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J.At.Mol.Sci.doi:10.4208/jams.032510.042010a Vol.1,No.3,pp.201-214 August2010Theoretical Raman and IR spectra of tegafur andcomparison of molecular electrostatic potentialsurfaces,polarizability and hyerpolarizability oftegafur with5-ﬂuoro-uracil by density functionaltheoryOnkar Prasad∗,Leena Sinha,and Naveen KumarDepartment of Physics,University of Lucknow,Lucknow,Pin Code-226007,IndiaReceived25March2010;Accepted(in revised version)20April2010Published Online28June2010Abstract.The5-ﬂuoro-1-(tetrahydrofuran-2-yl)pyrimidine-2,4(1H,3H)-dione,also knownas tegafur,is an important component of Tegafur-uracil(UFUR),a chemotherapy drugused in the treatment of cancer.The equilibrium geometries of”Tegafur”and5-ﬂuoro-uracil(5-FU)have been determined and analyzed at DFT level employing the basis set6-311+G(d,p).The molecular electrostatic potential surface which displays the activitycentres of a molecule,has been used along with frontier orbital energy gap,electricmoments,ﬁrst static hyperpolarizability,to interpret the better selectivity of prodrugtegafur over the drug5-FU.The harmonic frequencies of prodrug tegafur have alsobeen calculated to understand its complete vibrational dynamics.In general,a goodagreement between experimental and calculated normal modes of vibrations has beenobserved.PACS:31.15.E-,31.15.ap,33.20.TpKey words:prodrug,polarizability,hyperpolarizability,frontier orbital energy gap,molecular electrostatic potential surface.1IntroductionThe use of a prodrug strategy increases the selectivity and thus results in improved bioavailability of the drug for its intended target.In case of chemotherapy treatments,the reduction of adverse effects is always of paramount importance.The prodrug whichis used to target the cancer cell has a low cytotoxicity,prior to its activation into cytotoxic form in the cell and hence there is a markedly lower chance of it”attacking”the healthy∗Corresponding author.Email address:prasad onkar@lkouniv.ac.in(O.Prasad)/jams201c 2010Global-Science Press202O.Prasad,L.Sinha,and N.Kumar/J.At.Mol.Sci.1(2010)201-214 non-cancerous cells and thus reducing the side-effects associated with the chemothera-peutic agents.Tegafur,a prodrug and chemically known as5-ﬂuoro-1-(tetrahydrofuran-2-yl)pyrimidine-2,4(1H,3H)-dione,is an important component of’Tegafur-uracil’(UFUR), a chemotherapy drug used in the treatment of cancer,primarily bowel cancer.UFUR is a ﬁrst generation Dihydro-Pyrimidine-Dehydrogenase(DPD)inhibitory Flouropyrimidine drug.UFUR is an oral agent which combines uracil,a competitive inhibitor of DPD,with the5-FU prodrug tegafur in a4:1molar ratio.Excess uracil competes with5-FU for DPD, thus inhibiting5-FU catabolism.The tegafur is taken up by the cancer cells and breaks down into5-FU,a substance that kills tumor cells.The uracil causes higher amounts of 5-FU to stay inside the cells and kill them[1–4].The present communication deals with the investigation of the structural,electronic and vibrational properties of tegafur due to its biological and medical importance inﬁeld of cancer treatment.The structure and harmonic frequencies have been determined and analyzed at DFT level employing the basis set6-311+G(d,p).The optimized geometry of tegafur and5-FU and their molecular properties such as equilibrium energy,frontier orbital energy gap,molecular electrostatic potential energy map,dipole moment,polar-izability,ﬁrst static hyperpolarizability have also been used to understand the properties and activity of the drug and prodrug.The normal mode analysis has also been carried out for better understanding of the vibrational dynamics of the molecule under investi-gation.2Computational detailsGeometry optimization is one of the most important steps in the theoretical calculations. The X-ray diffraction data of the tegafur monohydrate and the drug5-FU,obtained from Cambridge Crystallographic Data Center(CCDC)were used to generate the initial co-ordinates of the prodrug tegafur and drug5-FU to optimize the structures.The Becke’s three parameter hybrid exchange functionals[5]with Lee-Yang-Parr correlation func-tionals(B3LYP)[6,7]of the density functional theory[8]and6-311+G(d,p)basis set were chosen.All the calculations were performed using the Gaussian03program[9].TheFigure1:Optimized structure of Tegafur and5-ﬂuoro-uracil at B3LYP/6-311+G(d,p).O.Prasad,L.Sinha,and N.Kumar/J.At.Mol.Sci.1(2010)201-214203Figure2:Experimental and theoretical Raman spectra of Tegafur.model molecular structure of prodrug tegafur and drug5-FU are given in the Fig.1.Pos-itive values of all the calculated vibrational wave numbers conﬁrmed the geometry to be located on true local minima on the potential energy surface.As the DFT hybrid B3LYP functional tends to overestimate the fundamental normal modes of vibration,a scaling factor of0.9679has been applied and a good agreement of calculated modes with ex-perimental ones has been obtained[10,11].The vibrational frequency assignments have been carried out by combining the results of the Gaussview3.07program[12],symmetry considerations and the VEDA4program[13].The Raman intensities were calculated from the Raman activities(Si)obtained with the Gaussian03program,using the following relationship derived from the intensity theory of Raman scattering[14,15]I i=f(v0−v i)4S iv i{1−exp(−hc v i/kT)},(1)where v0being the exciting wave number in cm−1,v i the vibrational wave number of i th normal mode,h,c and k universal constants and f is a suitably chosen common nor-malization factor for all peak intensities.Raman spectra has been calculated according to the spectral database for organic compounds(SDBS)literature,using4880˚A as excit-ing wavelength of laser source with200mW power[16].The calculated Raman and IR spectra have been plotted using the pure Lorentzian band shape with a band width of FWHM of3cm−1and are shown in Fig.2and Fig.3,respectively.204O.Prasad,L.Sinha,and N.Kumar/J.At.Mol.Sci.1(2010)201-214Figure3:Experimental and theoretical IR spectra of Tegafur.The density functional theory has also been used to calculate the dipole moment, mean polarizability<α>and the totalﬁrst static hyperpolarizabilityβ[17,18]are given as for both the molecules in terms of x,y,z components and are given by following equationsµ=(µ2x+µ2y+µ2z)1/2(2)<α>=13αxx+αyy+αzz,(3)βTOTAL=β2x+β2y+β2z1/2=(βxxx+βxyy+βxzz)2+(βyyy+βyxx+βyzz)2+(βzzz+βzxx+βzyy)21/2.(4)Theβcomponents of Gaussian output are reported in atomic units and therefore the calculated values are converted into e.s.u.units(1a.u.=8.3693×10−33e.s.u.).O.Prasad,L.Sinha,and N.Kumar/J.At.Mol.Sci.1(2010)201-214205 3Results and discussion3.1Geometric structureThe electronic structure of prodrug tegafur and the drug5-FU have been investigated, in order to assess the effect of introduction ofﬁve-membered ring having an electron withdrawing carbonyl group to the drug5-FU for better selectivity of target cancer cells. The optimized molecular structures with the numbering scheme of the atoms are shown in Fig. 1.The ground state optimized parameters are reported in Table1.Theﬁve-membered ring in case of tegafur adopts an envelope conformation,with the C(14)atom, acting as theﬂap atom,deviating from the plane through the remaining four carbon atoms.The C-C and C-H bond lengths ofﬁve-membered rings lie in the range1.518˚A ∼1.556˚A and1.091˚A∼1.096˚A respectively.The endocyclic angles ofﬁve-membered ring lie between103.50to108.00whereas there is a sharp rise in the endohedral angle values(129.1◦)at N(6)atom and sharp fall in the angle values(111.3◦)at C(8)atom in the six-membered hetrocyclic ring.The C(7)=O(2)/C(8)=O(3)/C(12)=O(4)bond lengths are equal to1.217/1.211/1.202˚A and are found to be close to the standard C=O bond length(1.220˚A).These calculated bond length,bond angles are in full agreement with those reported in[19,20].The skeleton of tegafur molecule is non-planar while the5-FU skeleton is planar.The optimized parameters agree well with the work reported by Teobald et al.[21].The angle between the hetrocyclic six-membered ring plane andﬁve-membered ring plane represented byζ(N(5)-C(11)-C(15)-C(12))is calculated at126.1◦.It is seen that most of the bond distances are similar in tegafur and5-FU molecules,al-though there are differences in molecular formula.In the six-membered ring all the C-C and C-N bond distances are in the range1.344∼1.457˚A and1.382∼1.463˚A.Accord-ing to our calculations all the carbonyl oxygen atoms carry net negative charges.The signiﬁcance of this is further discussed in terms of its activity in the next section.Table1:Parameters corresponding to optimized geometry at DFT/B3LYP level of theory for Tegafur and5-FUParameters Tegafur5-FUGround state energy(in Hartree)-783.639204-514.200506Frontier orbital energy gap(in Hartree)0.185850.19593Dipole moment(in Debye) 6.43 4.213.2Electronic propertiesThe frontier orbitals,HOMO and LUMO determine the way a molecule interacts with other species.The frontier orbital gap helps characterize the chemical reactivity and ki-netic stability of the molecule.A molecule with a small frontier orbital gap is more po-larizable and is generally associated with a high chemical reactivity,low kinetic stability206O.Prasad,L.Sinha,and N.Kumar/J.At.Mol.Sci.1(2010)201-214 and is also termed as soft molecule[22].The frontier orbital gap in case of prodrug tega-fur is found to be0.27429eV lower than the5-FU molecule.The HOMO is the orbital that primarily acts as an electron donor and the LUMO is the orbital that largely acts as the electron acceptor.The3D plots of the frontier orbitals HOMO and LUMO,electron density(ED)and the molecular electrostatic potential map(MESP)for both the molecules are shown in Fig.4and Fig.5.It can be seen from theﬁgures that,the HOMO is almost distributed uniformly in case of prodrug except the nitrogen atom between the two car-bonyl groups but in case of5-FU the HOMO is spread over the entire molecule.Homo’s of both the molecules show considerable sigma bond character.The LUMO in case of tegafur is found to be shifted mainly towards hetrocyclic ring and the carbonyl group ofﬁve-membered ring and shows more antibonding character as compared to LUMO of 5-FU in which the spread of LUMO is over the entire molecule.The nodes in HOMO’s and LUMO’s are placed almost symmetrically.The ED plots for both molecules show a uniform distribution.The molecular electrostatic potential surface MESP which is a plot of electrostatic potential mapped onto the iso-electron density surface,simultaneously displays molecular shape,size and electrostatic potential values and has been plotted for both the molecules.Molecular electrostatic potential(MESP)mapping is very use-ful in the investigation of the molecular structure with its physiochemical property rela-tionships[22–27].The MESP map in case of tegafur clearly suggests that each carbonyl oxygen atom of theﬁve and six-membered rings represent the most negative potential region(dark red)but theﬂuorine atom seems to exert comparatively small negative po-tential as compared to oxygen atoms.The hydrogen atoms attached to the six andﬁve-membered ring bear the maximum brunt of positive charge(blue region).The MESP of tegafur shows clearly the three major electrophyllic active centres characterized by red colour,whereas the MESP of the5-FU reveals two major electrophyllic active centres,the ﬂuorine atom seems to exert almost neutral electric potential.The values of the extreme potentials on the colour scale for plotting MESP maps of both molecules have been taken same for the sake of comparison and drawing the conclusions.The predominance of green region in the MESP surfaces corresponds to a potential halfway between the two extremes red and dark blue colour.From a closer inspection of various plots given in Fig. 4and Fig.5and the electronic properties listed in Table1,one can easily conclude how the substitution of the hydrogen atom by theﬁve-membered ring containing an electron withdrawing carbonyl group modiﬁes the properties of the drug5-FU.3.3Electric momentsThe dipole moment in a molecule is an important property that is mainly used to study the intermolecular interactions involving the non bonded type dipole-dipole interactions, because higher the dipole moment,stronger will be the intermolecular interactions.The calculated value of dipole moment in case of tegafur is found to be quite higher than the drug5-FU molecule and is attributed due to the presence of an extra highly electron withdrawing carbonyl group.The calculated dipole moment for both the molecules areO.Prasad,L.Sinha,and N.Kumar/J.At.Mol.Sci.1(2010)201-214207Table2:Polarizability data/a.u.for Tegafur at DFT/B3LYP level of theoryPolarizability TegafurαXX173.315αXY-2.494αYY111.365αXZ-4.149αYZ0.399αZZ92.930<α>125.870Table3:Allβcomponents andβTotal for Tegafur calculated at DFT/B3LYP level of theoryPolarizability TegafurβXXX-54.9411βXXY-57.5539βXYY-13.4605βYYY95.0387βXXZ31.8370βXYZ9.2943βYYZ-22.0880βXZZ57.6657βYZZ-21.7419βZZZ-37.3655βTotal(e.s.u.)0.2808×10−30also given in Table1.The lower frontier orbital energy gap and very high dipole moment for the tegafur are manifested in its high reactivity and consequently higher selectivity for the target carcinogenic/tumor cells as compared to5-FU(refer to Table1).According to the present calculations,the mean polarizability of tegafur(125.870/ a.u.,refer to Table2)is found signiﬁcantly higher than5-FU(66.751/a.u.calculated at the same level of theory as well as same basis set).This is related very well to the smaller frontier orbital gaps of tegafur as compared to5-FU[22].The different components of polarizability are reported in the Table2.Theﬁrst static hyperpolarizabilityβcalculated value is found to be appreciably lowered in case of tegafur(0.2808x10−30e.s.u.,refer to Table3)as compared to5-FU(0.6218x10−30e.s.u.calculated at B3LYP/6-311+G(d,p)). Table3presents the different components of static hyperpolarizability.In addition,βval-ues do not seem to follow the same trend asαdoes,with the frontier orbital energy gaps. This behavior could be explained by a poor communication between the two frontier or-bitals of tegafur.Although the HOMO is almost distributed uniformly in case of tegafur208O.Prasad,L.Sinha,and N.Kumar/J.At.Mol.Sci.1(2010)201-214Figure4:Plots of Homo,Lumo and the energy gaps in Tegafur and5-FU.Figure5:Total Density and MESP of Tegafur and5-FU.but the LUMO is found to be shrunk and shifted mainly towards hetrocyclic ring and the carbonyl group ofﬁve-membered ring and shows more antibonding character than the LUMO of5-FU.It may thus be concluded that the higher”selectivity”of the prodrug tegafur as compared to the drug5-FU may be attributed due to the higher dipole mo-ment and lower values of frontier energy band gap coupled with the lowerﬁrst static hyperpolarizability.3.4Vibrational spectral analysisAs the molecule has no symmetry,all the fundamental modes are Raman and IR active. The66fundamental modes of vibrations of tegafur are distributed among the functional and theﬁnger print region.The experimental and computed vibrational wave num-O.Prasad,L.Sinha,and N.Kumar/J.At.Mol.Sci.1(2010)201-214209 bers,their IR and Raman intensities and the detailed description of each normal mode of vibration of the prodrug tegafur,carried out in terms of their contribution to the total potential energy are given in Table4.The calculated Raman and IR spectra of prodrugTable4:Theoretical and experimental a wave numbers(in cm−1)of TegafurExp a Exp a Calc.Calc.Calc.Calc.Assignment of dominantIR Raman(Unscaled(Scaled IR Raman modes in order of Wave no.Wave no.Wave no.Wave no.Intensity Intensity decreasing potentialin cm−1in cm−1in cm−1)in cm−1)energy distribution(PED)3426-3592347779.8317.38υ(N-H)(100)3076310032193115 3.0919.49υ(C-H)R(99)3033-3117301714.2012.97υas methylene(C-H)(82)30333004310730079.8732.29υas methylene(C-H)(90)-29763097299818.5945.83υas methylene(C-H)(80)--3065296720.6530.88υs methylene(C-H)(96)--305029527.8416.11υ(C-H)pr(98)--3044294610.2419.02υs methylene(C-H)(91)2911-3033293624.9745.77υs methylene(C-H)(84)1721-183********.637.65υ(C12=O)pr(90)1693172317821725461.2581.78υ(C8=O)R(72)1668170717661709871.67 3.93υ(C7=O)R(66)165816611701164776.0842.39υ(C9-C10)(66)+β(H17-C10-C9)(11)14711473151114628.71 2.05sc CH2(93)14661469149314457.829.82sc CH2(87)140014381467142042.97 1.93υ(N5-C)10)(23)+β(N5-C10-C9)(13) +υ(N6-C8)(11)+β(N5-C11-H18)(10)140014031450140320.857.15sc(CH2)(88)13621367141913738.94 3.78β(H16-N6-C7)(52)+υ(C=O)R(20) +β(H17-C10-N5)(11)135613401393134971.90 4.40β(H18-C11-N5)(35) +β(H16-N6-C7)(13)1339-138********.7460.20β(H17-C10-C9)(21)+υ(C9-C10)(14) +υ(N5-C10)(13)+υ(N6-C7)(12)--1343130010.26 1.21methylene(C14)wag(62)+methylene(C15)twisting(13)--1337129414.487.82methylene(C15)wag(56)+methylene(C14)twisting(16)1264126113071266 4.21 1.73methylene(C13)wag(56)+methylene(C14),(C15)twisting(16)1264-12991257 1.958.16Methylene twisting(60)1231-12671225199.09 4.95β(H17-C10-N5)(23)+methylene(C13)twisting(15) +υ(N5-C10)(10)1187-1244120485.739.03Ring deformation1179119912281189 4.29 1.65Methylene twisting(40) +(C11-H18)wag(35)--1193115522.238.09methylene(C13)wag(10) +β(H17-C10-C9)(10)210O.Prasad,L.Sinha,and N.Kumar/J.At.Mol.Sci.1(2010)201-214(continued)Exp a Exp a Calc.Calc.Calc.Calc.Assignment of dominantIR Raman(Unscaled(Scaled IR Raman modes in order of Wave no.Wave no.Wave no.Wave no.Intensity Intensity decreasing potentialin cm−1in cm−1in cm−1)in cm−1)energy distribution(PED)1115-11681131134.60 4.73β(H23-C15-C11)(21) +β(H22-C13-C14)(18)β(H16-N6-C7)(17)1115-11571120 5.9920.48υ(N6-C7)(30)+υ(N5-C10)(16) +methylene twisting(14)1065104510621028 3.60 4.26υ(C-C)pr(28)+β(H18-C11-C12)(13) +methylene twisting(11)1087-1126109020.609.14υ(C-C)pr(35)+β(C12-C13-C14)(12) --10139808.56 6.79υ(C-C)pr(54)+methylene wag(25)941942965934 2.79 1.53υ(C-C)pr(20)+β(H18-C11-C15)(17) +methylene twisting(10)9139219268970.27 6.28methylene rocking(33) +υ(C-C)pr(11)--916886 4.1310.06υ(C-C)pr(59)867-896868 2.20 5.99C-H out of plane Ring wag(79)840-8868570.48 4.53β(H16-N6-C7)(20)+β(H17-C10-C9)(13)+methylene(C13)rocking(13) +methylene(C14)twisting(11)--82780011.31 6.48methylene rocking(69)77378281578950.9325.00β(C10-N5-C7)(27)+β(C9-C10-N5)(16) +υ(F-C)(11)749-760736 5.940.73βout(O-C-N)(78)--75473052.72 2.02βout(O-C-N)(77)+(N-H)wag(10) --746722 5.537.78Ring Breathing mode(51)687704728705 1.7330.18methylene rocking(39) +β(O2-C7-N6)(18)-6466686479.5512.38β(O-C-N)(45)+β(F-C-C)(11) -64665863742.75 2.90(N-H)wag(90)608-6266069.55 2.91β(C-C-C)Pr(18)+β(O-C-C)Pr(18) +(N-H)wag(12)--58256320.4212.86βout(C-C-C)Pr(17)+β(C8-N6-C7)(12) +β(C9-C10-N5)(10)542-550532 2.497.84βout(C-C-C)Pr(31)+β(O-C-C)Pr(15)48249051850110.7119.07β(O-C-C)Pr(32)+Pr torsional mode(12) +Ring Tors.mode(12)430-4694548.9916.04Pr tors.mode(31)+β(N-C-N)(23) +β(N5-C10-C9)(10)-421418405 2.01 1.44Pr tors.mode(29)+Ring Tors.mode(17)--4103967.608.21Ring Tors.mode(54)(continued)Exp a Exp a Calc.Calc.Calc.Calc.Assignment of dominant IR Raman(Unscaled(Scaled IR Raman modes in order ofWave no.Wave no.Wave no.Wave no.Intensity Intensity decreasing potential in cm−1in cm−1in cm−1)in cm−1)energy distribution(PED)-38138937719.530.39β(O2-C7-N6)(22)+Ring Tors.(21) Tors.(O4-C11-C13-C12)(12)-352364352 3.228.17Tors.(F1-C8-C10-C9)(59) +Tors.(O3-N6-C9-C8)(10)-319312302 1.680.76β(C10-C9-F1)(26)+β(C8-N6-C7)(18) +β(C10-N5-C11)(29)+β(C10-N5-C7)(12)--2872787.10 4.57Ring Tors.(24)+βout(C10-C9-F1)(22) +β(C15-C11-N5)(20)--2432360.17 1.90Pr tors.mode(32)+Ring Tors.(30) +βout(C10-C9-F1)(12)--230223 1.08 1.61Pr tors.mode(30) +β(C10-N5-C11)(29)--166160 4.74 3.08Ring Tors.(64)--152147 2.75 4.58Pr tors.mode(20)+Tors.(C15-C11-N5-C7)(19)+Ring Tors(10)+β(C10-N5-C11)(10)--1281230.78 3.22Tors.(C15-C11-N5-C7)(35)+Ring Tors.(33)+Pr tors.mode(17)--7471 1.78 1.29Tors.(C14-C15-C11-N5)(61) +β(C11-N5-C10)(10)--6159 1.36 1.94Ring Tors.(36)+Tors.(C15-C11-N5-C7)(35)--4543 1.18 1.74Tors.(C11-C7-C10-N5)(67) +Tors.(C12-C11-N5-C7)(11)The experimental IR and Raman data have been taken from http://riodb01.ibase.aist.go.jp/sdbs website.Note:υ:stretching;υs:symmetric stretching;υas:asymmetric stretching;β:in plane bending;βout:out of plane bending;Tors:torsion;sc:scissoring;ωag:wagging;Pr:Five-membered ring;Ring:Hetroaromatic six-membered ring tegafur agree well with the experimental spectral data taken from the Spectral Database for Organic Compounds(SDBS)[16].3.4.1N-H vibrationsThe N-H stretching of hetrocyclic six-membered ring of tegafur is calculated at3477 cm−1.As expected,this is a pure stretching mode and is evident from P.E.D.table con-tributing100%to the total P.E.D.,and is assigned to IR wave number at3426cm−1.The discrepancy in the calculated and experimental N-H stretching wave number is due to the intermolecular hydrogen bonding.The mode calculated at637cm−1represents the pure N-H wagging mode which is assigned well with the peak at646cm−1in Raman spectra.3.4.2C-C and C-H vibrationsC-C stretching are observed as mixed modes in the frequency range1600cm−1to980 cm−1for tegafur with general appearance of C-H and C-C stretching modes and are in good agreement with experimentally observed frequencies.C-C stretches are calcu-lated to be1090,980,934and886cm−1.The functional group region in aromatic het-rocyclic compounds exhibits weak multiple bands in the region3100∼3000cm−1.The six-membered ring stretching vibrations as well as the C-H symmetric and asymmet-ric stretching vibrations of methylene group in tegafur are found in the region3125to 2925cm−1.In the present investigation,the strengthening and contraction of C-H bond C(10)-H(17)=108.147pm in hetrocyclic six-membered ring may have caused the C-H stretching peak to appear at3115cm−1having almost100%contribution to total P.E.D. in calculation.This C-H stretching vibration is assigned to the3076cm−1IR spectra. The calculated peaks at3017,3007,2998cm−1and2967cm−1are identiﬁed as methylene asymmetric and symmetric stretching vibrations with more than80%contribution to the total P.E.D.are matched moderately and have been assigned at3033cm−1in the IR and at3004and2976cm−1in Raman spectra respectively.The calculated peaks in the frequency range1475∼1400cm−1of tegafur correspond methylene scissoring modes with more than85%contribution to the total P.E.D.are as-signed at1471/1473and1466/1469cm−1in the IR/Raman spectra.Methylene wagging calculated at1300cm−1(62%P.E.D.),1294and1266cm−1(56%P.E.D.each),show con-siderable mixing with methylene twisting mode,whereas dominant twisting modes are calculated at1257cm−1and1189cm−1with60%and40%contribution to P.E.D.The mode calculated at897,800and705cm−1are identiﬁed as methylene rocking with their respective33%,69%and39%contribution to the total P.E.D.3.4.3Ring vibrationsThe calculated modes at868cm−1and722cm−1represent the pure six-membered ring wagging and breathing modes.As expected the skeletal out of plane deformations/ the torsional modes appear dominantly below the600cm−1.The mode calculated at 789cm−1represent mixed mode with(C-C-N)and(C-N-C)in-plane bending and F-C stretching and corresponds to Raman/IR mode at782/773cm−1.The experimental wave number at646cm−1in Raman spectra is assigned to the in-plane(O-C-N)and(F-C-C) bending at647cm−1.3.4.4C=O vibrationsThe appearance of strong bands in Raman and IR spectra around1700to1880cm−1show the presence of carbonyl group and is due to the C=O stretch.The frequency of the stretch due to carbonyl group mainly depends on the bond strength which in turn depends upon inductive,conjugative,ﬁeld and steric effects.The three strong bands in the IR spectra at 1721,1693and1668cm−1are due to C=O stretching vibrations corresponding to the three C=O groups at C(12),C(8)and C(7)respectively in tegafur.These bands are calculatedat1771,1725and1709cm−1.The discrepancy between the calculated and the observed frequencies may be due to the intermolecular hydrogen bonding.4ConclusionsThe equilibrium geometries of tegafur and5-FU and harmonic frequencies of tegafur molecule under investigation have been analyzed at DFT/6-311+G(d,p)level.In general, a good agreement between experimental and calculated normal modes of vibrations has been was observed.The skeleton of optimized tegafur molecule is non-planar.The lower frontier orbital energy gap and the higher dipole moment values make tegafur the more reactive and more polar as compared to the drug5-FU and results in improved target cell selectivity.The molecular electrostatic potential surface andﬁrst static hyperpolarizabil-ity have also been employed successfully to explain the higher activity of tegafur over its drug5-FU.The present study of tegafur and the corresponding drug in general may lead to the knowledge of chemical properties which are likely to improve absorption of the drug and the major metabolic pathways in the body and allow the modiﬁcation of the structure of new chemical entities(drug)for the improved bioavailability. Acknowledgments.We would like to thank Prof.Jenny Field for providing the crystal data of Tegafur and5-FU from Cambridge Crystallographic data centre(CCDC),U.K. and Prof.M.H.Jamroz for providing his VEDA4software.References[1]L.W.Li,D.D.Wang,D.Z.Sun,M.Liu,Y.Y.Di,and H.C.Yan,Chinese Chem.Lett.18(2007)891.[2] D.Engel, A.Nudelman,N.Tarasenko,I.Levovich,I.Makarovsky,S.Sochotnikov,I.Tarasenko,and A.Rephaeli,J.Med.Chem.51(2008)314.[3]Z.Zeng,X.L.Wang,Y.D.Zhang,X.Y.Liu,W H Zhou,and N.F.Li,Pharmaceutical Devel-opment and Technology14(2009)350.[4]ura,A Azucena,C Carmen,and G Joaquin,Therapeutic Drug Monitoring25(2003)221.[5] A.D.Becke,J.Chem.Phys.98(1993)5648.[6] C.Lee,W.Yang,and R.G.Parr,Phys.Rev.B37(1988)785.[7] B.Miehlich,A.Savin,H.Stoll,and H.Preuss,Chem.Phys.Lett.157(1989)200.[8]W.Kohn and L.J.Sham,Phys.Rev.140(1965)A1133.[9]M.J.Frisch,G.W.Trucks,H.B.Schlegel,et al.,Gaussian03,Rev.C.01(Gaussian,Inc.,Wallingford CT,2004).[10] A.P.Scott and L.Random,J.Phys.Chem.100(1996)16502.[11]P.Pulay,G.Fogarasi,G.Pongor,J.E.Boggs,and A.Vargha,J.Am.Chem.Soc.105(1983)7037.[12]R.Dennington,T.Keith,lam,K.Eppinnett,W.L.Hovell,and R.Gilliland,GaussView,Version3.07(Semichem,Inc.,Shawnee Mission,KS,2003).[13]M.H.Jamroz,Vibrational Energy Distribution Analysis:VEDA4Program(Warsaw,Poland,2004).[14]G.Keresztury,S.Holly,J.Varga,G.Besenyei,A.Y.Wang,and J.R.Durig,Spectrochim.Acta49A(1993)2007.[15]G.Keresztury,Raman spectroscopy theory,in:Handbook of Vibrational Spectroscopy,Vol.1,eds.J.M.Chalmers and P.R.Grifﬁth(John Wiley&Sons,New York,2002)pp.1.[16]http://riodb01.ibase.aist.go.jp/sdbs/(National Institute of Advanced Industrial Scienceand Technologys,Japan)[17] D.A.Kleinman,Phys,Rev.126(1962)1977.[18]J.Pipek and P.Z.Mezey,J.Chem.Phys.90(1989)4916.[19]dd,Introduction to Physical Chemistry,third ed.(Cambridge University Press,Cam-bridge,1998).[20] F.H.Allen,O.Kennard,and D.G.Watson,J.Chem.Soc.,Perkin Trans.2(S1)(1987)12.[21] B.Blicharska and T.Kupka,J.Mol.Struct.613(2002)153.[22]I.Fleming,Frontier Orbitals and Organic Chemical Reactions(John Wiley and Sons,NewYork,1976)pp.5-27.[23]J.S.Murray and K.Sen,Molecular Electrostatic Potentials,Concepts and Applications(El-sevier,Amsterdam,1996).[24]I.Alkorta and J.J.Perez,Int.J.Quant.Chem.57(1996)123.[25] E.Scrocco and J.Tomasi,Advances in Quantum Chemistry,Vol.11(Academic Press,NewYork,1978)pp.115.[26] F.J.Luque,M.Orozco,P.K.Bhadane,and S.R.Gadre,J.Phys.Chem.97(1993)9380.[27]J.Sponer and P.Hobza,Int.J.Quant.Chem.57(1996)959.。

学术交际英语第一部分第4章

eg.3 对该电路作一定量分析是很复杂的。 W: Quantitative analysis of this circuit is complicated. R: A quantitative analysis of this circuit is complicated.
3）Overuse of articles
4）Confusion of “a” and “an”
eg.1 这里应该使用8伏的电池。 W: A 8-volt battery should be used here. R: An 8-volt battery should be used here. eg.2 在这里我们使用一个S形的管子。 W: A S-shaped tube is used here. R: An S-shaped tube is used here. eg.3 这是一个单位。 W: This is an unit. R: This is a unit.
eg.8 通过观察一种新药对病人的影响才能看出它的治疗效果。 W: Through observing the effect of a new kind of drug to patient, one can see its efficiency of cure. R: By observing the effect of a new drug on patients, one can see its therapeutic effect. eg.9 我们在讨论微分方程的时候，将把注意力集中在一次方程上。 W: During our discussion of differential equations, we shall restrict our attention to equations of the first degree. R: In our discussion of differential equations, we shall restrict our attention to equations of the first degree. eg.10 除了该电子外，氢原子还含有一个正质子。 W: Except the electron, hydrogen atom also contains a positive proton. R: In addition to the electron, a hydrogen atom also contains a positive proton.

中考英语作文评分标准及评分说明四川

中考英语作文评分标准及评分说明四川全文共3篇示例，供读者参考篇1Scoring Criteria and Explanation for Middle School English Composition in SichuanThe middle school English composition in Sichuan is an important part of the standardized test for students. The composition test aims to assess the students' English writing skills, vocabulary, grammar, coherence, and creativity. In order to evaluate the students' work fairly and accurately, the examiners use a specific scoring criteria and provide detailed explanations for each score.Scoring Criteria:1. Content (30 points): The content refers to the topic relevance, originality, and coherence of the composition. The students should stick to the topic, present their ideas clearly, and develop the content logically.2. Vocabulary and Grammar (25 points): The vocabulary and grammar score assesses the students' use of vocabulary, sentence structure, and grammar accuracy. The students shoulddemonstrate a good range of vocabulary and use them appropriately in sentences with correct grammar.3. Organization (20 points): The organization score evaluates the coherence and cohesion of the composition. The students should use appropriate paragraph structures, transitions, and connectives to ensure the smooth flow of ideas.4. Creativity (15 points): The creativity score measures the students' ability to present their ideas in an original and engaging way. The students should use imaginative language, examples, and descriptions to make their composition more interesting.5. Language Use (10 points): The language use score focuses on the students' language proficiency, including pronunciation, intonation, and fluency. The students should demonstrate a clear and natural use of English language.Explanation for each score:1. Excellent (100-90): The composition demonstrates a deep understanding of the topic, original ideas, coherent organization, rich vocabulary, accurate grammar, and creative language use. The writing is engaging, persuasive, and error-free.2. Good (89-80): The composition shows a clear understanding of the topic, coherent structure, varied vocabulary, mostly accurate grammar, and some creative language use. The writing is interesting and well-developed with minor errors.3. Average (79-70): The composition presents a basic understanding of the topic, somewhat coherent organization, limited vocabulary, some grammar errors, and little creativity. The writing is somewhat engaging but lacks depth and originality.4. Below average (69-60): The composition demonstrates a weak understanding of the topic, poor organization, limited vocabulary, frequent grammar errors, and lack of creativity. The writing is dull, disjointed, and difficult to follow.5. Poor (59-0): The composition shows a lack of understanding of the topic, incoherent organization, repetitive vocabulary, numerous grammar errors, and no creativity. The writing is confusing, incomprehensible, and full of mistakes.In conclusion, the scoring criteria for the middle school English composition in Sichuan provide a clear and detailed assessment of the students' writing abilities. By following the scoring guidelines and explanations, the examiners can evaluate the students' work objectively and fairly. It is important for thestudents to pay attention to these criteria and strive to improve their writing skills in order to achieve higher scores in the composition test.篇2Grading Criteria and Scoring Explanation for the Middle School English Composition in Sichuan ProvinceThe English composition is an important part of the middle school entrance exam in Sichuan Province. It not only tests the students' language ability but also evaluates their thinking skills and creativity. In order to ensure a fair and accurate assessment of the students' writing, a detailed grading criteria and scoring explanation are provided below.1. Content and Organization (30 points)- Ideas: The composition should have a clear main idea and supporting details that are relevant to the topic. (10 points)- Organization: The composition should have a logical structure with a clear introduction, body paragraphs, and conclusion. (10 points)- Development: The ideas should be well-developed with examples, explanations, and details to support the main points.(10 points)2. Vocabulary and Grammar (30 points)- Vocabulary: The composition should demonstrate a range of vocabulary, including words and phrases that are appropriate for the topic. (15 points)- Grammar: The composition should have correct grammar usage, including verb tenses, subject-verb agreement, and sentence structure. (15 points)3. Language Use and Fluency (20 points)- Clarity: The composition should be clear and easy to understand, with smooth transitions between ideas. (10 points)- Fluency: The composition should be well-written with a variety of sentence structures and language devices. (10 points)4. Creativity and Originality (20 points)- Creativity: The composition should show creativity in the use of language, ideas, and organization. (10 points)- Originality: The composition should be original and unique, showing the student's personal thoughts and perspectives. (10 points)Scoring Explanation:- Excellent (26-30 points): The composition demonstrates a high level of proficiency in all aspects. It is well-organized, with clear ideas, accurate grammar, and a wide range of vocabulary. The language use is fluent and engaging, showing creativity and originality.- Good (21-25 points): The composition is well-written with minor errors in content, vocabulary, or grammar. It shows a good understanding of the topic and demonstrates creativity and originality.- Fair (16-20 points): The composition has some weaknesses in content, vocabulary, or grammar. It may lack clarity or organization, but still conveys the main ideas. It shows some creativity and originality.- Needs Improvement (15 points or below): The composition has significant errors in content, vocabulary, or grammar. It may be unclear or poorly organized, with limited creativity and originality.In conclusion, the grading criteria and scoring explanation provide a clear framework for evaluating the students' English compositions in the middle school entrance exam in Sichuan Province. By focusing on content, vocabulary, grammar, language use, creativity, and originality, the examiners can assess the students' writing skills accurately and fairly.篇3Grading Criteria and Explanation for English Composition in the Middle School Entrance Examination in SichuanEnglish composition is an important part of the middle school entrance examination in Sichuan. It is aimed at assessing students' ability to express ideas clearly and coherently in English. In order to ensure fairness and consistency in grading, a set of grading criteria and explanations have been established for English compositions.1. Content (30 points)- Relevance: Does the composition address the giventopic/task?- Completeness: Is the composition well-developed with relevant details and examples?- Originality: Does the composition show creativity and original thinking?2. Organization (20 points)- Introduction: Does the composition have a clear and engaging introduction?- Body: Is the main idea supported with well-organized paragraphs and logical transitions?- Conclusion: Does the composition have a satisfactory conclusion that ties back to the main idea?3. Vocabulary and Grammar (20 points)- Vocabulary: Is a wide range of vocabulary used appropriately and accurately?- Grammar: Are grammatical structures used correctly, including verb tenses, pronouns, and sentence structures?4. Cohesion and Coherence (15 points)- Cohesion: Are cohesive devices (e.g., transition words, pronouns) used effectively to connect ideas?- Coherence: Is the composition logically and clearly organized?5. Creativity and Style (15 points)- Creativity: Does the composition show originality and creativity in ideas and language use?- Style: Is the composition written in a clear and engaging style that holds the reader's attention?Explanation of Grading- Excellent (26-30 points): The composition is outstanding in all aspects, with a clear and original idea, well-developed content, excellent organization, precise vocabulary and grammar, effective cohesion and coherence, and creative style.- Good (21-25 points): The composition is good in most aspects, with a relevant idea, well-developed content, good organization, mostly accurate vocabulary and grammar, adequate cohesion and coherence, and a clear style.- Average (15-20 points): The composition is average in most aspects, with a somewhat relevant idea, basic content, average organization, basic vocabulary and grammar, some cohesion and coherence issues, and a basic style.- Below Average (0-14 points): The composition is below average in most aspects, with an irrelevant or incomplete idea,poor content, weak organization, limited vocabulary and grammar, lack of cohesion and coherence, and a basic style.In conclusion, the grading criteria and explanations for English composition in the middle school entrance examination in Sichuan are designed to assess students' ability to communicate effectively in English. By following these criteria, examiners can ensure fairness and consistency in grading, and students can understand the expectations for their compositions.。

冲刺讲义

一、Listening Comprehension（听力）Exercise oneSection A:1. Me? Just a little.我？只听懂一点点4. Don’t mention it. （借钱）不客气5. It is really unimaginable. 真的超出想象Section B:6. classmates 同学7. Last Christmas. 上个圣诞节见的面9. USD＄280.280美元10. He hadn’t realized he was speeding. 他还没有意识到超速15. Carry his groceries home. 帮他把杂货带回家Exercise twoSection A:3. perhaps I got to read through them again.也许我该再看一遍4. yes, identical同一的ones. 是的，是同卵双胞胎Section B:9. they try to be friendly to them.他们尽力对他们友好10. at 2:00 两点12. his car was hit from behind.他的车尾被撞了（追尾了）13. he has to finish his report 他得完成他的报告14. See the Niagara.游览尼亚加拉瀑布15. In a bookstore 在书店16. a timetable of events.参观时刻表17. they live far away.他家住得很远（500公里）Exercise threeSection A:2. yes, it is worth your while to do so.是的。

值得你去做3. oh, I am sorry, I didn’t notice it.对不起，我没注意到5. How much do you want to change?你想兑换多少零钱？Section B:8. long holidays attract her 长假期吸引她10. a book store 书店（没提到）12. a couple of items 几件东西13. he is tired of厌倦his work 他厌倦邮局的工作14. sample cutting 切片样品（标本）16. he once gave a book as a present他曾经送他人一本书作为礼物五年前出版的一本小说18. she planned house and other buildings她设计房子和其他建筑物19. the architects were men 建筑设计师都是男的20. storage buildings（她主要设计）仓库Exercise fourSection A:1. no, it is really freezing 是的，天气真寒冷2. maybe tomorrow if I hurry up 如果快些，也许明天能完成Section B:6. it has plenty of light 房间光线很好7. to see a new type of boiler来看新款的热水器9. in the women’s dormitory.在女生宿舍10. their schoolmates 他们的同学16. they may support the employers他们会支持雇主17. a third party would impose a settle 第三方来裁决Exercise fiveSection A:1. no, I don’t mind at all 我一点也不介意3. thank you for saying so很感激你这麽说5. I’m afraid I don’t我恐怕不喜欢Section B:6. toothpaste, coffee and a doll 牙膏，咖啡，洋娃娃12. a bookstore书店16. receptionist and guest接待员和顾客。

植物油中内源性成分的抗氧化作用

马宇晨，王光宜，刘乐乐，等. 植物油中内源性成分的抗氧化作用[J]. 食品工业科技，2023，44（24）：119−130. doi:10.13386/j.issn1002-0306.2023040195MA Yuchen, WANG Guangyi, LIU Lele, et al. Antioxidant Effects of Endogenous Components in Vegetable Oils[J]. Science and Technology of Food Industry, 2023, 44(24): 119−130. (in Chinese with English abstract). doi: 10.13386/j.issn1002-0306.2023040195· 研究与探讨 ·植物油中内源性成分的抗氧化作用马宇晨，王光宜，刘乐乐，李红艳*（南昌大学食品科学与资源挖掘全国重点实验室，江西南昌 330047）摘　要：本研究通过在复配植物油中添加不同的植物油内源性抗氧化物（生育酚、植物甾醇、多酚和角鲨烯），研究不同植物油内源性成分对植物油的抗氧化作用。

采用Schaal 烘箱加速实验，通过脂肪酸组成、酸价、过氧化值、茴香胺值、总氧化值等氧化稳定性指标的变化，评价内源性抗氧化物对复配油氧化稳定性的影响。

结果表明，生育酚和多酚单独作用时抗氧化效果明显，且随浓度的增加而增强。

生育酚和角鲨烯组合作用时，随着生育酚和角鲨烯浓度的升高，呈现先拮抗后协同效应，当生育酚含量大于480 mg/kg ，角鲨烯的存在会显著提高生育酚的抗氧化能力（P <0.05）。

从加速氧化的结果来看，未经预处理去除抗氧化成分的复配油脂肪酸组成只有微小的变化，经过预处理的复配油脂肪酸组成变化范围较大。

经过预处理的复配油酸价和总氧化值在氧化前后的变化量也显著高于未经预处理的复配油（P <0.05），添加生育酚和多酚后，复配油的氧化稳定性得到提高，表明内源性抗氧化成分含量虽少，但对延缓植物油氧化过程起到了至关重要的作用。

教材知识解读选择性必修第二册 Unit 1 Science and Scientists

Ⅰ.认阅读单词1．cholera n．霍乱2．diarrhoea n．腹泻3．dehydration n．脱水4．contradictory adj.相互冲突的；对立的；不全都的5．germ n．微生物；细菌；病菌6．pump n．泵；抽水机；打气筒7．water pump水泵8．household n．一家人；家庭；同住一所(套)房子的人9．raw adj.未煮的；生的；未经处理的；原始的10．statistic n．[pl.]统计数字；统计资料；统计学11．epidemiology n．流行病学12．microscope n．显微镜13．protein n．蛋白质14．cell n．细胞；小房间；单间牢房15．virus n．病毒16．vaccine n．疫苗17．framework n．框架；结构18．theoretical framework理论框架19．rainbow n．彩虹20．concrete n．混凝土adj.混凝土制的；的确的；具体的21．plasma n．血浆22．aerospace n．航空航天工业23．patriotic adj.爱国的24．mechanical adj.机械的；发动机的；机器的25．mechanic n．机械师；机械修理工26．aviation n．航空制造业；航空；飞行27．jet n．喷气式飞机28．missile n．导弹29．astronomer n．天文学家30．astronomy n．天文学31．telescope n．望远镜Ⅱ.记重点单词1．severe adj.极为恶劣的；格外严峻的；严峻的2．subscribe v i.认购(股份)；定期订购；定期交纳(会费)3．suspect v t.& v i.怀疑；疑有；不信任n．犯罪嫌疑人；可疑对象4．blame v t.把……归咎于；责怪；指责n．责怪；指责5．handle n．把手；拉手；柄v t.处理；搬动；操纵(车辆、动物、工具等)；(用手)触碰6．link n．联系；纽带v t.把……连接起来；相关联7．substantial adj.大量的；价值巨大的；重大的8．decrease n．削减；降低；削减量v t.& v i.(使大小、数量等)削减；减小；降低9．transform v t.使改观；使转变形态v i.转变；转变10．thinking n．思想；思维；见解11．finding n．发觉；调查结果；(法律)判决12．initial adj.最初的；开头的；第一的13．solid adj.牢靠的；固体的；坚实的n．固体14．cast v t.(cast，cast)投射；向……投以(视线、笑容等)；投掷15．shadow n．阴影；影子；背光处16．pour v t.倒出；倾泻；斟(饮料)17．leadership n．领导；领导地位；领导才能18．trace v t.追溯；追踪；查出n．痕迹；遗迹；踪迹19．outstanding adj.优秀的；杰出的；明显的20．abstract adj.抽象的；理论上的n．(文献等的)摘要21．concept n．概念；观念22．besides prep.除……之外(还) ad v.而且；此外23．brilliant adj.聪颖的；绝妙的；光明的24．furthermore ad v.此外；再者25．fault n．弱点；过错26．shift n．转变；转换；轮班v i.& v t.转移；挪动；转向Ⅲ.知拓展单词1．frustrated adj.懊恼的；懊丧的；失意的→frustrate v t.使懊恼；使懊丧→frustration n．懊丧；懊恼；挫败2．infection n．感染；传染→infect v t.使感染；传染→infectious adj.感染的；传染的3．proof n．证据；证明；检验→prove v t.证明link v．证明是4．multiple adj.数量多的；多种多样的→multiply v i.& v t.乘；繁殖5．intervention n．介入；出面；干涉→intervene v i.干扰；介入6．pure adj.洁净的；纯的；纯粹的→purely ad v.完全地；纯粹地→purify v t.净化；使……洁净7．defend v t.保卫；防守；辩解→defense/defence n．防备；保卫；爱护8．assistant n．助理；助手→assist v t.& v i.挂念；帮忙→assistance n．挂念；帮忙；救济9．gifted adj.有天赋的；有天才的；天资聪慧的→gift n．礼物；天赋10．steady adj.稳定的；平稳的；稳步的→steadily ad v.稳定地；持续地11．vivid adj.生动的；鲜亮的；丰富的→vividly ad v.生动地；逼真地；鲜亮地1．idiom n．习语；成语2．ignore v t.忽视3．illegal adj.非法的；不合法的4．immediately ad v.马上5．immigration n．移民6．import v t.& n．进口；输入7．impression n．印象；感觉8．incorrect adj.不正确的；错误的Ⅳ.背核心短语1．once and for all最终地；彻底地2．subscribe to同意；赞同3．thanks to幸亏；由于4．break out(战斗、打斗等不开心的事情)突然开头；爆发5．in charge of主管；掌管6．come down患(病)；染上(小病)7．above all最重要的是；尤其是8．die from/of死于9．in time准时；迟早10．be likely to do sth 很可能做某事Ⅴ.悟经典句式1．Cholera used to be one of the most feared diseases in the world，until a British doctor，John Snow，showed how it could be overcome.(until引导的时间状语从句)在英国医生约翰·斯诺向人们呈现如何战胜霍乱之前，霍乱曾是世界上最令人恐惊的疾病之一。

全国大学英语CET四级考试试题及解答参考(2025年)

2025年全国大学英语CET四级考试复习试题及解答参考一、写作（15分）Part I Writing (30 points)Directions: For this part, you are allowed 30 minutes to write a short essay on the topic “The Impact of Artificial Intelligence on Daily Life.” You should start your essay with a brief introduction to the topic, then give specific examples to illustrate your point, and finally, provide a conclusion with your personal view. Your essay should be about 120 to 150 words but no less than 100 words.Writing Sample:The advent of artificial intelligence (AI) has revolutionized our daily lives in numerous ways. From smart homes to advanced medical diagnosis, AI has become an integral part of modern society.In smart homes, AI systems like voice assistants and smart security cameras enhance our convenience and safety. These systems learn from our habits and preferences, making our homes more comfortable and efficient. Moreover, in the healthcare sector, AI algorithms are being used to analyze medical images and identify potential diseases at an early stage, which can significantly improvepatient outcomes.However, the rise of AI also brings challenges. For example, job displacement is a major concern, as AI can perform certain tasks more efficiently than humans. Additionally, there are ethical questions about privacy, data security, and the potential misuse of AI technology.In conclusion, while AI has brought substantial benefits to our daily lives, we must also address its challenges to ensure a balanced and ethical integration of AI into our society.Writing Analysis:•Introduction: The essay starts with a clear introduction to the topic of AI and its impact on daily life, providing a broad perspective.•Body Paragraphs: The body of the essay presents two distinct impacts of AI:•The positive impact of AI in smart homes and healthcare.•The negative impacts of job displacement and ethical concerns.•Conclusion: The essay concludes with a balanced view, acknowledging both the benefits and challenges of AI, and emphasizing the need for ethical considerations.•Structure and Coherence: The essay has a clear structure and is well-organized, making the flow of ideas easy to follow.•Length: The essay meets the required word count, with 120 words, demonstrating the writer’s ability to convey the main points concisely.二、听力理解-短篇新闻（选择题，共7分）第一题News:In recent years, global attention has been drawn to the rapid development of electric vehicles (EVs). According to a recent report by the International Energy Agency (IEA), the number of electric vehicles on the roads worldwide reached 13 million in 2021, up from just 2 million in 2015. The report also indicates that by 2030, the number of electric vehicles is expected to surpass 145 million.Question 1:What has the number of electric vehicles on the roads reached as of 2021 according to the recent report by the IEA?A) 1 millionB) 13 millionC) 2 millionAnswer: BQuestion 2:How many years is it mentioned from 2015 to 2021 in the report?A) 5 yearsB) 6 yearsC) 7 yearsAnswer: BQuestion 3:What is the expected number of electric vehicles by 2030 according to the report?A) 13 millionB) 2 millionC) 145 millionAnswer: C第二题News Item 1:A new study reveals that the global use of electric scooters has increased significantly in recent years. These scooters are becoming a popular form of transportation in cities around the world. However, the study also highlights the environmental and safety concerns associated with the rapid growth in electric scooter usage.Cities are faced with the challenge of managing the increased demand for parking spaces, as well as the potential risks of accidents involving these scooters. Improved infrastructure and regulations are being considered to address these issues.Questions:1、What is the primary topic of the news item?A. The decline of traditional scootersB. The environmental impact of electric scootersC. The safety concerns of using electric scootersD. The rise in global use of electric scooters2、“These scooters are becoming a popular form of transportation in cities around the world.” Which of the following is true regarding the use of electric scooters?A. They are only popular in developed countries.B. They have no environmental impact.C. They are causing a decrease in car usage.D. They have become a common mode of transportation globally.3、“Improved infrastructure and regulations are being considered to address these issues.” What is the implied issue that needs to be addressed?A. The overuse of public transportation.B. The need for more parking spaces for cars.C. The decline in bicycle usage.D. The potential safety risks and management challenges posed by electric scooters.Answers:1.D2.D3.D三、听力理解-长对话（选择题，共8分）First QuestionConversationA: Hey, Sarah! Did you finish listening to the podcast this morning?B: Yeah, I did. It was quite fascinating. Have you checked the transcript on their webpage?A: Not yet. I plan to review what we heard today after work. By the way, I was thinking it would be nice to form a study circle this semester.B: That sounds like a good idea. Could you host a meeting this weekend?A: Sure, I can. I’ll prepare some questio ns for us to discuss, and you can bring in your notes. It’ll make our learning more productive.B: Great! Should we stick to the topics in the podcast or choose something else?A: Let’s talk about the topics in the podcast first. That way, it’ll help us understand the context better.B: Sounds perfect. I have a couple of questions for you. How long have you been listening to podcasts?A: Since about a year now. I find it’s a great way to learn English while doing something productive.B: I agree. What’s your favorite podcast?A: Hmm, I really like “The Economist Briefing.” It covers current events and history, which are topics I find interesting.B: Nice choice. I’m a fan of “TED Talks Daily.” It’s a bit different from “The Economist Briefing” but still educational.A: That’s true. We can switch up the topics as we like. What are youstudying?B: I’m majoring in international relations. The podcast really helps me get more insights into what I’m studying.A: That’s awesome. What about yo ur plans for the future?B: I hope to travel around Europe for my study abroad program next year, so I’m trying to learn more European languages. It would be a great opportunity to practice my English as well.A: That sounds exciting! This weekend, let’s m eet for an hour at my place, okay?B: Sure, that works for me.Q1. What is one reason Sarah likes listening to this podcast?a)To practice her English.b)To pass CET-4.c)To prepare for a trip.d)To learn her major subject.Answer: aQ2. How long has the speaker been listening to podcasts?a)One yearb)Two yearsc)Three yearsd)Half a yearAnswer: aQ3. Who does the speaker admire for choosing “TED Talks Daily”?a)Sarahb) A friendc) A professord)Another studentAnswer: aQ4. What will they do this weekend?a)Meet for an hour at the speaker’s place.b)Join a club activity.c)Go to a coffee shop.d)Attend a lecture on English.Answer: aQuestion 2:Why does Liu feel a bit nervous about the exam?A) He is preparing for it for too long.B) He hasn’t studied hard enough.C) His friends are also enrolled in CET-4 course classes.D) He needs to take a break soon.Answer: AQuestion 3:What advice does Amy give to Liu?A) Enroll in a CET-4 course class.B) Review the past papers.C) Study every day.D) Take a break.Answer: BQuestion 4:What can be inferred about Liu from the conversation?A) He is confident about the exam.B) He has been preparing for the exam for a long time.C) He is ready for the upcoming exam.D) He doesn’t like studying hard.Answer: B四、听力理解-听力篇章（选择题，共20分）第一题Directions: In this section, you will hear a passage. Listen carefully and answer the questions that follow.Passage:In today’s fast-paced digital world, it has become increasingly important for businesses to adopt technologies that improve their efficiency and customer satisfaction. The rise of artificial intelligence (AI) and machine learning (ML) has led to significant advancements in the field of business operations. Companies are now exploring various ways to integrate these technologies to enhance their processes.1、What aspect of business operations has seen significant advancements dueto AI and ML integration?A) Customer serviceB) LogisticsC) Financial managementD) A2、Why is the adoption of AI and ML technologies regarded as important for businesses?A) To reduce operational costsB) To improve customer satisfactionC) To increase operational efficiencyD) C3、Which of the following is NOT an example of how businesses can integrate AI and ML?A) Enhancing predictive analyticsB) Automating routine tasksC) Increasing manual data entryD) C第二题Passage 1The globalization of the economy has brought about significant changes in the world, and one area that has been heavily affected is the sports industry. In this essay, we will explore how globalization has impacted the sports industry,focusing on the growth of international sports events and the role of sports in global culture.1、Why is globalization having a profound impact on the sports industry?A) Because it allows sports to be practiced anywhere in the world.B) Because it has led to the growth of international sports events.C) Because it has changed the way people culture around the world.D) Because it has increased the salaries of professional athletes.2、Which of the following is not mentioned as a change brought about by globalization in the sports industry?A) The increase in cross-cultural interactions.B) The decline in local sports teams.C) The rise of regional sports leagues.D) The increase in global fan bases for various sports.3、What is the main argument made by the essay about the role of sports in global culture?A) Sports have a单一 focus on winning and losing.B) Sports help to foster national pride and identity.C) Sports have become a way for countries to cooperatively compete.D) Sports have lost their relevance due to increased commercialization.Answer Key:1、B2、BThird Question: Listening Comprehension - Listening PassagePassage:Welcome to our final research trip to India. We are in a small village in the state of Kerala, known for its rich cultural heritage and scenic beauty. The village, named Paravoor, has a population of approximately 15,000. Today, we focus on the local economy, which is largely dependent on farming, tourism, and small-scale industries. Currently, the village is facing several challenges, including water scarcity and lack of proper infrastructure. The government plans to implement a new irrigation project, which will provide a significant boost to the agricultural sector. In addition, the village is promoting eco-tourism to diversify its economic base. However, these initiatives require support and investment from both the government and the local community.1、Which of the following is NOT a challenge facing Paravoor Village?A、Water scarcityB、Lack of proper infrastructureC、Dependence on large-scale industriesD、C、2、What is the villagers’ plan to diversify their economic base?A、Developing new industriesB、Promoting eco-tourismC、Increasing agricultural production3、Which of the following is a potential benefit of the new irrigation project?A、It will help diversify the local economy.B、It will improve the infrastructure.C、It will provide water to the entire state.D、C、五、阅读理解-词汇理解（填空题，共5分）第一题Reading PassageAlice, receiving a ring, was extremely pleased. Her father promptly asked, “Have you made up your mind, my dear?” “Not quite,” said Alice ominously, stepping out of her ring. “But I will do so directly,” she declared.With a faint shiver of delight, the father experienced her civil but firm decision and then together they went to bet {?1?} her little servant girl a seventeen-pound horse. While they were thus occupied, the children saw their disagreement. The richest and keenest-uprisinguchepest, perfectly struck their fancy, and though their(Game) competitive position was, by no means, satisfactory, they had no objection to feel very sorry for the seller.1、civil A. 非常高兴的B. 礼貌的；文明的C. 无数的；无休止的D. 非常出色的2、competititive A. 竞争性的；竞赛的B. 嫉妒的；充满敌意的C. 令人厌恶的；讨厌的D. 无能的；不称职的3、keen A. 苦涩的；尖利的B. 明锐的；敏锐的C. 高兴的；愉快的D. 枯燥的；乏味的4、Ominous A. 不吉利的；不祥的B. 温和的；文雅的C. 欢快的；愉快的D. 兴奋的；激动的5、shiver A. 战栗；发抖B. 淡水C. 快速降雨D. 柔软的动物答案:1、B2、A3、B4、A5、A第二题Directions: Read the following text and complete the sentences below. There is one word or phrase missing in each sentence. Choose the most appropriate word or phrase from the options given below each sentence.Reading Passage:The rapid growth of technology has profoundly transformed our social fabric. From the emergence of the internet to the advent of smartphones, our daily interactions and work routines have been fundamentally altered. These technological advancements have not only facilitated instant communication but also expanded our access to information. However, this shift comes with its own set of challenges. For instance, while the internet provides a vast array of resources, it also exposes us to misinformation and the need for digital literacy is increasingly important. Moreover, the reliance on technology in the workplace has raised concerns about job security, as automation and artificial intelligence continue to evolve and change the nature of work.1、The word “fabric” (Line 1) most closely r elates to the following word: _[Options: a) fabric b) structure c) society d) clothing_]•1、c) society2、The phrase “emergence of the internet” (Line 3) can be replaced with which of the following: _[Options: a) the start of the internet b) the appearance of the internet c) the deployment of the internet d) the invention of the internet_]•2、b) the appearance of the internet3、The word “instant” (Line 4) is synonymous with: _[Options: a) immediate b) brief c) quick d) rapid_]•3、a) immediate4、The challenge mentioned in the passage regarding the internet is: _[Options: a) accessing information b) exposure to misinformation c) maintaining digital literacy d) balancing physical and digital interactions_]•4、b) exposure to misinformation5、The phrase “nature of work” (Line 7) refers to: _[Options: a) the quality of work b) the purpose of work c) the essence of work d) the value of work_]•5、c) the essence of work六、阅读理解-长篇阅读（选择题，共10分）第一题Reading Passage OneIt is widely accepted that education is of great importance to all people. However, there are many arguments on its necessity. While some people believe it is important to receive an education, others argue that education is not essential in one’s life.One of the main arguments for education is that it offers opportunities for personal development. With a good education, individuals can acquire the knowledge and skills needed to succeed in life. They can also improve theircritical thinking abilities and make informed decisions. Furthermore, an education can help individuals become more adaptable and flexible, enabling them to thrive in a changing world.Opponents of education argue that people can succeed without it. They cite examples of successful individuals who dropped out of school, such as Steve Jobs and比尔·盖茨. They believe that talent and opportunities can compensate for a lack of formal education.In the following passage, there are some statements about education. Choose the most suitable answer for each of the following questions.Questions 1-51、Which of the following is the main issue discussed in the reading passage?A. The benefits of educationB. The drawbacks of educationC. The importance of personal developmentD. The relationship between education and success2、What do the proponents of education believe about the role of education in personal development?A. Education hinders personal growth.B. Education does not contribute to skill acquisition.C. Education improves critical thinking and decision-making skills.D. Education makes individuals less adaptable.3、What is the main argument against education mentioned in the passage?A. Education limits personal development.B. Successful individuals can compensate for a lack of education.C. Education stifles creativity and innovation.D. Education takes away opportunities for self-betterment.4、Which of the following does the reading passage NOT mention as a reason for supporting education?A. Increased opportunities for employment.B. Enhanced critical thinking abilities.C. Improved adaptability and flexibility.D. Theernenment in international cooperation.5、What is the author’s attitude towards the debate on education?A. The author believes that education is unnecessary.B. The author supports the idea that education is essential for personal development.C. The author prefers talent and opportunities over education.D. The author is neutral on the issue of education.Answer Key:1、A2、C3、B4、D5、B第二题Passage:The concept of cloud computing has been discussed for decades, but it has only recently become a practical solution for businesses and individuals. Itall began with the idea of using the Internet as a transmission medium for data and applications. As technology advanced, the costs of storage and bandwidth became more affordable, making cloud computing a viable option. Today, cloud services range from simple file storage to complex application delivery, and they are accessible via web browsers or special software applications.The benefits of cloud computing are numerous. First, there is no need for costly hardware or maintenance. Cloud providers handle all the backend operations, ensuring that the service runs smoothly without requiring any intervention from users. Second, cloud services are highly scalable, meaning they can handle sudden increases in demand without additional investment. Third, cloud computing encourages collaboration and mobility, as users can access data and applications from anywhere with an internet connection. Finally, cloud services often come with robust security features, which are continuously updated, minimizing the risk of data breaches.However, cloud computing also comes with challenges. Security remains a significant concern, as data is stored remotely and vulnerable to cyberattacks. Additionally, there is the issue of data sovereignty, where data stored outside a country’s borders may be subject to the laws of that country. Furthermore, some companies may be hesitant to switch to cloud services due to the lack of control over their data, a common concern known as “control issues.”Questions:1、What is the main idea of the passage?a) The history of cloud computing.b) The benefits and challenges of cloud computing.c) The security concerns of cloud computing.d) The scalability of cloud computing.2、Why did cloud computing become practical recently?a) Because of the decreased costs of storage and bandwidth.b) Because of the widespread availability of the Internet.c) Because of the advancement in technology.d) Because of the decreasing demand for hardware.3、What are the benefits of cloud computing mentioned in the passage?a) No need for costly hardware, scalability, collaboration and mobility, and robust security features.b) High scalability, easy maintenance, and data sovereignty.c) Low costs, easy access, and increased data security.d) Remote access, data availability, and decreased bandwidth requirements.4、Which of the following is a challenge of cloud computing?a) The lack of mobility.b) The high costs of hardware.c) The security risks associated with remote data storage.d) The limited availability of web browsers.5、What is the common concern known as “control issues” mentioned in the passage?a) Users have no control over their data.b) Users have control over their data, but it is stored remotely.c) Data stored outside a country’s borders may be subject to the laws of that country.d) Users can choose to control their data through special software applications.Answers:1、b) The benefits and challenges of cloud computing.2、a) Because of the decreased costs of storage and bandwidth.3、a) No need for costly hardware, scalability, collaboration and mobility, and robust security features.4、c) The security risks associated with remote data storage.5、a) Users have no control over their data.七、阅读理解-仔细阅读（选择题，共20分）First Reading Comprehension Part AReading PassageThe following is a passage about the importance of exercise for mental health and productivity. This passage is followed by some questions to which the answers can be found in the passage.In today’s fast-paced world, stress has become an integral part of our lives. It’s essential to find ways to manage and reduce stress to maintain both our mental and physical health. One effective way to combat stress is through regularexercise. Research has consistently shown that physical activity can have a profound impact on our mental well-being and productivity.1.Physical activity has been found to:A) improve mental healthB) enhance productivityC) both improve mental health and enhance productivityD) have no effect on mental health2.The passage primarily discusses:A) the negative impact of stress on mental healthB) the benefits of exercise in reducing stressC) the effectiveness of various stress management techniquesD) the effects of different types of stress on the body3.It is mentioned that physical activity can have a “profound impact” on our:A) attention spanB) moodC) ability to sleepD) All of the above4.The word “integral” in the first paragraph most closely means:A) essentialB) foundationC) simpleD) occasional5.According to the passage, what is one effective way to combat stress?A) Avoiding situations that cause stressB) Seeking professional helpC) Regular physical activityD) Meditating for a few minutes dailyOptions:1、C2、B3、D4、A5、C第二题阅读下面的文章，然后回答问题。

A theory of weak bisimulation for core cml

J.Functional Programming1(1):1–000,January1993c1993Cambridge University Press1A Theory of Weak Bisimulation for Core CMLWILLIAM FERREIRA†Computing LaboratoryUniversity of CambridgeMATTHEW HENNESSY AND ALAN JEFFREY‡School of Cognitive and Computing SciencesUniversity of Sussex1IntroductionThere have been various attempts to extend standard programming languages with con-current or distributed features,(Giacalone et al.,1989;Holmstr¨o m,1983;Nikhil,1990). Concurrent ML(CML)(Reppy,1991a;Reppy,1992;Panangaden&Reppy,1996)is a practical and elegant example.The language Standard ML is extended with two new type constructors,one for generating communication channels,and the other for delayed com-putations,and a new function for spawning concurrent threads of computation.Thus the language has all the functional and higher-order features of ML,but in addition pro-grams also have the ability to communicate with each other by transmitting values along communication channels.In(Reppy,1992),a reduction style operational semantics is given for a subset of CML calledλcv,which may be viewed as a concurrent version of the call-by-valueλ-calculus of(Plotkin,1975).Reppy’s semantics gives reduction rules for whole programs,not for program fragments.It is not compositional,in that the semantics of a program is not deﬁned in terms of the semantics of its subterms.Reppy’s semantics is designed to prove properties about programs(for example type safety),and not about program fragments(for example equational reasoning).In this paper we construct a compositional operational semantics in terms of a labelled †William Ferreira was funded by a CASE studentship from British Telecom.‡This work is carried out in the context of EC BRA7166CONCUR2.2W.Ferreira,M.Hennessy and A.S.A.Jeffreytransition system,for a core subset of CML which we callµCML.This semantics not only describes the evaluation steps of programs,as in(Reppy,1992),but also their communi-cation potentials in terms of their ability to input and output values along communication channels.This semantics extends the semantics of higher-order processes(Thomsen,1995) with types andﬁrst-class functions.We then proceed to demonstrate the usefulness of this semantics by using it to deﬁne a version of weak bisimulation,(Milner,1989),suitable forµCML.We prove that,modulo the usual problems associated with the choice operator of CCS,our chosen equivalence is preserved by allµCML contexts and therefore may be used as the basis for reasoning about CML programs.In this paper we do not investigate in detail the resulting theory but conﬁne ourselves to pointing out some of its salient features;for example standard identities one would expect of a call-by-valueλ-calculus are given and we also show that certain algebraic laws common to process algebras,(Milner,1989),hold.We now explain in more detail the contents of the remainder of the paper.In Section2we describeµCML,a monomorphically typed core subset of CML,which nonetheless includes base types for channel names,booleans and integers,and type con-structors for pairs,functions,and delayed computations which are known as events.µCML also includes a selection of the constructs and constants for manipulating event types,such as and for constructing basic events for sending and receiving values, for combining delayed computations,for selecting between delayed compu-tations,and a function for launching new concurrent threads of computation within a program.The major omission is thatµCML has no facility for generating new channel names.However we believe that this can be remedied by using techniques common to the π-calculus,(Milner,1991;Milner et al.,1992;Sangiorgi,1992).In the remainder of this section we present the operational semantics ofµCML in terms of a labelled transition system.In order to describe all possible states which can arise dur-ing the computation of a well-typedµCML program we need to extend the language.This extension is twofold.Theﬁrst consists in adding the constants of event type used by Reppy in(Reppy,1992)to deﬁneλcv,i.e.constants to denote certain delayed computations.This extended language,which we callµCML cv,essentially coincides with theλcv,the lan-guage used in(Reppy,1992),except for the omissions cited above.However to obtain a compositional semantics we make further extensions toµCML cv.We add a parallel oper-ator,commonly used in process algebras,which allows us to use programs in place of the multisets of programs of(Reppy,1992).Theﬁnal addition is more subtle;we include inµCML cv expressions which correspond to the ed versions of Reppy’s constants for representing delayed computations.Thus the labelled transition system uses as states programs from a language which we call µCML.This language is a superset ofµCML cv,which is our version of Reppy’sλcv, which in turn is a superset ofµCML,our mini-version of CML.The following diagramA Theory of Weak Bisimulation for Core CML3indicates the relationships between these languages:µCMLλcvCMLIn Section3we discuss semantic equivalences deﬁned on the labelled transition of Sec-tion2.We demonstrate the inadequacies of the obvious adaptations of strong and weak bisimulation equivalence,(Milner,1989),and then consider adaptations of higher-order and irreﬂexive bisimulations from(Thomsen,1995).Finally we suggest a new variation called hereditary bisimulation equivalence which overcomes some of the problems en-countered with using higher-order and irreﬂexive bisimulations.In Section4we show that hereditary bisimulation is preserved by allµCML contexts.This is an application of the proof method originally suggested in(Howe,1989)but the proof is further complicated by the fact that hereditary bisimulations are deﬁned in terms of pairs of relations satisfying mutually dependent properties.In Section5we brieﬂy discuss the resulting algebraic theory ofµCML expressions.This paper is intended only to lay the foundations of this theory and so here we simply indicate that our theory extends both that of call-by-valueλ-calculus(Plotkin,1975)and process algebras(Milner,1989).In Section6we show that,up to weak bisimulation equivalence,our semantics coincides with the reduction semantics forλcv presented in(Reppy,1992).This technical result ap-plies only to the common sub-language,namelyµCML cv.In Section7we brieﬂy consider other approaches to the semantics of CML and related languages and we end with some suggestions for further work.2The LanguageIn this section we introduce our languageµCML,a subset of Concurrent ML(Reppy, 1991a;Reppy,1992;Panangaden&Reppy,1996).We describe the syntax,including a typing system,and an operational semantics in terms of a labelled transition system. Unfortunately,there is not enough space in this paper to provide an introduction to pro-gramming in CML:see(Panangaden&Reppy,1996)for a discussion of the design and philosophy of CML.The type expressions for our language are given by:A::A A A A A AThus we have three base types,,and;the latter two are simply examples of useful base types and one could easily include more.These types are closed under four con-structors:pairing,function space,and the less common and type constructors.4W.Ferreira,M.Hennessy and A.S.A.JeffreyOur language may be viewed as a typedλ-calculus augmented with the type constructors A for communication channels sending and receiving data of type A,and A for constructing delayed computations of type A.Let Chan A be a type-indexed family of disjoint sets of channel names,ranged over by k, and let Var denote a set of variables ranged over by x,y and z.The expressions ofµCML are given by the following abstract syntax:e f g Exp::v ce e e e e e x e e eev w Val::x y e x k01c Const::The main syntactic category is that of Exp which look very much like the set of expressions for an applied call-by-value version of theλ-calculus.There are the usual pairing,let-binding and branching constructors,and two forms of application:the application of one expression to another,ee,the application of a constant to an expression,ce.There is also a syntactic category of value expressions Val,used in giving a semantics to call-by-value functions and communicate-by-value channels.They are restricted in form: either a variable,a recursively deﬁned function,x y e,or a predeﬁned literal value for the base types.We will use some syntax sugar,writing y e for x y e when x does not occur in e,and e;f for x e f when x does not occur in f. Finally there are a small collection of constant functions.These consist of a representa-tive sample of constants for manipulating objects of base type,,which could easily be extended,the projection functions and,together with the set of constants for manipulating delayed computations taken directly from(Reppy,1992):and,for constructing delayed computations which can send and receive values,,for constructing alternatives between delayed computations,,for spawning new computational threads,,for launching delayed computations,,for combining delayed computations,,for a delayed computation which always deadlocks,and,for a delayed computation which immediately terminates with a value. Note that there is no method for generating channel names other than using the predeﬁned set of names Chan A.There are two constructs in the language which bind occurrences of variables,xe1e2where free occurrences of x in e2are bound and x y e where free oc-currences of both x and y in e are bound.We will not dwell on the precise deﬁnitions of free and bound variables but simply use f v e to denote the set of variables which have free occurrences in e.If f v e/0then e is said to be a closed expression,which we sometimes refer to as a program.We also use the standard notation of e v x to denote the substitution of the value v for all free occurrences of x in e where bound names may be changed in order to avoid the capture of free variables in v.(Since we are modelling aA Theory of Weak Bisimulation for Core CML5:A B A:A A:A B B:A A::A A A::::A A B B:A A:A:A AFigure1a.Type rules forµCML constant functionsx yΓx:A y:BΓ:Γ:Γx y e:A BΓe:AΓf:BΓe:AΓe f:BΓe:AΓx:A f:BΓe f g:A6W.Ferreira,M.Hennessy and A.S.A.Jeffreythis reduction semantics are of the form:CτCwhere C C are conﬁgurations which combine a closed expression with a run-time envi-ronment necessary for its evaluation,andτis Milner’s notation for a silent action.However this semantics is not compositional as the reductions of an expression can not be deduced directly from the reductions of it constituent components.Here we give a compositional operational semantics with four kinds of judgements:eτe,representing a one step evaluation or reduction,e v e,representing the production of the value v,with a side effect e,e k?x e,representing the potential to input a value x along the channel k,ande k!v e,representing the output of the value v along the channel k.These are formally deﬁned in Figure2,but weﬁrst give an informal overview.In order to deﬁne these relations we introduce extra syntactic constructs.These are introduced as required in the overview but are summarized in Figure3.The rules for one step evaluation or reduction have much in common with those for a standard call-by-valueλ-calculus.But in addition a closed expression e of type A should evaluate to a value of type A and it is this production of values which is the subject of the second kind of judgement.HoweverµCML expressions can spawn subprocesses before returning a value,so we have to allow expressions to continue evaluation even after they have returned a result.For example in the expression:0a;aone possible reduction is(whereτindicates a sequence ofτ-reductions):0a;aτa?11a!0where the process returns the value1before outputting0.For this reason we need a reduc-tion e v e rather than the more usual termination e v.The following diagram illustrates all of the possible transitions from this expression:0a;aτa!0τa?vva!0vA Theory of Weak Bisimulation for Core CML7 judgements of the operational semantics apply to these conﬁgurations.The second,more common in work on process algebras,(Bergstra&Klop,1985;Milner,1989),extends the syntax of the language being interpreted to encompass conﬁgurations.We choose the latter approach and one extra construct we add to the language is a parallel operator,e f.This has the same operational rules as in CCS,allowing reduction of both processes:eαee fαe fand communication between the processes:e k!v ef k?x fe fτe v x fThe assymetry is introduced by termination(a feature missing from CCS).A CML process has a main thread of control,and only the main thread can return a value.By convention, we write the main thread on the right,so the rule is:f v feαeSecondly,e may have spawned some concurrent processes before returning a function,and these should carry on evaluation,so we use the silent rule for constant application:e v e8W.Ferreira,M.Hennessy and A.S.A.JeffreyThe well-typedness of the operational semantics will ensure that v is a function of the appropriate type,.With this method of representing newly created computation threads more of the rules corresponding toβ-reduction in a call-by-valueλ-calculus may now be given.To evaluate an application expression e f,ﬁrst e is evaluated to a value of functional form and then the evaluation of f is initiated.This is represented by the rules:eαee fτe yf g(In fact we use a slightly more complicated version of the latter rule as functions are al-lowed to be recursive.)Continuing with the evaluation of e f,we now evaluate f to a value which is then substituted into g for y.This is represented by the two rules:fτfx f gτf g v xThe evaluation of the application expression c f is similar;f is evaluated to a value and then the constant c is applied to the resulting value.This is represented by the two rulesfτfc fτfδc vHere,borrowing the notation of(Reppy,1992),we use the functionδto represent the effect of applying the constant c to the value v.This effect depends on the constant in question and we have already seen one instance of this rule,for the constant,which result from the fact thatδv v.The deﬁnition ofδfor all constants in the language is given in Figure2f.For the constants associated with the base types this is self-explanatory; the others will be explained below as the constant in question is considered.Note that because of the introduction of into the language we can treat all constants uniformly, unlike(Reppy,1992)where and have to considered in a special manner.In order to implement the standard left-to-right evaluation of pairs of expressions we introduce a new value v w representing a pair which has been fully evaluated.Then to evaluate e f:ﬁrst allow e to evaluate:eαee fτe xf v xThese value pairs may then be used by being applied to functions of type A B.For example the following inferences result from the deﬁnition of the functionδfor the constants and:e v w eeτe m nIt remains to explain how delayed computations,i.e.programs of type A,are han-dled.It is important to realise that expressions of type A represent potential rather than actual computations and this potential can only be activated by an application of theA Theory of Weak Bisimulation for Core CML9eαee fαe feαee f gαe f geαee fαef fαfe f v e fFigure2a.Operational semantics:static rules ge1αege1ge2αegeαeceτeδc v e ee f gτe ge v ee fτe yfg v xv x y g e v ee fτef v xe k?x ef k!v fv vΛk?k?x x10W.Ferreira,M.Hennessy and A.S.A.Jeffreye f g Exp::v ce e e e e e x e e eev w Val::x y e x k01c Const::Figure3a.Syntax ofµCMLv w Val::v v gege GExp::v!v v?ge v ge geΛA vFigure3b.Syntax ofµCML cve f g Exp::ge e eFigure3c.Syntax ofµCMLconstant,of type A A.Thus for example the expression k is of type A and represents a delayed computation which has the potential to receive a value of type A along the channel k.The expression k can actually receive such a value v along channel k,or more accurately can evaluate to such a value,provided some other computation thread can send the value along channel k.The semantics of is handled by introducing a new constructor for values.For certain kinds of expressions ge of type A,which we call guarded expressions,let ge be a value of type A;this represents a delayed computation which when launched initiates a new computation thread which evaluates the expression ge.Then the expression ge reduces in one step to the expression ge.More generally the evaluation of the expressione proceeds as follows:First evaluate e until it can produce a value:eτeeτe geNote that here,as always,the production of a value may have as a side-effect the generation of a new computation thread e and this is launched concurrently with the delayed compu-tation ge.Also both of these rules are instances of more general rules already considered. Theﬁrst is obtained from the rule for the evaluation of applications of the form ce and the second by deﬁningδge to be ge.The precise syntax for guarded expressions will emerge by considering what types of values of the form e can result from the evaluation of expressions of type from the basic languageµCML.The constant is of type A A and thereforethe evaluation of the expression e proceeds byﬁrst evaluating e to a value of type A until it returns a value k,and then returning a delayed computation consisting of an event which can receive any value of type A on the channel k.To represent this event we extend the syntax further by letting k?be a guarded expression for any k and A,with the associated rule:e k eeτe k!vIt is these two new expressions k?and k!v which perform communication between compu-tation threads.Formally k!v is of type and we have the axiom:k?k?x xTherefore in general input moves are of the form e k?x f where e:B and x:A f:B. Communication can now be modelled as in CCS by the simultaneous occurrence of input and output actions:e k?x ef k!v feτeΛobtained,once more,by deﬁningδto beΛ.The constant is of type A A B B.The evaluation of e proceeds in the standard way by evaluating e until it produces a value,which must be of the form ge v,where ge is a guarded expression of type A and v has type A B.Then the evaluation of e continues by the construction of the new delayed computation ge v.Bearing in mind the fact that the production of values can generate new computation threads,this is formally represented by the inference rule:e ge v ege vαveThe construct,of type A A,evaluates its argument to a value v,and thenreturns a trivial a delayed computation;this computation,when activated,immediately evaluates to the value v.In order to represent these trivial computations we introduce a new constructor for guarded expressions,A and the semantics of is then captured by the rule:e v eA vτvThe choice construct e is a choice between delayed computations as has the type A A A.To interpret it we introduce a new choice constructor ge1ge2where ge1and ge2are guarded expressions of the same type.Then e pro-ceeds by evaluating e until it can produce a value,which must be of the form ge1ge2, and the evaluation continues by constructing the delayed computation ge1ge2.This is represented by the rule:e ge1ge2ege2αege1ge2αeΓv:AΓw:BΓge:AΓv:AΓw:AΓv?:AΓge:AΓv:A BΓge1ge2:AΓA v:AΓe:AΓf:BΓτ:A Γv:AΓk?x:AΓw:Bof the form e k ?xf where f may be an open expression we need to consider relations over open expressions.Let an open type-indexed relation R be a family of relations R ΓA such that if e R ΓA f then Γe :A and Γf :A .We will often elide the subscripts from relations,for example writing e R f for e R ΓA f when context makes the type obvious.Let a closed type-indexed relation R be an open type-indexed relation where Γis everywhere the empty context,and can therefore be elided.For any closed type-indexed relation R ,let its open extension R be deﬁned as:e R x :A Bf iff e v x R B f v x for allv :AA closed type-indexed relation R is structure preserving iff:if v R A w and A is a base type then v w ,if v 1v 2R A 1A 2w 1w 2then v i R A i w i ,if ge 1R A ge 2then ge 1R A ge 2,andif v R A B v then for all w :A we have vw R B v w .With this notation we can now deﬁne strong bisimulations over µCML expressions.A closed type-indexed relation R is a ﬁrst-order strong simulation iff it is structure-preserving and the following diagram can be completed:e 1R e 2e 1R e 2ase 1lRe 2lsince the deﬁnition of strong bisimulation demands that the actions performed by expres-sions match up to syntactic identity.This counter-example can also be reproduced using only µCML contexts:kx121kx21since the left hand side can perform the move:kx12τk !x12but this can only be matched by the right hand side up to strong bisimulation:kx21τk !x21In fact,it is easy to verify that the only ﬁrst-order strong bisimulation which is a congruence for µCML is the identity relation.To ﬁnd a satisfactory treatment of bisimulation for µCML,we need to look to higher-order bisimulation ,where the structure of the labels is accounted for.To this end,given a closed type-indexed relation R ,deﬁne its extension to labels R l as:v R l A wk !v R l A k !wkChan BThen R is a higher-order strong simulation iff it is structure-preserving and the followingdiagram can be completed:e 1R e 2e 1R e 2aswhere l 1R l l 2e 1l 1Re 2l 2lotherwise.Then R is a ﬁrst-order weak simulation iff it is structure-preserving and the following diagram can be completed:e 1R e 2e 1R e 2ase 1lRe 2ˆl Let1be the largest ﬁrst-order weak bisimulation.Proposition 3.31is an equivalence.ProofSimilar to the proof of Proposition 3.1.Unfortunately,1is not a congruence,for the same reason as 1,and so we can attempt the same modiﬁcation.R is a higher-order weak simulation iff it is structure-preserving and the following diagram can be completed:e 1R e 2e 1R e 2aswhere l 1R ll 2e 1l 1Re 2ˆl 2Lethbe the largest higher-order weak bisimulation.Proposition 3.4h is an equivalence.ProofSimilar to the proof of Proposition 3.1.However,h is still not a congruence,for the usual reason that weak bisimulation equiva-lence is not a congruence for CCS summation.Recall from (Milner,1989)that in CCS 0τ0but a 00a 0τ0.We can duplicate this counter-example in µCML since the CCS operator corresponds to the µCML operator and 0corresponds to Λ.However may only be applied to guarded expressions and therefore we need a guarded expressionwhich behaves like τ0;the required expression is A Λ.Thus:ΛhA Λsince the right hand side has only one reduction:A ΛτΛτΛbut:Λk !0hA Λk !0because the only reduction of Λk !0is Λk !0k !0ΛΛand:A Λk !0τΛτΛThis counter-example can also be replicated using the restricted syntax of µCML.We have:hsince the left hand side has only one reduction:ΛΛand the right hand side can match this with:A ΛΛand we have seen:ΛhA ΛHowever:k 0hk 0since the left hand side has only one reduction:k 0τΛk !0whereas the right hand side has the reduction:k 0τA Λk !0A ﬁrst attempt to rectify this is to adapt Milner’s observational equivalence for µCML,and to deﬁne h as the smallest symmetric relation such that the following diagram can be completed:e 1he 2e 1he 2aswhere l 1h ll 2e 1l 1he 2l 2Proposition 3.5h is an equivalence.ProofSimilar to the proof of Proposition 3.1.This attempt fails,however,since it only looks at the ﬁrst move of a process,and not at theﬁrst moves of any processes in its transitions.Thus,the above µCML counter-example for h being a congruence also applies to h ;i.e.hbut:k 0hk 0This failure was ﬁrst noted in (Thomsen,1995)for CHOCS.Thomsen’s solution to this problem is to require that τ-moves can always be matched by at least one τ-move,which produces his deﬁnition of an irreﬂexive simulation as a structure-preserving relation where the following diagram can be completed:e 1R e 2e 1R e 2aswhere l 1R l l 2e 1l 1Re 2l 2Letibe the largest irreﬂexive bisimulation.Proposition 3.6iis a congruence.ProofThe proof that i is an equivalence is similar to the proof of Proposition 3.1.The proof that it is a congruence is similar to the proof of Theorem 4.7in the next section.However this relation is rather too strong for many purposes,for example 12i111since the right hand side can perform more τ-moves than the left hand side.This is similar to the problem in CHOCS where a τP i a P .In order to ﬁnd an appropriate deﬁnition of bisimulation for µCML,we observe that µCML only allows to be used on guarded expressions ,and not on arbitrary expressions.We can thus ignore the initial τ-moves of all expressions except for guarded expressions.For this reason,we have to provide two equivalences:one on terms where we are not interested in initial τ-moves,and one on terms where we are.A pair of closed type-indexed relations R R n R s form a hereditary simulation (we call R n an insensitive simulation and R s a sensitive simulation )iff R s is structure-preserving and we can complete the following diagrams:e 1R ne 2e 1R ne 2aswhere l 1R sll 2e 1l 1R ne 2ˆl 2and:e 1R se 2e 1R se 2aswhere l 1R s l l 2e 1l 1R ne 2l 2Let n sbe the largest hereditary bisimulation.Note that we require R s to be structure-preserving because it is used to compare the labels in transitions,which may contain ab-stractions or guarded events.In the operational semantics of µCML expressions,guarded expressions can only appear in labels,and not as the residuals of transitions.This explains why in the deﬁnition of n labels are compared with respect to the sensitive relation s whereas the insensitive relation is used for the residuals.For example,if ge 1n s ge 2then we have:xge 1nxge 2since once either side is applied to an argument,their ﬁrst action will be a τ-step.On the other hand:ge 1nge 2sinceis precisely the construct which allows us to embed ge 1and ge 2in acontext.Theorem 3.7s is a congruence for µCML ,andnis a congruence for µCML.ProofThe proof that s and n are equivalences is similar to the proof of Proposition 3.1.The proof that they form congruences is the subject of the next section.Proposition 3.8The equivalences on µCML have the following strict inclusions:1shh111x1xk k i h k12s i1111n s x1xh n1h h x1xwhere:x x(Note that this settles an open question(Thomsen,1995)as to whether i is the largestcongruence contained in h.)It is the operator which differentiates between the two equivalences n and h.Howeverin order to demonstrate the difference we need to be able to apply to guarded expressionswhich can spontaneously evolve,i.e.performτ-moves.The onlyµCML constructor for guarded expressions which allows this is A,and in turn occurrences of this can only begenerated by theµCML constructor.Therefore:Proposition3.9For the subset ofµCML without and A,n is the same as h,and s is the same as h.ProofFrom Proposition3.8n h.For the subset ofµCML without and A,deﬁne R s as:v w v h w ge1ge2ge1h ge2v1w v2w v1h v2Then since no event without A can perform aτ-move,and since the only initial moves ofv i w areβ-reductions,we can show that h R s forms an hereditary bisimulation,and so h n.From this it is routine to show that s h.Unfortunately we have not been able to show that n is the largestµCML congruence con-tained in weak higher-order bisimulation equivalence.However we do have the following characterisation:Theorem3.10n is the largest higher-order weak bisimulation which respectsµCML contexts.ProofBy deﬁnition,n is a higher-order weak bisimulation,and we have shown that it respectsµCML contexts.All that remains is to show that it is the largest such.Let R be a higher-order weak bisimulation which respectsµCML contexts.Then deﬁne: R n R v1w e2v1R v2v2wτe2e1v2w v1R v2v1wτe1R s v w v R w ge1ge2ge1R ge2v1w v2w v1R v2We will now show that R n R s forms an hereditary simulation,from which we can de-duce R R n n.。

AJMV], #L [AJ93b, Vin91, AO94], and #NC

On TC,AC,and Arithmetic CircuitsManindra Agrawal Department of Computer Science Indian Institute of Technology Kanpur208016,Indiamanindra@iitk.ernet.inEric Allender Department of Computer Science Rutgers UniversityP.O.Box1179 Piscataway,NJ08855-1179,USA allender@Samir DattaDepartment of Computer ScienceRutgers UniversityP.O.Box1179Piscataway,NJ08855-1179,USAsdatta@AbstractContinuing a line of investigation that has studiedthe function classes#P[V al79b],#SAC[V al79a,Vin91,AJMV],#L[AJ93b,Vin91,AO94],and#NC[CMTV96],we study the class of functions#AC.One way to deﬁne#AC is as the class of functions computed by constant-depth polynomial-size arithmetic circuits of unbounded fan-in addition and multiplication gates.In contrast to the pre-ceding function classes,for which we know no nontriviallower bounds,lower bounds for#AC follow easily fromestablished circuit lower bounds.One of our main results is a characterization of TCin terms of#AC:A language is in TC if and onlyif there is a#AC function and a number such that.Using the naming conventions of[FFK94,CMTV96],this yields:TC PAC C ACAnother restatement of this characterization is that TC canbe simulated by constant-depth arithmetic circuits,with asingle threshold gate.We hope that perhaps this character-ization of TC in terms of AC circuits might provide a newavenue of attack for proving lower bounds.cuss counting and enumeration classes.1.1.Counting ClassesCertainly the best-known counting class is V aliant’s class#P[V al79b],consisting of functions that map to the num-ber of accepting computations of an NP-machine on input .Recently,the class#L(counting accepting computations of an NL-machine)has also received considerable attention[AJ93b,Vin91,Tod,MV].#P characterizes the complexityof computing the permanent of a matrix[V al79b],while#L characterizes the complexity of computing the determinant [Vin91,Tod,V al92,MV].It should be noted that#P and#L can also be char-acterized in terms of uniform arithmetic circuits,as fol-lows:NP and NL both have characterizations in terms ofuniform Boolean circuits.(NP sets are accepted by uni-form exponential-size circuits of“polynomial algebraic de-gree,”and NL sets are accepted by uniform polynomial-size“skew”circuits[V en92].We will not need to deﬁne these concepts further here.)The classes#P and#L result if we“arithmetize”these Boolean circuits,replacing each OR gate by a+gate,and replacing each AND gate by a gate,where the input variables now take as values the Natural Numbers(instead of the Boolean values),and negated input literals1Tomo Yamakami[Yam96]has recently deﬁned#AC somewhat dif-ferently,and his deﬁnition does not appear comparable to ours.plexity.As we shall see,#AC straddles the boundary mark-ing the limits of current circuit lower bound technology. #AC provides a characterization of TC(for which no cir-cuit lower bounds are known),but on the other hand#AC is closely related to the classes AC and AC[2],and as a consequence we can prove that many simple functions are not in#AC.(This stands in contrast to the related classes #NC,#L,#SAC,and#P which,for all we know,may contain all of the functions in P.)We can also show that #AC is properly contained in#AC for every.A better understanding of#AC should aid in advancing our store of lower bound techniques.nguage ClassesCounting classes such as#P and#L are closely related to associated language classes such as PP and PL.In order to develop this in a general setting,it is useful to deﬁne the “Gap”classes.The class GapP was deﬁned in[FFK94],and by anal-ogy GapL was studied in[Vin91,AO94],and GapNC was studied in[CMTV96].In all of these cases,there are two equivalent deﬁnitions:1.Gap is the class of functions that are the difference oftwo#functions.2.Gap is the class of functions computed by the classof arithmetic circuits that characterize#,when these circuits are augmented by having the constant. (In fact,for the cases when is one of NC,L,and P, the cited papers give many other equivalent deﬁnitions,as well.)Now,for a given class,Gap gives rise to two language classes:P=Gap,,C=Gap,.PP and PL wereﬁrst studied in[Gil77]and have been considered in many papers;C P was studied in[Wag86] and elsewhere,and C L was studied in[ABO96](see also [ST]).PNC and C NC were deﬁned and studied in [CMTV96](see also[Mac]).A main result of this paper is that PAC and C AC co-incide with TC.However,there are two difﬁculties that must be overcome before we can even state this theorem. We must deal with(a)uniformity,and(b)the fact that the two most natural ways to deﬁne GapAC do not seem to be equivalent(although both ways give rise to the same class PAC=C AC=TC).Deﬁnition2DiffAC is the class of functions expressible as the difference of two#AC functions.Deﬁnition3For any,GapAC is the class of functions computed by depth circuits with-gates(theusual arithmetic sum and product)having unbounded fan-in where inputs to the circuits are fromwhere each.Let GapAC GapAC.Recall that for all the classes NC,L,SAC,P,Gap can be deﬁned equivalently either as orin terms of arithmetic circuits with access to the constant .However,in all of those cases,the proof of equivalence relies on the fact that the PARITY language is in;and ofcourse this is not true for=AC.Open Question1Is DiffAC=GapAC?Open Question2Is DiffAC?(Note that DiffAC is clearly contained in GapAC,andthat GapAC).The classes DiffAC and GapAC each provide reason-able ways to deﬁne PAC and C AC.This leads to the following two deﬁnitions:Deﬁnition4The class C AC(C AC)consists ofthose languages for which there exists a function inDiffAC(GapAC)such that for all bit strings,If then.If then.Deﬁnition5The class PAC(PAC)consists of thoselanguages for which there exists a function in DiffAC (GapAC)such that for all bit strings,If thenIf thenAt this point,the reader may fear that we are introducingtoo many complexity classes,with relatively little motiva-tion.The good news is that all of these classes are different names for TC—at least in the P-uniform and non-uniform settings.1.2.1.UniformityA(non-uniform)circuit family consists of a circuit for each input length.If there is an“efﬁcient”al-gorithm for constructing,given,then the family is said to be uniform,where different notions of“efﬁcient”give rise to different notions of uniformity.We will con-sider P-uniform,logspace-uniform,and Dlogtime-uniform circuit families.For P-uniform circuits[BCH86,All89], the mapping is computable in polynomial time,for logspace-uniform circuits[Ruz81],the mapping is com-putable in logspace.Dlogtime-uniformity requires a some-what more careful deﬁnition;we refer the reader to[BIS90]. Although Dlogtime-uniformity is widely-regarded as be-ing the“right”notion of uniformity to use when discussing small circuit complexity classes such as TC and AC,only a few of our theorems mention Dlogtime-uniformity. Open Question3Can the characterizations of TC that we present in the P-uniform and logspace-uniform setting also be shown to hold in the Dlogtime-uniform setting?1.3.The CharacterizationsIn the P-Uniform and Non-Uniform SettingsC AC PAC TC C AC PACIn the Logspace-Uniform SettingC AC PAC TC C AC PACIn the Dlogtime-Uniform SettingTC C AC PACis the required circuit showing that#AC. whereLemma4Let,be integers,where.Forall:Proof.We use induction on.This proves the base case(=1).For the inductive stepobserve that,(End of the proof of Theorem3.)Theorem9#AC,DiffAC and GapAC are closed under the choose operation(i.e.if is a function in one of these classes,then so is for any positive constant). Proof.(of Theorem9)Notice that once we know that#AC is closed under the choose operation,it follows immediately that DiffAC is closed as well(using essentially the same proof as that of Closure Property5in[FFK94]).We proceed by induction on the depth of the counting circuit computing the#AC function.If the circuit has depth0,then the claim follows trivially as assumes values0and1only.In order to prove the inductive step, we just need to prove that if are#AC functions and for some constant and all,are#AC functions,then so are and .Consider the identity:The coefﬁcient of on the right hand side is,where the sum is taken over all distinct tu-ples,satisfying.Thus comparing the coefﬁcients of on both sides of the identity we get:Here is a partition of into parts.(Note that this shows that two multivariable polynomials agree on an inﬁnite domain(the naturals);hence these polynomials agree also on the integers.)Hence,in order to show that is in#AC,we just need to show that the above expression involving a sum of products has polynomially many terms.But a simple inductive argument shows that it has less than terms: letting denote the number of terms in the sum and giving values successively,we get the following equation:Noting that is1for each and using a simple induction on we get the result.In order to prove that is in#AC,weﬁrst consider.Note that is exactly the number of ways of choosing distinct cells out of an matrix.For any choice of cells,let denote the number of columns containing of the chosen cells.Then an alternative way of choosing cells out of this matrix is toﬁrst choose the integers,then choose the columns containing exactly one chosen cell and the chosen cell within each of these,then choose the columns con-taining exactly two chosen cells and the the two chosen cells within them and so on.Consider all distinct partitions of in the formWe denote by one such partition and by,the set of all such partitions.Also deﬁne as the cardinality of the set.Then,Then using the above identity involving,we have:Let denote the number of terms in this sum once the right hand side has been completely expanded as a sum of products.Then,Claim10.Proof.The claim clearly holds for.Now assume that the claim holds for all and all,and consider the induction step.Let be.Then,where the last inequality holds inductively.Thus,This is a good time to observe that#AC is not closed under some more general choose operations.For instance,let;is clearly in#AC.For any func-tion,the function is not in#AC, since this function is0iff,and thus the under-lying Boolean AC circuit would be computing the-threshold function,which is not in AC[FKPS85,DGS86].This argument leaves open the question of what happens when but.For in this range,the threshold is computable in AC[FKPS85,DGS86],but the currently-known proofs of this fact do notpreserve the number of accepting subtrees.Open Question6Are the functions andin#AC?4.C AC PAC TCThe most important step in proving this characterizationinvolves showing how to simulate threshold circuits.Theorem11P-uniform TC P-uniform C AC and Dlogtime-uniform TC Dlogtime-uniform C AC.Proof.We will need to use the following well-known fact (see e.g.[PS88]),Fact12A problem is in TC if and only if it is accepted by a constant-depth family of“exact-threshold”gates ET (an ET gate has s inputs and outputs1iff exactly r of them are1).Let be.First we will show that there exists a P-uniform DiffAC(Dlogtime-uniform GapAC)function whose value on a string of bits isif the string contains exactly1’s and0otherwise.It is easy to see that the functionHere(.)and(.)are polynomials with coefﬁcients in#AC.They are obtained by expanding the product(where)and sepa-rating the positive and negative terms.Just as in the basecase their coefﬁcients have polynomially long binary repre-sentations and hence can be computed by P-uniform#AC circuits.Obtaining a Dlogtime-uniform GapAC is even simpler. Inductively suppose the GapAC function corresponding to is.Then proceeding the same way as for DiffAC functions we getProposition13C AC PAC(under all considered no-tions of uniformity).Proposition14P-uniform(non-uniform)GapAC P-uniform(non-uniform)FTC.(This is a simple consequence of the fact that unbounded fan-in addition and multiplication are in P-uniform TC [RT92].)Corollary15In the P-Uniform and Non-Uniform Settings,C AC PAC TC C AC PACNote that one interpretation of the preceding corollary is that TC languages can be computed with just constant-depth arithmetic and a single threshold gate.Also note that, although we do not know if DiffAC=GapAC,we ob-tain a characterization of TC using either function class. Finally,note that our normal form theorems yield an even more restrictive characterization of TC.Corollary16For any set in non-uniform or P-uniform TC,there exist a constant,a function in#AC,and a (non-uniform or P-uniform,respectively)#AC function with the following property:If,then.If,then.Proof.From the proof of Theorem11,we know that there is a DiffAC function such that if,then,and if is in,then where for some,and.Let.By Corollary6,is of the formfor some#AC function and some constant.And if any satisﬁes the congruences above then,where.More explicitly,whereAnd the following variant of the prime-number theorem: Theorem19(see e.g.[HW79])For sufﬁciently large val-ues of,the product of all primes less than exceeds. As a consequence of Theorems18and19we get the fol-lowing corollary:Corollary20If,then can uniquely be repre-sented as,where(for )and are the primes smaller than .is called the Chinese Remainder Representation of.Lemma21There is a Logspace-uniform TC circuit that decides whether a number less than is actually less than,given the residues modulo(here are theﬁrst primes and is their product). Proof.We consistently use the notation(viz.etc.)introduced in Theorem18and Corollary20.Let(in the remaining portion of the proof any unqualiﬁed or refers to an integer in the range).From the Chinese Remainder Theorem we know that the number in question (i.e.the number with residues modulo)isEssentially we need toﬁnd out theﬁrst bit of the frac-tional representation of.[DMS94]shows how to do this in Logspace.We show that their method is amenable to a TC circuit implementation.The essential idea is to compute theﬁrst bits of each of the fractions(for)andﬁnd the sumsapproximating.[DMS94]show that if the fractional part of contains any zeros,then theﬁrst bit of the frac-tional part of is equal to theﬁrst bit of the fractional part of(which is the bit that we need to compute).If, instead,the fractional part of is all ones,then consider the number that results byﬂipping the bit(recording the residue mod2of).In the Chinese Remainder Representa-tion,the number is equal to or;note that if and only if,thus if the frac-tional part of contains any zeros,we again know the value we want.If the fractional parts of and ofare both all ones,then[DMS94]show that the computa-tion can be repeated using approximating(which in this case has the same bit as).Thus our answer can be computed byﬁnding the value,which is the largest for which theﬁrst bits of the fractional part of or of are not all1.So we just need to show that each of the’s and can be computed using Logspace-uniform TC circuits.But this follows from Lemma23-7,8below.(of Lemma22-5)By successively testing each integerfor primality compute the,prime.Nowsuccessively(re)compute(for)and if,thenﬁnd the modulo-inverse of(by reducingmodulo and checking for each positive numberwhether).Keep accumulatingthe inverses in a product modulo-.Theﬁnal value ofthe product is the modulo-inverse of.(of Lemma22-6)Compute,and then computeusing pute the productand then produce theﬁrst bits of us-ing the standard long division algorithm.Proof.(of Theorem17)Let be the constant such that for alllarge,the value of the given GapAC circuit has absolutevalue less than.(Such a exists,since#AC#P.)Weuse Lemmas23-4and Lemmas23-5to construct a TC cir-cuit that computes the answer modulo the primes less than.This way any positive number is mapped intoand any negative number into.Thus it is suf-ﬁcient to test whether theﬁnal answer is greater than,which can be done with the help of Lemma21.Theorem25(Dirichlet)(see e.g.[HW79])For any two rel-atively prime numbers and,there exist inﬁnitely manyprimes in the sequence.Let be aﬁniteﬁeld,and let#AC denote the class offunctions computed by#AC circuits,where now+andare operations over theﬁeld.Theorem26A language is in ACC if and only if its char-acteristic function is in#AC for someﬁniteﬁeld. Proof.Let be a language in ACC;thus is in AC[]for some.Without loss of generality the only gates areand Mod(since can be simulated by and Mod).Ourﬁrst step is toﬁnd a prime of the form for some, using Dirichlet’s theorem(Theorem25)above.Now make copies of each gate,and replace all Mod gates with Mod gates(keeping in mind that).Thus at this stage the only gates are and Mod.Nowan gate can be replaced by a product gate modulo(sincethe value of each gate is Boolean).It remains only to simu-late the Mod gates.Let an arbitrary Mod gate have inputs.Consider(where is a generator of the multiplicative group modulo );this has value1iff the number of’s that are1is di-visible by(-1).Further,is0if is and is1otherwise.This gives us the arithmetic circuit equivalent to the Mod gate.The other direction is equally simple.We will builda circuit that computes,for each gate,a representa-tion of theﬁeld element to which evaluates.Let theﬁniteﬁeld be GF().We will use two representa-tions.One representation rep will be as a-tuple ofstrings of the form,where corresponds to ele-ment when is viewed as a vector space over GF.Note that,when given such-tuples,their sum can easily be computed by AC circuits.(When adding up the components,test for each if Mod holds.If so,then out-put as the value of the component.)The other representation rep will be of the form where,where is a generator of the multi-plicative group of.Since isﬁnite,each representation is only bits,and conversion between representations can be computed in AC.Now the product can be computed by computing rep,which can clearly be computed in AC[].This completes the proof.A similar argument shows that,for all prime and for all,#AC corresponds exactly to AC[]. We close this section with another question concerning the relationship between#AC and DiffAC.Open Question7Is there any set AC such that DiffAC?6.Lower Bounds,and ConclusionsWe know many lower bounds for#AC.For instance,the Mod function is not in#AC,as a consequence of Propo-sition27and the circuit lower bounds in[Raz87].At the end of Section3.2we saw that some functions related to the symmetric polynomials are not in#AC.Other examples can easily be generated as easy consequences of known cir-cuit lower bounds.(In contrast,no function in#P or in Pis known not to be in#NC.)We can also show that the #AC and GapAC hierarchies are strict using the known lower bounds.Theorem28For any,#AC#AC,and GapAC GapAC.Proof.We prove the theorem for#AC,the proof for GapAC is identical.Assume that#AC#AC for some.It fol-lows then that#AC#AC.Let be a language in AC but not in depth AC[2].(See,for instance Proposition11 in[AH94].We can choose to be the mod3of theﬁrst bits,for some.)The characteristic function of is in#AC,and therefore,in#AC by our assumption.But this gives a depth AC[2]circuit for,in contradiction to our choice of.[All89] E.Allender.P-uniform circuit complexity.J.ACM,36:912–928,1989.[All96] E.Allender.A note on uniform circuit lower bounds for the counting hierarchy.InInternational Conference on Computing andCombinatorics Conference(COCOON),vol-ume1090of Lecture Notes in Computer Sci-ence,pages127–135.Springer-V erlag,1996. 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Open Types and Bidirectional Relationships as an Alternative to Classes and Inheritance

Vol.6,No.3,March–April2007 Open Types and Bidirectional Relationships as an Alternative to Classes and InheritanceChristian Heinlein,Dept.of Computer Science,University of Ulm,GermanyOpen types are presented as a simple yet powerful data model for statically typed pro-cedural and object-oriented programming languages,that overcomes the limitationsof the traditional record-oriented model.The basic idea is to separate type deﬁnitionsfrom the deﬁnitions of their attributes in order to allow incremental deﬁnitions of the latter.Furthermore,bidirectional relationships are introduced as pairs of mutually in-verse attributes whose values will be kept consistent automatically.Finally,anonymousand automatic attributes are presented as a simple extension of attributes that uni-ﬁes the concepts of aggregation,inheritance(including subtype polymorphism),anduser-deﬁned type conversions.Since open types do not possess methods in the object-oriented sense,global virtual functions are used as an alternative and moreﬂexiblemeans to deﬁne behaviour,while modules are employed to achieve information hidingand type-safe separate compilation.The basic implementation ideas of open types asa language extension for C++are described.1INTRODUCTIONSince the advent of procedural programming languages in the1960s,data structures appearing in programs are typically modeled as records,and even the object-oriented notion of a class is basically a record equipped with accompanying procedures or methods.Even though data modeling based on records,e.g.,modeling a person as a record possessingﬁelds(or members)such as name,date of birth,address (which might itself be a record),etc.,is rather natural and straightforward,a severe limitation of records is the fact that they areﬁxed:Once a record type has been deﬁned,the set of itsﬁelds is invariably determined,and all its instances will possess exactly theseﬁelds.Variant records in procedural languages and subclasses in object-oriented lan-guages provide some moreﬂexibility in this regard,but a particular type or class still remainsﬁxed once it has been deﬁned.So,even though it is possible,for in-stance,to“extend”a given class Person by deﬁning a subclass PersonWithSsno in order to model persons with a social security number(ssno),the base class Person actually remains unchanged(so the term“extend”is quite misleading).This is par-ticularly problematic when an existing program(e.g.,a person management system) shall be extended later in an unanticipated way:If the original source code is not available or shall not be modiﬁed for reasons of modularity,introducing a subclassCite this article as follows:Christian Heinlein:“Open Types and Bidirectional Relationships as an Alternative to Classes and Inheritance”,in Journal of Object Technology,vol.6,no.3, March–April2007,pp.101–151,http://www.jot.fm/issues/issue200703/article3OPEN TYPES AND BIDIRECTIONAL RELATIONSHIPS AS AN ALTERNATIVE TO CLASSES AND INHERITANCE of Person does not help since the original code still creates instances of the originalclass.To overcome these kinds of problems,aspect-oriented programming languages provide so-called inter-type member declarations[22]or introductions[32]in order to actually extend an existing class deﬁnition with new dataﬁelds(and methods)in a modular way(i.e.,without needing to touch existing source code),without deﬁning a new class for that purpose.Interestingly,the possibility to truly extend the set of dataﬁelds of a class later actually makes the original possibility to deﬁne a class with dataﬁelds superﬂuous:It is always possible in principle to deﬁne a class empty, i.e.,without anyﬁelds,and to add them incrementally later.If a particular class has been extended with additional dataﬁelds multiple times, typically by diﬀerent“aspects”of a program,it might happen that many instances of the class do not actually need all theﬁelds introduced that way.For example, the social security number might be stored only for persons having an employment, while information about a person’s spouse and children might be needed only for those receiving child beneﬁt.But even for“conventionally”deﬁned data structures, where all dataﬁelds are deﬁned at once,it might happen thatﬁelds of particular instances remain unused simply because particular information is either unknown or irrelevant.Depending on the total number of unused dataﬁelds in a program,it might be worthwhile to have an underlying data representation format that stores only those dataﬁelds of an object which are actually used,similar to the way database systems optimize storage of objects containing null values.Finally,bidirectional relationships between data types,e.g.,between a person and the cars it owns,are hard to express naturally with record-based data models, since conceptually they do not belong to either type,but rather constitute entities in their own right.In order to implement them in procedural or object-oriented programming languages,it is necessary to model them as dual pairs of dataﬁelds of the participating record types,one for each“direction”of the relationship,which must be kept consistent explicitly.If,for instance,a car changes its owner,not only must its ownerﬁeld be changed accordingly,but also the carsﬁelds of both the old and the new owner must be modiﬁed to correctly reﬂect the new situation.To overcome all these limitations of traditional record and class types men-tioned above,open types will be presented in this paper as an alternative data model for statically typed procedural and object-oriented programming languages. Beforehand,however,Sec.2gives some introductory remarks about the decision to provide open types as a syntactical extension of an existing language(viz.C++) instead of developing either a completely new language or a library for an existing one.Afterwards,Sec.3brieﬂy presents null values as a generally useful concept which is particularly relevant for the design of open types.After these preparations,Sec.4introduces the basic notion of open types,to-gether with single-and multi-valued attributes,while Sec.5describes bidirectional relationships as pairs of mutually inverse attributes whose values will be kept con-102JOURNAL OF OBJECT TECHNOLOGY VOL6,NO.32DESIGN ALTERNATIVESsistent automatically.Section6presents anonymous and automatic attributes as a simple extension of attributes that uniﬁes the concepts of aggregation,inheritance (including subtype polymorphism),and user-deﬁned type conversions.Since open types are only one of two fundamental concepts of so-called advanced procedural programming languages1,the complementary concept of global virtual functions published earlier[14,16]is recapitulated in Sec.7,followed by a descrip-tion of modules to support encapsulation,information hiding,and type-safe separate compilation in Sec.8.To give a coherent example for the application of these con-cepts in concert,Sec.9presents a solution of the well-known expression problem [35].The basic ideas to implement open types,both on the linguistic level and in terms of low-level memory management and garbage collection,are presented in Sec.10,before the paper is concluded with a discussion of related work in Sec.11 and a general conclusion in Sec.12.2DESIGN ALTERNATIVESGenerally speaking,there are at least three diﬀerent possibilities for providing a new programming language concept:It might be implemented either as a library for an existing language,possibly accompanied by a framework of design patterns or coding rules(e.g.,JBoss AOP[17],which implements aspect-oriented concepts as a Java library),or as a syntactical extension of an extension language(e.g.,AspectJ[22], which extends Java with aspect-oriented language constructs),or in a completely new language.After careful evaluation of the pros and cons of these alternatives,it has been decided to implement open types as a precompiler-based language extension for the following reasons:•Providing them as a pure library framework for a statically typed procedural or object-oriented language turned out to be too complex and unwieldy to use.In fact,the code generated by the precompiler for open types and attributes is so verbose and complicated that no programmer would volunteer to write it manually.•The eﬀort for developing a completely new advanced procedural programming language based on open types,global virtual functions,and modules,has been regarded too high for now,even though it is still considered a long-term goal.•Even though a precompiler-based implementation of a language extension has some well-known limitations,e.g.,with respect to proper diagnosis of and recovery from syntax errors,it allows to construct a working environment 1See rmatik.uni-ulm.de/rs/mitarbeiter/ch/apples.VOL6,NO.3JOURNAL OF OBJECT TECHNOLOGY103OPEN TYPES AND BIDIRECTIONAL RELATIONSHIPS AS AN ALTERNATIVE TO CLASSES AND INHERITANCE for the new language concept,which can be used to gain valuable practical experience with it,in a comparatively short amount of time.The decision to actually use C++as the base language has been inﬂuenced,amongst others,by the following considerations:•Since open types are designed as a statically type-safe concept,the base lan-guage must at least support the notion of static types and provide a suﬃcient amount of static type checking.Therefore,purely dynamically typed languages such as Smalltalk or Lisp have been ruled out.The fact that static type check-ing in C++can always be circumvented by dirty tricks(such as taking the address of an object,casting it to a diﬀerent pointer type,and dereferencing it)has been accepted as a minor drawback,since accidental violations of the static type system are detected by the compiler.•In contrast to(more)pure object-oriented languages such as Eiﬀel or Java, C++is actually a multi-paradigm language[24]that supports traditional pro-cedural programming as well.Since open types and global virtual functions are more related to traditional record types and procedures than to classes and methods,theyﬁt in more naturally with a language providing these concepts than with a bare object-oriented language.Since the resulting language called C+++supports object-oriented programming alongside with traditional and advanced procedural programming,a programmer can(and should)select a particular subset of the language whichﬁts his needs and personal preferences.In particular,when using open types,all stuﬀrelated to classes with all its accompanying complexity becomes dispensable.•C++provides a rich set of independently useful concepts(one might also say that it is conceptually overloaded),such as templates,function and operator overloading,default arguments,etc.,which are not only useful for application programmers,but also for the code generated by the precompiler,which,for instance,makes heavy use of templates.Despite these arguments for C++(and against pure object-oriented languages),it should be noted that the basic concept of open types is actually language-independent and might in fact be incorporated into any statically typed procedural or object-oriented programming language.3NULL VALUESThe concept of null values,i.e.,special“values”representing the absence of any real value,is provided in various forms by some programming languages,e.g.,nil in Lisp,None in Python,null in Java,or NaN(not a number)in languages providing IEEEﬂoating point arithmetics[12].While the latter can be used with well-deﬁned 104JOURNAL OF OBJECT TECHNOLOGY VOL6,NO.34OPEN TYPES AND ATTRIBUTESsemantics just like real values(where the value of an expression containing one or more NaN operands is NaN,too),using any of the former in an operation usually leads to a run time error.Furthermore,statically typed languages typically do not provide null values for all types of the language,but mainly for reference types.2 As has been shown in more detail in[15],however,providing null values with well-deﬁned behaviour as a general concept for all types of a language yields several beneﬁts and naturally solves some otherwise intractable problems,in particular:•If a variable is not explicitly initialized,it naturally possesses no value,i.e., null,instead of an undeﬁned value or a default value such as zero.•If a function does not explicitly return a value,because it does not contain or execute a return statement,it naturally returns no value,i.e.,null.In fact,many dynamically typed languages actually exhibit such a behaviour.On the other hand,attempts to statically detect these situations at compile time(as,e.g., in Java)are necessarily limited to conservativeﬂow analyses due to the theoretical undecidability of the underlying problems,which frequently lead to annoying“false”error messages.To incorporate such a general notion of null values into C++,wrapper types called integer,character,etc.are provided for the built-in types int,char,etc. whose parameterless constructor yields a null value which is diﬀerent from any real value of the type(including zero).This implies that variables of such a type which are not explicitly initialized,are implicitly initialized to null.To conveniently check whether a given value is null,an implicit conversion to a Boolean value is provided that returns true for all real values(including zero!)and false for a null value.To achieve that functions that do not explicitly return a value implicitly return null, a corresponding return statement is added by the precompiler at the end of every function body.For the design of open types,only the fact that the parameterless constructor of a type logically returns nothing,will be essential,while the other aspects of null values might be considered independently useful.4OPEN TYPES AND ATTRIBUTESBased on the preparations of the previous section,this section introduces the core concepts of open types and attributes,using the simple conceptual data model de-picted in Fig.1as an example,while subsequent sections about bidirectional rela-tionships and anonymous and automatic attributes and relationships will describe some important extensions of this basic model.2Besides IEEE NaN values forﬂoating point types,C#’s Nullable types constitute a partial exception;however,instead of actually providing null values for all types of the language,there is a separate nullable type T?for each non-nullable type T.VOL6,NO.3JOURNAL OF OBJECT TECHNOLOGY105OPEN TYPES AND BIDIRECTIONAL RELATIONSHIPS AS AN ALTERNATIVE TO CLASSES AND INHERITANCEFigure1:Conceptual data modelType and Attribute DeﬁnitionsAn open type is simply deﬁned by declaring its name with the keyword typename, e.g.:typename Person;typename Car;This corresponds to drawing the rectangles labeled Person and Car in the graphical data model.Afterwards,a single-valued attribute such as name,corresponding to a dataﬁeld in record notion,can be deﬁned by declaring it as a kind of mapping from Person s to string s(where the latter type constitutes a predeﬁned atomic type depicted by an ellipse instead of a rectangle in order to distinguish it from user-deﬁned open types):Person->string name;This corresponds to drawing an arrow labeled name from Person to string in the graphical data model.Simultaneously,the right hand side of the deﬁnition(string name;)looks identical to a C++(member)variable deﬁnition.Similarly,a multi-valued attribute such as gnames(given names),corresponding to a dataﬁeld whose type is an array or container type,is deﬁned by using a double instead of a single arrow to indicate the multi-valuedness:Person->>string gnames;Again,this corresponds directly to drawing a corresponding arrow in the graphical 106JOURNAL OF OBJECT TECHNOLOGY VOL6,NO.34OPEN TYPES AND ATTRIBUTESdata model.Since type and attribute deﬁnitions are separated,it is easily possible to add new attributes of a type on demand,either in the same or in a diﬀerent translation unit,without needing to change the original type deﬁnition.It is even possible to dynamically load modules containing additional attribute deﬁnitions for a type,even after objects of this type have been created.Objects and ReferencesThe value of an open type variable or expression is either an internal pointer or reference3to an object of that type or a null reference,in the same way as the value of a variable or expression whose type is a Java class is either a reference to an object of that class or the special value null.As a consequence,copying an open type value simply means to copy the reference instead of the referenced object,while comparing two values simply means to compare their references.In contrast to Java,however,where null constitutes a generic value compatible with all reference types,there is a separate null value for each open type that can be obtained by calling its parameterless constructor.To check whether a given value is null,an implicit conversion to a Boolean value is provided that returns true if the value actually references an object and false if it constitutes a null reference(cf. Sec.3).Constructors and MutatorsTo create,initialize,and modify objects of an open type T,the following constructors and mutators are provided.As already mentioned,the parameterless constructor T(),which might either be called explicitly or is called implicitly for variables of type T which are not initialized explicitly[33],returns the null reference of type T,i.e.,a reference to no object.In contrast,the attribute-initialization constructor T(@attr,val)creates a distinct new object of type T,i.e.,an object that is diﬀerent from null and any other object, initializes its attribute attr with value val,and returns a reference to it.Since open types are designed to be statically type-safe,attr must have been declared as an attribute of type T,and val must be assignment-compatible with its target type.Similarly,the attribute mutator obj(@attr,val)modiﬁes the object(referenced by)obj by setting the value of its attribute attr to val(if attr is a single-valued attribute)or by appending val to its values of attribute attr(if attr is a multi-valued attribute).Expressed diﬀerently,obj(@attr,val)always adds val to obj’s values of attr,after discarding any previous value if attr is single-valued.4Again, 3The term“reference”is used in its general meaning here,which is somewhat diﬀerent from the C++notion of references[33].4For multi-valued attributes,there are also variants of the mutator to remove a previously added value and to insert a new value at a particular position.VOL6,NO.3JOURNAL OF OBJECT TECHNOLOGY107OPEN TYPES AND BIDIRECTIONAL RELATIONSHIPS AS AN ALTERNATIVE TO CLASSES AND INHERITANCE to ensure static type safety,attr must have been declared as an attribute of obj’s (static)type,and val must be assignment-compatible with its target type.As a result of the operation,the object(reference)obj is returned,which allows straight-forward combinations of a constructor call with one or more mutator calls to create an object with multiple initial attribute values,e.g.:Person p=Person(@name,"Hoare")(@gnames,"Charles")(@gnames,"Anthony")(@gnames,"Richard"); Here,the constructor call Person(@name,"Hoare")creates a new Person object, initializes its attribute name with the string"Hoare",and returns(a reference to) the object.This object(reference)is directly used in the mutator call...(@gnames, "Charles")which initializes its attribute gnames with"Charles"and returns the same object(reference).This is again used in and returned by the subsequent muta-tor calls...(@gnames,"Anthony")and...(@gnames,"Richard")which in turn add the strings"Anthony"and"Richard"to the values of attribute gnames.Finally, the object(reference)returned by the last mutator call is assigned to the Person variable p.Of course,it is also possible to perform constructor and mutator calls separately, e.g.:Person p=Person(@name,"Hoare");p(@gnames,"Charles");p(@gnames,"Anthony")(@gnames,"Richard");To create an empty object,i.e.,a distinct object which is diﬀerent from null and any other object,but does not possess any attribute values yet,the empty constructor T(@)can be used,which is called with a pseudo-argument@to distinguish it from the parameterless constructor T().Therefore,a call T(@attr,val)to the attribute-initialization constructor is actually just a shorthand for T(@)(@attr,val),i.e.,a call to the empty constructor followed by an appropriate mutator call.In addition to these predeﬁned constructors of open types,it is possible to deﬁne arbitrary user-deﬁned constructors,e.g.://Create person with given name g and name n.Person(string g,string n){return Person(@name,n)(@gnames,g);}In contrast to normal C++constructors(and constructors in other object-oriented programming languages),which must be deﬁned(or at least declared)inside their class and must not explicitly return anything,but rather initialize the implicitly available object this,user-deﬁned constructors of open types are much like ordi-nary(global)functions whose result type and name coincide(and therefore only one of them is speciﬁed in their deﬁnition).In particular,there is no implicitly available object this,and the constructor must explicitly(create and)return an object,typi-cally by calling one of the predeﬁned constructors.Furthermore,just like attributes, 108JOURNAL OF OBJECT TECHNOLOGY VOL6,NO.34OPEN TYPES AND ATTRIBUTESconstructors can be deﬁned incrementally on demand.Attribute InspectionsTo inspect the attribute values of a given object,the attribute inspection operator@ can be used,quite similar to the way the dot operator is used to access class members in C++and other languages,e.g.,p@name or p@gnames.5For a single-valued attribute such as name,its current value is returned,i.e.,the value that has been set for this attribute by the most recent mutator or attribute-initialization constructor call for this object.If none of these operations has been performed for the object yet,i.e.,the attribute does not possess any value,nothing is returned conceptually,i.e.,a null value of the attribute’s target type(i.e.,string in the current example)that is obtained by calling its parameterless constructor(cf. Sec.3).6If a multi-valued attribute such as gnames is inspected with the@operator, the values added to this attribute by all mutator(and attribute-initialization con-structor)calls performed for this object so far are returned as a(possibly empty) ordered sequence.Even though it is possible to grasp such a sequence as a whole,it is typically processed element by element using a tailored iteration statement,e.g.: for(string g:p@gnames)cout<<g<<"";This prints p’s given names in the order in which they have been added,i.e.,Charles Anthony Richard.Alternatively,it is possible to directly inspect individual values of such a sequence by applying the standard index operator,e.g.,p@gnames[2],to obtain the second given name of p,i.e.,"Anthony".Similarly to inspecting the value of a non-existent single-valued attribute,inspecting a non-existent value of a multi-valued attribute by using an out-of-range index yields nothing,i.e.,a null value that is obtained in the same way as described above.Therefore,expressions such as p@gnames[0]or p@gnames[4]will return a null string in the current example.Similar to an attribute mutator operation,an attribute inspection obj@attr is type-correct,if attr has been declared as an attribute of obj’s static type,and the 5It would have been possible to reuse the existing dot or->operator for that purpose,too,just like existing keywords such as typename have been reused to avoid the introduction of new ones. Introducing a new operator,however,cannot create any incompatibilities with existing C++code, while introducing a new keyword(e.g.,type)would cause programs using this as an identiﬁer to become invalid.6If the target type of an attribute is a user-deﬁned or built-in C++type(such as int)that does not possess a distinct null value,its parameterless constructor would return a default value such as zero,which is conceptually quite diﬀerent from no value.Therefore,such types should ideally be prohibited as target types of attributes,which could actually be enforced by the precompiler. For practical reasons,however,in particular to simplify the integration of C++legacy code into C+++programs,any kind of target type is allowed.By means of a compile-time switch,it is possible to specify whether the default value returned by the parameterless constructor shall be returned or an exception shall be raised when a non-existent attribute value of such a target type is accessed.If a type does not possess a public parameterless constructor,the former alternative will lead to a compile-time error.VOL6,NO.3JOURNAL OF OBJECT TECHNOLOGY109OPEN TYPES AND BIDIRECTIONAL RELATIONSHIPS AS AN ALTERNATIVE TO CLASSES AND INHERITANCE result type of the operation is equal to the attribute’s target type(for single-valued attributes)or a sequence of it(for multi-valued attributes),where a sequence is deﬁned as a type-safe container similar to an array.In either case,the attribute inspection operator returns an R-value[33],i.e.,a value which must not occur on the left hand side of an assignment operator.Therefore,attribute update operations must only be performed by mutator calls,not directly by assignments such as: p@name="Hoare";//Syntax error!If such an assignment would be allowed,the attribute inspection operator could not simply return a null value for a non-existent attribute,but would be forced to implicitly create the attribute in that case,i.e.,to allocate space for it,in order to be able to return an L-value referring to it.This would lead to many unnecessary attribute creations in practice.Inspecting and Modifying Null ObjectsTrying to inspect or modify the“object”referenced by a null pointer is illegal in C++and many other languages and usually leads to a run time error such as a SIGSEGV(segmentation violation signal)or a NullPointerException.In contrast, inspecting and modifying attributes of open types is well-deﬁned even for null ob-jects/references:While inspecting such an attribute is equivalent to inspecting a non-existent attribute,i.e.,returns null,modifying such an attribute simply has no eﬀect.The main reason for these unusual deﬁnitions is convenience,since they allow to omit many otherwise necessary checks.To test,for example,whether p’s name is"Hoare",one can simply write if(p@name=="Hoare")–instead of if(p&& p@name=="Hoare")–even if p might be null;if it actually is,p@name is null, too,and therefore,as expected,diﬀerent from"Hoare".Similarly,testing whether the third given name of p is"Richard",one simply writes if(p@gnames[3]== "Richard"),without needing to check explicitly whether p is not null,whether it has given names at all,and whether it has a third given name.Simultaneously,pro-grams tend to become more robust since inadvertently omitted checks will not lead to run time errors,but usually merely to unsatisﬁed conditions.Similarly,the fact that mutator calls on null objects are silently ignored,fre-quently reduces the need to explicitly distinguish between real and null objects,and again,inadvertently omitting such distinctions does not lead to run time errors.Ref-erence[15]contains a more detailed discussion of the pros and cons of this unusual deﬁnition.Garbage Collection and Object DeletionIn contrast to normal C++objects,which must be explicitly deleted by the pro-grammer to reclaim their storage,objects of open types are automatically garbage-collected when they have become unreachable,quite similar to objects of classes in Java,Eiﬀel,Smalltalk,and many other programming languages.110JOURNAL OF OBJECT TECHNOLOGY VOL6,NO.3。

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Abstract In general few components are reused as they are.Often,available components are incompatible with what is required.This necessitates component adaptationsor the use of adapters between components.In this paper we develop algorithmsfor the synthesis of adapters,coercing incompatible components into meeting re-quirements.We concentrate on adapters for concurrent systems,where adaptersare able to resolve synchronisation problems of concurrent components.A newinterface model for components,which includes protocol information,allows usto generate these adapters semi-automatically.Keywords:Component interfaces,interoperability,adapter generation,ﬁnite state machines One of the anticipated beneﬁts of component oriented software develop-ment is,that a component can be deployed in several contexts.Unfortunately, practice shows,that components rarely can be deployed as they ually they have to be adapted to achieve interoperability with the environment.Since components are reused mainly as black-boxes,the component user usually can only perform adaptations as conﬁgurations of the component,which must be foreseen by the component developer.But in practice,the component devel-oper cannot foresee in advance all contexts of the component’s future deploy-ment.The middleware,in which the components are deployed,acts as a(more or less)transparent medium,while the actual interoperability problem occursbetween components working together via the middleware.One way to solve this interoperability problem is,that the middleware,in which the component is deployed,provides mechanisms to achieve interoperability between compo-nents automatically.This interoperability can be realised in two ways:(a)by automatic adaptations of the component(Reussner,2001)or(b)by generating adaptors,which reside between a component and its environment(Yellin and Strom,1997).Adaptor generation requires a detailed information about component in-teractions.Unfortunately,the interface descriptions of common component models do not include a lot of such information.Whereas the IDL’s known form Java or CORBA only provide method signatures(which can be seen a very rough contracts for methods deployment),interactions between methods are not described within these interface models.Especially,there is a de-mand for information concerning the valid sequences of method calls(Nier-strasz,1993;Kr¨a mer,1998;Vallecillo et al.,1999;Reussner,2001;de Al-faro and Henzinger,2001).For adaptor generation in particular,information about(a)the supported sequences of methods provided by a component and (b)the sequences of calls to external methods,which a component can per-form,is required(Yellin and Strom,1997).These protocols are formed by the application-level components and are independent of the underlying commu-nication protocols(such as TCP/IP,UDP,etc.)In section2.1we propose an approach for modelling component interfaces withﬁnite state machines.This enrichment of interface speciﬁcations can be used to(semi)-automatically gen-erate adapters for bridging component protocol incompatibilities.Subsection 2.2reviews the terms compatibility and conformance in the context of architec-tural connections.Three different kind of adapters to overcome common cases of component incompatibility are described in section3:(A)One component uses two(or more)other components.(B)Two components simultaneously use a third one.Here the mediating adapter has to perform synchronisation between the two using components.(C)One component uses another one but with conﬂicting protocols.In section4we present related work concerning other architectural component models and protocol speciﬁcation for compo-nents.Section5concludes and describes future work.More background in-formation and details about the algorithms presented in section3is given in( Schmidt and Reussner,2000).In our methods and tools we termed a self-contained component a ken(En-glish:range of knowledge;Japanese:area(of local autonomy)(Schmidt and Chen1995;Schmidt1998)).Such a composite ken may be hierarchically de-ﬁned in terms of other more primitive kens.But most importantly it deﬁnes a protection domain with well deﬁned connections from and to other kens.The ken encompasses a cluster of“internal”objects.It separates them from,and controls their interoperation with,the outside world.The connection control is exercised by so-called gates.Gates contain a signature list(like classical inter-faces do)and,additionally,a protocol speciﬁcation,i.e.,a description of a set of call sequences,as described below.Gates also may contain speciﬁcations of non-functional properties(i.e.,quality of services),where appropriate and nec-essary.(In this paper we do not further pursue analyses using non-functional ken properties.)Using the term“ken”rather than component emphasises the usage of gates instead of classical interfaces.Gates tell us how to enter or interoperate with a ken.In this way,they enable a black-box view of kens.We distinguish between required and provided gates.A provided gate de-scribes possible connections to the external world for purpose of providing a service.A required gate represents possible connections to other components that required to perform the services provided.In our architecture description,required gates are connected to provided gates(of other components)to show,as part of the architectural design,the kind of distributed components and their interoperation necessary to perform the overall function of the system.Each gate describes a component interface,by listing a method signature and deﬁning the protocol for method calls.The protocol is speciﬁed as aﬁnite state machine(FSM).The sequences of method calls accepted by this FSM are call sequences supported by the component.An example of a valid call sequence to a video-player component may be the sequence play-pause-play-stop,whereas the sequence pause-stop is commonly not supported.The provided gate FSM is abbreviated by P-FSM for short.Analogously to the provided gates,the required gates model the required external methods and components and all possible sequences of calls to these external methods.These sequences are again modelled in a FSM.For short,the required gate FSM is abbreviated R-FSM.In the following we use the common notion of deterministic FSMs(e.g.,like used in the UML). Deﬁnition1(Finite State Machine)A FSM comprises an input alphabet(),a set of states (),a set ofﬁnal states(),a start state(),and a total transition function.The P-FSMs input alphabet is the set of methods provided by the compo-nent.In the reverse,the input alphabet of the the R-FSM is the set of (external)methods required by the component.To introduce the usage of adapters a proper architectural context,ﬁrst we have to discuss how kens are related to their environment.Therefore,we re-view the terms compatibility and conformance.In design-by-contract we distinguish between correctness and conformance.A component implementation is correct in relation to its interface contract when it is both consistent and complete .Roughly,consistency means that two behaviours distinct according to the speciﬁcation,are distinct in the imple-mentation’s behaviour.A trivial example is the distinction between true and false,or that between returning from a call and raising a deﬁned pleteness means roughly that any behaviour observable according to the speciﬁcation is indeed implemented.A simple form of completeness implies that all features listed in the interface are actually implemented;more complex forms of speciﬁcation require all possible orders of calls permitted according to the speciﬁcation to be served by the implementation.Correctness is thus a relation between implementation and interfaces.Quite distinct from correctness,we deﬁne conformance as a relation between inter-faces of two different components such that either these components can in-teroperate adequately or one can replace the other.Regarding substitutability,conformance is deﬁned between two instances of the same kind.The confor-mance between two kens can be reduced to the conformance between their provided gates and that of their required gates.Conformance regarding inter-operability is deﬁned for patibility ﬁnally,extends the abovebinding provided mapping kenprovided gate required gate required mappingExample:Kens,Gates,Bindings and Mappingsrelationships.A component is compatible to its environment if its contracts (more generally its precode)are conformant to a given architectural context,its implementation must be correct,and possibly compliance may entail a num-ber of other aspects including compliance to standard notations for its precode, standard protocols,possibly domain-speciﬁc,etc.In our gray-box approach to kens we show the hierarchical decomposition of kens into lower-level kens and gates.A conﬁguration of sub-kens with their interoperation connections is shown inside the box for the encompassing ken.This leads to the distinction of gate mapping from gate binding(seeﬁg.1).When the required gate of a ken is connected to the provided gate of a neighbour ken,this is called a binding.A binding is considered legitimate if the provided gate conforms to the required gate.Intuitively this means that every call sequence generated by the FSM of the required gate is accepted by the provided gate’s FSM.This includes a form of subtyping and thus permits signiﬁcant variation-again in contrast to DARWIN which always requires identity:the required FSM deﬁnes a sublanguage of the provided one-in the sense of formal automata theory.In contrast to a binding,a mapping relates a provided gate of the composite ken to the provided gate of one of its interior kens,or one of its required gates to the required gate of an interior ken.Because there are many provided and required gates to one ken,confor-mance under substitution has two forms(in accordance with(Frick et al., 1996)):Conformance demands that1in each provided mapping,the interior gate conforms to the exterior gate (contravariant conformance);2in each required mapping,the exterior gate conforms to the interior gate (covariant conformance);3there may be unmapped interior provided gates;4there may be unmapped exterior required gates;A weaker variant is partial(or context-dependent)conformance which is like conformance except that1there may be unmapped exterior provided gates,if these are not used in the encompassing ken’s context;2there may be unmapped interior required gates,if these cannot be reached from required gates;Hence,when ken is to replace ken one has to check(a)whether the provides interface of includes the provides interface of and(b),whether the requires interface of is included in the requires interface of.Checking whether is bound correctly to(i.e.,whether can use)is realised by testing whether the requires interface of is included in the provides interface of.These tests are applicable in general;they must hold for normal signature-based interface models as for protocol-modelling interfaces.For the latter,the inclusion of the languages,described by the interface FSMs must be checked.Most commonly synchronisation problems arise(a)when one component uses two other components or(b)through concurrent use of a component by two other components.For this purpose a split-operator(handling case(a)) and a join-operator(for case(b))is introduced.The former provides a single gate and requires two gates to which incoming calls are dispatched appropri-ately.The latter,conversely,joins the incoming call streams of two provided gates and channels them its sole required gate.With these two operators,all other kens can be normalised in the canonical representation by merging their gates into a single provided and a single required gate by using the shufﬂe-FSM construction deﬁned in a subsequent section.The shufﬂe-FSM represents all possible interleavings of the original component behaviours.These adapters also lead to an architectural simpliﬁcation.This simpliﬁcation normalises con-nections such that each gate has a unique binding or mapping.The last adapter we present adapters for a speciﬁc class of protocol in-compatibilities where a component’s protocol needs some extra methods calls which are not performed by the using component.In this subsection we describe the generation of an adapter between a ken and two kens and which are used by.The adapter dispatches the calls of to the right ken(or).The beneﬁt of this adapter is the pre-sentation of’s and’s provides interfaces in a single interface.That allows interoperability checking,like described in section2.2.Problem1(1:n Adapter)Given two provided gates and,how can one merge their behaviours into a single combined behaviour.To solve this problem we apply the construction of the shufﬂe-FSM. The concept of a shufﬂe-FSM is,that both constituent FSMs(in our case the P-FSMs)can switch states independently.In each state of all,events acceptable in that state are acceptable in the combined FSM.The converse also holds.The resulting interleaving is modelled exactly by the shufﬂe language of the provided gates.The formal construction of the shufﬂe of two FSMs is a well known operation(motivated by shufﬂe languages(Shaw,1978)).Hence, the general concept of a shufﬂe-FSM is applicable to our problem.Applied to our problem,the constrcution works as follows.Algorithm 1(Construction of Shufﬂe-FSM)Given two FSMs and the resulting shufﬂe-FSMis constructed as followsthe input alphabet is the union of and .Note that the inputalphabetsand must be disjoint.This can always be achieved by preﬁxing the method names with the name of their ken).the set of states is the Cartesian product of the state sets and :.a stateis in the set of accepting states ,iff or .the start-state is ,and the transition function is deﬁnediff iff (1)Note that the resulting FSM is deterministic,since both FSMs are deterministic and have a disjoint input alphabet.From the construction of the transition function of the shufﬂe-FSM as deﬁned in equation 1it follow:Lemma 1The shufﬂe-FSM (constructed fromand )contains all allowed call se-quences to a combined interface of and .P-FSM VideoPlayerP-FSM SoundPlayer P-FSM VideoPlayer (left)and P-FSM SoundPlayer (right)Figure 3shows an example,where the shufﬂe-FSM of the provided gate of the VideoPlayer ken (Figure 2,left)and the provided gate of a Sound-Player (Figure 2,right)is shown.Now,for example,we can adapt the functionality of the VideoMail (us-ing VideoPlayer and SoundPlayer )according the functionality of that shufﬂe FSM.The complexity of this algorithm lies mainly in the deﬁnition of transitions.The number of resulting transitions is never larger than.The algorithm produces an 1:2-adaptor,which can be applied associatively multiple times to create an 1:n -adaptor.P-FSM P-FSM VideoPlayer SoundPlayerFig.6shows a producer-consumer system 4.A producer writes to a buffer,then a consumer reads and clears the buffers.The producer can continue writ-ing the next symbol to the buffer.(For sake of brevity,lets assume buffer size1.This means,producer and consumer communicate using a simple handshake protocol.)It is clear that synchronisation between producer and consumer is necessary.The consumer hasto wait for the producer to ﬁll the buffer.Like-wise,the producer has to wait for the consumer to read and clear the buffer.The task of the join-operator is to automatically ﬁnd these points of synchro-nisation.ProducerConsumerBuffer Writer as producer,Reader as Consumer and Buffer as input for the join-operator generation.Problem 2(Synchronisation)Given two required gates and ,how can one merge their behaviours into a single combined behaviour such that1.conﬂicting calls exclude each other (calls are conﬂicting,when they bothcall the same method of a provided gate.2.calls fromand are synchronised relative to a shared provided gate .The algorithm to ﬁnd these synchronisation points works as follows:Algorithm2pute the shufﬂe-FSM as deﬁned in algorithm1from and.Note that the input alphabets and are not necessarily disjoint.So,the resulting shufﬂe-FSM may be non-deterministic.But for later use, we annotate each transition with the name of the required gate it came from(either or)and we refer to that annotation as the owner of.A method of or called from an edge is denoted by method.When constructing the shufﬂe-FSM,we deﬁne a mapping,which maps each transition of to its originating transition in or.2.Build the intersection FSM of the shufﬂe-FSM and the providedgate FSM.The resulting is non-deterministic,iffis non-deterministic.3.Derive synchronisation information from and:for each path in from to an accepting statedoin paths with circles,circle only twiceold null;for each edge doannotate with excludes;if old null thenif owner old owner thenannotate old with”-,enables”;enabling the other transitionannotate with”enables,-”;waiting on the other transitionfifiold;ododThe set denotes all edges from the state that originates from,having the owner owner and method method.The intermediate Writer Reader and the Writer Reader Buffer are shown in Figure5.The annotations are given in statechart event syntax(Harel,11,2-/readIntermediate FSM constructions:Writer Reader and Writer Reader Buffer.1987),as also used for the dynamic models in UML.An annotation a/b means that this transition has to wait on event a andﬁres event b(when the transition is used,i.e.,event a arrives).The result of the algorithm are the annotations “-/enables R-FSM Writer::write1”and“enables R-FSM Reader::read1/-”for the read operation.Both anno-tations can be combined to“enables R-FSM Reader::read1/enables R-FSM Writer::write1”.Similarly,the result for the R-FSM Writer:write operation is “enables R-FSM Writer:write1/enables R-FSM Reader:read1”.Toﬁnd the dependency between the write-and the read-operation,we have to visit the states in the order1,2,1,2,1.That is,we have to take the loop twice. To see,why this algorithm solves problem2,we state the following lemma Lemma2The FSM describes all possible sequences of calls from and to the ken.Proof1Analogous to lemma1the FSM describes all possible sequences of calls to external methods,which and can emit simultaneously.The inter-section with the provided gate FSM restricts to the call sequences supported by.Theorem1Algorithm2solves the synchronisation problem2.Proof2From lemma2we know that describes all possible sequences of calls from and to the ken.If a state has several edges,which are all calling the same method from then only one call can be performed,that is the other calls are excluded.Synchronisation is required between consecutive calls,when theﬁrst call is emitted by another component than the second call.These dependencies are detected by traversing all paths(while taking loops only twice).Taking loops only twice sufﬁces to detect in theﬁrst cycle the dependencies with in the loop.The second circle detect the dependency between the last and theﬁrst statement in the loop.Note that Algorithm2does not resolve conﬂicting method calls.It just de-tects conﬂicting calls.An appropriate resolving strategy might be implemented manually by the programmer,or could be an additional parameter for the adapter generator.The complexity of this algorithm lies mainly in the construction of the shufﬂe-FSM and the cross product.Both constructions require maximummax steps.(Since the input alphabets are overlapping we take their maximum instead of their sum.)Again,this algorithm produces an 2:1-adaptor,which can be applied associatively multiple times to create an n:1-adaptor for an arbitrary n .In the above section we concentrated on the synchronisation of two (or in general several)components simultaneously using another component.All us-ing components and the used component were given.We looked for the set of synchronisation points (if existing).In this section we tackle the case where one ken ()uses another ken (),but the protocols R-FSM and P-FSM are not compatible.Because of simplicity,in the latter we refer with and to R-FSM and P-FSM .In some cases we can compute a restriction of ’s functionality (i.e.,adaptation of P-FSM (Reussner,2001)).But this works only if the intersection of the languages described by and is not empty.One interesting case of incompatible protocols (which results in an empty in-tersection)is that the methodcalled by exists in principle,but is not yet ready in the current state of .Some such protocol incompatibilities can be resolved by ’preﬁxing’each call to with a sequence of calls to .These ’preﬁx calls’bring into a state,in which the concerned method of can be called.For example imagine a required gate of a simple CD player GUI,which only can start,stop,and pause the current CD.Now couple this to a more powerful provided CDPlayer gate additionally offering to select one of ﬁve CDs,before playing them.The R-FSM SimpleCDPlayer and the P-FSM CDPlayer are shown in Figure 6.P-FSM selectCD1/-selectCD2/-R-FSM SimpleCDPlayer (left)and P-FSM CDPlayer (right)In this example we need to preﬁx R-FSM SimpleCDPlayer ’s method play in state one with calls to init and selectCDn .Here we can recognise two simple facts:(a)there may be several different possible preﬁxes.This ambi-guity must be resolved by the software designer(here one might choose se-lectCD1for example).(b)not every call of play must be preﬁxed.Only calls to play must be preﬁxed,when P-FSM CDPlayer is in state one.(In gen-eral the preﬁx depends on the state of,the state of and the method of tobe called).One problem occurs:It is not sufﬁcient to generate a preﬁx to bring into a appropriate state(say),where can handle a call to a method(say ).We must also ensure that in state can handle all possible sequencesof calls to its methods that can emit after the call to.This clearly restrictsthe set of preﬁing preﬁxes means that a call to a method of mustﬁrstbring into an appropriate state.After that call,might be left in this state–yet this state is not aﬁnal state.In order to coerce to move to aﬁnalstate,some additional postﬁx transitions need to occur.It is noteworthy,thatnot all component incompatibilities can be resolved by preﬁxing or postﬁxing.A valid preﬁx or postﬁx may not exist.Problem3(Initialising/Finalising problem)Given a R-FSM and a P-FSM,we look for a function prefix which given a triplet method returns a sequence of methods such that:(a)They are called in state to driveinto a state enabling the method.(b)the methods of that can be called from after being in state are also supported by.Furthermore,we require a function postfix,which given a triplet method returns a sequences of method calls such that the sequence starts in and takes into aﬁnal state after method was called by.The main step to compute this functions,is to create a so-called asymmetricshufﬂe-FSM.The set of states of this FSM is a subset of the Cartesian productof the state set of and.The main idea is that this FSM contains two kindsof transitions:marked and unmarked transitions.Marked transitions go from a tuple with an input,where in both FSMs is handled in state (resp.).In an unmarked transition,the input is only handled in,but not in.(Since we do not consider the case,that inputs are accepted in and not in,we call this shufﬂe-FSM asymmetric.)Now we can look for a preﬁx as a path in this asymmetric shufﬂe-FSM from a state tuple to a marked transition.Similarly the postﬁxes are deﬁned as paths from to a ﬁnal state.The asymmetric shufﬂe-FSM of our example is shown in Figure7.As theresult of our example the preﬁx for CDPlayer:Play in state1is:init,SelectCD1.Note that the selection of theﬁrst CD is a choice of the pro-grammer.The algorithm would present all possible CD’s here(1–5).The rest of the section describes the algorithm and argues why it solves theproblem.Before we can state the algorithm,we have to deﬁne three predicates.Ac-cording to Kleene(Kleene,1956),eachﬁnite FSM describes a regular lan-selectCD1AShuffle-FSM SimpleCDPlayer + CDPlayerThe asymmetric shufﬂe-FSM of the CDPlayer and the SimpleCDPlayerguage.This language clearly depends on the start state of the FSM.When not assuming a ﬁxed start state,we can parameterise the language recognisedby an FSM with the start state.Letdenote the language recognised by FSM ,when state is takes as its start state.A ﬁnite FSM may containtransitions,i.e.transitions which do not consume any input symbol (and so are used non-deterministicly).The set RL (restricted language in depen-dence of the start state)is deﬁned as,where is the FSM with every transitionreplaced with an transition iff Now we can state the predicate (language contained),used in thealgorithm.is true iff the language is contained in the language.Algorithm 3(Construction of the Asymmetric Shufﬂe-FSM)Given one requires-FSM and one provides-FSM the resulting asymmetricshufﬂe-FSMis deﬁned as follows the input alphabet is .the set of states is a subset of the Cartesian product of the state setsand :.After creating the transition function (as deﬁned below)one has to check for each stateif (predicates also deﬁned below).In case this condition is not true,the stateis removed from the state set (and the transition function adapted accordingly).a state is in the set of accepting states ,iff andand the predicate (deﬁned below)is true.Note that the requirement that both states andare required to be ﬁnal states.(That differs from the deﬁnition of the ’symmetric’shufﬂe-FSM.)the start-state is ,and the transition function is deﬁnediffundeﬁnedundeﬁnediff undeﬁnedundeﬁnedthe set of marked transitions:a transitionundeﬁned undeﬁnedAfter the construction of this FSM,one may have to remove unreachable or dead states.The function Set:prefix()returns for a state in and a state in and for each input symbol a(possibly empty)set of preﬁxes (method calls)which must be injected in before method can be called.preﬁx()return pathesstarting from and ending in undeﬁned Likewise,the function Set:postfix()returns for aﬁnal state in and a state in and for each input symbol a(possibly empty)set of postﬁxes(i.e.a set of sequences of method calls)which must be injected in after method was called to bring inﬁnal state.This function postfix is necessary,because when FSM is in aﬁnal state,but is not,we cannot wait on a next call of a method of since is in aﬁnal state.postﬁx()return pathesstarting from and ending inAs speciﬁed in the functions prefix and postfix,we are looking for paths to(resp.from)marked transitions,because a marked transition originating from a state is supported in state by,and in state by.Due to the construction of the asymmetric shufﬂe-FSM,a path from a stateto is a sequence of method calls.This sequence must be called in. It brings to a state where the transition is supported by.(Similar rea-soning holds for the postfix function).Formal deﬁnitions of the functions prefix and postfix are given in(Schmidt and Reussner,2000).When se-lecting a preﬁx in state,we must ensure that can accept all possible sequences which can emit.If necessary we use further preﬁxing to ensure the acceptance.This is ensured by predicate LC.Putting this together,the functions prefix and postfix solve the initialising/ﬁnalising problem.The complexity of this algorithm lies mainly in the construction of the asym-metric shufﬂe-FSM and the cross product(max).Architecture deﬁnitions take a mix of black-box and glass-box approach in which successively some interior architectural and conﬁguration aspects。

On spatial reasoning with description logics - position paper

On Spatial Reasoning with Description Logics—Position PaperMichael WesselUniversity of Hamburg,Computer Science Department,Vogt-K¨o lln-Str.30,22527Hamburg,GermanyEmail:mwessel@informatik.uni-hamburg.deAbstractWe discuss a family of DLs called ALCI RCC which are suitable for qualitativespatial reasoning on various levels of granularity.In contrast to our previouswork where we investigated concept satisﬁability in the basic description logicALC in combination with composition–based role inclusion axioms of the formS◦T⊑R1⊔···⊔R n and role disjointness,we are now only considering the roleaxioms that are derived from the so-called RCC composition tables.In order tocorrectly capture the semantics of these relationships,inverse and disjoint rolesare needed.We discuss what we have found out so far.We make some remarksonﬁnite model reasoning,which is especially useful in database applications;e.g.the deductive qualitative Geographic Information System(GIS)scenario we havein mind.1Introduction and MotivationAt DL2001,we presented an overview of various ALC-extensions with composition based role inclusion axioms of the form S◦T⊑R1⊔···⊔R n,enforcing S I◦T I⊆R I1∪···∪R I n on the models I(see[4]).A set of these role axioms was called a role box,and the resulting logic was called ALC RA⊖.In previous work we have shown that concept satisﬁability in ALC RA⊖(and even in smaller sublanguages)becomes undecidable if concept satisﬁability w.r.t.arbitrary role boxes is considered.However, certain classes of so-called“admissible”role boxes satisfying additional conditions were shown to be decidable(e.g.the logic we called ALC RASG).One of the original motivations for extending ALC in that way was to augment a description logic like ALC with some kind of qualitative spatial reasoning capabilities(see also[2]).Since role disjointness is an important requirement if one considers roles as spatially exclusive base relationships,we also investigated the logic ALC RA,enforcing role disjointness on all roles(R,S∈N R,R=S:R I∩S I=∅).ALC RA turned out to be undecidable as well(see[4]).What is the relationship of these ALC extensions to qualitative spatial reasoning? In theﬁeld,the so-called RCC-family of spatial reasoning calculi is well-known(see [3]).A description of a concrete spatial scene with RCC-relationships can be seen as a complete edge-colored graph—between any two spatial objects,exactly one so-calledbase relation holds.This is called the JEPD-property(jointly exhaustive and pairwise disjoint).In the case of RCC8,we can distinguish eight,and in the case of RCC5only ﬁve base relations–some qualitative distinctions are ignored,see Figure1.It even makes sense to deﬁne RCC3,RCC2,and RCC1,oﬀering coarser and coarser spatial description capabilities.We admit that the main purpose for us to consider them here is to get a better understanding of the problems involved.Given that we do not have complete deﬁnite knowledge concerning a scene(some spatial relationships might be unknown or only vaguely known),we can combine general logical inferences with spatial inferences in order to either infer more speciﬁc spatial relationships,or to get more appropriate descriptions of the objects involved in that scene(see also[2]).For example,if the relationship between object a and c is not speciﬁed(in fact,this corresponds to the disjunction of all base relations)but given that we know the relation between a and another object b(say,S)and also between b and c(e.g.T),then we can read oﬀthe possible base relations between a and c from the entry in the so-called RCC composition table for S◦T(see Figure2a). Each entry represents an inference pattern of the form∀x,y,z:S(x,y)∧T(y,z)⇒(R1(x,z)∨...∨R n(x,z)),which is translated into a corresponding ALC RA role axiom S◦T⊑R1⊔···⊔R n.Corresponding to the underlying composition table,we call these special ALC RA specializations ALC RCC8,ALC RCC5,and so on.If we handle these relations as roles in ALC RA,we can use universal quantiﬁcation(concepts of the form∀R.D)to pose additional constraints on c.It is our conviction that the ability to quantify over roles corresponding to spatial relationships is a key-ability andﬁrst-order requirement for the qualitative spatial reasoning applications that we are trying to realize.1However,the class of concepts that might be used as qualiﬁcations within universal quantiﬁers is subject to discussion.It is obvious that quantiﬁcation involving only pure propositional concepts is much easier to handle than full quantiﬁcation. It should be noted that there are various(space and time)logics that do not oﬀer universal quantiﬁcation at all.However,ALC RA—with arbitrary role boxes—is undecidable,and the qualitative spatial reasoning specialization ALC RCC only make sense if also the appropriate inverse relationships of the base relations are respected.It is of course important that the inverse relationship must be respected,since some spatial inferences cannot be drawn otherwise.For example,the concept(∃DR.(C⊓∀DR.C))⊓∃P P I.¬C is unsatisﬁable in ALCI RCC5,but satisﬁable in ALC RCC5.This is due to the fact that DR◦P P I→DR, and therefore,the two∃-successors are linked via DR in the case of ALCI RCC5due to the requirement that DR I=(DR I)−1which is only respected in ALCI RCC5,but not in ALC RCC5.Concerning ALCI RCC8,the question whether it might be decidable or not was already raised by Cohn in(slightly diﬀerent form in)[1],where he suggests to use a pair of modal operators2R and3R for each available spatial base relationship R of RCC.Subsequent work with Bennett then focused on encoding of RCC relationships and networks in modal and intuitionistic(propositional)logic.However,they did not investigate quantiﬁcation over RCC relationships.1Currently,only the logic ALCRP(S2)oﬀers this ability(see[2]).Unfortunately,ALCRP(S2)somehow suﬀers from a severe restriction regarding the allowed quantiﬁer patterns in order to achieve decidability.We use the function inv to refer to the corresponding converse role(e.g.PPI= inv(PP),DR=inv(DR)).Please note that inv is total on N R.A model of a concept is an interpretation I=def(∆I,·I)that is a usual ALC model for that concept,i.e.maps concept names to subsets of∆I,roles to subsets of∆I×∆I, but additionally satisﬁes the disjointness,converse and composition requirements as speciﬁed by the corresponding RCC composition table.That is,for all roles R,S∈N R,R=S we have R I∩S I=∅,and if S◦T⊑R1⊔···⊔R n is an entry in the RCC composition table,then S I◦T I⊆R I1∪···∪R I n holds,and if R=inv(S),then R I=(inv(S)I)−1.Please note that we are working with a purely abstract semantics-we do not give a speciﬁc truly spatial interpretation for the objects as two-dimensional regions or the like here.Obviously,SR has to be an equivalence relation–every object is spatially re-lated to every other object(including itself).In the case of RCC2we additionally require that{<x,x>|x∈∆I}⊆O I,and in the case of RCC3,RCC5and RCC8 {<x,x>|x∈∆I}⊆EQ I must hold.This is plausible if we think of EQ as equal-ity—it might even be plausible to require that the interpretation of EQ is exactly the identity relation:EQ I={<x,x>|x∈∆I}.We call this the strong(er)EQ se-mantics(or the weak(er)EQ semantics,respectively).The stronger EQ semantics is appealing from a practical point of view since it makes the plausible assumption that no two diﬀerent congruent objects in the world might exist.As usually,we say that an interpretation I is a model of a concept C,written I|= C,if and only if C I=∅.2 In the following we make some observations concerning the considered DLs.First of all,none hast the tree model property,but we claim that some have theﬁnite model property(see below).ALCI RCC1is decidable and equivalent to the modal logic“S5”.It is well-known that“S5”is NP-complete.We refer to the nesting depth of2and3modalities as modal degree.From modal logics we know that every“S5”formula having a modal degree higher than one can be reduced to an equivalent“S5”formula having degree one.This is due to the equivalences3p≡23p(equivalently,∃SR.C⇔∀SR.∃SR.C for all concepts C),2p≡32p,3p≡33p,2p≡22p that are valid in“S5”,and which allow us to discard all nested modalities but the last one in an“S5”formula. Each“S5”formula can therefore be brought into modal conjunctive normal form, where each conjunct is a disjunction of the formβ∨2γ1∨...∨2γn∨3δ1∨...∨3δm, such that allβ,δi andγj are propositional formulas.ALCI RCC2is decidable as well.The composition table is trivial:{DR◦O→{DR,O},DR◦DR→{DR,O},O◦O→{DR,O}}.It is obvious that every com-plete and{DR,O}-colored graph satisﬁes the role box axioms.The validities(ax-iom schemas)of this logic include the axioms∃O.C⇒∀O.(C⊔∃{O,DR}.C)⊓∀DR.∃{O,DR}.C),∃DR.C⇒∀DR.(C⊔∃{O,DR}.C)⊓∀O.∃{O,DR}.C,∀O.C⇒C. It is open whether ALCI RCC2is still NP-complete.In fact,it seems to be impossible to enforce exponentially large models.We therefore conjecture it has the polysize-model property.In the case of ALCI RCC3we have to distinguish between ALCI RCC3with the strong EQ semantics and the weak EQ semantics:for example,∃EQ.(C⊓∃EQ.¬C)is satisﬁ-able only under the weak EQ semantics,but unsatisﬁable otherwise.The composition table is as expected(without symmetric entries):{DR◦ONE→{DR,ONE},DR◦DR→{DR,ONE,EQ},ONE◦ONE→{DR,ONE,EQ},EQ◦DR→{DR},EQ◦ONE→{ONE},EQ◦EQ→{EQ}}.In order to prove decidability of ALCI RCC3, we now give a reduction from concept satisﬁability in ALCI RCC3to satisﬁability in ﬁrst order predicate logic with two variables and equality,which is a decidable logic. Deﬁnition2Let C be an ALCI RCC3concept in negation normal norm(NNF).More-over,we assume that each concept C occurring within∃R.C and∀R.C is in disjunctive normal form(DNF),such that each conjunct in the disjunction of conjunctions is ei-ther an atomic concept,a negated atomic concept,or a concept of the form∃S.D or∀S.D,where D is again in DNF and NFF,etc.We then assume that there is a functionα,which,applied to a disjunct D of the above DNF(note that D is itself a conjunction),returns the modal part of D,and that there is a corresponding function βwhich returns the propositional part of D,e.g.if D=A1⊓(¬A2)⊓∃R.E⊓∀S.F, thenα(D)={∃R.E,∀S.F}andβ(D)={A1,(¬A2)}.We skip the(easy)deﬁnitions ofαandβhere,as well as for DNF and NNF.The following two mutually recursive functionsφx andφy do the main job(φy is obtained fromφx by swapping x and y):φx(C)=def C(x),if C is an atomic conceptφx(¬C)=def¬φx(C)φx(C1⊓...⊓C n)=defφx(C1)∧...∧φx(C n)φx(C1⊔...⊔C n)=defφx(C1)∨...∨φx(C n)φx(∃EQ.C)=def( mp∈α(C)φx(mp)∧(∃y:EQ′(x,y)∧EQN(y)∧bp∈β(C)φy(bp))∨φx(C)),if C is not a disjunctionφx(∃EQ.(C1⊔...⊔C n))=defφx(∃EQ.C1)∨...∨φx(∃EQ.C n)φx(∃R.C)=def(∃y:R(x,y)∧φy(∃EQ.C)),if R=EQφx(∀EQ.C)=def( mp∈α(C)φx(mp)∧(∀y:EQ′(x,y)∧EQN(y)⇒ bp∈β(C)φy(bp))∧φx(C)),if C is not a disjunctionφx(∀EQ.(C1⊔...⊔C n))=def¬(φx(∃EQ.DNF(NNF((¬C1⊓...⊓¬C n)))))φx(∀R.C)=def(∀y:R(x,y)⇒φy(∀EQ.C)),if R=EQThe“FO2=”translation of C is then deﬁned as follows(note the use of“=”):∀x,y:DR(x,y)⊕ONE(x,y)⊕x=y⊕(EQN(x)∨EQN(y))∧∀x,y:DR(x,y)⇔DR(y,x)∧∀x,y:ONE(x,y)⇔ONE(y,x)∧φx(C)2 We claim that the resulting formula is equi-satisﬁable with C under the weak EQ semantics in ALCI RCC3.The proof can be found in a forthcoming report.It is obvious that already FO2without equality is suﬃcient if one translates ALCI RCC3 with the strong EQ semantics into FOPL.But considering the weak EQ semantics, we have to ensure that∀x,y,z:EQ(x,z)⇔DR(x,y)∧DR(y,z)⊕ONE(x,y)∧ONE(y,z)⊕EQ(x,y)∧EQ(y,z)is satisﬁed.In order to achieve an equi-satisﬁable FO2formula(using only two variables!)we have to exploit the special properties of“=”,which ensures that equal objects are in fact interpreted as identical domain objects.The trick is that“x=y”is used to represent EQ(x,y).Whenever two objects are forced to be EQ,the“=”relationship ensures that the RCC network cannot become inconsistent without being recognized as inconsistent.Suppose that EQ(x,y), and that for some z,we have DR(x,z)and ONE(z,y).The network is obviously inconsistent.Fortunately,due to“x=y”,representing EQ(x,y),the inconsistency will be detected:DR(x,z)implies DR(y,z)and DR(z,y)due to symmetry,together with ONE(z,y)violating the disjointness requirement.However,note that under the weak EQ semantics,x and y could very well have diﬀerent propositional descriptions in ALCI RCC3,even if EQ(x,y)holds.Thus,one has to separate the modal and the propositional point of view of the“EQ”-connected objects.For example,∃EQ.C⊓∃EQ.¬C is consistent,but translating this into∃x,y,z:x=y∧C(y)∧y=z∧¬C(z) obviously yields an unsatisﬁable formula.The separation is therefore achieved by using a further binary predicate“EQ′”.Nested occurrences of∃EQ....and∀EQ....-concepts areﬂattened during the translation,similar to the“S5”modal conjunctive normal form which has a modal degree of one(see above).It should be noted that the diﬀerence between ALCI RCC3with the strong and the weak EQ semantics is that the former requires that EQ I is a congruence relation for all present unary and binary predicates(that is,concepts and roles),whereas the latter only enforces that EQ I is a congruence relation for all present binary predi-cates.The weak EQ semantics can,of course,be made“strong”by conjoining,for all relevant concept names C,the global axioms C→∀EQ.C to the original concept (add∀{EQ,DR,ONE}.(C→∀EQ.C)as a conjunct to the original concept).Then, it is easy to see that all EQ-connected nodes in a model(they form an EQ-clique)can be collapsed into a single node,and we still have a model.Considering ALCI RCC5and ALCI RCC8we can observe that neither has theﬁ-nite model property,unlike ALCI RCC3and its sub-languages.Due to the asymmet-ric and transitive PP relation in ALCI RCC5,for example,the concept((∃P P.⊤)⊓(∀P P.∃P P.⊤))has noﬁnite models.See below for a short discussion.There is some indication that ALCI RCC5could possibly be computationally easier to handle than ALCI RCC8,since the latter seems to have more expressive power. More speciﬁcally,unlike ALCI RCC5,ALCI RCC8somehow allows the distinction of a role and its transitive orbit(this is a role whose interpretation contains at least the transitive closure of the interpretation of the generating role;“somehow”because it is not strictly a transitive orbit,see below).The following concept enforces an inﬁnite chain of even-odd-...-marked individu-als,see the“spatial illustrations”in Figure2b.Each node can distinguish its direct TPPI-successor from all its indirect xly speaking,we can con-sider NTPPI somehow as the transitive orbit of TPPI;more speciﬁcally,we have ((T P P I I)+−T P P I I)⊆NT P P I I(please assume that odd=def¬even):◦DR(a,b)PO(a,b)EQ(a,b)PPI(a,b)PP(a,b)DR(b,c)T DR PO PPI DR DR PO PPI DR PO(b,c)DR PO PP T PO PO PPI DR PO PP EQ(b,c)DR PO EQ PPI PP PP(b,c)DRPOPPPO PP PP PO EQ PP PPI PP PPI(b,c)DR DR POPPIPPI PPI T a)RCC5Composition Table;T =def {DR,P O,EQ,P P,P P I }ALCI RCC 8model of even odd chainFigure 2:RCC5table and inﬁnitely descending modeleven odd chain =def even ⊓(∃TPPI .∃TPPI .⊤)⊓(even ⇒∀TPPI .odd )⊓(odd ⇒∀TPPI .even )⊓(∀NTPPI .((even ⇒∀TPPI .odd )⊓(odd ⇒∀TPPI .even )))⊓(∀TPPI .((even ⇒∀TPPI .odd )⊓(odd ⇒∀TPPI .even )))⊓(∀NTPPI .∃TPPI .⊤)Due to the RCC8composition table,we haveTPPI ◦TPPI →{TPPI ,NTPPI },TPPI ◦NTPPI →{NT P P I },NTPPI ◦TPPI →{NT P P I },NTPPI ◦NTPPI →{NT P P I }.This possibility came to us as a surprise.Once a role and its transitive orbit (or closure)can be distinguished,it is easy to see that even ﬁnite pseudo-models repre-senting inﬁnite ALCI RCC 8models would have to be exponential in size of the length of the input concept.Finite pseudo-models are,for example,constructed by tableau calculi for logics like SHIQ that also lack the ﬁnite model property and whose inﬁnite models can be represented ﬁnitely by means of a so-called blocked tableau,which can be understood as a pseudo-model.We can observe that a calculus for ALCI RCC 8would at least have to construct pseudo-models of exponential size in the length of the input concept.This is demonstrated with the following classical “binary n-bit counter”concept:counter =def even odd chain ⊓∃TPPI .∃TPPI .(¬bit 0⊓¬bit 1⊓...⊓¬bit n −1)⊓∀NTPPI .(toggle bit 0⊓toggle bit 1⊓...⊓toggle bit n −1)toggle bit 0=def (bit 0⊓∀TPPI .¬bit 0)⊔(¬bit 0⊓∀TPPI .bit 0)toggle bit i =def ((⊓0≤j<i bit j )⊓((bit i ⊓∀TPPI .¬bit i )⊔(¬bit i ⊓∀TPPI .bit i )))⊔(¬(⊓0≤j<i bit j )⊓((bit i ⊓∀TPPI .bit i )⊔(¬bit i ⊓∀TPPI .¬bit i )))There does not seem to be a way to achieve a similar eﬀect in ALCI RCC 5.Please note that each pseudo-model would most likely have to represent an exponential number of nodes (e.g.2+2n here),since even propositional clashes could not be detected otherwise —say,the conjunction ⊓0≤j<n bit j turns out to be unsatisﬁable which can only be detected in the 2+2n th node.3Future Work-Finite Model Reasoning with ALCI RCC5? If we have such problems showing decidability or undecidability of ALCI RCC5and ALCI RCC8,then might it probably be easier to restrict ourselves toﬁnite model rea-soning,i.e.impose a semantics where concepts that have only inﬁnite models are considered as unsatisﬁable?This would also be appealing from an application point of view.Generally speaking,ﬁnite model reasoning is not necessarily easier than reasoning with general models(Trakhtenbrot).However,it may be easier.For ex-ample,(∃P P.⊤)⊓(∀P P.∃P P.⊤),(∃DR.⊤)⊓(∀DR.∃P P I.⊤),and(∃DR.∃P O.C)⊓(∀P O.¬C)⊓(∀DR.¬C)⊓(∀P P.((∃DR.∃P O.C)⊓(∀P O.¬C)⊓(∀DR.¬C)))only have inﬁnite models.It is tempting to suspect that“‘PP”and/or“PPI”within universal and/or existential value restrictions are responsible for spawning the inﬁnite models.Aﬁnite model reasoning ALCI RCC5calculus would have to detect the unsatis-ﬁability of all given examples.We were experimenting with some kind of“inﬁnity checker”that tried to detect whenever an inﬁnite structure is enforced by the current tableau expansion history(of course,this might be undecidable as well).But note that an“inﬁnity checker”is in fact a stronger predicate than a blocking condition —the blocking condition would have to ensure that whenever it returns TRUE,an inﬁnite model can be constructed.In contrast,the inﬁnity checker must not know whether the concept under consideration is satisﬁable in the inﬁnite or not.The problem we are trying to solve seems to be related to the well-foundedness problem in part-whole-reasoning.Summing up,we have made someﬁrst steps from the general ALC RA⊖,ALC RA and ALC RASG logics,missing inverse roles,to logics that are useful for qualitative spa-tial reasoning.We are optimistic that at least for ALCI RCC5the mentioned problems can be overcome.It is also easy to see that there are restricted versions of ALCI RCC5 and ALCI RCC8whose decidability can easily be shown;e.g.allow only propositional concepts in universal quantiﬁers,etc.But this is not our mission.References[1]A.G.Cohn.Modal and Non Modal Qualitative Spatial Logics.In F.D.Anger,H.M.Gues-gen,and J.van Benthem,editors,Proceedings of the Workshop on Spatial and Temporal Reasoning,IJCAI,1993.[2]V.Haarslev,C.Lutz,and R.M¨o ller.A description logic with concrete domains and arole-forming predicate operator.Journal of Logic and Computation,9(3):351–384,June 1999.[3]D.A.Randell,Z.Cui,and A.G.Cohn.A Spatial Logic based on Regions and Connections.In B.Nebel,C.Rich,and W.Swartout,editors,Principles of Knowledge Representation and Reasoning,pages165–176,1992.[4]M.Wessel.Obstacles on the way to spatial reasoning with description logics–some unde-cidability results.In Carole Goble Deborah L.McGuinness,Peter F.Patel-Schneider and Ralf M¨o ller,editors,Proceedings of the International Workshop in Description Logics2001(DL2001),number49in CEUR-WS,pages122–131,Stanford University, California,USA,August1-32001.RWTH Aachen.Proceedings online available from rmatik.RWTH-Aachen.DE/Publications/CEUR-WS/Vol-49/.。

Cohesion in English

Cohesion in EnglishThe various kinds of cohesion had been out lined by MAK Halliday in his writings on stylistics and the concept was developed by Ruqayia Hasan in her University of Edinburgh doctoral thesis.Cohesive relations are relations between two or more elements in a text that are independent of the structure: for example between a personal pronoun and an antecedent proper name, such as John ….he. A semantic relation of this kind may be set up either within a sentence with the consequence that when it crosses a sentence boundary it has the effect of making the two sentences cohere with one another.The major function of cohesion is text formation. As defined: text is a unified whole of linguistic items, this unity of text as a semantic whole is source for the concept of cohesion.So first we will explore the concept of text.TextText in linguistics refers to any passage spoken written of whatever length that forms a unified whole. A reader can easily identify whether the passage he is reading is a text or otherwise a collection of unrelated sentences. A text may be: spoken, written, prose, verse, dialogue, monologue, single proverb, a single cry for help or all day discussion on a committee. A text is a unit of language in use. A grammatical unit that is larger than a sentence. A text is not something that is like a sentence only bigger or larger. It is misleading. Rather text can be best defined as a semantic unit; a unit not of form but of meaning. If it is semantic unit, we will not expect to find it in structure of a sentence as a grammatical unit as phrase, clause etc.So text is not consist of sentence but it is realized by sentence or encoded in sentences.There are certain objective factors involved that constitute a text.Constituents of Text1.Texture:2.Ties:3.Cohesion1. Texture:Texture is that feature of text which made it a unified whole.According to ‘The Concise Oxford Dictionary of Linguistics by P.H. Mathews’ cohesion and coherence are sources which create texture. Crys tal adds ‘informativeness’ to cohesion and coherence.Example:Wash and core six cooking apples. Put them into a fireproof dish.Here them reference back to six cooking apples to create cohesion between the two sentences. Here we make a presupposition about the relationship between them and six cooking apples but it is not enough only to make a presupposition rather that presupposition must be satisfied to create texture as shown in the example . These two items are co referential and this coreferentiality creates texture.Here are five cohesive devices to create texture:(i)Reference(ii)Substitution(iii)Ellipses(iv)Conjunction(v)Lexical Cohesion2. TiesThe term refers to a single instance of cohesion.Example:Wash and core six cooking apples. Put them into a fireproof dish.Them and six cooking apples show reference as tie.If we take the Example:Wash and core six cooking apples. Put the apples into a fireproof dish.Here are two ties(i)Reference(ii)RepetitionCohesive analysis of text is made in terms of tie for a systematic account of its patterns which area source for texture. Onward we will use the term ‘cohesive tie’ in place of ‘tie’.Here are five different kinds of cohesive ties that are also called cohesive devices:(i)Reference(ii)Substitution(iii)Ellipses(iv)Conjunction(v)Lexical cohesionMAKH and RH have based their model of cohesion on these cohesive ties. A detailed review is given here in the proceeding discussion.3. Cohesion‘The Concise Oxford Dictionary of Lin guisti cs by P.H. Mathews (1997)’ defines cohesion in term of syntactic unit (sentence).‘ A Dictionary Of Linguistics And Phonetics by David Crystal (1997)’ defines cohesion in terms of a grammatical unit (words)MAKH and RH (1976) argued that the concept of cohesion is semantic one. For them it refers to relation of meaning that:exists with in textgives the text texturedefines the text as textThis relation of meaning between the elements gives the reader presupposition. This is another way of approaching the notion of cohesion that presupposing and the presupposed give us a presupposition at semantic level as a relation of meaning: The one element presupposes the otheri.e. the one element cannot be decoded without the presupposed.Example:Time fliesYou can’t; they fly too quickly.You can’t (Ellipses)They (Reference)Fly (Lexical Cohesion)Types OF CohesionLanguage is multiple coding system comprising three levels of coding:➢Meaning The semantic system➢Wording The lexicogrammatical system(grammar an vocabulary)➢Sounding/writing The phonological and orthographical systemCohesive relation fit into the overall pattern of language. Cohesion is expressed partly through vocabulary and partly through grammar.:1. Grammatical Cohesion(i) Reference(ii) Substitution(iii) Ellipses2. Lexical CohesionThe distinction between grammatical cohesion and Lexical cohesion is a matter of degree and MAHK RH suggested not to go in the depth of these overlapping areas and that conjunction is on the border line of the two types mainly it is grammatical but with the lexical component so we cannot clearly distinguish between the two types.Cohesion and the Linguistics StructureTexture and StructureStructure is one mean of expressing texture. Text consists of one sentence are fairly rare but they can be single sentences as well for ExampleNo smokingWonder never ceaseBut most of the text extends beyond the confines of single sentences so structure is important in a text as structural units such as phrase, clause and sentence which express the unity of text. But our use of term Cohesion refers especially to the non structural text forming relation. They are semantic relations and the text is a semantic unit.Cohesion With in the TextSince cohesive relation is not concerned with structure, they may be found just as well with in the sentence as between sentences cohesive relation are beyond the sentences boundaries. Cohesion is semantic relation between one element in the text and some other element that is crucial for its interpretation. This other element must also be found with in the text. Cohesion refers to the range of possibilities that exist for linking something with what has gone before. The Place of Cohesion in the Linguistics SystemHalliday (1985) has described three major functional semantic components:(i)The Ideational(ii)The Interpersonal(iii)The TextualTable: the place of cohesion in the description of English functional components of semantic systemConclusionCohesion is a part of text forming component in the linguistics system. It links together the elements that are structurally unrelated through the dependence of one on the other for its interpretation. Without cohesion the semantic system cannot be effectively activated at all. Cohesive Devices(i)Reference(ii)Substitution(iii)Ellipses(iv)Conjunction(v)Lexical cohesion1. ReferenceThere are certain items in any language which cannot be interpreted semantically in their own right rather they make reference to something else within the text for their interpretation. Here is an example of referenceDoctor Foster went to Gloucester in a shower of rainHe stepped in puddle right up to his middleAnd never went there againHere in the above exampleHe refers back to Doctor FosterThere refers back to GloucesterHe and there show that information about them is retrieved elsewhere within the text. It characterizes a particular type of cohesion which is called reference. The relationship of referenceis on semantic level. The reference items must not match the grammatical item it refers to. What must match or the semantic properties of reference item in relation to the items it refers to. Reference can be sub-categorize as followReferenceExophora EndophoraAnaphora CataphoraExophoraIt indicates situational references. Anaphora signals that reference must be made to the context of situation. It is outside the text so it is called anaphoric reference.Example;Fo r he’s a jolly good fellow and so say all of us.Here text is not indicating who he is?He can be recognized by the situation in which expression is used. They are not source of cohesion because there presupposition cannot be resolved within the text rather the presupposition is found outside the text.EndophoraIt is a general name for reference within the text. This reference can be of two types.(i)Anaphora: Reference back(ii)Cataphora: Reference forwardExample:Child: Why does that one come out?Parent: That whatChild: That one.Parent: That one what?Child: That lever there that you push to let the water out.That one that lever (cataphoric reference)That lever that one (anaphoric reference)Types of referenceThere are three types of reference(i)Personal Reference(ii)Demonstrative Reference(iii)Comparative ReferenceIt is better first explain the structure of nominal group then proceed towards three types of Reference. It is because we will analyze nominal group for cohesive analysis of these cohesive devices.Nominal GroupThe logical structure of the nominal group (noun phrase) is that it consists of head with optional modifier the modifying elements include some which precede the head and some which follow it. They can be referred as Pre modifier and Post modifier respectively.ExampleThe two high stone wall along the roadside.Wall ------------ HeadThe two high stone ------------ Pre modifierAlong the roadside ------------ Post modifierThe modifier can be further subcategorized as:(i)Deictic(ii)Numerative(iii)Epithet(iv)Classifier(v)Qualifier(vi)ThingExampleTheir famous old red wine.Deictic Deictic epithet classifier thingDeterminer adjective adjective adjective nounI. Personal ReferenceIt is a reference by means of function into a speech situation through the category of the person in the form of personal pronouns. The category of persons includes the three classes of personal pronouns. The category of person includes the three classes of personal pronouns. During the communication process the speech roles are assigned to the participants through the person system as:SpeakerAddresseeIt/one are used as a generalized form for other itemsExampleIf the buyer wants to look the condition of the property, he has to have another survey. One carried out on his own behalf.Here in the above example the use of personal pronouns is a source of personal referenceBuyer he hisSurvey oneIf possessive pronouns are used, they give two more notions other than Speaker and Addressee. They are that of Possessor and Possessed as I the following exampleThat new house is John’s. I didn’t know it was hisPossessor JohnPossessed house shown by the use of his and ‘sThe following table shows the system of person for personal reference.Table: Personal ReferenceSemantic categoryGrammatical functionClassPerson:speaker (only)addressee (s), with/without other person(s)speaker and other person other person, male other person, female other persons, objects object; passage of text generalized personII. Demonstrative ReferenceIt is essentially a form of verbal pointing. The speaker identifies or points pout the referentby locating it on scale of proximity. The system of demonstrative pronoun is given in the following table.Table: Demonstrative ReferenceSemantic category Grammatical functionProximity: near far neutralExamplesLeave that there and come here.Where do you come from?I like the lions and I like the polar bears. These are my favorites and those are myfavorites too.III. Comparative ReferenceHere two types of comparison are given:(i)General Comparison(ii)Particular Comparison(i)General ComparisonHere things compared show likeness or unlikeness without considering any particular property. Likeness or unlikeness is referential property as something is can be like something else.ExampleIt’s the sa me cat as the one we saw yesterday.Its different cat from the one we saw yesterday(ii)Particular ComparisonHere comparison is made on the scale of quantity or quality it is a matter of degree compare things on this scale. In other words we can say it expresses the comparability between things. ExampleTake some more teaWe are demanding higher living standard.There are twice as many people there as the last time.Table: Comparative referenceClassGeneral comparison:Identitygeneral similaritydifference (i.e. non-identity or similarity)Particular comparison:2. SubstitutionSubstitution is replacement of one linguistic item by another. Ellipses is also a kind of Substitution where one linguistic item is replaced by nothing/ zero. Therefore it is an omission of an item.When we talk about replacement of one item by another, we mean replacement of one word/phrase with another word or phrase. We can say substitution is a relation on lexicogrammatical level. It is used to avoid repetition of a particular item. But while locating cohesion through substitution semantic is involved.ExampleMy axe is too blunt. I mist get a sharper one.You know John already knows. I think everybody does.Substitution is confined to text so exophoric substitution is rare. Most of the substitutions are endophoric and that of anaphoric type. But cataphoric substitution can also found in certain circumstances.Types of SubstitutionThere are three types of substitution.(i)Nominal Substitution(ii)Verbal Substitution(iii)Clausal substitution1.Nominal SubstitutionThere are three nominal substitutes.one, ones, same.The nominal substitute one/onesThe substitute one/ones always function as head of a nominal group and can substitute only for an item which is itself head a nominal group.ExampleI’ve heard some strange stories in my time. But this one was perhaps the strangest one of all.Note: The word other than a substitute can be used as(i)The personal pronoun one(ii)Cardinal numeral one(iii)Determiner oneThe nominal substitute sameSame typically accompanied by the presuppose an entire nominal group.ExampleA:I’ll have two poached eggs on toast, please.B: I’ll have the sameThe Same can have following expressions as:Say the sameDO the sameBe the same2. Verbal SubstitutionThe verbal substitute is do.This operates as head of a verbal group. Lexical verb is replaced by do and its position is on the final in the group.Example from AliceThe words did not come the same as they used to do.It can also substitute for a verb plus certain other elements in the clause.ExampleI don’t know the meaning of half those language words and what’s more, I don’t believe you do either.Note: The word Do other than as substituteLexical verb do (he is doing)General verb do (they did a dance)Pro-verb do {do(action), happen(event)} Clausal substitutionHere presupposed is not an element within the clause but an entire clause. So and Not are clausal substitutesExampleIs there going to be an earth quake? - it says soTypes of Clausal SubstitutionThere are three types of clausal substitution.➢Substitution of reported clause➢Substitution of conditional clause➢Substitution of modalized clause1. Substitution of Reported ClauseThe reported clausal that is substituted by so or not is always declarative whatever the mood of the presupposed clause is whether interrogative or imperative.ExampleHas everyone gone home? I hope not.I didn’t think so.(I hope not (that) every one has gone home)Is this mango ripe? – It seems so.The essential distinction to be made here is that between reports and facts. Reports can be substituted whereas facts can not, reason is that facts are encoded at semantic level while clausal substitute works at lexicogrammatical level only.2.Substitution of Conditional ClauseConditional clause are also substituted by so and not especially following if /assuming so / suppose so etc.Example11Everyone seems to think he’s guilty. If so, no doubt he’ll offer to resignWe should recognize the place when we come to it. Yes, but supposing not then what do we do?3.Substitution of Modalized ClauseSo and not also occur as substitute for clauses expressing modality.Example‘May I give you a slice?’ she said.‘Certainly not’ the red queen said.。

基于时间资源共享的分配方法在丰富的协作OFDM中的运用

P ri m a ry L i n k Figure 1. Model of the cognitive OFDM networkA Time-Sharing Resource Allocation Method in Heterogeneous Cognitive OFDM NetworkLei Li, Baoyu Zheng, Member, IEEEInstitute of Signal Processing and TransmissionNanjing University of Posts and Telecommunications, Nanjing, P.R. ChinaEmail: {y080601, zby}@Abstract —For a multiuser cognitive OFDM network, most existing adaptive resource allocation methods focus solely on fixed data-rate requirement (QoS guaranteed) or variable data-rate (no QoS guaranteed) conditions without any fairness consideration. In this paper, we investigate the resource allocation problem in a heterogeneous cognitive network with different QoS requirements. By decomposing the problem as a convex optimization, an optimal time-sharing resource allocation method is proposed to maximize the throughput of cognitive network under both subcarrier interference temperature limits and heterogeneous data-rate requirements. Finally, the performance of our proposed resource allocation algorithm is investigated by numerical results.Keywords-Cognitive Wireless Network; Orthogonal Frequency Division Multiplexing (OFDM); Resource Allocation; Quality of Service (QoS)I. I NTRODUCTIONThe cognitive wireless network was proposed as the "NeXt generation" dynamic access technology in [1], which is considered as a reliable, seamless, high-efficient network that support a variety of different QoS guaranteed services. QoS guaranteed services such as voice transmission and video phone are very sensitive to delay and require a fixed data-rate (FDR). Whereas, no QoS guaranteed services like file transmission and web browsing could tolerate large delay and variable data-rate (VDR). Therefore, the cognitive network should dynamically allocate its resource in real-time so as to provide available QoS for different cognitive user while maintaining the performance of primary network. This restriction of primary users is equivalent to the interference temperature limit on all cognitive users' transmission power [2]. Since the design of OFDM ensures that each sub-carrier has a bandwidth less than the coherence bandwidth of the channel resulting sub-carriers experience relatively flat fading [3; 4], the system performance can be significantly enhanced by adaptive resource allocation, especially in multiuser system. Most multiuser OFDM resource allocation methods have focused solely on homogeneous QoS requirements. For a pure FDR QoS, Wong converted the problem to minimizing total transmitting power while maintaining constant rate for each user [5], which is also referred to Margin Adaption (MA). However, cognitive OFDM network usually experiences strict interference constraint by primary network, which can not provide such constant rate for all users. On the other hand, for a pure adaptive rate system, Jang formulated the problem to maximizing network throughput subjected to total transmittingpower limit [6], which is also referred to Rate Adaption (RA). Unfortunately, this technique never takes any fairness among all users into consideration and leads some user to not be assigned any subcarrier if all its subcarrier gains are relatively worse. With the consideration of fairness, Shen proposed a sub-optimal algorithm based on proportional rates constraints among all users in [7], and Tao proposed a time-sharing algorithm based on partly delay-constrained requirement in [8]. In this paper, under the interference temperature limit on each subcarrier, we discuss a time-sharing resource allocation method for heterogeneous cognitive OFDM network, where both FDR and VDR users are supported simultaneously. The rest of the paper is organized as follows: We introduce our system model and decompose the allocation problem by time-sharing in Section II. The multi-level water-filling algorithm for given time-sharing factors is given in Section III. In Section IV, we discuss the calculation of time-sharing factors based on heterogeneous requirements. The performance of our proposed resource allocation method is investigated by numerical results in Section V. Finally, conclusions are given in Section VI. II. S YSTEM M ODELWe consider a heterogeneous cognitive OFDM network depicted in Fig.1. The system consists of N cognitive users(CU) sharing Ksubcarriers licensed to primary network. According to the "receiver-centricity" concept [2], interference caused by cognitive transmitter must keep below a certain upper-bound determined by the primary user (PU) receiver using the same subcarrier. These interference temperature limits on particular subcarriers is gathered by primary base station and delivered to cognitive control center (CCC). Cognitive channel gains ,n k g and interference channel gains,n k h are assumed perfectly estimated at user terminal and collected by CCC via a feedback channel. Typically, CCCThis work is partly supported by National Natural Science Foundation of China (Grant No. 60972039), The National High Technology Research and Development Program of China (Grant No. 2009AA01Z241).978-1-4244-7554-4/10/$26.00 ©2010 IEEEexecutes all resource allocation calculations and maintains the reliable communication in the cognitive OFDM network. Let ,n k R denotes the throughput of cognitive user n on subcarrier k in bits/OFDM-symbol, which depends on channel gain ,n k g and allocated power ,n k p , and can be expressed as2,,,22,log 1n k n k n k n k n g p R σ⎛⎞⎜⎟=+⎜⎟Γ⎝⎠, (1) where 2,n k σ denotes the noise estimated by cognitive receiver. And n Γis a constant related to a given BER requirement, which is suitable for estimating practical data-rate. If practicaluncoded MQAM modulation constellation is used, according to [9], we have()ln 51.5n n BER ⋅Γ=−. (2)For a set f Φof FDR cognitive users, the QoS guaranteed constant rates ,f n R n ∈Φshould be satisfied. And for a set v Φ of VDR cognitive users, best-effort rates ,v m R m ∈Φ should be maximized. Undoubtedly, {}1,2,,f vN ΦΦ=∪ .These QoS requirements were also considered in [8] withoutfairness considerations among VDR users, which may make some VDR user not be able to communicate if all its subcarriergains are relatively worse.In [8], the author creatively proposed a time-sharing resource allocation by relaxing the constraint that each subcarrier is used by one user only. This method introduced a sharing factor [],0,1n k ρ∈ indicating the portion of time that subcarrier k is assigned to user n during each time fragment,which was first noticed in [5] and widely used in multiuserOFDM systems to convert a mixed integer optimizationproblem into a convex optimization [6;7;8]. In our work, wemove forward this time-sharing method by introducingmutually exclusion in time fragment, which can be written as{},,,maxn n k n n k nkp R ττ∑∑(3)subject to,0,,n k p n k ≥∀,(4) ,,n k n kp P n ≤∀∑,(5) 2,,,,n k n k k h p T n k ≤∀,(6),ffn nR R n =∀∈Φ,(7)::,,vi j i j R R i j γγ=∀∈Φ, (8){}1,2,,f v N ΦΦ=∪ ,(9)[]0,1,1n n n ττ∈≤∑.(10) The object function (3) is to maximize cognitive network throughout, where n τ denotes the time-sharing factor that the portion of time subcarriers occupied by user n . Meanwhile, ,n k R is calculated by (1) and the actual rate of user n is,n n n k k R R τ=∑. Constraint (5) is the total transmitting powerlimit of user n . Constraint (6) is the interference temperaturelimit given by primary network on each subcarrier. Note that although most existing allocation methods in cognitive radio treat interference limit as a summed-up value over all subcarriers, we hold our opinion that it should be separatelyconsidered on each subcarrier, since primary network allocatesdifferent subcarriers for different users, and then resultsdifferent interference channel gains ,n k h .Constraint (7) denotesthe QoS requirements of FDR users. Constraint (8) is theproportional rates requirement for VDR users, which is firstly introduced in [7] to maintain the fairness among all users.The sharing factor n τ in (3) under constraint (10) make the resource allocation more tractable by relaxing its exclusionon k subcarriers under our model assumption, i.e., allsubcarriers are allocated to a single user over a portion of time. This make our optimization problem significantly reduced intotwo sub-problems:• For a given sharing factor set {}n τ, objective function(3) turn to be {},,max n k n k k p R ∑for each user under the power constraints (4)-(6);• For a given maximized rate set {},,max n k n k k p n R ⎧⎫⎨⎬⎩⎭∑, findthe sharing factor n τ for each user under the QoS constraints (7)-(9). The first issue is a power allocation and control problem, aswell as the second belongs to a rate allocation and schedulingproblem. Both these issues will be solved separately andintegrated jointly as the solution of the resource allocationproblem in the following two sections.III. M ULTI -L EVEL W ATER -F ILLING P OWER A LLOCATION As discussed above, by a given time-sharing factor set {}n τ,maximizing network's total throughput is equivalent to maximizing each user's throughput, that is{},,max ,n k n k k p R n ∀∑ (11)subject to,,n k n kp P ≤∑(12) 2,,,n k n k k h p T k ≤∀,(13),0,n k p k ≥∀.(14)The object (11) is concave because positive linearcombination of concave function (1) is concave. Furthermore,Subcarrier IndexW a t e r F i l l i n g P o w e rFigure 2. Illustration of multi-level water-fillingsince the inequality constraints (12)-(14) are all convex, the feasible set of this problem is convex. For that reason, the power allocation problem defined in (11)-(14) is a convex optimization problem and there exists a unique global optimal point, which can be acquired by iteration. Now we formulate the optimal power allocation. The Lagrangian of the problem is,{}(),2,,2,2,log 1nn knn k n kn n k n kk k n J p g p p P λλ⎛⎞⎛⎞⎜⎟=+−−⎜⎟⎜⎟Γ⎝⎠⎝⎠∑∑, (15) where n λ is the Lagrange multiplier of user n . The boundary conditions in (12) and (14) will be absorbed in Karush-Kuhn-Tucker (KKT) conditions [10] for short Lagrangian ()n J i . Ifwe let ,n k p ∗as the optimal solution there exist for ,n k ∀, applying the KKT conditions, we formulate the sufficient andnecessary conditions for ,n k p ∗by differentiating the Lagrange,{}()2,,,2,,,,0,,0,0,0,0n k k n knn knn k k n k n kn k p T h J p p T h k p p λ∗∗∗∗∗⎧>=⎪∂⎪=<<∀⎨∂⎪<=⎪⎩. (16) Moreover, this differentiating of Lagrangian with respect to ,n k p ∗and substituting into the KKT condition (16) follows,2,2,22,,,,,,2,222,,,10,0ln 211,0ln 2ln 21,ln 2n k nn n k n k n n k nk n kn n n kn k n k n k n k k n n k n k n k g T p g g h T T h g h σλσσσλ∗⎧Γ⎪−<⎪⎪⎪ΓΓ⎪=−<−<⎨⎪⎪Γ⎪−>⎪⎪⎩,(17)which can also be simplified as,2,,22,,1min max 0,,,ln 2n k nk n kn n k n k Tp k g h σλ∗⎡⎤⎛⎞Γ⎢⎥⎜⎟=−∀⎢⎥⎜⎟⎝⎠⎣⎦. (18) Meanwhile, the Lagrange multiplier n λ is obtained when we substitute (17) into the total power constraint (12), 2,22,,1min max 0,,ln 2n k nk n k n n k n kTP g h σλ⎧⎫⎡⎤⎛⎞Γ⎪⎪⎢⎥⎜⎟−=⎨⎬⎢⎥⎜⎟⎪⎪⎝⎠⎣⎦⎩⎭∑. (19)This multi-level water-filling optimal power allocation method given by (17) and (19) is similar to traditional OFDM water-filling principle [11], however, being some difference summarized as follows and illustrated in Fig. 2:•The line sketched out the bottom is no longer channelnoise 2,n k σ, but 22,,,n k n k nn kg σΩ=Γas EquivalentNoise adjusted by cognitive channel gains; •The power filled on each subcarrier ,n k p does not only depend on the water-line 1ln 2n n L λ=, but also the interference limit 2,,n k kn kI T h =, which is illustratedin Fig. 2 as Interference Limit Line ,,n k n k I Ω+. Thus, the filled power can exceed neither the water-line nor the interference-line; •For different user n , the water-line n L may vary.However, the water-line 1ln 2n L λ= given by (19) cannotbe calculated in closed-form. Thus, a numerical iterative algorithm is given as follows that incessantly pours total power n P into all subcarriers until total power is used up or interference limits are reached on all subcarriers with least algorithm complexity ()2log K K Ο: 1) Initialization,a) Set (),min n n k kL ←Ω as initial water-line;b) Set 0n F ← as initial total filled-power. 2) Loop until n F approchs n P numerically,a) Update current water-line ()n n n n L L P F ←+−;b) Update (),,min max 0,,n n n k n k k F L I ⎡⎤←−Ω⎣⎦∑ascurrent total filled-power;c) If ,,max()n n k n k L I >Ω+, set ,,max()n n k n k L I ←Ω+and break the loop. 3) Obtain allocation results,a) Return current n L as final water-line;b) Return (),,,min max 0,,n k n n k n k p L I ⎡⎤←−Ω⎣⎦ as finalpower on subcarrier k .Figure 3. Procedure of time-sharing resource allocation2C o g n i t i v e N e t w o r k T h r o u g h p u t2Figure 4. Throughput versus cognitive and interference channel gainsIV. T IME -S HARING A LLOCATION WITH Q O S R EQUIREMTS Although the transmitting power is given by (17) and (19), the actual transmitting rate of user n also depends on its time-sharing factor n τ, i.e., ,n n n k k R R τ=∑. As discussed above, time-sharing factors denote the portion of time subcarriers occupied by user n , which play a leading role in multiuser scheduling under heterogeneous QoS requirements. Thus, the sharing factors allocation problem can be expressed as, {},max n n n kn k R ττ∑∑ (20) subject to,f f n n R R n =∀∈Φ, (21) ::,,vi j i j R R i j γγ=∀∈Φ, (22){}1,2,,f v N ΦΦ=∪ , (23) []0,1,1n n n ττ∈≤∑, (24)Fortunately, this convex optimization problem is a linear program (LP) without any inequality constraint, which leads to the existence of close-form solution [10]. The FDR constraint (21) should be satisfied foremost not only for its reliable requirement, but also for its equality property, which yields,,,f fn n n kk R n R τ=∀∈Φ∑. (25) Note that these factors may dissatisfy constraint (24) when the FDR requirements are beyond the capacity of cognitive network, which is also called service outage. In this situation, there is no feasible point for (20)-(24).On the other hand, all VDR users share the remainingthroughput of cognitive network under the proportional rate fairness constraint (22). Their total sharing factors must satisfy,1,,v fm n m n m n ττ=−∀∈Φ∀∈Φ∑∑. (26) Additionally, proportional rates constraint (22) implies ,,:(/):(/)i j i i k j j k k k R R ττγγ=∑∑, ,v i j ∀∈Φas theproportional sharing factors constraint, which yields, (),,,m m kvk m mm m m km k R m R γττγ=∀∈Φ∑∑∑∑. (27) Hence, the time-sharing factors allocation including both FDR and VDR users and given by (25) and (27) respectively.As a summarization, the diagram of our time-sharing resource allocation is given in Fig. 3, where the right dashed box represents the heterogeneous QoS requirements of cognitive users. Furthermore, each resource allocation cycle must be finished in a stable cognitive period, during which thechannel parameters and interference limit do not change.V. S IMULATION AND A NALYSISIn our simulations, we consider a heterogeneous cognitiveOFDM network with 8 users and 64 subcarriers. UncodedMQAM constellation is used and the BER for both FDR and VDR users are set to 510−. Noise gap 2,n k σ for every cognitivereceiver on each subcarrier in normalized to unit, i.e. 0dB. Inaddition, all cognitive and interference channel gains are treatas i.i.d. Rayleigh variables with mean square 2,E[||]n k g and2,E[||]n k h respectively. Thus, Monte Carlo simulations are applied over 310 times to reduce the influence of various channel realizations.Fig. 4 shows the relation between cognitive networkthroughput ,n n k n k R τ∑∑ in unit bits/OFDM-symbol and two average channel gains. We vary one channel gain from -20 dB to 0 dB and lock another at -10 dB. Meanwhile, all usersare set as VDR equal proportional rates (1:1::1 ) on powerconstraint n P =+∞for a independent comparison between different k T . We see that throughput rises when 2,E[||]n kgincreases or 2,E[||]n k h decreases for fixed k T . This is becausecognitive network enjoys advantageous access capacity in goodcognitive or bad interference channel conditions. Moreover, as expected, throughput rises with k T since more interferenceprimary network can endure. Last but not least, the gaps growup as shown in the figure for the joint beneficial impact ofinterference limit and channel gains. Owing to the direct constraint of cognitive transmittingpower by (5) and (6), cognitive network throughput definitelydepends on both user power constraint n P and subcarrier interference limit k T . This relation is given in Fig. 5 as a mesh plot with all channel gains at a same mean value -10dB. Above102030P n(dB)T k(dB)C o g n i t i v e N e t w o r k T h r o u g h p u tFigure 5. Throughput versus sub-carrier interference temperature limit anduser transmitting power limit51015202500.20.40.60.81Average Throughput of FDR UsersS e r v i c e O u t a g e P r o b a l i t yFigure 6. Service outage probability versus average throughput requirementof each fixed data-rate userall, at small value of n P or k T , no matter how large the other is, the throughput hardly increases. This trend is expected because the low value constraint plays a dominant role in transmitting power limitation. In addition, for a fixed large k T (corresponding large 2,E[||]k k n k I T h =), the throughput's variation can be generalized into three phases: Power Limited Phase — small n P restricts transmitting power and then makes the cognitive network in a low throughput, i.e., n k P I <; Boost Phase — median n P brings effective multi-level water-filling among all subcarriers and then makes rapid growth in throughput, i.e., k n k k I P I <<∑; Interference Limited Phase — large n Pexceeds the interference temperature limit and then makes little change in throughput, i.e.,n k k P I >∑.Note that a similar phenomenon occurs if we extend the value rangeof k T for a fixed large n P .For a cognitive heterogeneous network, access availability of FDR users can only be guaranteed in a probabilistic manner for the variable cognitive conditions and finite transmitting power. The service is said to be in an outage if FDR users' requirements exceed system capacity and then cannot be satisfied. This relation is illustrated in Fig. 6 with parameters n P =∞ and 0dB k T =. We define the range of average FDR users' requirements with outage probability lower than 1% asNon-Outage Range, and the range with outage probability between 1% and 99% as Partial-Outage Range. Undoubtedly, FDR users' requirements by (7) can be supported in probability 1out P − in both these ranges, but hardly guaranteed after the partial-outage range. In our simulation, both these two ranges shrink with the growth in FDR users' amount rapidly. This characteristic tells us that FDR users' requirements should be set at most in the non-outage range or low values of partial outage range to reduce service outage probability in a real system.VI. C ONCLUSIONA time-sharing resource allocation method for cognitive heterogeneous OFDM network under the constraint of each subcarrier interference limit is considered in this paper. FDR and VDR users are simultaneously supported by constant rate and proportional rate access respectively. We investigated the problem of maximizing network throughput while satisfying both interference and total power constraints. This problem was transformed into two sub-problems of convex optimization by introducing the time-sharing factor, and solved separately. Simulation results showed that network throughput increases with the increasing of cognitive channel gains, the decline of interference channel gains, the increment of each subcarrier interference temperature limit, and the growth of user power constraint. Moreover, the upper-bound of FDR requirements is determined in a service outage probabilistic manner.R EFERENCES[1] I. F. Akyildiz, W. Y. Lee, M. C. Vuran, S. Mohanty, "NeXt generation /dynamic spectrum access / cognitive radio wireless networks: A survey," Computer Networks Journal (Elsevier), vol. 50, no. 13, pp. 2127-2159, Sep. 2006.[2] S. Haykin, "Cognitive Radios: Brain-Empowered WirelessCommunication," IEEE J. Selected Aeras Comm., vol. 23, no. 2, pp. 12-18, Feb. 2005.[3] E. Biglieri, J. Proakis, and S. Shamai, "Fading channels: Information-Theoretic and Communications Aspects," IEEE Trans. on Information Theory, vol. 44, no. 6, pp. 2619-2692, 1998.[4] A. Babai, B. Saltzberg, and M. Ergen, "Multi-Carrier DigitalCommunications - Theory and Applications of OFDM," 2nd ed., Springer-Verlag, New York, 2004.[5] C. Y. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, "MultiuserOFDM with adaptive subcarrier, bit and power allocation," IEEE J. Select. Areas Commun., vol. 17, no. 10, pp. 1747-1758, Oct. 1999.[6] J. Jang, K. B. Lee, "Transmit power adaptation for multi-user OFDMsystems, IEEE J. Select. Areas Commun., vol. 21, no. 2, pp. 171-178, Feb. 2003.[7] Z. Shen, J. G. Andrews, and B. L. Evans, "Adaptive resource allocationin multiuser OFDM systems with proportional fainess," IEEE trans. Wirelss Commun., vol. 4, no. 6, pp. 2726-2737, Nov. 2005.[8] M. Tao, Y. Liang, and F. Zhang, "Adaptive Resource Allocation forDelay Differentiated Traffic in Multiuser OFDM Systems," IEEE ICC'06 proceedings, 2006.[9] A. J. Goldsmith, S. Chua, "Variable-Rate Variable-Power MQAM forFading Channels," IEEE trans. Commun., vol. 45, no. 10, pp. 1218-1230, Oct. 1997.[10] S. Boyd and L. Vandenberghe, Convex Optimization, CambridgeUniversity Press, 2004.[11] T. M. Cover and J. A. Thomas, Elements of Information Theory, Willey,1991.。

有关于分类的英语作文初一

When it comes to writing an essay about classification in English,especially for a seventhgrade student,its essential to approach the topic in a structured and clear manner. Here are some key points to consider when writing such an essay:1.Introduction:Begin by introducing the concept of classification.Explain that classification is a way of organizing information into groups based on shared characteristics.2.Importance of Classification:Discuss why classification is important.It helps in making sense of the world around us,whether its in biology,where animals and plants are classified into different species,or in everyday life,where we classify objects to keep our environment organized.3.Types of Classification:Describe the different types of classification.For example: Hierarchical Classification:This involves grouping items into a series of categories that are subdivided into smaller categories.Cross Classification:This is when items are classified based on multiple criteria. Binary Classification:This is a simple form of classification where items are divided into two categories.4.Examples in Daily Life:Provide examples of classification that students can relate to, such as:Organizing books in a library by genre and author.Sorting clothes by color or type.Classifying food into categories like fruits,vegetables,proteins,etc.5.Classification in Science:Explain how classification is used in various scientific fields. For instance:In Biology,the Linnaean system classifies organisms into kingdoms,phyla,classes, orders,families,genera,and species.In Geology,rocks are classified into three main types:igneous,sedimentary,and metamorphic.6.Classification in Technology:Discuss how technology uses classification,such as: Categorizing software applications based on their function.Organizing digital files and folders on a computer.7.Challenges in Classification:Mention some of the challenges that can arise when classifying,such as ambiguity in the criteria used for classification or the difficulty in categorizing items that dont fit neatly into one category.8.Conclusion:Sum up the essay by reiterating the importance of classification in organizing and understanding the world.Encourage students to think critically about the categories they use in their own lives and to consider how classification can be used to solve problems or make decisions.9.Personal Reflection:Optionally,you can include a personal reflection on how the student uses classification in their life or how they have learned to classify things in a new way.Remember to use simple and clear language appropriate for a seventhgrade level,and ensure that the essay is wellstructured with a logical flow of ideas.。

Conductance of a Conjugated Molecule with Carbon Nanotube Contacts

Conductance of a Conjugated Molecule with Carbon NanotubeContactsNicolas A.Bruque,∗M.K.Ashraf,and Roger keDepartment of Electrical Engineering,University of California Riverside,CA 92521Abstract Calculations of the conductance of a carbon nanotube (CNT)-molecule-CNT structure are in agreement with experimental measurements [1].The features in the transmission correspond directly to the features of the isolated molecular orbitals.The HOMO provides conductance at low bias that is relatively insensitive to the end groups of the cut CNTs,the cut angle,or the number of molecular bridges.A molecular conformation change not directly in the path of the carrier transport increases the resistance by over 2orders of magnitude.Keywords :Electron transport,F IREBALL ,CNT,DFT,NEGF,conductance,molecularelectronics ∗Electronic address:nbruque@a r X i v :0806.2851v 1 [c o n d -m a t .o t h e r ] 17 J u n 2008Individual molecules have been proposed as the ultimately scaled electronic device in future electronics.Gold metal contacts to molecules has been studied the longest and given the most attention both experimentally and theoretically [2,3,4,5].The agreement between the experimentally measured currents and the theoretically predicted currents in these systems was diﬃcult to obtain due to the strong dependence of the conductance on the contact geometry [5,6,7,8,9,10].The correspondence has greatly improved with the introduction of amine linkers [11,12,13].The carbon nanotube (CNT)has been utilized as an alternative contact to single molecules [1,14,15].The CNT-molecule-CNT amide interface chemistry provides a well deﬁned covalent bond to attach CNT contacts to single molecules.The CNT contacts can provide both metallic and semiconducting properties governed by the CNT chirality.Prior transport studies report that the current response of CNT-molecule-CNT systems is greatly inﬂuenced by the chirality of the CNT contacts [16,17,18]while others report changes when examining the passivation chemistry at the cut ends of the CNTs [19].The CNT-molecule-CNT transport studies published to date have been limited to model or pro-posed systems [16,17,18,19,20,21,22,23]where the CNT-molecule interface chemistry,interface geometry,CNT chirality,or molecular conformation were the areas of -parisons between theory and experiment for these systems have not yet been performed.In this paper we present transport calculations of a CNT-molecule-CNT system that was built and measured [1],we make quantitative comparisons,and we show how the features in the transmission spectrum result from the features of the molecular orbitals of the isolated molecules.To calculate the equilibrium transmission of a CNT-molecule-CNT system,our method uses density functional theory (DFT)implemented by the ab initio tight-binding molecular dynamics code F IREBALL [24,25,26]coupled with a non-equilibrium Greeen’s functional (NEGF)algorithm [21,27,28,29,30].The BLYP exchange-correlation functional is used to perform a self-consistent calculation [31,32]using a double numeric sp 3localized orbital F IREBALL basis.We relax the system using periodic boundary conditions until forces are <0.05eV ˚A −1using a self-consistent convergence factor of 10−5.These matrix elements are used to calculate the surface self-energies,Green’s function of the device,and the result-ing transmission.To calculate the room temperature conductance,we take the derivative of the current equation with respect to voltage,G =2e h dET (E )(−∂f ∂E),where f is theFermi-Dirac factor and T is the transmission probabality.The relaxation and transmission calculations are both performed using a double numeric orbital basis to avoid any discrep-ancies that may arise using a single numeric basis[9].Additional details on our approach can be found in Ref.[21].We model the experimental CNT-molecule-CNT system in Ref.[1]using metallic(7,7) CNT contacts attached to theπ-cruciform molecule[33]shown in Fig. 1.The molecule is referred to as molecule1in Ref.[1].To build the structure,we begin by relaxing the isolated molecule with amide groups attached.We build the CNT out of optimized unit cells.We then cut the CNT to provide the closestﬁt to the molecule with amide linkers attached.We assume that after the etching step,the CNT contacts areﬁxed in their position and the molecular window is governed by the one-dimensional atomic layer spacing of the CNTs[1,14].Weﬁnd that9unit cells of a(7,7)CNT are comparable in length to the relaxed molecule plus amide groups.At the dodecyloxybenzene cross-arm ring ends we attach a truncated C2H5alkane chain instead of C12H25used in the experiment since,being insulating,they do not aﬀect the electronic properties of the conjugated central molecule. The system is constructed such that each CNT contact is at least5unit-cells in length on either side of the molecule.The CNT at the interface is passivated with hydrogen atoms to minimize localized surface states.Weﬁnd that four CNT unit cells(8atomic layers)for each CNT contact are long enough to damp out charge oscillations at the end layer(where the self-energies are added)that result from the C-H charge dipoles at the cut interfaces [21].We show in Fig.1(B)a planar conformation of molecule1and in(C)a perpendicular conformation rotating only the cross-arm dodecyloxybenzene rings in each conﬁguration. Both systems remain stable when relaxed with the plane of the amide groups at no more than14.1degrees from parallel to the tangential plane of the CNTs at the point of contact. This dihedral angle was found to have minimal eﬀect on transmission up to15degrees from parallel[16].The orientation of the planar molecule in Fig.1contrastsﬁndings by Ke et.al. modeling a comparable CNT-benzenediamide-CNT system[17].Ke et al.found a lowπorbital overlap between the(5,5)CNT contacts and molecule where the molecular plane was above the surface of two(5,5)CNTs.Weﬁnd that the larger1nm diameter(7,7)CNT allows the amide linker to align nearly co-planarly with the CNT surface possibly due to a larger spacing between H atoms around CNT ends.The discrepancy could also be aﬀectedby the diﬀerent lengths of the molecules studied.In Fig.1(A),we show the calculated transmission as a function of the diﬀerence E−E F for the two structures.The transmission of the planar molecule has a resonant peak near the Fermi energy which results in a room temperature(300K)resistance of6.4MΩ.The resistance of the perpendicular molecule is1.6GΩ.The experimental measured resistance is5MΩ[1].To understand the diﬀerence in the transmission curves of the two molecules in Fig.1, we examine the relaxed isolated molecular orbitals,shown in Fig.2.Both molecules remain stable during relaxation with the planar conformation energetically favorable by1.4eV.Fig. 2shows the LUMO,HOMO,HOMO-1,HOMO-2and HOMO-3(top to bottom)for both molecules with the amide groups attached at the left and right ends.The diﬀerence between the two molecules is notably the HOMO.In the planar conformation,the HOMO lies across the molecule perpendicular to the LUMO and the path of transport.The HOMO in the perpendicular conformation is localized strongly around the amide linkers and is oriented parallel to the LUMO.Because theπ-conjugations extends across both arms of the cross in the planar molecule,the orbitals are more extended than in the perpendicular conformation. This spreading of the orbital wavefunction reduces the HOMO-LUMO gap to1.69eV in the planar conformation from2.17eV in the perpendicular conformation.The HOMO-1and HOMO-2states in both molecules are split by a few meV and are essentially degenerate.We next compare the covariant spectral functions[21]at each transmission peak shown in Fig.3to the orbitals of the isolated molecules.The spectral function labels(1-4)correspond to the labeled transmission peaks in Fig.1.The broad transmission peak(1)corresponds to the molecular LUMO in both systems.The broad transmission peak and the LUMO that extends across the entire CNT-molecule-CNT structure indicate that the coupling of the CNT orbital to the molecular LUMO is strong.This is consistent with results found by others[16,17].Peak(2)in the transmission curve results from the coupling of the CNT states to the HOMO of the planar molecule.This state is localized on the cross-arm of the molecule away from the CNTs and is weakly coupled to the contacts.The Fano resonance at peak(2)results from the two parallel paths through the molecule.An electron can tunnel through the tail of the extended state(1)or it can tunnel through the localized state(2).Transmission peak(3)results from the resonant tunneling through the degenerate HOMO-1/HOMO-2states of the planar molecule localized on the oxygen atoms linkingthe dodecyloxybenzene rings to the C2H5alkane chains.Transmission peak(4)results from coupling to the HOMO-3orbital of the planar molecule and the HOMO orbital of the perpendicular molecule.The spectral functions for peaks(1)and(4)are qualitatively the same for both molecular conformations,so we only show the spectral function of the planar molecule.Transmission peak(3)is also a Fano resonance arising from the two parallel paths corresponding to the HOMO-1/HOMO-2states localized on the cross-arms and the HOMO-3state extended across the molecule.This comparison clearly maps the features in the transmission directly to the features of the isolated molecular orbitals.The examinations of the transmission,molecular orbitals and spectral functions explains the diﬀerence in resistance of the two molecular conformations in Fig.1.Rotating the the dodecyloxybenzene rings breaks the conjugation with the rings on the horizontal axis of the molecule and removes the HOMO localized on the cross-arms.The HOMO-LUMO gap widens leaving no states near the Fermi energy to carry current,and the resistance increases by over2orders of magnitude.The use of conformation change for molecular switching is well known.Several examples are rotaxane[34,35],1,4-bis-phenylethynyl-benzene[10],and2’-amino-4-ethylphenyl-4’-ethylphenyl-5’-nitro-1-benzenethiolate[36,37]which we refer to as the nitro molecule.In all cases the conformation change of the molecules alters the molecular orbitals along the path of the electron transport.In the nitro molecule,the conjugation is broken directly in the transport path between each contact.In rotaxane,the orbital changes from extended to localized along the transmission path of the molecule.For the cruciform molecule,shown in Fig.1,the eﬀect of conformation is diﬀerent.The rotation of the vertical rings does not aﬀect the conjugation along the horizontal axis of the molecule,and it does not localize a previously extended state along the axis of the molecule.Instead,it removes the HOMO that lies on the cross rings,puts it back onto the horizontal axis of the molecule but at a lower energy resulting in exponentially decreased transmission near the Fermi energy and a several order of magnitude reduction in the conductance.This is a new twist on the conformation-change paradigm of molecular switching.Experimentally it has been suggested that up to two molecular bridges might be estab-lished across the gap[1]during the dehydration reaction.While the molecular end groups on the cut ends of the CNTs are not known,it is reasonable to assume that the CNT ends remain functionalized with carboxyl groups(COOH),rather than H atoms,after de-hydration reaction[1].To explore these issues,weﬁrst add one additional molecule to our CNT-molecule-CNT system.Fig.4(A)shows a relaxed CNT-molecule-CNT system where an additional planar molecule is attached parallel to the original molecule shown in Fig.1 (B).The maximally separated conﬁguration of the two molecules shown here is known to be energetically favorable.[19].The two molecule transmission is shown in Fig.4(B)where we observe a doubling of peaks near the Fermi level giving a calculated resistance of4.7MΩ.As expected,the peaks are associated with the same orbitals previously discussed in relation to Figs.1-3.The addition of one molecular bridge reduces the resistance,but not by a factor of two.The resistance is sensitive to the position of the HOMO resonant transmission peaks with respect to the Fermi level,and the two peaks from the two molecules split and shift compared to the single peak from a single molecule.Finally,we cut a CNT non-vertically and passivate the side walls with carboxyl groups. We attach a single planar molecule shown in Fig.4(C)at the shortest portion of the molecular gap.The relaxed plane of the amide CONH groups is at no more than24.2degrees from parallel to the tangential plane of the CNTs at the point of contact.The transmission is shown in Fig.4(D)where the features remain qualitatively comparable to the features of the planar transmission in Fig.1(A).Quantitatively,weﬁnd a narrowing of each resonant peak.The LUMO and HOMO-3peaks shift slightly deeper into the conductance and valence bands respectively.The spectral function at each peak again matches the features of the isolated molecular orbitals shown in Fig. 2.The calculated resistance is40MΩ.The increase is the result of the narrowing of the HOMO resonance.The transmission curve for the carboxyl passivated system contrasts to work done by Ren et.al.[19]where passivated carboxyl groups where compared to H passivation on semi-conducting(13,0)CNTs connected by a single diaminobenzene molecule.Ren et.al. found that the resonant peaks broaden in the valence and conduction band regions when the side-walls are passivated with carboxyl.The narrowing of the valence band resonances in our case,shown in Fig.4(D),indicate a lower coupling of the molecular states to the continuum of states in the CNT contacts.The decrease in coupling is partially due to the increased dihedral angle between the molecule and the plane of the CNT at the point of contact.The increase of the dihedral angle is caused by the increase of the steric hindrance of the carboyxl groups compared to the H atoms.The CNT sidewall chemistry,when relaxed, aﬀects the orientation of the molecular junction due to negatively charged oxygen atoms onthe cut surface of the CNTs repelling the CONH linker oxygen atoms.This repulsion forces the amide horizontal axis to twist,aﬀecting theπ-bond overlap between the CNT contacts and the amide linkers.We note that although the resistance has increased compared to the hydrogen passivation conﬁguration,the overall transmission curve remains similar to the original system with the HOMO level near the Fermi energy.Overall the resistances listed in Table I are close to the experimental measurements,(excluding the perpendicular conformation).The proximity of the HOMO state near the Fermi energy provides a weakly-coupled transport path through the molecule at low bias regardless of the interface orientation,the number of molecular bridges,or the presence of carboxyl groups.In summary,we have found good theoretical agreement with theﬁrst experimental mea-surement of a CNT-molecule-CNT system.The features in the transmission correspond directly to the features of the isolated molecular orbitals.The rotation of the dodecyloxy-benzene rings of the cross-arm alters the resistance by over2orders of magnitude even though it does not aﬀect the conjugation along the transport path.The HOMO lying on the cross-arms of the planar molecule provides conductance at low bias that is relatively insensitive to the end groups of the cut CNTs,the cut angle,or the number of molecular bridges.AcknowledgementsThis work is supported by the NSF(ECS-0524501)and the Semiconductor Research Cor-poration Focus Center Research Program on Nano Materials(FENA).TABLE I:Resistance of four CNT-molecule-CNT systems studied where‘Planar’indicates the planar conformation of the molecule.System Conductance(MΩ)Perpendicular1590Planar 6.4Planar/2molecules 4.7Planar/carboxyl40.Experimental5Figure CaptionsFig. 1.(A)Calculated transmission of the CNT-molecule-CNT structures where the solid line(red)is for the planar dodecyloxybenzene cross-arm conformation and the dashed line (blue)is for the perpendicular dodecyloxybenzene cross-arm conformation.(B and C) Relaxed CNT-molecule-CNT planar and perpendicular structures respectively.Fig. 2.Calculated molecular orbitals for the isolated molecule in both the planar (left)and perpendicular(right)conformations.Amide groups are included at the left and right ends of each molecule.Fig. 3.3D contour plots of the covariant spectral function corresponding to the res-onant transmission peaks marked in1calculated using the planar CNT-molecule-CNT structure.Fig. 4.(A)CNT-molecule-CNT structure with two planar molecules attached.(B) Calculated transmission of CNT-molecule-CNT system shown in(A).(C)CNT-molecule-CNT structure with the CNT side walls passivated with carboxyl group molecules.(D) Calculated transmission of CNT-molecule-CNT system shown in(C).FIG.1:FIG.2:FIG.3:FIG.4:[1]X.Guo,J.P.Small,J.E.Klare,Y.Wang,M.S.Purewal,I.W.Tam,B.H.Hong,R.Caldwell,L.Huang,S.O’Brien,et al.,Science311,356(2006),URL / cgi/content/abstract/311/5759/356.[2]M.A.Reed,C.Zhou,C.J.Muller,T.P.Burgin,and J.M.Tour,Science278,252(1997).[3]J.Taylor,M.Brandbyge,and K.Stokbro,Phys.Rev.Lett.89,138301/1(2002).[4]P.Damle,A.Ghosh,and S.Datta,Chem.Phys.281,171(2002).[5]H.Basch,R.Cohen,and M.A.Ratner,Nano Letters5,1668(2005),URL 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暨南大学《项目管理》chapter12outsourcingmanaginginterorganizationalrelations

• A lack of incentive for continuous improvement by contractors participating in the partnering relationship.
12–16
Advantages of Long-term Partnerships
Partnering Relationships Traditional Practices
Mutual trust forms the basis for strong working relationships. Shared goals and objectives ensure common direction.
• Extensive training and team-building activities.
• Well-established conflict management processes in place. • Frequent review and status updates. • Co-location when needed. • Fair and incentive-laden contracts.
12–13
Project Completion—Celebrating Success
• Conduct a joint review of accomplishments and disappointments. • Hold a celebration for all project participants. • Recognize special contributions.
• Voluntary, experienced, willing, with committed top management.

spanning trees of hypergraph

Advances in Applied Mathematics47(2011)840–868Contents lists available at ScienceDirectAdvances in Applied Mathematics/locate/yaamaSpanning trees of3-uniform hypergraphsAndrew Goodall a,1,Anna de Mier b,∗,2a Department of Applied Mathematics and Institute of Theoretical Computer Science(ITI),Charles University,Malostranskénám.25, 11800Praha1,Czech Republicb Departament de Matemàtica Aplicada II,Universitat Politècnica de Catalunya,Jordi Girona1-3,08034Barcelona,Spaina r t i c l e i n f o ab s t r ac tArticle history:Received15February2010 Revised12April2011 Accepted15April2011 Available online5May2011MSC:05C6505C70Keywords:3-Uniform hypergraph Spanning treePfaﬃanMatrix-tree theorem Orientations Masbaum and Vaintrob’s“Pfaﬃan matrix-tree theorem”implies that counting spanning trees of a3-uniform hypergraph(abbre-viated to3-graph)can be done in polynomial time for a class of“3-Pfaﬃan”3-graphs,comparable to and related to the class of Pfaﬃan graphs.We prove a complexity result for recognizing a3-Pfaﬃan3-graph and describe two large classes of3-Pfaﬃan 3-graphs–one of these is given by a forbidden subgraph charac-terization analogous to Little’s for bipartite Pfaﬃan graphs,and the other consists of a class of partial Steiner triple systems for which the property of being3-Pfaﬃan can be reduced to the property of an associated graph being Pfaﬃan.We exhibit an inﬁnite set of partial Steiner triple systems that are not3-Pfaﬃan,none of which can be reduced to any other by deletion or contraction of triples. We alsoﬁnd some necessary or suﬃcient conditions for the ex-istence of a spanning tree of a3-graph(much more succinct than can be obtained by the currently fastest polynomial-time algorithm of Gabow and Stallmann forﬁnding a spanning tree)and a su-perexponential lower bound on the number of spanning trees of a Steiner triple system.©2011Elsevier Inc.All rights reserved.*Corresponding author.E-mail addresses:goodall.aj@(A.Goodall),anna.de.mier@(A.de Mier).1Research supported in part by the hosting department while visiting the other author and Marc Noy at various times in 2008–2010.2Research supported in part by projects MTM2008-03020and DGR2009-SGR1040.0196-8858/$–see front matter©2011Elsevier Inc.All rights reserved.doi:10.1016/j.aam.2011.04.006A.Goodall,A.de Mier/Advances in Applied Mathematics47(2011)840–8688411.Introduction1.1.Spanning trees of3-uniform hypergraphsIn this paper we investigate the problem of the existence,ﬁnding and counting of spanning trees of3-uniform hypergraphs(henceforth called3-graphs for short).The initial motivation for our work was Masbaum and Vaintrob’s Pfaﬃan matrix-tree theorem[21].They introduce the notion of an ori-entation(or equivalently a sign)of a spanning tree of a3-graph.The Pfaﬃan matrix-tree theorem gives a generating function for signed spanning trees of a3-graph.We shall be particularly interested in how this spanning tree orientation can be used to identify a large class of3-graphs for which the problem of counting the number of spanning trees can be done in polynomial time.This class is comparable to that of Pfaﬃan graphs,for which there is a polynomial-time algorithm for counting the number of perfect matchings.A classical theorem of Kasteleyn[14]is that planar graphs are Pfaﬃan: can weﬁnd a similar class of3-graphs for which counting the number of spanning trees can be done in polynomial time?We should be clear at the outset about how we are deﬁning a spanning tree of a3-graph,for there are various natural alternatives.(More detailed deﬁnitions of these and other terms from the theory of hypergraphs are given in Section2below.)A spanning tree of a3-graph H is an inclusion-maximal subset T of the hyperedges of H that covers all the vertices subject to the condition that T does not contain a cycle of hyperedges.If B H is the usual bipartite vertex-hyperedge incidence graph associated with H,then a spanning tree of H in this sense corresponds precisely to a spanning tree of B H with the property that either all three edges of B H incident with a given hyperedge belong to the tree or none of them do.Alternatively,if each hyperedge{a,b,c}of H is represented as a triangle of edges ab,bc,ca in a graph G H on the same vertex set as H,then a spanning tree of H corresponds to a cactus subgraph of G H covering all vertices.See[1]for a generalization of the Masbaum–Vaintrob theorem to arbitrary hypergraphs in which spanning trees are now cacti with cycles of any odd length and not just triangles.Spanning trees of3-graphs differ in fundamental ways from spanning trees of ordinary graphs: a closer correspondence is to be found with perfect matchings,as will become clearer later in the paper.Whereas for spanning trees of graphs the problems of the existence,ﬁnding and counting of spanning trees each have a straightforward polynomial-time algorithm,the same is not true for spanning trees of3-graphs.As for the algorithmic complexity of matching problems,recall that the augmenting path algorithm ﬁnds a maximum matching of a bipartite graph in polynomial time.Consequently,both the problem of whether there is a perfect matching of a bipartite graph and the problem ofﬁnding one can be solved in polynomial time.Edmonds’maximum matching algorithm[6]solves in polynomial time the existence and search problems for whether an arbitrary graph has a perfect matching.Lovász’s matroid matching algorithm[16,18]provides a polynomial-time algorithm solving the problem of the existence andﬁnding of a spanning tree of a3-graph.However,since it solves such a general and complicated problem,the algorithm is involved,has running time a polynomial of high degree and is not optimal when restricting attention from linear matroids to the graphic matroids underlying the case of3-graphs.The augmenting path algorithm for linear matroids of Gabow and Stallmann[8]has running time O(mn2)with O(mn)space for graphic matroids of rank n and size m, improved to using O(m)space(alternatively O(mn log6n)time using O(m log4n)space)by the same authors in[7].In this paper we give some straightforward necessary or suﬃcient conditions that give simple criteria for the existence of a spanning tree of a3-graph and in the case of Steiner triple systems a superexponential lower bound on the number of spanning trees.Our focus then turns to the problem of counting spanning trees of3-graphs.This problem is #P-complete even for a very restricted class of3-graphs,which is a consequence of the fact that counting perfect matchings is#P-complete for general graphs[28].Masbaum and Vaintrob deﬁne an orientation or sign of a spanning tree of a3-graph using orientations of hyperedges in a way that closely follows the deﬁnition of the sign of a perfect matching,as elucidated by Hirschman and Reiner[12].Just as the existence of a Pfaﬃan orientation of the edges of a graph enables the number of perfect matchings of a graph to be computed in polynomial time,so the existence of what we shall842 A.Goodall,A.de Mier/Advances in Applied Mathematics47(2011)840–868call a“3-Pfaﬃan orientation”of a3-graph allows the number of spanning trees to be calculated in polynomial time.This observation was made by Caracciolo et al.in the conclusion of their paper[5].Having identiﬁed a property of3-graphs that enables counting of spanning trees to be done in polynomial time,how quickly can we verify that a graph has this property?Compare the case of Pfaﬃan graphs:it is not known whether there is a polynomial-time checkable certiﬁcate for a graph to have a Pfaﬃan orientation.Vazirani and Yannakakis[29]show that the problem of determining whether a graph G has a Pfaﬃan orientation and that of determining whether a given orientation of G is Pfaﬃan are polynomial-time equivalent.They appeal to Lovász’polynomial-time algorithm[20]for computing the binary rank andﬁnding a basis of the vector space of matchings of a graph.They also show that the problem of deciding whether a graph has a Pfaﬃan orientation is in co-NP.We show that the problem of deciding the existence of a3-Pfaﬃan orientation is also in co-NP,but we do not know if it is equivalent to deciding if a given orientation of hyperedges is3-Pfaﬃan.Although checking whether a graph is Pfaﬃan is not known to be polynomial time,Little[15]gave a structural characterization of Pfaﬃan bipartite graphs as those that do not contain an even subdivi-sion of K3,3with a perfect matching in the complement.A natural question is whether there is any similar characterization of3-Pfaﬃan3-graphs:we prove such a characterization for a special subclass of tripartite3-graphs.Whether tripartite3-Pfaﬃan3-graphs in general have a similar description in terms of forbidden subgraphs remains open.1.2.Outline of the paperIn Section2we introduce some of the basic notions and notation required in the paper.We assume the reader is familiar with the theory of Pfaﬃan orientations of graphs,of which[26]is a recent survey.We refer to[19]for a general reference on matching theory.In Section3we present some elementary results about the problem of deciding if there is a span-ning tree of a3-graph and about the problem of counting them.We begin in Section 3.1with a summary of what is known about the complexity of these problems in general.In Section 3.2 we consider the case of the complete3-graph,for which we can enumerate the number of spanning trees,and,more importantly,thereby establish in Lemma2a correspondence between spanning trees of a3-graph and perfect matchings of a graph that is basic to the rest of the paper.In Section3.3 we describe some straightforward necessary or suﬃcient conditions for the existence of a spanning tree of a3-graph.Theorem4gives a lower bound on the number of spanning trees of a Steiner triple system.In Section4we initiate our study of orientations of spanning trees of3-graphs and the property of a3-graph having a“3-Pfaﬃan orientation”,which by Masbaum and Vaintrob’s Pfaﬃan matrix-tree theorem[21]implies a polynomial-time algorithm for counting spanning trees.We begin in Section4.1by deﬁning orientations of spanning trees,which are deﬁned relative to an orientation of triples.Theorem9gives an explicit formula for the number of positively and negatively oriented spanning trees of the complete3-graph under a canonical orientation of its triples.In Section4.2we introduce the notion of a“3-Pfaﬃan orientation”,analogous to a Pfaﬃan orientation of a graph.We state a theorem of Hirschman and Reiner and use it to characterize the property of having a3-Pfaﬃan orientation for a subclass of partial Steiner triple systems.In particular,if we make a3-graph H by adding an extra vertex to every edge of a graph G then a3-Pfaﬃan orientation of H corresponds exactly to a Pfaﬃan orientation of G.In Section4.4we prove that the general problem of deciding if a3-graph has a3-Pfaﬃan orientation is in co-NP.Just as for Pfaﬃan graphs,it is not known whether there is a polynomial-time algorithm.We return to this question in Section6.The main result of this paper is contained in Section5.Weﬁnd a large family of3-graphs for which we can characterize the property of having a3-Pfaﬃan orientation in terms of forbidden sub-graphs,similar to Little’s characterization of Pfaﬃan bipartite graphs(Theorem27and Corollary28).We conclude by highlighting some open problems in Section6.2.Notation and terminologyA3-graph is a3-uniform hypergraph H=(V, ),where ⊆V3.There are no repeated hyper-edges and no hyperedges of size2or1.We shall use the name triple for a hyperedge of H.The under-A.Goodall,A.de Mier /Advances in Applied Mathematics 47(2011)840–868843lying graph of a 3-graph H =(V , )is the multigraph G =(V ,E )with edge set E ={{a ,b }:∃c ∈V ,{a ,b ,c }∈ },an edge {a ,b }occurring with multiplicity |{c ∈V :{a ,b ,c }∈ }|.We identify a triple of H with its corresponding triangle in the underlying graph G .We write abc for the triple {a ,b ,c }of H or triangle of G and ab for the edge {a ,b }of G .Deleting a triple abc ∈ gives the 3-graph H \abc =(V , \abc ).A sub-3-graph of H is a 3-graph obtained from H by deleting some subset of triples.Contracting a triple abc gives the 3-graph H /abc =(V \{b ,c }, )where is deﬁned as follows.A triple ijk belongs to if (i)ijk and abc are disjoint,or (ii)ijk is obtained from a triple that meets abc in one vertex by relabeling this common vertex by a if it is equal to b or c .In other words,to form H /abc from H we set a =b =c and remove all triples that have decreased in size to a pair or singleton and also any repeated triples.In terms of the underlying graph G of H ,deleting a triple abc of H corresponds to deleting the edges ab ,bc ,ca of G .Contracting abc corresponds to contracting ab ,bc ,ca and removing any edges that are no longer an edge of a triangle.The degree of a vertex a ∈V in H is deﬁned by d (a )=#{t ∈ :a ∈t },equal to half the degree of a in the underlying graph G .The multiplicity of a pair ab ∈ V 2 in H is deﬁned by m (ab )=#{t ∈ :{a ,b }⊆t },equal to the multiplicity of the edge ab in the underlying graph G .A path in a 3-graph H =(V , )is an alternating sequence of +1distinct vertices and distinct triples,a 0,t 1,a 1,...,a −1,t ,a ,with the property that a i −1∈t i a i for i ∈[ ].A path is usually identiﬁed with its set of triples {t 1,...,t }.Observe that it is not required that a path with triples spans 2 +1vertices,although most of the paths that appear in the paper have this property.The 3-graph H is connected if for each pair of vertices u ,v ∈V there is a path u ,t 1,...,t ,v in H that joins them.H is connected if and only if its underlying graph is connected.A cycle in H is a closed path,i.e.,an alternating sequence of distinct vertices and distinct triples a 0,t 1,...,a −1,t terminated by the starting vertex a =a 0,with the property that a i −1∈t i a i .A cycle is usually identiﬁed with its set of triples {t 1,...,t }.Two triples sharing two vertices form a cycle.A forest of H is a set of triples T ⊆ with the property that there is no cycle C ⊆T .Between any two vertices in a forest there is at most one path.A spanning tree of H is a sub-3-graph T containingno cycles such that T =V ,i.e.,a connected forest spanning V .If H has a spanning tree then |V |is necessarily odd and T contains |V |−12triples.The connected 3-graph on {u ,v ,a ,b ,c }with triples uva ,uvb ,uvc has no spanning tree.A leaf of a tree T is a triple with two vertices of degree 1(belonging to no other triple of T ).A spanning tree of H has at least one leaf abc ,and at least two leaves if |V | 5.The 3-graph T −{b ,c }obtained by deleting vertices b ,c is a spanning tree of H −{b ,c }if and only if abc is a leaf of T for some a and where b ,c have degree 1.3.Elementary results on the existence and counting of spanning treesplexity of existence,ﬁnding and counting of spanning trees of 3-graphsThe problem of determining whether a 3-graph has a spanning tree is a special case of the matroid matching problem.The latter consists in,given a matroid with ground set E and a collection P of unordered pairs of E ,ﬁnding the largest size of a subset M ⊆P such that r ( p ∈M p )=2|M |,where r is the rank function of the matroid;such a set M is called a maximum matching of the matroid.Now,given a 3-graph H =(V , )and triples abc put in arbitrary linear order a <b <c ,deﬁne the subgraph G of its underlying graph G =(V ,E )on edge set E ={ab ,ac :abc ∈ ,a <b <c }of size 2| |.Partition E into pairs ab ,ac with abc ∈ ,a <b <c .Taking as the matroid the graphic matroid deﬁned by G and as the collection P all the pairs above,the existence of a spanning tree in the 3-graph H amounts to having a maximum matroid matching of size |V |−1.As mentioned in the introduction,this gives a polynomial-time algorithm for ﬁnding a spanning tree of a 3-graph.For k 4the problem of deciding if a k -uniform hypergraph has a spanning tree is NP -complete [3].Counting spanning trees of a 3-graph is #P -complete.This follows since counting perfect match-ings of a graph is a #P -complete problem in general [28]and this reduces to the problem of counting844 A.Goodall,A.de Mier/Advances in Applied Mathematics47(2011)840–868spanning trees for the class of3-graphs with the property that there is a vertex that is contained in all triples.On the other hand,counting perfect matchings is polynomial time for the class of graphs that have a Pfaﬃan orientation.One of the aims of this paper is to develop the analogous notion of a Pfaﬃan orientation for3-graphs and thereby characterize a class of3-graphs with the property that counting spanning trees has a polynomial-time algorithm.3.2.Spanning trees of complete3-graphsFor a3-graph H=(V, )let T(H)={T⊆ :T is a spanning tree of H}.Note that T(H\abc)= {T∈T(H):abc/∈T}and there is a bijection between T(H/abc)and{T∈T(H):abc∈T}.If abc is in no spanning tree of H then T(H)=T(H\abc).If abc is in every spanning tree of H then contracting the triple abc deﬁnes a bijection from T(H)to T(H/abc).Fix n∈N and denote by K(3)2n+1the complete3-graph with vertex set[2n+1]and triple set[2n+1]3,the set all3-subsets of[2n+1].For short we write T for the set of spanning trees of K(3)2n+1.The following result can be found for example in[24],but we include a proof as it prepares the ground for the next lemma and for Theorem9later.Theorem1.The number of spanning trees of K(3)2n+1is given by|T|=(2n−1)!!(2n+1)n−1.Proof.The proof uses a similar construction to the Prüfer code for spanning trees of ordinary graphs.A tree spanning at leastﬁve vertices always has at least two leaves;a rooted tree spanningﬁve or more vertices has at least one leaf not containing the root as a vertex of degree1.Suppose we are given a spanning tree T on[2n+1].We remove triples from T leaf by leaf in a canonical way until we are left with a tree consisting of just one triple.At the end of the algorithm described below we obtain a sequenceγ=γn∈[2n+1]n−1and a perfect matching M=M n of[2n]. If n=1,we takeγto be the empty sequence and M={12}.For n 2,the algorithm proceeds as follows.(1)Initializeγ1as the empty sequence,M0as the empty matching and T1=T as the spanning treeof K(3)2n+1that is to be encoded.Root T at vertex2n+1.Start with i=1.(2)At step i consider the rooted tree T i.Remove the leaf containing the smallest vertex label in T iwhile not containing the root2n+1as a vertex of degree1,thereby obtaining the next rooted tree T i+1.(If a leaf contains2n+1as a vertex of degree1it is ignored and the leaf with the next smallest vertex is taken.)Record as c i the vertex of degree greater than1in this leaf and setγi+1=γi c i.The other two vertices of degree1in the leaf a i b i c i are paired in the matching M i=M i−1∪{a i b i}.(3)If the remaining tree T i+1has only one triple(i.e.,i=n−1)then this triple takes the forma nb n(2n+1);in this case set M=M n=M n−1∪{a n b n},γ=γn,and stop.Otherwise increment ito i+1and go to(2).Conversely,given a sequenceγ=c1c2···c n−1∈[2n+1]n−1and a perfect matching M={a1b1,...,a nb n}of[2n]a unique spanning tree of K(3)2n+1is constructed as follows.(1)Initialize i=1,γ1=γ,M1=M,T1the empty tree(no triples or vertices).(2)Find the vertex a i with smallest label that does not occur as an element of the sequenceγi andthat occurs in the matching M i,but is not paired with c i.Let b i be the vertex such that a i b i∈M i.Set T i+1=T i∪{a i b i c i},M i+1=M i\{a i b i}andγi+1=c i+1···c n−1.(3)After step i=n−1the sequenceγn is empty and M n={a n b n}.Set T=T n∪{a n b n(2n+1)}andstop.Otherwise,increment i to i+1and go to(2).A.Goodall,A.de Mier/Advances in Applied Mathematics47(2011)840–868845Fig.1.Smallest connected3-graph on an odd number of vertices without a spanning tree.(Shaded triangles are triples.)Spanning trees of K(3)2n+1are thus in bijection with pairs(γ,M),whereγ∈[2n+1]n−1and M isa perfect matching of[2n].Since there are(2n−1)!!such perfect matchings,the result follows.2Theﬁrst part of the proof of Theorem1can be applied to any3-graph H,yielding a correspon-dence between spanning trees of H and pairs(M,f),where M is a perfect matching of H−v and f:M→V is a function satisfying a certain condition.Lemma2.Let H=(V, )be a3-graph with underlying graph G,and let v∈V.Given a spanning tree T of H,there is a unique perfect matching M of G−v and a function f:M→V such that the set of triples of T is equal to{ijf(ij):ij∈M}.Conversely,a perfect matching M of G−v and a function f:M→V determine a spanning tree of H if{ijf(ij):ij∈M}⊆ and there is no set of edges{i0j0,...,i −1j −1,i j =i0j0}⊆M such that f(i m−1j m−1)∈{i m,j m}for m∈[ ].Proof.Rooting a spanning tree T of H at the vertex v,we construct a unique perfect matching M of G−v and associated function f:M→V as follows.If|V|=3then T={vij}and set M={ij}and f(ij)=v.Assume now that|V|>3.Then every leaf of T has one vertex of degree greater than1,by which it is attached to the rest of the tree,and the remaining two vertices are of degree1.Let ijk be a leaf of T with vertices i,j of degree1.Remove this leaf from T.Inductively the remaining tree T\ijk determines a unique perfect matching M of G−{v,i,j}and function f:M →V\{i,j}.Extend M to a perfect matching M of G−v by adding the edge ij and the function f by setting f(ij)=k.Conversely,given a perfect matching M of G−v and a function f:M→V,the3-graph on V having as set of triples T={ijf(ij):ij∈M}is a spanning tree of H if T⊆ and there is no cycle of triples.It is easy to see that this amounts to the condition on f in the statement of the theorem. For such an f,the3-graph T is a tree with(|V|−1)/2triples,and therefore it spans the|V|vertices of H.23.3.Necessary or suﬃcient conditions for the existence of spanning treesThe most straightforward necessary conditions for the existence of a spanning tree of a3-graph H=(V, )is that H is connected and that|V|is odd.The3-graph in Fig.1shows that these condi-tions are not suﬃcient.Ourﬁrst non-trivial condition for the existence of spanning trees is a suﬃcient one and is as follows.Theorem3.Suppose H=(V, )is a3-graph such that|V|is odd and each pair of vertices has multiplicity at least1in H.Then H has a spanning tree.Proof.Assume T⊆ is a tree of maximum size and suppose that|T|<|V|−12.Let U⊂V be the setof vertices not spanned by T.Then|U|is even,containing at least two vertices u,v.Since there is some triple containing{u,v},there is w∈V such that uv w∈ and in fact w∈U for otherwise we could add the triple uv w as a leaf to T and obtain a larger tree of H.Set S={uv w},vertex-disjoint from T.For any leaf abc of T with vertices a,b of degree1in T there is a triple uai containing the pair{u,a}.By the remark in the previous paragraph i∈V\U.If uai is a triple for some i=b then deleting abc from T and adding the triples uai and uv w gives846 A.Goodall,A.de Mier /Advances in Applied Mathematics 47(2011)840–868a larger tree,contradicting the fact that T has maximum size.So we may assume that the only triple that contains u and at least one of a ,b is uab ,and that this is true for every leaf abc of T .We then remove all the leaves abc of T and put the triples uab in S .We repeat this argument,at each stage looking at triples containing u and vertices of degree 1in the leaves of what is left of the initial tree T .There are just two possible outcomes:either (i)at some stage we can join the remaining subtree of T and the tree S containing uv w by a triple to make a larger tree than the original tree T ,or (ii)we remove all the leaves of T and end up with a larger tree S that spans all but one of the vertices that are spanned by T and also the vertices u ,v ,w .Both possibilities contradict the hypothesis that T has maximum size.Hence the maximum tree T spans all the vertices of H ,i.e.,T is a spanning tree of H .2An extremal case of Theorem 3is when each pair of vertices is contained in exactly one triple,i.e.,H is a Steiner triple system.The condition on the multiplicity of pairs of vertices implies thata Steiner triple system on n points also has the property that every vertex is of degree n −12,and that n is congruent with 1or 3modulo 6.Wilson [30]showed that the number of non-isomorphic Steinertriple systems on n ≡1or 3(mod 6)points lies between (e −5n )n 2/12and (e −1n )n 2/6.(Given the truth of the then conjecture of Van der Waerden on the size of permanents,Wilson improved the lower bound,and further conjectured that the actual number is in fact asymptotically (e −1n )n 2/6.)There is just one isomorphism class for n ∈{3,7,9},two for n =13,eighty for n =15.For Steiner triple systems not only can we assert the existence of a spanning tree but we can also give a superexponential lower bound on the number of spanning trees.Theorem 4.If H =(V , )is a Steiner triple system on |V |=n vertices then H has Ω((n /6)n /12)spanning trees.Proof.Brouwer [4]proved that any Steiner triple system on n vertices has a transversal (set of pair-wise disjoint triples)covering all but 5n 2/3vertices,and Alon,Kim and Spencer [2]improved this to all but O (n 1/2ln 3/2n )vertices.Let P ⊆ be such a set of pairwise disjoint triples that together cover U ⊆V ,with |U |=n −k and k =o (n ).Let r =(n −1)/2.We give a procedure that generates s i =0(r −k −1−6i )spanning trees,where s is the largest integer such that r −k −1−6s >0(s is n /12−o (n )).However,this procedure may give repeated trees;we then show that each tree cannot appear more than n /6times.Recall that in a Steiner triple system every vertex belongs to r triples.In H |U every vertex belongs to at least r −k triples.Let u 0be a vertex of U .The construction of a spanning tree consists in ﬁrst using P to construct a “comb-like”tree of H |U and then extending this tree to a spanning tree of H .So let us begin by considering the restriction H |U .Let t 0be any triple containing u 0,subject only to the condition that t 0/∈P .Say t 0={u 0,u 0,u 0}.Let p 0,p 1,p 2be the triples in P that contain u 0,u 0,u 0,respectively.Clearly the triples t 0,p 0,p 1,p 2form a tree T 0.Let u 1be any of the four vertices in (p 1∪p 2)\t 0.There are at least r −k −7triples that contain u 1but no other vertex of T 0.Let t 1={u 1,u 1,u 1}be any one of them.Let p 3and p 4be the triples in P that contain u 1and u 1,respectively.Let T 1=T 0∪{t 1,p 3,p 4}.We proceed iteratively in this way as long as r −k −1−6i is positive:we choose u i to be any of the four vertices in p 2i −1∪p 2i that are not in t i −1and we choose t i ={u i ,u i ,u i }a triple containing u i and no other vertex in T i −1.Then we take the two triples p 2i +1,p 2i +2in P that contain u i ,u i and set T i =T i −1∪{t i ,p 2i +1,p 2i +2}.Once we have a tree T s ,covering 6s +9vertices,we need to complete it to a spanning tree of H .We repeatedly use the following claim.Claim.Let T be a tree of H and let W be the set of vertices not spanned by T.Then there are vertices a,b of W such that the triple that contains them has its third vertex in T.Proof.Suppose it were not the case.Then the triples on W would form a Steiner triple system.But since W has even cardinality this is impossible.2A.Goodall,A.de Mier /Advances in Applied Mathematics 47(2011)840–868847Fig.2.A spanning tree and its skeleton (here s =2).Red triples are shown as thick long lines,blue triples are thin dashed lines and green triples are depicted as bags.Therefore,by adding a leaf at a time,we can complete T s to a spanning tree of H .There may be many ways of completing T s ,but we just take one of them arbitrarily.If we ﬁx the starting vertex u 0,by applying the procedure just described we obtain 4s s i =0(r −k −1−6i )spanning trees of H .Indeed,at step i we need to choose one of four vertices and then we know that this vertex belongs to at least r −k −1−6i triples that are contained in H |U but do not contain any vertex already in the tree.It could be,however,that the same tree is produced several times.For instance,the tree in Fig.2could appear in two different ways.Next we bound the number of possible repetitions of a given spanning tree T .Let us ﬁrst color the triples of T in the following way.The triples from P are colored blue;the triples entirely contained in U and that intersect three triples of P are colored red,and the remaining triples are colored green.Observe that green triples are only included in the ﬁnal stage of the construction of a tree (when the claim is used),whereas blue and red triples can appear both during the ﬁrst steps of the construction and also at the end.The skeleton of T is the graph whose vertices are the red triples and where two vertices are adjacent if there is a blue edge in the tree intersecting the corresponding red triples in different vertices.The skeleton is a forest (it will be a tree if there is only one red triple containing u 0);root each component of the forest at the vertex corresponding to the triple that contains u 0.Observe that the skeleton contains at least one rooted path of length s .If by the above procedure the same tree is produced more than once,the corresponding skeleton has at least two different rooted paths of length s .The skeleton of a spanning tree contains at most n /6vertices,since in the tree every red triple has two blue triples attached.There are at most n /6−s vertices that can be the end of a rooted path of length s .Since we are only interested in a lower bound for the number of trees,certainly there are no more than n /6rooted paths of length s in the skeleton,so each tree is produced at most n /6times.Therefore the number of spanning trees of a Steiner triple system is a least4s si =0(n −k −1−6i )n /6.This is Ω((n −k −1)!1/6)and since k =o (n )we thus have Ω((n /2)!1/6)spanning trees,which by Stirling’s approximation gives the statement of the theorem.2We now return to the question of the existence of spanning trees and will this time present a necessary condition.Consider again a 3-graph H =(V , )with underlying graph G =(V ,E ).The hypergraph obtained from H by deleting vertices in S ⊆V is denoted by H −S .This may contain hyperedges of size 1,2or 3.The underlying graph G −S consists of triangles for each triple,edges for each pair,and isolated vertices for each singleton of H −S .A connected component of H −S corresponds exactly to a connected component of the graph G −S .Let q (H −S )denote the num-。

环保功能材料 SCI

New Method of Water Purification Based on the Particle-Exclusion PhenomenonI V A N K L Y U Z H I N,A N D R E W S Y M O N D S,†J E F F R E Y M A G U L A,A N DG E R A L D H.P O L L A C K*Department of Bioengineering,Box355061,University of Washington,Seattle,Washington98195Received December17,2007.Revised manuscript received April29,2008.Accepted May7,2008.Colloidal particles in suspension are excluded from the vicinity of various hydrophilic surfaces.On the basis of this phenomenon,a novel method of water puriﬁcation is proposed and tested.Proof-of-concept is demonstrated using a custom-made extractor that collected clean water from the annular “exclusion zone”within a Naﬁon tube.Up to99.6%of particles could be removed from the suspension.The experimental results suggest that particle exclusion may provide a new framework for water puriﬁcation from both organic and inorganic matter,as well as from harmful pathogens.IntroductionRecent studies have shown unexpected particle behavior next to various hydrophilic surfaces(1–3).Particles,such as microspheres,migrate away from these surfaces,leaving unexpectedly large regions of particle-free water(Figure1). At equilibrium,these regions may be as large as several hundred micrometers,and their physical properties differ from those of bulk water.These interfacial areas have been termed“exclusion zones”because of their distinctive ability to exclude particles and solutes.Exclusion zones had in fact been noted as early as1970,when microspheres were shown to be excluded from the vicinity of certain biological tissues (4).More recently,extensive studies have shown that the exclusion phenomenon is quite general,both in biological and non-biological systems(1,2).The phenomenon of exclusion provides a new basis for water puriﬁcation.With a large enough exclusion zone next to the exclusion-generating surface,clean water can be easily collected,leaving behind particle-containing and solute-containing water.We chose Naﬁon as the excluding surface. Naﬁon is a perﬂuorosulfonic ionomer that consists of a polytetraﬂuoroethylene backbone and regularly spaced side chains terminated by sulfonate ionic groups(5).Previous studies have demonstrated that Naﬁon has negative charge in deionized water,with a surface electrical potential of-160 mV(2).The advantages of using Naﬁon as the excluding surface are its relatively large exclusion zone and its com-mercially availability in convenient tubular shape.We developed a system in which water could be drawn continu-ously along the tube’s annular exclusion zone and extracted at the end of the tube,with promising levels of separation of both artiﬁcial and natural water-borne particles. Materials and MethodsThe puriﬁcation process employed a Naﬁon tube.With a pressure gradient imposed along the tube,suspensions could be forced toﬂow inside.An annular exclusion zone developed with distance along the tube(Figure2).By drawing water from the annular zone using an extractor at the end,virtually particle-free water could be obtained.Flow Chamber.To observe whether various particle types were excluded from the zones next to the Naﬁon surface, both in static conditions and duringﬂow,the experimental chamber illustrated schematically in Figure2was used.A 5-mm-thick transparent plastic sheet with window cut out was set on a glass plate.A3-mm hole was drilled on either end of the sheet,allowing the Naﬁon tube(O.D.2.5mm, TT-110,Perma Pure LLC,NJ)to traverse the chamber.The chamber wasﬁlled with distilled,deionized water and sealed with a second glass plate.The tube was connected via Tygon tubing to a container on the input end and to a syringe pump (YA-12,Yale Apparatus)on the output end.The pump worked in the withdraw mode,diminishing the pressure and forcing theﬂuid suspension toﬂow through the tube.To observe particle behavior near the Naﬁon surface in static situations,the syringe pump was engaged until the tube was primed;then,after5to10min,the equilibration time required to ensure that the exclusion zone was fully formed,the near-surface regions were examined.To observe particle behavior duringﬂow,the syringe pump was set to operate at a constant rate.Once theﬂow was established, the interfacial region within the Naﬁon tube was examined in an inverted microscope(Diaphot,Nikon)equipped with a5×objective lens.Images were acquired and analyzed using a digital CMOS camera(DFC290,Leica).Images were also taken occasionally using a digital camera(EasyShare P880, Kodak)through an eyepiece of the microscope.Observations of bacterial and viral suspensions were made in a biosafe laboratory,where high magniﬁcation objectives (20×or higher)were the only ones available for use.The short focal distances prompted the use of thinner Naﬁon tubes(TT-030,ID0.64mm,Perma Pure)that wereﬁxed between a microscope slide and a coverslip.The Naﬁon tube was superfused with the bacterial suspension and observed under an upright microscope(Axioskop,Zeiss).Bacteria were imaged close to the Naﬁon tube under both brightﬁeld and ﬂuorescent illumination.Adenoviruses were also studied and imaged via a laser scanning confocal microscope(Leica SP-1,Keck Imaging Center at University of Washington).Because they were small(cylindrical,80nm long)and could not therefore be resolved with light microscopy,the viruses were ﬂuorescently labeled so that the exclusion zone would appear as aﬂuorescence“void”next to the surface of the Naﬁon tube.Differential Extractor and Separation.The experimental setup used for the separation experiments is shown in Figure 3.A custom-made“differential extractor”was employed to separate exclusion zone water and bulk solution.The extractor was made of two concentric stainless steel tubes of different diameter held together by low temperature silver solder.The Naﬁon tube clasped the extractor’s outer tube. The extractor’s inner tube extended out0.5mm into the Naﬁon tube,which made it possible to visualize the puriﬁcation process under the microscope.The inner and outer channels of the extractor led to separate outputs,each connected to a syringe pumps via Tygon tubing.*Corresponding author phone:(206)685-1880;fax:(206)685-3300;e-mail:ghp@.†Current address:MRC Centre for Developmental Neurobiology,King’s College London,Strand,London WC2R2LS,England,U.K.Environ.Sci.Technol.2008,42,6160–616661609ENVIRONMENTAL SCIENCE&TECHNOLOGY/VOL.42,NO.16,200810.1021/es703159q CCC:$40.75 2008American Chemical SocietyPublished on Web07/11/2008The pumps generated reduced pressures inside the extractor’s inner and outer channels,forcing the suspension to ﬂow.When the suspension reached the extractor’s interface,the contents of the tube’s core was sucked into the inner channel,while the annular water was sucked into the outer channel (Figure 3).Thus,the solution near the Naﬁon surface was separated from the core solution.Suspension Preparation.To test the method’s effective-ness,particle suspensions of varied composition were prepared.They included topsoil,clay soil,silt,bacteria,viruses,and microspheres.Turbidity,expressed in NTUs (nephelometric turbidity units)was used as a measure of particle concentration.This approach is commonly used forthat purpose (6–9).Turbidity was measured using a turbi-dimeter (2020i,LaMotte,MD).The instrument was calibrated using 0.5,10,and 100NTU standards (Amco Clear,GFS Chemicals,OH).Although turbidity of river and lake waters can reach hundreds of NTUs during rains and ﬂoods,typical values lie within 1-20NTU (7,8),well within the range of calibration.The suspensions of topsoil,clay soil,and silt were prepared by mixing the soil samples (Ward’s Natural Science,Rochester NY)with deionized water in a commercial blender (51BL32,Waring,New Hartford,CT).After they were mixed,the suspensions were ﬁltered through a paper ﬁlter with 8-to 12-µm pore size (Sharkskin General-Purpose ﬁlter paper,Whatman).This procedure removed the larger particles that would ordinarily settle out inside the Naﬁon tube.The turbidity of the ﬁltered solutions lay within a 100-300NTU range,and this required further dilution for experiments.Dilution yielded input suspensions with turbidities 5,20,and 100NTU.To supplement the studies of natural particles,carboxy-late-coated 3-µm latex microspheres (Polybead,Polysciences Inc.;coefﬁcient of variance,5%)were used as synthetic test particles.Concentrated stock suspensions (1.68×1012particles/L)were diluted with distilled,deionized water.For the experiments that employed ﬂow,the stock solution was diluted to yield 5,20,and 100NTU suspensions.Water for the experiments (Type 1,HPLC grade,18.2ΜΩ)was obtained from a standard water puriﬁcation system (Diamond TII,Barnstead).Because of their hazardous nature,bacterial and viral suspensions were observed under static conditions only,near the surface of the Naﬁon tube.No ﬂow experiments were carried out.Two gram-negative bacterial species were studied,Escherichia coli and Nitrousomonus europea .E.coli were cultured overnight at 37°C in liquid broth media.N.europea were grown in special media at room temperature until fully grown.Cells were spun down and washed three times in 10%glycerol solution to remove salt,which has been shown to reduce the size of exclusion zones (3).The washed bacteria were then diluted 1:1with sterile deionized water,giving a ﬁnal concentration of approximately 5×108particles/mL.Some bacterial preparations wereincubatedFIGURE 1.Example of development of exclusion zone (EZ)near the edge of Naﬁon ﬁlm.An aqueous microsphere suspension was injected between two microscope slides with a ﬂat Naﬁon ﬁlm squeezed between.Following injection,the microspheres migrated away from the edges of the Naﬁon ﬁlm,leaving a region of particle-free water.Carboxylate-coated 3-µm microspheres were used.Images were acquired with an invertedmicroscope.FIGURE 2.Experimental chamber used for exclusion-zone observations,not to scale.A motor pulled on the syringe plunger at a constant,controllable rate.Particles condensed in the tube’s core,as shown schematically.For exclusion-zone observations in static situations,the syringe motor could be stopped.Observation point marked with dashedcircle.FIGURE 3.Experimental setup used for water puriﬁcation experiments,not to scale.Syringe pumps (not shown)generated ﬂow through Naﬁon tube and channels of differential extractor.Arrows denote direction of ﬂow.VOL.42,NO.16,2008/ENVIRONMENTAL SCIENCE &TECHNOLOGY96161with a ﬂuorescent cell-viability marker SYTO-9(Molecular Probes)for 15min.Viral particles were obtained from the University of Washington Molecular Genetics Laboratory.The preparation used was an aerosol adenovirus of rare serotype,usually seen in patients with compromised immune systems.Viral particles were labeled with Cy3dye by dialysis and then frozen in 0.5mL aliquots at -80°C for storage.Once the virus preparation was thawed on ice,it was dialyzed against 500mL sterile deionized water for 3.5h to remove the salt from the virus particle buffer (initially 150mM NaCl).For the preparation used in these experiments,the stock concentra-tion was 1.4×1012viral particles/mL.This was diluted 3:2with deionized water,giving a working concentration of 8.4×1011viral particles/mL.ResultsSolute Exclusion.To determine if topsoil particles,clay soil,and silt are excluded,the Naﬁon tube was primed with the respective suspension at 100NTU and observed as described in Figure 2.Exclusion zones were seen with all suspensions (Figure 4).Their size at equilibrium depended on suspension type.For clay particles,the size (∼170µm)was generally larger than that of topsoil and silt particles (∼120µm).By comparison,the exclusion zone of 3-µm carboxylate mi-crospheres under the same conditions was greater than 300µm.Soil-exclusion zones were also more ambiguously deﬁned than microsphere-exclusion zones,that is,their termination boundaries were less sharp.Exclusion zones were also seen with bacterial particles.Both bacterial species (N.europea and E.coli )were excluded.An example is shown in Figure 5.The exclusion zone was revealed by a ﬂuorescence gap.Viral suspensions revealed a different kind of behavior.After the viral suspension was superfused around the Naﬁon tube,“clusters”were observed which were much larger than the individual particles (Figure 6).These ﬂuorescent clusters,2-5µm in diameter,were absent from a region approximately 150-µm wide.They were also adsorbed onto the Naﬁon tube’s outer wall,possibly as a result of immediate binding to the Naﬁon upon infusion.Whether or not individual viral particles might be present within the cluster-exclusion zone remains uncertain.Flow Observations.To study particle exclusion during ﬂow,the experimental chamber illustrated in Figure 2wasmodiﬁed so that Naﬁon tubing of different i.d.’s (2.2,1.6and 1.2mm)could be employed.The exclusion zone inside the tube was measured at midlength along the tube and studied at different ﬂow rates.Starting from 5mL/h,the ﬂow rate was increased in 5mL/h increments to 50mL/h.AteachFIGURE 4.Exclusion zones within static colloidal suspensions.Photographs were taken with a 5×objective 5min afterpriming.FIGURE 5.Exclusion of E.coli inside and outside the Naﬁontube.FIGURE 6.Medium of viral particles near Naﬁon surface.Observed ﬂuorescent clusters were absent in the zone next to Naﬁon (EZ).Some clusters attached to the Naﬁon surface.61629ENVIRONMENTAL SCIENCE &TECHNOLOGY /VOL.42,NO.16,2008ﬂow rate,approximately ﬁve minutes were allowed for the exclusion zone to come to steady state,for measurement.An example showing the development of the steady state is presented in Figure 7.Along the length of the Naﬁon tube,the exclusion zone was not uniform.At the tube’s entry,particles were evenly distributed over the full cross-section.As particles moved through the tube during steady ﬂow,they were progressively excluded from the vicinity of the wall,both with distance and time.At a ﬂow rate of 15mL/hr,for example,the exclusion zone reached its steady-state size at a distance of 1-2mm.At that position and ﬂow rate,the exclusion-zone size was smaller than in the static condition (see Figure 7).When the ﬂow rate was increased,the exclusion-zone size diminished.This dependence,for each of several tube diameters,is shown in Figure 8.Note that the tube with the largest i.d.showed the largest exclusion zones.When solutions of topsoil,clay soil,or silt were pumped through the Naﬁon tube,sediment formed.The sedimented particles accumulated progressively on the bottom of the tube in a thin layer.In general,sediment was heavier toward the tube’s distal end,although the amounts were not quantiﬁed.Sediment formation did not obscure the ﬂow through the tube.It is apparent from Figure 8that lower ﬂow rates yielded larger exclusion zones.However,lower ﬂow rates also brought lower overall water-collection rates.As a compromise,an intermediate ﬂow rate of 15mL/h was selected for the separation experiments,below.At this ﬂow rate,the linear velocity at the centerline was 1.91(0.06mm/s.Pure-Water Extraction.Extraction experiments were carried out according to the setup shown in Figure 3.When particles reached the differential extractor,the exclusion zone was fully formed (Figure 9).The differential extractor separated the suspension into core and annular fractions (c.f.,Figure 3).The latter fraction contained relatively puriﬁed water.We deﬁne R as the ratio of turbidity in the collected puriﬁed suspension to that in the input suspension.Lower R values mean better puriﬁcation.It was more convenient to express results in terms of 1-R ,which we deﬁne as puriﬁcation efﬁcacy.Higher values imply higher efﬁcacy.Puriﬁed-water yield,on the other hand,depends on how fast water within the exclusion zone is delivered to the differential extractor.Both yield and efﬁcacy are increased with larger exclusion zones.To determine efﬁcacy and yield at various levels of contamination,the turbidities of the input suspensions were varied.Suspensions of topsoil,clay soil,silt,and microspheres were used.The inner channel intake rate was kept at 13mL/h,and the outer channel intake rate was 2mL/h.Together,this created a 15mL/h ﬂow through the Naﬁon tube.Thus,for every 15mL of input suspension,2mL of puriﬁed annular fraction were extracted.Sample collection continued for two hours,yielding 4mL of exclusion-zone water.Because the minimum amount of solution required for turbidity mea-surement was 10mL,the collected annular fractions were diluted with 6mL of deionized water.After the turbidity was measured,the result was multiplied by 2.5to take into account the dilution.The results are presented in Table 1.The puriﬁcation efﬁcacy depended on suspension type.The highest was achieved with the microspheres.With 100NTU input suspension,99.6%efﬁcacy was achieved.For the input suspensions of lower turbidity (20and 5NTU),efﬁcacy was 98%.Results obtained with the soil suspensions showed the opposite tendency:higher initial particle concentrations resulted in lower efﬁcacy.Approximately 70-90%of particles were removed.Overall,the microsphere suspensions were puriﬁed with greater efﬁcacy than the soil suspensions.To determine how efﬁcacy varied with annular ﬂow rate,the ratio of outer/inner intake rate ratio was varied,without changing either input turbidity (20NTU)or overall ﬂow rate (15mL/h).The differential extractor separated an annular layer from the solution in the core.The width of the annular layer collected depended on the outer-channel intake rate:higher intake rates tended to suck water closer to the core,which was “dirtier”.Thus,with lower outer-channel intake rate,cleaner water should be collectible.To test this premise,the outer/inner channel ﬂow ratio was changed in ﬁve steps,from 14/1to 7/8mL/hr,and the turbidities were measured.Changing the ratio did not affect the size of exclusion zone because the ﬂow rate was maintained constant.The results are presented in Table 2.With all suspensions,puriﬁcation efﬁcacy decreased as the intake rate through the outer channel was increased.Values of puriﬁcation efﬁcacy were always highest for the microsphere suspensions.However,with the 1mL/h intake rate,topsoil and clay results were similar to that of microspheres.In general,reductionFIGURE 7.Development of exclusion zone during ﬂow at a ﬁxed observation point.Flow rate of 15mL/h was used.A steady state was reached after approximately 60s.Right:microsphere exclusion in staticsituation.FIGURE 8.Effect of ﬂow rate on exclusion-zone size.VOL.42,NO.16,2008/ENVIRONMENTAL SCIENCE &TECHNOLOGY96163of the intake rate through the outer channel resulted in cleaner water.This was observed for all particle types.Results varied somewhat among experiments.For ex-ample,the conditions in the second data column of Table 2(2mL/h)and the second data row of Table 1(20NTU)are similar:both represent collection rates of 2mL/h at 20NTU.Yet the results varied somewhat.Variation was typically on the order of 10-20%.Tables 1and 2show the best results among those achieved under nearly similar conditions,typically among ﬁve trials.The deviations were mainly the result of technical deﬁcits,such as slightly noncircular tubular cross-section or off-center collector position,and because the goal was to test proof-of-principle,the data presented in the tables report the best results achieved,rather than the means.In the absence of the noted technical deﬁcits,it is estimated that the best results would have been achieved with more consistency.DiscussionSolutes are excluded from an unexpectedly large zone next to many hydrophilic surfaces (1–4).On the basis of this phenomenon,we constructed a device that separates variousparticulates from water and collects the puriﬁed fraction.Representative particulates commonly found in water were effectively removed,without the need for a ﬁne physical ﬁlter.The scientiﬁc basis of this phenomenon is under intense study.Exclusion of particles and solutes from zones spanning hundreds of micrometers from surfaces is not expected from conventional theory,although some aspects such as double-layer and osmotic phenomena may play a role.The bulk of evidence suggests that a major player is a long-range reorganization of water molecules in the vicinity of hydro-philic surfaces,including Naﬁon,the reorganized,or struc-tured “phase”of water excluding particles and solutes (2).A presentation of the evidence and implications is available at /programs/displayevent.aspx?rID )22222,the link to the 2007/2008University of Washington Annual Lectureship Award,where this phenomenon is featured.Exclusion of Water-Borne Particles.The experiments incorporated various soil suspensions and biological particles.The fact that they were excluded from the region next to Naﬁon adds to the growing list of particles and solutes conﬁrmed to be excluded from the zone next to hydrophilic surfaces (1–4).Soil suspensions had smaller exclusion zones than mi-crospheres (Figure 4).This difference may result from two factors.One is particle-size distribution.The exclusion-zone size is larger for larger particles (1).Soil suspensions,after having passed through a 12-µm ﬁlter,contained an array of smaller particle sizes,including those smaller than the 3-µm microsphere size used here.The presence of these smaller particles may explain the relatively smaller exclusion zones.Another reason for the relatively smaller zones may be the presence of dissolved substances.Soils usually contain salts and other molecular compounds such as proteins,peptides,and polysaccharides (10),which are known to cause dimi-nution of exclusion-zone size (3).We found also that the boundaries of the exclusion zone were less sharp for soil than for microspheres (Figure 4).This fuzziness also may arise from the soil’s particle-size diversity.For the 3-µm carboxylate microspheres,by contrast,the standard deviation of size was only 0.112µm,generating a very distinct border (Figure 4).Exclusion zones observed for bacterial particles and viral clusters imply that a disinfection device may be possible.Currently,bacterial particles are ﬁltered out by membranes or ﬁlters,and the residual organisms are deactivated by various disinfectants such as chlorine,ozone,or UV (11,12).If bacterial particles are separable in a same manner as soil particles,then a new disinfection method could be on the horizon.Exclusion-Based Puriﬁcation.Built on the observation that water-borne particles are excluded fromnear-surfaceFIGURE 9.Photographs of the zones near the extractor.Left:Microsphere suspension.Right:Clay suspension.Intake rate of the outer channel:2mL/h.Inner channel:13mL/h.TABLE 1.Purification Efficacy for Various Suspensions As a Function of Particle Concentration apuriﬁcation efﬁcacy (%)input turbidity (NTU)microspherestopsoil silt clay soil 598938490209873938410099.6768679aSolution intake rates:inner channel,13mL/h;outer channel,2mL/h.Samples collected for 2h.TABLE 2.Purification Efficacy Achieved with Various Outer Channel Intake Rates apuriﬁcation efﬁcacy (%)intake rate through outer channel (mL/h)suspension type 12467microsphere 9891807056clay soil 9871474846topsoil9680595039aInner channel intake rate was changed to maintain a 15mL/h ﬂow rate through the tube.Samples were collected for two hours and then diluted to yield 10mL.61649ENVIRONMENTAL SCIENCE &TECHNOLOGY /VOL.42,NO.16,2008regions of hydrophilic substances,the prototypeﬁltration system performed well.Various soils could be separated, resulting in relatively pure water.Puriﬁcation of soil suspensions depended on concen-tration(Table1).Lower-concentration suspensions gener-ally showed higher puriﬁcation efﬁcacy than those with higher concentrations.This may be a result of the lower salt concentration associated with lower soil concentration. On the other hand,the efﬁcacy of microsphere-suspension puriﬁcation did not depend signiﬁcantly on concentration. This result agrees with the previous observation that microsphere concentration does not affect the exclusion-zone size(1).The observed relation between exclusion-zone size and ﬂow rate(Figure8)sheds light on the conditions under which pure-water yield may be maximized.Pure-water yield depends mainly on two features:exclusion zone size andﬂow rger exclusion zones allow extraction of more clean water per unit volume of original suspension. Higherﬂow rate should allow faster collection.On the other hand,higherﬂow rate also reduces the size of exclusion zone(Figure8).Hence,to maintain high puriﬁcation efﬁcacy a lower outer-channel intake rate must be used,which in turn decreases the pure water collection rate.However,the curves on the graph in Figure8suggest a plateau atﬂow rate of approximately50mL/h;thus,at ﬂow rates higher than50mL/h,the exclusion-zone size should not change signiﬁcantly.Potentially,this may allow pure water collection at much faster rates.At an expedient outer-channelﬂow rate of2mL/h,soil turbidity was reduced by90%,whereas the reduction for microspheres was up to99.6%(Table1).This difference stems from the observation that microsphere-exclusion zones were larger than soil-particle exclusion zones;the ﬂow collected by the differential extractor’s outer channel was therefore essentially all exclusion-zone water.If the exclusion zone is smaller than200µm,as in the case of soil suspensions,then the particles from the core are sucked into the outer channel,contaminating the annular fraction. This problem was solved by lowering the outer channel’s intake rate.Although this procedure increased the puri-ﬁcation efﬁcacy(Table2),it also reduced pure water yield, the tradeoff between pure water yield and puriﬁcation efﬁcacy.Methodological Limitations.Execution of the experi-ments revealed several shortcomings of the approach.They arise both from the exclusion phenomenon itself and the speciﬁc implementation of the principle.Geometrical Limitations.Geometric uniformity was an important consideration.To prevent particles fromﬂowing into the extractor’s outer channel,the gap between the extractor’s two concentric tubes had to be uniform over the circumference;otherwise,some core solution couldﬂow into the outer channel.This contaminates the annular fraction and reduces puriﬁcation efﬁcacy.To minimize this problem, the setup had to be carefully aligned each time prior to the experiment and not always perfectly.If this concentric approach were adapted for larger scale puriﬁcation,careful engineering would need to address this limitation.Similarly,the Naﬁon-tube shape is also critical.If the cross-section is noncircular,then theﬂow proﬁle will be nonuniform,and particles in some core regions may enter the annulus.Indeed,some samples coming from the manufacturer had a distinctly elliptical cross-section.Such tubes could be forced into an almost circular cross-section by feeding them through a hole made in the chamber wall. When the tube was dry,itﬁt through the hole easily.Upon swelling in water,the tube sealed the hole and acquired a more circular cross-section.Noncircularity is a lingering problem that could be circumvented by using a system design based onﬂat surfaces.Sediment Formation.The observed sediment formation is probably caused by the rapid settling of the heavier particles or by some chemical change inside the Naﬁon tube that created heavier particles.If sedimentation is caused by the weight of the larger particles,then the problem could probably be solved throughﬁner preﬁltering,or the issue could be circumvented altogether through use of a vertically oriented Naﬁon tube.Although the amount of sediment was minute relative to the total number of particles within the suspension,its existence must have affected the results presented in Table 1,presumably elevating the apparent puriﬁcation efﬁcacy. Indeed,one could argue that the turbidity reduction in the annular fraction originated entirely from sediment formation, the clear water arising entirely because of settling.However, sediment fallout was not observed at all with microspheres, which showed the greatest turbidity reduction(Table1). Hence,the effect seems to be relatively minor,although further consideration is warranted.Low Puriﬁcation Rate.The relatively small size of the exclusion zone places a limit on the water-puriﬁcation rate.Flow rates were considerably smaller than those involved in standard puriﬁcation techniques.To increase throughput,multiple units could be arranged in parallel, or relatively larger exclusion zones could be generated by using surfaces that might be better exclusion-zone nuclea-tors than Naﬁon.On the other hand,the tubular design employed here was adopted solely for obtaining proof of principle,with no consideration given to generating high throughput.For commercial applications,other designs may be more effective.If these improved designs cannot yield puriﬁcation efﬁcacies beyond the80-90%obtainable here with common particles,then cascading of units in series might eventually be necessary.The current design is preliminary;it reﬂects only the modest level of engi-neering required for obtaining proof-of-principle.Advantages.The principal advantage of this approach is its inherent simplicity.Removal of particles occurs naturally; in principle,it is merely a matter of collecting the puriﬁed water.Modern puriﬁcation techniques,by contrast require the use of physicalﬁlters or membranes that eventually become clogged and must be cleaned(backwashed)or replaced(11,13–15).Here,there are no physicalﬁlters.On the other hand,scaling up this new approach for imple-mentation in realistic settings will evidently require ap-preciable engineering.This is for the future.Another advantage of this approach is its inherent capacity to remove pathogens.Bacterial particles were excluded,and preliminary data indicate that viruses might be excluded as well(Figures7and8).This feature would make the method especially useful in locales where drinking water may contain biological contaminants.In summary,the exclusion-zone phenomenon offers a new,previously unforeseen route toward water puriﬁcation. Proof-of-principle has been demonstrated,with good sepa-ration ratios in a simple design.The prototype could easily be improved for both faster and cleaner collection,making it a practical approach with considerable promise because of its inherent simplicity.AcknowledgmentsThis research was supported by ONR Grant N00014-05-1-0773and NIH Grant1R21AT-002362.We thank Chenyang Wang,Vincent Thuc Wu,and Iris Pang for help with preliminary measurements that aided in the initial design. Literature Cited(1)Zheng,J.-M.;Pollack,G.H.Long-range forces extending frompolymer-gel surfaces.Phys.Rev.E2003,68,031408.VOL.42,NO.16,2008/ENVIRONMENTAL SCIENCE&TECHNOLOGY96165。

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1
Coherence relations
Introduction
In this paper, I would like to address a methodological question that starts from the following observation: There is a growing number of corpus studies in the area of the use of coherence relations and discourse markers in natural texts. Most of these studies try to establish a relationship between the coherence relations found in the text and the discourse markers used to signal them linguistically, very often inter-clausal connectives (Degand 1996, 1998; Grote, Lenke & Stede 1997; Knott 1996; Mann & Thompson 1992; Oversteegen 1997; Pit, Pander Maat & Sanders 1997; Pander Maat & Sanders 1995, Sanders 1997). However, the results of these studies are hardly ever straightforward to compare. The main reason for this is that the methods used to classify both the coherence relations and their linguistic markers are very often divergent and in the best cases only partially overlapping. So, in order to enable comparison of the different studies, there is a need for clear and explicit classification criteria. In this paper, I will try to set out a number of such (operationalisable) elements that could function as tools in the categorisation task.
The goal will be reached if the categorisation criteria are formulated in such an explicit way that they can be applied by different analysts to all kinds of h assistant at the Belgian National Fund for Scientific Research (F.N.R.S.). 29
justification, motivation, evidence, conclusion, etc. Furthermore, a distinction can be made between (i) epistemic (knowledge of a fact leads to conclusion of a belief), and (ii) speechact relations (a fact leads to the utterance of a speech-act). • _Textual / sequential relations establish a sequential, text organising relation between ideationally and interpersonally only loosely or indirectly related adjacent discourse segments. Examples are: list, joint, etc. or any other ideational or interpersonal relations when they are used as comment, digression, excursus, etc.
2
From connective relation
to
coherence
While the characterisation of these relational domains is general enough so as to account for all different kinds of discourse structures, this generality poses a number of problems as soon as one starts to work with natural texts. Most of the time there is agreement on proto~.'pical examples (very often built-up examples for purposes of illustration), but in actual text analysis one gets rapidly confronted with an important number of ambiguous cases. That is, when one tries to establish what type of coherence relations are present in the text, it becomes rapidly impossible to classify found relations on the basis of these definitions alone. Different elements may account for these problems: (i) coherence relations are not always marked linguistically, (ii) there is no one to one mapping between coherence relation and linguistic discourse marker, and (iii) there is no general consensus on the type of linguistic constructions that may function as discourse markers (connectives, prepositions, adverbials, intonation patterns, cue phrases, etc.). In the literature, connectives are generally considered to be prototypical linguistic markers of coherence relations. In this paper, I will then concentrate on the problems that arise when one tries to relate to each other the discourse domains as described above, the coherence relations and the connectives that may signal these coherence relations. This will be exemplified on the hand of causal constructions.
A classical approach to coherence relations is to classify them into relational or discourse domains: semantic v s . pragmatic (van Dijk 1979; Sanders 1992; Pander Maat & Sanders 1995), content v s . epistemic vs. speech-act (Sweetser 1990), external vs. internal (Halliday & Hasan 1985, Martin 1992), subject matter vs. presentational (Mann & Thompson 1988), ideational vs. interpersonal vs. textual (Degand 1996, Maier & Hovy 1993), ideational vs. rhetorical vs. sequential (Redeker 1991). These classifications all account for the fact that there are different types of coherence relations that exist at several "levels", "strata", "planes" or "domains" of the discourse. It is striking to note that there is a great amount of agreement between the authors with respect to the different general types of coherence relations. They can be grossly characterised as follows: ® Ideational / semantic / content / external / subject matter relations establish a link between discourse units that denote states of affairs in the world described in the discourse. Examples are: cause, sequence, contrast, etc. Interpersonal / pragmatic / internal / presentational / rhetorical relations establish a link between the illocutionary meaning of one of the discourse units with the Iocutionary meaning of the other. Examples are: