A new heuristic for rectilinear steiner trees

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J G Speer -Influence of interface mobility on the evolution of austenite-martensite grain assemblies

Inﬂuence of interface mobility on the evolution of austenite–martensite grain assemblies during annealingM.J.Santoﬁmia a,b,*,J.G.Speer c ,A.J.Clarke d ,L.Zhao a,b ,J.Sietsma baMaterials Innovation Institute (M2i),Mekelweg 2,2628CD Delft,The NetherlandsbDepartment of Materials Science and Engineering,Delft University of Technology,Mekelweg 2,2628CD Delft,The NetherlandscAdvanced Steel Processing and Products Research Center,Colorado School of Mines,Golden,CO 80401,USAdMaterials Science and Technology Division,Mail Stop G770,Los Alamos National Laboratory,Los Alamos,NM 87545,USAReceived 9March 2009;accepted 17June 2009Available online 13July 2009AbstractThe quenching and partitioning (Q&P)process is a new heat treatment for the creation of advanced high-strength steels.This treatment consists of an initial partial or full austenitization,followed by a quench to form a controlled amount of martensite and an annealing step to partition carbon atoms from the martensite to the austenite.In this work,the microstructural evolution during annealing of martensite–austenite grain assemblies has been analyzed by means of a modeling approach that considers the inﬂuence of martensite–austenite interface migration on the kinetics of carbon partitioning.Carbide precipitation is precluded in the model,and three diﬀerent assumptions about interface mobility are considered,ranging from a completely immobile interface to the relatively high mobility of an incoherent ferrite–austenite interface.Simulations indicate that diﬀerent interface mobilities lead to profound diﬀer-ences in the evolution of microstructure that is predicted during annealing.Ó2009Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.Keywords:Quenching;Annealing;Steels;Diﬀusion;Thermodynamics1.IntroductionCurrent demands on fuel consumption and safety have led the automotive industry to search for new advanced steels with enhanced strength and ductility.One of the ideas being explored is the development of low-carbon steels with a microstructure consisting of martensite and a consider-able fraction of retained austenite.This combination of phases can lead to a high strength,because of the presence of martensite,and considerable formability.Although these microstructures have been observed in the past in quenched martensitic steels,the amount and stability of the retainedaustenite found were usually low [1,2].In addition,during subsequent tempering,reduction of carbon in the martens-ite occurred via carbide precipitation,whereas austenite was usually decomposed into ferrite and carbides.Knowledge of the eﬀect of some elements,e.g.silicon and aluminum,in inhibiting cementite precipitation has opened the possibility for obtaining carbon-enriched aus-tenite by partitioning of carbon from supersaturated mar-tensite.The recently proposed [3,4]‘‘quenching and partitioning ”(Q&P)process makes use of this idea.This new heat treatment consists of a partial martensite trans-formation (quenching step)from a fully or partially austen-itized condition,followed by an annealing treatment (partitioning step)at the same or higher temperature to promote carbon partitioning from the supersaturated martensite to the austenite.During the partitioning step it is intended that the austenite be enriched with carbon,thus allowing its stabilization at room temperature.The1359-6454/$36.00Ó2009Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.doi:10.1016/j.actamat.2009.06.024*Corresponding author.Present address:Instituto Madrilen ˜o de Estu-dios Avanzados en Materiales (IMDEA-Materiales),ETS de Ingenierı´a de Caminos 28040Madrid,Spain.Tel.:+34915493422;fax:+34915503047.E-mail address:mariajesus.santoﬁmia@ (M.J.Santoﬁmia)./locate/actamatAvailable online at Acta Materialia 57(2009)4548–4557resulting microstructure after the whole thermal cycle con-sists of ferrite(in the case of an initial partial austenitiza-tion),martensite and retained austenite.In this paper,the partitioning step will be further referred to as annealing, to avoid confusion with the process of carbon migration (partitioning).From the above,it is clear that the essential mechanism of the Q&P process is the transfer of carbon from the supersaturated martensite to the austenite.Given that this mechanism of carbon partitioning was not considered in detail in the past,the conditions under which it takes place are now under debate.Some authors[5–8]have postulated a‘‘constrained carbon equilibrium”(CCE)condition gov-erning the carbonﬂux from the martensite to the austenite. The CCE takes into account that iron and substitutional atoms are less mobile at temperatures at which carbon dif-fusion takes place and that the martensite–austenite inter-face can be assumed immobile or stationary.Therefore, only carbon equilibrates its chemical potential.There are some experimental observations that question whether the martensite–austenite interface remains station-ary during annealing.Zhong et al.[9]have reported the apparent migration of these interfaces in a low-carbon steel after annealing at480°C.Although the direction of migra-tion has not been established,this observation indicates the importance of understanding the transfer of iron atoms in relation to the partitioning of carbon.Another interesting observation that contradicts the simplifying assumption of a stationary interface is the reported expansion of the material during the annealing(partitioning step)observed by dilatometry[10],probably indicating changes in the fractions of phases.However,a deﬁnitive explanation of the causes of this expansion is not yet available,since it is unclear if the expansion is a result of the continued growth of already present athermal martensite,the nucle-ation of new isothermal martensite or bainite reaction [11].Another interesting unexplained feature is the pres-ence of two peaks in the representation of retained austen-ite fraction vs.annealing time,which has been attributed to the competition between carbon partitioning and carbide precipitation[12].Given these contradictions,Speer et al.[13]recently con-sidered the implications of iron atom movement on the evolution of the martensite–austenite interface during annealing.According to that work[13],‘‘the diﬀerence in iron potential between the ferrite and the austenite creates a driving force for iron to move from one structure to the other,which is accomplished via migration of the existing interface,assuming that nucleation of new crystals does not occur”.Under these considerations,Santoﬁmia et al.[14]quantitatively analyzed the motion of the martensite–austenite interface in a model based on thermodynamics and diﬀusion,assuming the same chemical potential of car-bon in martensite and austenite at the interface and allow-ing motion of the phase interface when a free-energy diﬀerence occurs.Simulations corresponding to a particu-lar realistic microstructure were presented,showing a sig-niﬁcant bidirectional movement of the martensite–austenite interface.These calculations were made assuming an activation energy for the migration of iron atoms corre-sponding to data on austenite to ferrite transformation in steels(140kJ molÀ1)[15,16],which implies the assumption of an incoherent martensite–austenite interface.In princi-ple,the use of this activation energy could seem inconsis-tent with the well-known semicoherent character of the martensite–austenite interface created during martensite formation[17].However,a treatment of annealing at the transformation temperature or at higher temperatures(that can be identiﬁed as the annealing or partitioning tempera-ture of the Q&P process,typically between250and500°C) can aﬀect the character and thus the mobility of the mar-tensite–austenite interface.In any case,there is a signiﬁcant lack of studies in this area.Therefore,the theoretical anal-ysis of phases and carbon behavior during annealing of martensite–austenite microstructures assuming diﬀerent interface characters is an alternative way to study mecha-nisms and provide an insight into the above-mentioned experimental observations.In this work,microstructural evolution during annealing of martensite–austenite grain assemblies has been analyzed by means of a modeling approach that considers the inﬂu-ence of the coupling between martensite–austenite interface migration and the kinetics of carbon partitioning.Assum-ing that the character of the martensite–austenite interface inﬂuences the activation energy for iron migration from one phase to the other,three diﬀerent activation energies are considered in this study:(i)‘‘inﬁnite”(i.e.immobile interface)which corresponds to CCE conditions;(ii) 140kJ molÀ1from data on the austenite to ferrite transfor-mation involving incoherent interfaces[15,16];and(iii)a higher value(180kJ molÀ1)which represents an estimated value for semicoherent interfaces.Carbon proﬁles and vol-ume fraction of phases predicted as a function of the quenching temperature,annealing temperature and mar-tensite–austenite interface mobility are analyzed.For sim-plicity,carbide precipitation is assumed to be suppressed completely.2.ModelThe interaction between carbon partitioning and inter-face migration is analyzed using the model presented by Santoﬁmia et al.[14].Some aspects of this model are reviewed here for a proper understanding of the analysis presented in the following sections.For modeling purposes,martensite is considered to have a body-centered cubic(bcc)structure supersaturated in carbon,whereas austenite is a face-centered cubic(fcc) phase.The model considers the same chemical potential of carbon in bcc and in fcc at the bcc–fcc interface because of the high atomic mobility of interstitial carbon,which is one of the CCE conditions.This condition is expressed in terms of carbon concentration by Eq.(1)presented in Ref.[14].M.J.Santoﬁmia et al./Acta Materialia57(2009)4548–45574549The motion of interfaces in a microstructure is a result of the repositioning of atoms from lattice positions in one grain to projected lattice positions in a neighboring grain.At a given temperature,the equilibrium concentra-tions of carbon in fcc,x fcc-eqC ,and bcc,x bcc-eqC,are given bythe metastable equilibrium phase diagram,excluding car-bide formation.If the carbon concentrations at the inter-face are diﬀerent from the equilibrium values,the phases will experience a driving pressure,D G,for a phase transfor-mation towards the equilibrium phase composition.This local driving pressure is experienced at the interface and results in an interface velocity,v,which is proportional to the driving pressure according to:v¼M D G;ð1Þwhere M is the interface mobility.In this work,the driving pressure is considered proportional to the diﬀerence be-tween the equilibrium concentration of carbon in fcc and the interface carbon concentration in fcc,for which the proportionality factor is calculated from Thermo-Calc[18].The driving pressure can be positive or negative, depending on the relative diﬀerence between the equilib-rium carbon content of the austenite and the actual carbon concentration in austenite at the interface.The relationship between the carbon content in the austenite at the fcc–bccinterface,x fcc–bccC ,and the interface migration behavior,according to the present model,is schematically repre-sented in Fig.1.If the interface is enriched in carbon rela-tive to equilibrium,then the chemical potential of iron is higher in martensite than in austenite and the driving pres-sure for the movement of the interface promotes interface migration from the austenite to the martensite(Fig.1a), whereas the interface would be promoted to move in the opposite direction if the interface is depleted in carbon relative to equilibrium(Fig.1b).The interface mobility,which is temperature dependent, can be expressed as a product of a pre-exponential factor and an exponential term:M¼M0expÀQM RT;ð2Þwhere Q M is the activation energy for iron atom motion at the interface.The pre-exponential factor,M0,can be expressed as[19]:M0¼d4m Dk B T;ð3Þwhere d is the average atomic spacing in the two phases separated by the interface in question,m D is the Debye fre-quency and k B is the Boltzmann constant.The value of d has been estimated to be2.55A˚for a martensite–austenite interface[20].The diﬀusion of carbon in martensite and austenite is modeled by solving Fick’s second law using a standard ﬁnite-diﬀerence method[21].Diﬀusion coeﬃcients are cal-culated referring to the carbon content in martensite[22] and austenite[23].3.Simulation conditionsIn order to study the inﬂuence of the martensite–austen-ite interface character on the interaction between carbon partitioning and iron migration during annealing,it is assumed that modiﬁcations to the interface character lead to diﬀerent values of the activation energy for iron migra-tion.This is a reasonable qualitative approximation,since the mobility of a martensite–austenite interface during annealing is related to the coherency of the interface.For example,iron atoms migrate more easily in incoherent interfaces.Although it is now not possible to exactly relate the value of the activation energy to the speciﬁc character of the interface,approximations can lead to insightful results,as will be shown in the following sections.In this work,three diﬀerent activation energies are assumed in the calculations.3.1.Case1:inﬁnite activation energyUsing the described model,it is possible to check that a very high value of the activation energy(higher than 300kJ molÀ1)leads to an interface mobility low enough to be considered nonexistent over any reasonabletimescale Fig.1.Schematic diagram illustrating the austenite interface composition under CCE conditions(dashed lines)and under equilibrium(dotted lines).(a) Carbon concentration in the austenite at the interface higher than the equilibrium concentration,and(b)carbon concentration in the austenite at the interface lower than the equilibrium concentration.4550M.J.Santoﬁmia et al./Acta Materialia57(2009)4548–4557(up to days)during annealing at temperatures up to 500°C.For simplicity,the simulations have been done assuming an inﬁnite value of the activation energy by set-ting the interface mobility equal to zero.This assumption leads to an immobile interface and to results corresponding to CCE conditions.3.2.Case2:Q M=180kJ molÀ1An activation energy for iron migration equal to 180kJ molÀ1was selected for this case in order to simulate the situation of limited martensite–austenite mobility, slower than for austenite to ferrite transformations.This value of the activation energy should be considered illustra-tive for coherent or semicoherent interfaces rather thanquantitatively accurate,since currently there is no basis for an accurate estimation of the activation energy for movement of iron atoms at the martensite–austenite interface.3.3.Case3:Q M=140kJ molÀ1In this case,the activation energy for interface migration was set equal to140kJ molÀ1,which is the value used by Krielaart and Van der Zwaag in a study on the austenite to ferrite transformation behavior of binary Fe–Mn alloys [15]and by Mecozzi et al.[16]to study the same phase transformation in a Nb microalloyed CMn steel.The resulting mobility can be seen as an upper limit,applying to incoherent interfaces.Model predictions are sensitive to the alloy used in the calculations.In this work,simulations have been per-formed assuming a binary Fe–0.25wt.%C system and a martensite–austeniteﬁlm morphology(also used in Ref.[14]).The corresponding martensite start temperature (M s)was calculated to be433°C[24].Simulations consid-ered two annealing temperatures(350and400°C)and dif-ferent quenching temperatures ranging from220to400°C. Values of the martensite–austenite interface mobility M, calculated according to Eqs.(2)and(3)for both annealing temperatures studied,are presented in Table1.Variations in the quenching temperatures lead to diﬀerent amounts of martensite and austenite prior to annealing.The volume fractions of phases present after the quenching step are esti-mated by the Koistinen–Marburger equation[25],leading to the values shown in Table2.The volume fractions of phases present at each quenching temperature and the lath widths of martensite and austenite are related using a‘‘con-stant ferrite width approach”[26].This approach is based on the transmission electron microscopy observations of Krauss and co-workers,indicating that most martensitic lath widths range approximately from0.15to0.2l m [27,28].Additionally,Marder[29]reported that a lath width of0.2l m was most frequently observed for 0.2wt.%C martensite.Therefore,a constant martensite lath width equal to0.2l m has been assumed for the initial conditions in the simulations.Corresponding austenite dimensions are obtained based on the appropriate austen-ite fraction predicted for every quenching temperature,and the results are shown in Table2.The volume fraction of martensite during annealing can be estimated from the size of the martensite domain at every annealing time.The local fraction of austenite that is stable upon quenching to room temperature is estimated by calculation of the M s temperature using Eq.(5),pre-sented in Ref.[24],across the austenite carbon proﬁle and by further use of the Koistinen–Marburger[25]rela-tionship to estimate the volume fraction of stable austenite at each point[30].Final retained austenite fractions are cal-culated by integration of the area under each local fraction of stable austenite curve for diﬀerent annealing times[31].Simulations of the interaction between carbon partition-ing and interface migration under the conditions explained above are presented and discussed with respect to the evo-lution of the phase fractions and phase compositions.4.Results and discussion4.1.Carbon proﬁles in martensite and austenite during annealingFigs.2and3show the evolution of carbon proﬁles in martensite and austenite during annealing at350and 400°C,respectively,assuming a quenching temperature of300°C and the three activation energies considered to describe interface mobility.The sameﬁgures also show the estimation of the local retained austenite fraction when the material isﬁnally quenched to room temperature after annealing.A general observation is,in all cases,a sharp increase in the carbon content in the austenite close to the martensite–austenite interface at short annealing times.Table1Mobility(m4JÀ1sÀ1)corresponding to two activation energies and annealing temperatures studied.Annealing temperature(°C)Mobility forQ M=180kJ molÀ1Mobility forQ M=140kJ molÀ1350 2.45Â10À20 5.53Â10À17 400 2.99Â10À19 3.81Â10À16Table2Calculated martensite and austenite fractions present at each quenching temperature and corresponding martensite and austenite widths using the constant ferrite width approach.Quenchingtemperature(°C)Approximate fractionat quench temperatureLath orﬁlmwidth(l m)Austenite Martensite Austenite Martensite 2200.100.900.020.20 2500.130.870.030.20 2700.170.830.040.20 2890.200.800.050.20 3000.230.770.060.20 3200.290.710.080.20 3500.400.600.130.20 4000.690.310.450.20M.J.Santoﬁmia et al./Acta Materialia57(2009)4548–45574551Starting with the results corresponding to annealing at 350°C,it is observed that,under stationary interface con-ditions (Fig.2a–c ),the sharp carbon proﬁles observed in the austenite at short annealing times are progressively reduced.After about 100s,the carbon concentration in both phases is equilibrated according to the conditions established by CCE,i.e.the same chemical potential of car-bon in the martensite and the austenite but with the limita-tion of an immobile interface.Fig.2c shows estimations of the local fraction of retained austenite,indicating that the ﬁnal state corresponds to the retention of about half of the austenite available during annealing.When the activation energy is assumed equal to 180kJ mol À1(Fig.2d–f ),the interface mobility is not high enough to produce interface migration during the time-frame in which carbon partitioning occurs from the mar-tensite to the austenite.This behavior results in evolution of carbon proﬁles similar to that obtained with a stationary interface for annealing times lower than 100s (the time necessary to obtain the ﬁnal proﬁles in the case of an immobile interface).However,at longer annealing times,there is interface migration from the martensite into the austenite until the establishment of full equilibrium in both phases,with a substantial reduction of the austenite frac-tion in this instance.The ﬁnal proﬁles are obtained after annealing for about 10,000s ($3h).In this case,the vol-ume fraction of retained austenite at the end of the process (Fig.2f)is less than half of the austenite available after the ﬁrst quench because of the reduction of the austenite thickness.When the activation energy is 140kJ mol À1(Fig.2g–i ),the interface mobility is high enough to produce migration of the martensite–austenite interface during carbon trans-fer between the two phases.Initially,the carbon content at the interface is higher than the equilibrium value and migration of the interface from the austenite into themar-Fig.2.Calculated carbon proﬁles in martensite (left column)and austenite (middle column)together with local austenite volume fraction that is stable to the ﬁnal quench (right column)during annealing at 350°C after quenching to 300°C:(a–c)immobile interface;(d–f)Q M =180kJ mol À1;(g–i)Q M =140kJ mol À1.Arrows in the upper part of the ﬁgures and dashed lines indicate the movement of the martensite–austenite interface.According to Table 2,the combined thickness of one martensite plus one austenite ﬁlm is 0.26l m when quenching at 300°C,but because of symmetry the calculation domain includes only the half-thickness,which is 0.13l m.4552M.J.Santoﬁmia et al./Acta Materialia 57(2009)4548–4557tensite takes place.However,carbon diﬀusion causes a reduction of this peak in the time interval between 0.1and 1s,to carbon levels at the interface that are lower than the equilibrium value.Consequently,the interface then migrates from the martensite to the austenite.The homog-enization of carbon in the austenite leads to further movement of the interface until the carbon content corre-sponding to full equilibrium in both phases is reached after annealing for about 100s.The time taken to attain the ﬁnal carbon proﬁles is similar to the that required in the case of an immobile interface,but considerably lower than for an activation energy of 180kJ mol À1.The ﬁnal fraction of local retained austenite (Fig.2i)is the same as that obtained in the previous case.From the above results,it is clear that the interface mobility has an important inﬂuence on the kinetics of the carbon partitioning process.In the case of a stationary interface or when the interface mobility corresponds to the value determined for reconstructive austenite to ferrite transformations (Q M =140kJ mol À1),the ﬁnal carbon proﬁles are obtained after annealing for a similar length of time (about 100s).However,in the case of an interme-diate interface mobility (Q M =180kJ mol À1),as might apply to a lower-energy semicoherent interface,the devel-opment of the carbon proﬁles is essentially similar to those obtained in the case of an immobile interface for times shorter than about 100s.However,longer annealing times lead to slow migration of the interface until full equilibrium conditions are reached after annealing for about 10,000s.In the case of annealing at 400°C (Fig.3),the evolution of the carbon proﬁles in martensite and austenite and local fractions of retained austenite is similar to those obtained for annealing at 350°C,but takes place on a diﬀerent time-scale.For example,uniform carbon concentration proﬁles in the case of an immobile interface (Fig.3a and b)and Q M =140kJ mol À1(Fig.3g and h)are obtained inbothFig.3.Calculated carbon proﬁles in martensite (left column)and austenite (middle column)together with local austenite volume fraction that is stable to the ﬁnal quench (right column)during annealing at 400°C after quenching to 300°C:(a–c)immobile interface;(d–f)Q M =180kJ mol À1;(g–i)Q M =140kJ mol À1.Arrows in the upper part of the ﬁgures and dashed lines indicate the movement of the martensite–austenite interface.According to Table 2,the combined thickness of one martensite plus one austenite ﬁlm is 0.26l m when quenching at 300°C,but because of symmetry the calculation domain includes only the half-thickness,which is 0.13l m.M.J.Santoﬁmia et al./Acta Materialia 57(2009)4548–45574553phases after annealing for about 10s.However,in the case of Q M =180kJ mol À1(Fig.3d and e),the time required to reach full equilibrium is substantially longer,in the range between 100and 1000s.This is a consequence of the low mobility of the interface.4.2.Evolution of the interface position during annealing Fig.4a and b shows the evolution of the interface posi-tion with annealing time for the case of quenching to 300°C and annealing at 350and 400°C,respectively.Fig.4c and d shows the corresponding evolution of the car-bon content in the austenite at the interface.The three curves give results for the three martensite–austenite inter-face mobilities considered in this work.Examination of these ﬁgures leads to the observations described below.In the case of an immobile interface,the carbon content in the austenite increases fast very early in the process (although this rapid increase in carbon is not represented in the timescale of Fig.4)and then decreases before reach-ing the value given by the constrained carbon equilibrium condition.For Q M =180kJ mol À1,the interface does not signiﬁcantly change its position for annealing times lower than about 10s in the case of annealing at 350°C and about 1s for annealing at 400°C.During this time,the car-bon content in the austenite at the interface reaches the value corresponding to CCE,i.e.evolves identically to the case of an immobile interface.However,longer anneal-ing times lead to the initiation of interface migration from the martensite into the austenite and the progressive enrichment of carbon at the interface until full equilibriumconditions are reached.Finally,consideringQ M =140kJ mol À1,the evolution of the interface position and the carbon concentration in the austenite at the inter-face largely occur simultaneously during the annealing pro-cess.In this case,carbon partitioning starts with an increase of the carbon content in the austenite at the inter-face,which is compensated by the movement of the inter-face from the austenite into the martensite.Once the carbon content of the austenite is lower than the equilib-rium value,the motion of the interface reverses its direc-tion,from the martensite into the austenite.This migration ends when full equilibrium conditions are reached.4.3.Evolution of the volume fraction of martensite during annealingThe predicted evolution of the volume fraction 1of mar-tensite during annealing for the case of quenching to 300°C and annealing at 350or 400°C is shown in Fig.5.As expected,the volume fraction of martensite for the case of an immobile interface is constant.In the case of Q M =180kJ mol À1,the volume fraction of martensite is constant for annealing times below about 100s (annealing at 350°C)or 10s (annealing at 400°C).Afterwards,the vol-ume fraction of martensite increases by about 0.16.The evo-lution of the martensite volume fraction with annealing time is more complex for the case of Q M =140kJ mol À1.First,Fig.4.(a and b)Position of the martensite–austenite interface for quenching to 300°C and annealing at (a)350°C and (b)400°C.Position 0.00refers to the initial position of the interface and any decrease or increase of the position represents a decrease or increase,respectively,of the martensite width.(c and d)Carbon content in the austenite at the interface for quenching at 300°C and annealing at (c)350°C and (d)400°C.1Predicted volume fractions ignore any slight changes in the phase densities associated with carbon partitioning.4554M.J.Santoﬁmia et al./Acta Materialia 57(2009)4548–4557。

一种求解RSMT布线问题的PSO算法

一种求解RSMT布线问题的PSO算法陈秀华;朱自然【摘要】最小直角斯坦纳树(RSMT)问题是超大规模集成电路布线中的重要问题之一,是典型的NP困难组合优化问题.为了有效地解决超大规模集成电路布线中的RSMT问题,提出一种粒子群优化算法,借助直角Steiner树的一些性质,采用Steiner点编码方案,寻找优化的Steiner点位置以减少直角Steiner树的长度.对几组布线模型实例进行了仿真测试,表明了该算法的有效性.【期刊名称】《闽江学院学报》【年(卷),期】2014(035)005【总页数】6页(P39-44)【关键词】超大规模集成电路(VLSI);最小直角斯坦纳树;布线算法【作者】陈秀华;朱自然【作者单位】福建船政交通职业学院公共教学部,福建福州350007;福州大学数学与计算机科学学院,福建福州350116【正文语种】中文【中图分类】TP301.6布线问题是超大规模集成电路（VLSI）物理设计的关键环节之一.一个电路芯片会有大量的线网需要连接，同时对于每个线网，又有几百种甚至更多的布线方案.随着设计规模的不断增长，尤其是百万门级芯片的普遍应用，对VLSI布线问题的算法设计提出了巨大的挑战.VLSI布线问题中连接树的目标是连接树的总长度最短，对于多端线网的最佳布线结果是构造最小直角Steiner树（RSMT）［1］，该问题已被证明是一个NP完全问题［2］.研究者提出了许多基于智能优化技术的解决方法［3－8］，这些智能算法主要有模拟退火算法［9－10］，遗传算法［11－15］和蚁群算法［16－18］等.文献［3］提出了关于最小直角Steiner树的混合遗传算法，表明智能优化算法在解决这类问题中具有较好的应用前景.粒子群优化算法PSO（particle swarm optimization）是Kenney和Eberhart于1995年提出的一种基于种群搜索策略的自适应随机算法.它源于对鸟群和鱼群等群体运动行为的研究，是一种基于迭代的智能优化算法，可用于求解大部分的优化问题.与常规的遗传算法（GA）相比较，它具有算法简单，收敛速度快，且对目标函数要求少等特点，已成为一种重要的优化工具.文献［5］首先提出了一种用于解决VLSI布线问题的离散粒子群优化算法.此方法通过设计基于惩罚的适应度函数，引入遗传算法的变异和交叉算子，增加了种群的多样性并适当地扩展了粒子的寻优范围.文献［19］提出使用PSO算法求解RSMT问题，通过引入遗传算法中的变异算子来改进PSO的求解性能.本研究通过借助直角Steiner树的一些性质，采用Steiner点编码方案，寻找优化的Steiner点位置以减少直角Steiner树的长度，提出了一种求解RSMT布线问题的的粒子群优化算法.对几组布线模型实例进行了仿真测试，结果表明该算法的有效性.1.1 RSMT问题模型斯坦纳树（Steiner－tree）是一棵连接特定要求点（demand point）集合和一些斯坦纳点（Steiner points）的连接树.由于它连接树总长度比其他方法更小，常被用作总体布线中构造连接树的方法.因此，VLSI总体布线问题可以看作是在总体布线图中，在目标函数最优化的条件下，针对每个线网寻找一棵斯坦纳树的问题.通常典型的目标函数是所选择的连接树的总长度最小.定义1［20］一棵斯坦纳树（Steiner－tree）的长度为所有边长度之和，即l（ei）为边ei的长度.斯坦纳树的长度也称为费用.定义2［5］一棵斯坦纳树（Steiner－tree）中，若该斯坦纳树的每条边均为直角矩形边，则此Steiner－tree称为直角斯坦纳树（rectilinear Steiner tree，RST）.定义3 给定一个无向图G（V，E），一个要连接的端点集合N（N⊆V），最小Steiner树（SMT）就是一棵通过V中的点连接N中所有点的生成树，以边长最短为目标.与欧氏距离Steiner树不同，最小直角Steiner树（rectilinear Steinerminimal tree，RSMT）两点间的距离是直线距离，横轴距离和纵轴距离之和，即连线只有水平和垂直两种形式.定义4［20］总体布线问题就是给定一个网表N＝｛N1，N2，…，Nn｝，和一个总体布线图G＝（V，E），对∀Ni∈N，1≤i≤n，找到一棵斯坦纳树Ti，使得其中，L（Ti）为Ti的长度；U（ei）是通过通道边ei的线网数，如果ei在Ti中则xij＝1；否则xij＝0．在集成电路的布线问题中，多端线网的最佳连接就是构造最小直角斯坦纳树.1.2 问题分析最小直角Steiner树（RSMT）的相关性质：性质1 设RSMT有n个端点，则RSMT的Steiner点个数≤n－2.性质2［21］（Hanan定理）任意一棵最小直角Steiner树T的Steiner点均在经过T的水平线和竖直线的交点（Hanna网格）上，如图1所示.性质3［20］若分别用Ls和Lm表示最小直角Steiner树和最小生成树的长度，则在RSMT问题所给定的待连接的布线端点集合N中，通过这些端点分别各自引一条水平线和竖直线，这些线的交叉点就形成Hanan点集合［21］.从Hanan点集合中按一定规则选取的部分点作为Steiner点集合，这些Steiner点与普通的生成树构成了直角斯坦纳树.求最小Steiner树的关键是确定点集S，即s点的个数和位置.图2和图3给出了连接4个顶点的最小生成树（minimum spanning tree，MST）与其对应的最小直角斯坦纳树（RSMT）.由于RSMT问题已经被证明是NP完全的，解决这类问题的主要方法就是启发式算法或智能优化算法.2.1 粒子群优化算法（PSO）PSO算法是一种基于群体和适应度的智能优化技术［22］.在求解过程中，首先初始化一群粒子，将每个粒子个体抽象为一个在搜索空间中没有质量和体积的微粒（点），并在搜索空间中以一定的速度飞行［23］.每个粒子所处的位置都表示问题的一个解，它们通过不断调整自己的位置来搜索新解，同时记住个体最优解和全局最优解.空间中的粒子追随当前种群中的最优粒子运动，直到在整个解空间中搜索到最优解为止.对于每一次迭代，粒子根据个体最优解和全局最优解来动态调整自身的速度.粒子i的第j维根据式（1）和式（2）更新速度和位置：式中，w是惯性系数，c1和c2是学习因子，r1和r2是介于［0，1］之间的随机数，xtij是t时刻粒子i的第j维分量值，vtij是t时刻粒子i的第j维速度分量值.2.2 粒子的编码提出的求解最小直角Steiner树的PSO算法，是通过找出优化的s点位置来得到输入端点集合N的RSMT，根据性质1，若输入n个端点，则RSMT的s点最多有n－2个.因此粒子位置编码是由n－2个s点的坐标位置构成：X＝（x1，x2，x3，…，xi，…，xn－2），其中第i维数据xi表示这个s点在平面上的坐标．同时定义num，表示有效s点的数量，只有前num个s点才会被加入．与粒子位置的数据结构一样，速度v也是由n－2个二维向量组成.2.3 粒子的适应度函数位置与速度的加法运算实现了粒子位置变换，适应度函数在PSO算法中用于判断种群进化过程中粒子所在位置的优劣.提出的PSO算法是以最小代价生成树算法为基础，粒子适应度函数定义如下：式中，N是RSMT问题的端点集合，L是N用最小生成树算法——kruskal法确定的MST的长度，l（e）是边e的直线距离.由公式（2）可以观察到新的位置的某些s点可能不会落在Hanan网格上，因此在求适应度的时候，用离这些点最近的Hanan点表示它，即：S1为X中离每个有效s点最近的Hanan网格上的点组成的集合.2.4 粒子的初始化为了避免初始粒子位置分布过于集中，所有粒子每维数据随机选取一个Hanan点.初始化时，所有粒子的初始速度都设为0，第i个粒子s点数numi＝rand（1，n －2），在之后的迭代过程中粒子i的s点数采用如下方法动态更新：若个体最优解s点数为pbestnum，全局最优解s点数为gbestnum，则numi＝max （numi，pbestnum，gbestnum）.由于加入过多无用的s点反而会降低适应度值，因此在迭代过程中通过动态增加s点数量，能够有效地加快收敛速度.2.5 粒子的更新式（1）中的惯性系数w，表示原先的速度能在多大程度上得到保留，对全局搜索，较好的方法是在前期有较高的探索能力以得到合适的种子，防止迭代陷入局部最优解而发生早熟，而在后期有较高的求精能力以加快收敛速度．为此，可将w设定成随着进化而线性减少．文献［24］也指出w线性减少取得了较好的实验结果，经笔者多次实验，在算法中将w设成从0.9到0.4线性递减取得比较好效果.其中MaxNumber是算法的最大迭代次数.2.6 算法步骤以下是求解RSMT布线问题的PSO算法（PSO-RSMT）具体步骤：输入：n个端点的坐标位置；输出：RSMT的值和对应s点坐标位置；Step 1：读入数据集，生成Hanan点；Step 2：初始化算法参数并随机生成初始群；Step 3：评价各个粒子的适应度函数值，并初始化个体最优解Xpbest和全局最优解Xgbest；Step 4：根据式（4）计算惯性权值w，按式（1）更新粒子速度，按式（2）更新粒子位置，按2.5中的策略动态更新s点数量；Step5：重新评价各个粒子的适应度函数值，并更新各个粒子的个体最优解Xpbest；Step6：更新种群的全局最优解；Step7：若满足终止条件，则循环结束，否则返回Step4.PSO算法模拟了群体模型中的信息共享机制，由于粒子的运动紧跟当前最优解，并且惯性系数可以调整其搜索能力，防止早熟，因此在搜索过程中用较小规模的种群就可以收敛到最优解.表1是采用本文PSO算法解RSMT的结果与用经典遗传算法［15］解RSMT的结果比较，每个输入端点的横纵坐标取0到10 000上的随机数.两种算法都用Microsoft Visual C＋＋编程实现，在Windows XP平台上运行通过，可以看到PSO算法在运行结果要比遗传算法好，速度也更快.（1）在RSMT长度上，PSO算法在输入端点数为9、12和15时，得到的结果与遗传算法相同，但是当输入端点数为18和20时，均得到了明显的优化，分别减少了0.88%和2.46%.（2）在使用时间上，对于表1的所有实例，PSO算法相较于遗传算法均有明显缩短，并且当输入端点数为9和12时，时间缩短量超过了50%，分别是69%和70%.在深入分析最小直角Steiner树（RSMT）问题的基础上，提出了一种基于粒子群优化的算法.采用Steiner点编码方案来实现粒子的编码，引入s点数量动态调整策略，以期加快收敛速度，并通过寻找优化的Steiner点位置来减少RSMT的长度.对几组布线模型实例进行了仿真实验，实验结果验证了算法在RSMT长度和运行时间方面都具有较好的性能.【相关文献】［1］Hwang F K，Richards D S，W inter P.The Steiner tree problem［M］.Amsterdam：North-Holland，1992.［2］Garey M R，Johnson D S.The rectilinear Steiner tree problem is NP－complete ［J］.SIAM Journal on Applied Mathematics，1977，32（4）：826-834.［3］杨昌玲，严晓浪.基于树型编码的MRST混合遗传算法及其并行处理［J］.微电子学，1999，29（2）：89－95.［4］杨文国，郭田德.求解最小Steiner树的蚁群优化算法及其收敛性［J］.应用数学学报，2006，29（2）：352－361.［5］刘耿耿，王小溪，陈国龙，等.求解VLSI布线问题的离散粒子群优化算法［J］.计算机科学，2010，37（10）：197－201.［6］Zhang Y H，Chu C.Interleaved global routing and detailed routing for ultimate routability［C］／／Design Automation Conference（DAC）.San Francisco：IEEE，2012：597－602.［7］Huang TW，Ho T Y，A two－stage 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福建省2024届高中毕业班适应性练习英语试卷(含答案)

福建省2024届高中毕业班适应性练习英语试卷学校：___________姓名：___________班级：___________考号：___________一、听力题1．Where does the conversation probably take place?A. In a library.B. In a supermarket.C. In a restaurant2．What sport do the speakers both like?A. Running.B. Swimming.C. Hiking.3．What are the speakers talking about?A. Pocket money.B. The value of money.C. Money saving.4．What is David busy doing?A. Visiting a flatB. Introducing a flat.C. Arranging a flat5．How much will the man pay for the magazines?A. $50.B. $80.C. $100.听一段材料, 回答以下小题。

6．How many multiple-choices remain unfinished?A. 3.B. 4.C. 7.7．How did Linda perform in the free response questions?A. Fairly well.B. Just so-so.C. Quite badly.听一段材料, 回答以下小题。

8．What do we know about Venice at the beginning of March?A. It has a travel off-season.B. It has a wonderful concert.C. It has a traditional celebration.9．Why are the speakers going to make up?A. To show love for Venetians.B. To adapt to the local custom.C. To make themselves elegant.10．What is the probable relationship between the speakers?A. Husband and wife.C. Director and actor.听一段材料, 回答以下小题。

The Physics of Ghost Imaging

obj
dρo f (ρo ) δ (ρo +
ρi ) m
(2)
where I (ρi ) is the intensity in the image plane, ρo and ρi are 2-D vectors of the transverse coordinates in the object and image planes, respectively, and m = si /so is the magniﬁcation factor. In reality, limited by the ﬁnite size of the imaging system, we may never have a perfect pointto-point correspondence. The incomplete constructive-destructive interference turns the pointto-point correspondence into a point-to-“spot” relationship. The δ -function in the convolution of Eq. (2) will be replaced by a point-spread function: I (ρ i ) =
obj
dρo f (ρo ) somb
R ω ρi ρo + so c m
(3)
where the sombrero-like function, or the Airy disk, is deﬁned as somb(x) = 2J1 (x) , x
and J1 (x) is the ﬁrst-order Bessel function, and R the radius of the imaging lens, and R/so is known as the numerical aperture of an imaging system. The ﬁnite size of the spot, which is deﬁned by the point-spread function or the Airy disk, determines the spatial resolution of the imaging setup. It is clear from Eq. (3) that a larger imaging lens and shorter wavelength will result in a narrower point-spread function, and thus a higher spatial resolution of the image. Ghost imaging, in certain aspects, has the same basic feature of classical imaging, such as the unique point-to-point image-forming relationship between the object plane and the image plane. Diﬀerent from classical imaging, the radiation stopped on the imaging plane does not “come” from the object plane, instead it comes directly from the light source. More importantly, the image is observed in the joint detection between two independent photodetectors, one measures the scattered or transmitted light from the object, another measures light directly coming from the source at each point in the image plane. The point-to-point correlation is determined by the nonlocal behavior of a pair of photons: neither photon-one nor photon-two “knows” where to arrive. However, if one of them is observed at a point on the object plane, its twin must arrive at a unique corresponding point on the image plane. The ﬁrst ghost imaging experiment was demonstrated by Pittman et al. in 1995 [1] [2]. The schematic setup of the experiment is shown in Fig. 2. A continuous wave (CW) laser is used to pump a nonlinear crystal to produce an entangled pair of orthogonally polarized signal (e-ray of the crystal) and idler (o-ray of the crystal) photons in the nonlinear optical process of spontaneous parametric down-conversion (SPDC). The pair emerges from the crystal collinearly with ωs ∼ = ωi ∼ = ωp /2 (degenerate SPDC). The pump is then separated from the signal-idler pair by a dispersion prism, and the signal and idler are sent in diﬀerent directions by a polarization beam splitting Thompson prism. The signal photon passes through a convex lens of 400mm focal 2

新视野大学英语2(第三版)unit8 textA课文翻译

Unit 8 Section A Animals or children?—A scientist's choice动物还是孩子？——一位科学家的选择1 I am the enemy! I am one of those cursed, cruel physician scientists involved in animal research. These rumors sting, for I have never thought of myself as an evil person. I became a children's doctor because of my love for children and my supreme desire to keep them healthy. During medical school and residency, I saw many children die of cancer and bloodshed from injury —circumstances against which medicine has made great progress but still has a long way to go. More importantly, I also saw children healthy thanks to advances in medical science such as infant breathing support, powerful new medicines and surgical techniques and the entire field of organ transplantation. My desire to tip the scales in favor of healthy, happy children drew me to medical research.1 我就是那个敌人！我就是那些被人诅咒的、残忍的、搞动物实验的医生科学家之一。

大学体验英语(第三版)课文原文及翻译

Frog Story蛙的故事A couple of odd things have happened lately.最近发生了几桩怪事儿。

I have a log cabin in those woods of Northern Wisconsin.I built it by hand and also added a greenho use to the front of it.It is a joy to live in.In fact,I work out of my home doing audio production and en vironmental work.As a tool of that trade I have a computer and a studio.我在北威斯康星州的树林中有一座小木屋。

是我亲手搭建的，前面还有一间花房。

住在里面相当惬意。

实际上我是在户外做音频制作和环境方面的工作——作为干这一行的工具，我还装备了一间带电脑的工作室。

I also have a tree frog that has taken up residence in my studio.还有一只树蛙也在我的工作室中住了下来。

How odd,I thought,last November when I first noticed him sitting atop my sound-board over my computer.I figured that he(and I say he,though I really don’t have a clue if she is a he or vice versa)would be more comfortable in the greenhouse.So I put him in the greenhouse.Back he ca me.And stayed.After a while I got quite used to the fact that as I would check my morning email and online news,he would be there with me surveying the world.去年十一月，我第一次惊讶地发现他（只是这样称呼罢了，事实上我并不知道该称“他”还是“她”）坐在电脑的音箱上。

New admissible heuristics for domain-independent planning

New Admissible Heuristics for Domain-Independent Planning
Dept. of Computer Science Link¨ opings Universitet Link¨ oping, Sweden pahas@ida.liu.se
Patrik Haslum
H´ ector Geffner
Abstract
Admissible heuristics are critical for effective domainindependent planning when optimal solutions must be guaranteed. Two useful heuristics are the hm heuristics, which generalize the reachability heuristic underlying the planning graph, and pattern database heuristics. These heuristics, however, have serious limitations: reachability heuristics capture only the cost of critical paths in a relaxed problem, ignoring the cost of other relevant paths, while PDB heuristics, additive or not, cannot accommodate too many variables in patterns, and methods for automatically selecting patterns that produce good estimates are not known. We introduce two reﬁnements of these heuristics: First, the additive hm heuristic which yields an admissible sum of hm heuristics using a partitioning of the set of actions. Second, the constrained PDB heuristic which uses constraints from the original problem to strengthen the lower bounds obtained from abstractions. The new heuristics depend on the way the actions or problem variables are partitioned. We advance methods for automatically deriving additive hm and PDB heuristics from STRIPS encodings. Evaluation shows improvement over existing heuristics in several domains, although, not surprisingly, no heuristic dominates all the others over all domains.

The greatest scientist of the 20th century--Albert Einstein

Great ahievements of Albert Einstein
(1) Theoretical Physics, and especially for his discovery of the law of the photoelectric effect. (2)On a Heuristic Viewpoint Concerning the Production and Transformation of Light (3)Theory of relativity which had been the subject of lively debate in philosophical circles and also has astrophysical implications which are being rigorously examined at the present time
The best well –known achievement: Special relativity and General relativity
• Special relativity: all physical laws for all inertial frame and all have the same form of expression. • General relativity: all physical laws for all noninertial reference frame of reference (including) all have the same form of expression • Special relativity of two axioms: • A), the constant principle: the speed of light in all inertial frame of reference remains unchanged, • B), relativity principle: for all inertial system using the frame of space and time of expression law of physics, they form is the same

建筑学毕业设计的外文文献及译文

建筑学毕业设计的外文文献及译文文献、资料题目：《Advanced Encryption Standard》文献、资料发表（出版）日期:2004.10.25系（部）：建筑工程系生：陆总LYY外文文献：Modern ArchitectureModern architecture, not to be confused with Contemporary architecture1, is a term given to a number of building styles with similar characteristics, primarily the simplification of form and the elimination of ornament. While the style was conceived early in the 20th century and heavily promoted by a few architects, architectural educators and exhibits, very few Modern buildings were built in the first half of the century. For three decades after the Second World War, however, it became the dominant architectural style for institutional and corporate building.1. OriginsSome historians see the evolution of Modern architecture as a social matter, closely tied to the project of Modernity and hence to the Enlightenment, a result of social and political revolutions.Others see Modern architecture as primarily driven by technological and engineering developments, and it is true that the availability of new building materials such as iron, steel, concrete and glass drove the invention of new building techniques as part of the Industrial Revolution. In 1796, Shrewsbury mill owner Charles Bage first used his "fireproof design, which relied on cast iron and brick with flag stone floors. Such construction greatly strengthened the structure of mills, which enabled them to accommodate much bigger machines. Due to poor knowledge of iron's properties as a construction material, a number of early mills collapsed. It was not until the early 1830s that Eaton Hodgkinson introduced the section beam, leading to widespread use of iron construction, this kind of austere industrial architecture utterly transformed the landscape of northern Britain, leading to the description, πDark satanic millsπof places like Manchester and parts of West Yorkshire. The Crystal Palace by Joseph Paxton at the Great Exhibition of 1851 was an early example of iron and glass construction; possibly the best example is the development of the tall steel skyscraper in Chicago around 1890 by William Le Baron Jenney and Louis Sullivan∙ Early structures to employ concrete as the chief means of architectural expression (rather than for purely utilitarian structure) include Frank Lloyd Wright,s Unity Temple, built in 1906 near Chicago, and Rudolf Steiner,s Second Goetheanum, built from1926 near Basel, Switzerland.Other historians regard Modernism as a matter of taste, a reaction against eclecticism and the lavish stylistic excesses of Victorian Era and Edwardian Art Nouveau.Whatever the cause, around 1900 a number of architects around the world began developing new architectural solutions to integrate traditional precedents (Gothic, for instance) with new technological possibilities- The work of Louis Sullivan and Frank Lloyd Wright in Chicago, Victor Horta in Brussels, Antoni Gaudi in Barcelona, Otto Wagner in Vienna and Charles Rennie Mackintosh in Glasgow, among many others, can be seen as a common struggle between old and new.2. Modernism as Dominant StyleBy the 1920s the most important figures in Modern architecture had established their reputations. The big three are commonly recognized as Le Corbusier in France, and Ludwig Mies van der Rohe and Walter Gropius in Germany. Mies van der Rohe and Gropius were both directors of the Bauhaus, one of a number of European schools and associations concerned with reconciling craft tradition and industrial technology.Frank Lloyd Wright r s career parallels and influences the work of the European modernists, particularly via the Wasmuth Portfolio, but he refused to be categorized with them. Wright was a major influence on both Gropius and van der Rohe, however, as well as on the whole of organic architecture.In 1932 came the important MOMA exhibition, the International Exhibition of Modem Architecture, curated by Philip Johnson. Johnson and collaborator Henry-Russell Hitchcock drew together many distinct threads and trends, identified them as stylistically similar and having a common purpose, and consolidated them into the International Style.This was an important turning point. With World War II the important figures of the Bauhaus fled to the United States, to Chicago, to the Harvard Graduate School of Design, and to Black Mountain College. While Modern architectural design never became a dominant style in single-dwelling residential buildings, in institutional and commercial architecture Modernism became the pre-eminent, and in the schools (for leaders of the profession) the only acceptable, design solution from about 1932 to about 1984.Architects who worked in the international style wanted to break with architectural tradition and design simple, unornamented buildings. The most commonly used materials are glass for the facade, steel for exterior support, and concrete for the floors and interior supports; floor plans were functional and logical. The style became most evident in the design of skyscrapers. Perhaps its most famous manifestations include the United Nations headquarters (Le Corbusier, Oscar Niemeyer, Sir Howard Robertson), the Seagram Building (Ludwig Mies van der Rohe), and Lever House (Skidmore, Owings, and Merrill), all in New York. A prominent residential example is the Lovell House (Richard Neutra) in Los Angeles.Detractors of the international style claim that its stark, uncompromisingly rectangular geometry is dehumanising. Le Corbusier once described buildings as πmachines for living,∖but people are not machines and it was suggested that they do not want to live in machines- Even Philip Johnson admitted he was πbored with the box∕,Since the early 1980s many architects have deliberately sought to move away from rectilinear designs, towards more eclectic styles. During the middle of the century, some architects began experimenting in organic forms that they felt were more human and accessible. Mid-century modernism, or organic modernism, was very popular, due to its democratic and playful nature. Alvar Aalto and Eero Saarinen were two of the most prolific architects and designers in this movement, which has influenced contemporary modernism.Although there is debate as to when and why the decline of the modern movement occurred, criticism of Modern architecture began in the 1960s on the grounds that it was universal, sterile, elitist and lacked meaning. Its approach had become ossified in a πstyleπthat threatened to degenerate into a set of mannerisms. Siegfried Giedion in the 1961 introduction to his evolving text, Space, Time and Architecture (first written in 1941), could begin ,,At the moment a certain confusion exists in contemporary architecture, as in painting; a kind of pause, even a kind of exhaustion/1At the Metropolitan Museum of Art, a 1961 symposium discussed the question πModern Architecture: Death or Metamorphosis?11In New York, the coup d r etat appeared to materialize in controversy around the Pan Am Building that loomed over Grand Central Station, taking advantage of the modernist real estate concept of πair rights,∖[l] In criticism by Ada Louise Huxtable and Douglas Haskell it was seen to ,,severπthe Park Avenue streetscape and πtarnishπthe reputations of its consortium of architects: Walter Gropius, Pietro Belluschi and thebuilders Emery Roth & Sons. The rise of postmodernism was attributed to disenchantment with Modern architecture. By the 1980s, postmodern architecture appeared triumphant over modernism, including the temple of the Light of the World, a futuristic design for its time Guadalajara Jalisco La Luz del Mundo Sede International; however, postmodern aesthetics lacked traction and by the mid-1990s, a neo-modern (or hypermodern) architecture had once again established international pre-eminence. As part of this revival, much of the criticism of the modernists has been revisited, refuted, and re-evaluated; and a modernistic idiom once again dominates in institutional and commercial contemporary practice, but must now compete with the revival of traditional architectural design in commercial and institutional architecture; residential design continues to be dominated by a traditional aesthetic.中文译文:现代建筑现代建筑，不被混淆与‘当代建筑’，是一个词给了一些建筑风格有类似的特点，主要的简化形式,消除装饰等.虽然风格的设想早在20世纪,并大量造就了一些建筑师、建筑教育家和展品，很少有现代的建筑物，建于20世纪上半叶.第二次大战后的三十年，但最终却成为主导建筑风格的机构和公司建设.1起源一些历史学家认为进化的现代建筑作为一个社会问题，息息相关的工程中的现代性, 从而影响了启蒙运动，导致社会和政治革命.另一些人认为现代建筑主要是靠技术和工程学的发展，那就是获得新的建筑材料，如钢铁，混凝土和玻璃驱车发明新的建筑技术，它作为工业革命的一部分.1796年，Shrewsbury查尔斯bage首先用他的‘火’的设计，后者则依靠铸铁及砖与石材地板.这些建设大大加强了结构，使它们能够容纳更大的机器.由于作为建筑材料特性知识缺乏,一些早期建筑失败.直到1830年初，伊顿Hodgkinson预计推出了型钢梁，导致广泛使用钢架建设，工业结构完全改变了这种窘迫的面貌,英国北部领导的描述，〃黑暗魔鬼作坊〃的地方如曼彻斯特和西约克郡.水晶宫由约瑟夫paxton的重大展览，1851年,是一个早期的例子, 钢铁及玻璃施工；可能是一个最好的例子，就是1890年由William乐男爵延长和路易沙利文在芝加哥附近发展的高层钢结构摩天楼.早期结构采用混凝土作为行政手段的建筑表达（而非纯粹功利结构），包括建于1906年在芝加哥附近，劳埃德赖特的统一宫，建于1926 年瑞士巴塞尔附近的鲁道夫斯坦纳的第二哥特堂,.但无论原因为何，约有1900多位建筑师，在世界各地开始制定新的建筑方法,将传统的先例（比如哥特式）与新的技术相结合的可能性.路易沙利文和赖特在芝加哥工作,维克多奥尔塔在布鲁塞尔，安东尼高迪在巴塞罗那，奥托瓦格纳和查尔斯景mackintosh格拉斯哥在维也纳，其中之一可以看作是一个新与旧的共同斗争.2现代主义风格由1920年代的最重要人物，在现代建筑里确立了自己的名声.三个是公认的柯布西耶在法国，密斯范德尔德罗和瓦尔特格罗皮乌斯在德国.密斯范德尔德罗和格罗皮乌斯为董事的包豪斯，其中欧洲有不少学校和有关团体学习调和工艺和传统工业技术.赖特的建筑生涯中，也影响了欧洲建筑的现代艺术,特别是通过瓦斯穆特组合但他拒绝被归类与他们.赖特与格罗皮乌斯和Van der德罗对整个有机体系有重大的影响.在1932年来到的重要moma展览,是现代建筑艺术的国际展览，艺术家菲利普约翰逊. 约翰逊和合作者亨利-罗素阁纠集许多鲜明的线索和趋势，内容相似,有一个共同的目的, 巩固了他们融入国际化风格这是一个重要的转折点.在二战的时间包豪斯的代表人物逃到美国，芝加哥，到哈佛大学设计黑山书院.当现代建筑设计从未成为主导风格单一的住宅楼，在成为现代卓越的体制和商业建筑，是学校（专业领导）的唯一可接受的，设计解决方案，从约1932年至约1984 年.那些从事国际风格的建筑师想要打破传统建筑和简单的没有装饰的建筑物。

2022届上海市实验学校高三上学期10月摸底考试英语试题(解析版)

C.The woman hadn't expected the maintenance service to take so long.
D.The woman was satisfied with the improvement in the garage's service
9.A.The man didn't intend to make the woman unhappy.
C.Ask the woman which floor she's going to. D.Stay in the same lift to go down to his floor.7.
7.A.The size of the electric vehicle market.
B.A new trend in the car making industry.
10.A.The man may need to re-evaluate her priorities.
B.The man should deal with the urgent matters first.
C.The man has failed to take care of the urgent matters.
B.The man thought the woman was being unreasonable.
C.The man believed the woman had misunderstood him.
D.The man wanted to say something upsetting to the woman.
Questions 11through 13are based on the following passage.

NONLINEAR TIME SERIES ANALYSIS

More informationNONLINEAR TIME SERIES ANALYSISThis book represents a modern approach to time series analysis which is based onthe theory of dynamical systems.It starts from a sound outline of the underlyingtheory to arrive at very practical issues,which are illustrated using a large number ofempirical data sets taken from variousﬁelds.This book will hence be highly usefulfor scientists and engineers from all disciplines who study time variable signals,including the earth,life and social sciences.The paradigm of deterministic chaos has inﬂuenced thinking in manyﬁelds ofscience.Chaotic systems show rich and surprising mathematical structures.In theapplied sciences,deterministic chaos provides a striking explanation for irregulartemporal behaviour and anomalies in systems which do not seem to be inherentlystochastic.The most direct link between chaos theory and the real world is the anal-ysis of time series from real systems in terms of nonlinear dynamics.Experimentaltechnique and data analysis have seen such dramatic progress that,by now,mostfundamental properties of nonlinear dynamical systems have been observed in thelaboratory.Great efforts are being made to exploit ideas from chaos theory where-ver the data display more structure than can be captured by traditional methods.Problems of this kind are typical in biology and physiology but also in geophysics,economics and many other sciences.This revised edition has been signiﬁcantly rewritten an expanded,includingseveral new chapters.In view of applications,the most relevant novelties will be thetreatment of non-stationary data sets and of nonlinear stochastic processes insidethe framework of a state space reconstruction by the method of delays.Hence,non-linear time series analysis has left the rather narrow niche of strictly deterministicsystems.Moreover,the analysis of multivariate data sets has gained more atten-tion.For a direct application of the methods of this book to the reader’s own datasets,this book closely refers to the publicly available software package TISEAN.The availability of this software will facilitate the solution of the exercises,so thatreaders now can easily gain their own experience with the analysis of data sets.Holger Kantz,born in November1960,received his diploma in physics fromthe University of Wuppertal in January1986with a thesis on transient chaos.InJanuary1989he obtained his Ph.D.in theoretical physics from the same place,having worked under the supervision of Peter Grassberger on Hamiltonian many-particle dynamics.During his postdoctoral time,he spent one year on a Marie Curiefellowship of the European Union at the physics department of the University ofMore informationFlorence in Italy.In January1995he took up an appointment at the newly foundedMax Planck Institute for the Physics of Complex Systems in Dresden,where heestablished the research group‘Nonlinear Dynamics and Time Series Analysis’.In1996he received his venia legendi and in2002he became adjunct professorin theoretical physics at Wuppertal University.In addition to time series analysis,he works on low-and high-dimensional nonlinear dynamics and its applications.More recently,he has been trying to bridge the gap between dynamics and statis-tical physics.He has(co-)authored more than75peer-reviewed articles in scien-tiﬁc journals and holds two international patents.For up-to-date information seehttp://www.mpipks-dresden.mpg.de/mpi-doc/kantzgruppe.html.Thomas Schreiber,born1963,did his diploma work with Peter Grassberger atWuppertal University on phase transitions and information transport in spatio-temporal chaos.He joined the chaos group of Predrag Cvitanovi´c at the Niels BohrInstitute in Copenhagen to study periodic orbit theory of diffusion and anomaloustransport.There he also developed a strong interest in real-world applications ofchaos theory,leading to his Ph.D.thesis on nonlinear time series analysis(Univer-sity of Wuppertal,1994).As a research assistant at Wuppertal University and duringseveral extended appointments at the Max Planck Institute for the Physics of Com-plex Systems in Dresden he published numerous research articles on time seriesmethods and applications ranging from physiology to the stock market.His habil-itation thesis(University of Wuppertal)appeared as a review in Physics Reportsin1999.Thomas Schreiber has extensive experience teaching nonlinear dynamicsto students and experts from variousﬁelds and at all levels.Recently,he has leftacademia to undertake industrial research.NONLINEAR TIME SERIES ANALYSIS HOLGER KANTZ AND THOMAS SCHREIBERMax Planck Institute for the Physics of Complex Systems,DresdenMore informationMore informationpublished by the press syndicate of the university of cambridgeThe Pitt Building,Trumpington Street,Cambridge,United Kingdomcambridge university pressThe Edinburgh Building,Cambridge CB22RU,UK40West20th Street,New York,NY10011–4211,USA477Williamstown Road,Port Melbourne,VIC3207,AustraliaRuiz de Alarc´o n13,28014Madrid,SpainDock House,The Waterfront,Cape Town8001,South AfricaC Holger Kantz and Thomas Schreiber,2000,2003This book is in copyright.Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.First published2000Second edition published2003Printed in the United Kingdom at the University Press,CambridgeTypeface Times11/14pt.System L A T E X2ε[tb]A catalogue record for this book is available from the British LibraryLibrary of Congress Cataloguing in Publication dataKantz,Holger,1960–Nonlinear time series analysis/Holger Kantz and Thomas Schreiber.–[2nd ed.].p.cm.Includes bibliographical references and index.ISBN0521821509–ISBN0521529026(paperback)1.Time-series analysis.2.Nonlinear theories.I.Schreiber,Thomas,1963–II.TitleQA280.K3552003519.5 5–dc212003044031ISBN0521821509hardbackISBN0521529026paperbackThe publisher has used its best endeavours to ensure that the URLs for external websites referred to in this bookare correct and active at the time of going to press.However,the publisher has no responsibility for the websites and can make no guarantee that a site will remain live or that the content is or will remain appropriate.More informationContentsPreface to theﬁrst edition page xiPreface to the second edition xiiiAcknowledgements xvI Basic topics11Introduction:why nonlinear methods?32Linear tools and general considerations132.1Stationarity and sampling132.2Testing for stationarity152.3Linear correlations and the power spectrum182.3.1Stationarity and the low-frequency component in thepower spectrum232.4Linearﬁlters242.5Linear predictions273Phase space methods303.1Determinism:uniqueness in phase space303.2Delay reconstruction353.3Finding a good embedding363.3.1False neighbours373.3.2The time lag393.4Visual inspection of data393.5Poincar´e surface of section413.6Recurrence plots434Determinism and predictability484.1Sources of predictability484.2Simple nonlinear prediction algorithm504.3Veriﬁcation of successful prediction534.4Cross-prediction errors:probing stationarity564.5Simple nonlinear noise reduction58vMore informationvi Contents5Instability:Lyapunov exponents655.1Sensitive dependence on initial conditions655.2Exponential divergence665.3Measuring the maximal exponent from data696Self-similarity:dimensions756.1Attractor geometry and fractals756.2Correlation dimension776.3Correlation sum from a time series786.4Interpretation and pitfalls826.5Temporal correlations,non-stationarity,and space timeseparation plots876.6Practical considerations916.7A useful application:determination of the noise level using thecorrelation integral926.8Multi-scale or self-similar signals956.8.1Scaling laws966.8.2Detrendedﬂuctuation analysis1007Using nonlinear methods when determinism is weak1057.1Testing for nonlinearity with surrogate data1077.1.1The null hypothesis1097.1.2How to make surrogate data sets1107.1.3Which statistics to use1137.1.4What can go wrong1157.1.5What we have learned1177.2Nonlinear statistics for system discrimination1187.3Extracting qualitative information from a time series1218Selected nonlinear phenomena1268.1Robustness and limit cycles1268.2Coexistence of attractors1288.3Transients1288.4Intermittency1298.5Structural stability1338.6Bifurcations1358.7Quasi-periodicity139II Advanced topics1419Advanced embedding methods1439.1Embedding theorems1439.1.1Whitney’s embedding theorem1449.1.2Takens’s delay embedding theorem1469.2The time lag148More informationContents vii9.3Filtered delay embeddings1529.3.1Derivative coordinates1529.3.2Principal component analysis1549.4Fluctuating time intervals1589.5Multichannel measurements1599.5.1Equivalent variables at different positions1609.5.2Variables with different physical meanings1619.5.3Distributed systems1619.6Embedding of interspike intervals1629.7High dimensional chaos and the limitations of the time delayembedding1659.8Embedding for systems with time delayed feedback17110Chaotic data and noise17410.1Measurement noise and dynamical noise17410.2Effects of noise17510.3Nonlinear noise reduction17810.3.1Noise reduction by gradient descent17910.3.2Local projective noise reduction18010.3.3Implementation of locally projective noise reduction18310.3.4How much noise is taken out?18610.3.5Consistency tests19110.4An application:foetal ECG extraction19311More about invariant quantities19711.1Ergodicity and strange attractors19711.2Lyapunov exponents II19911.2.1The spectrum of Lyapunov exponents and invariantmanifolds20011.2.2Flows versus maps20211.2.3Tangent space method20311.2.4Spurious exponents20511.2.5Almost two dimensionalﬂows21111.3Dimensions II21211.3.1Generalised dimensions,multi-fractals21311.3.2Information dimension from a time series21511.4Entropies21711.4.1Chaos and theﬂow of information21711.4.2Entropies of a static distribution21811.4.3The Kolmogorov–Sinai entropy22011.4.4The -entropy per unit time22211.4.5Entropies from time series data226More informationviii Contents11.5How things are related22911.5.1Pesin’s identity22911.5.2Kaplan–Yorke conjecture23112Modelling and forecasting23412.1Linear stochastic models andﬁlters23612.1.1Linearﬁlters23712.1.2Nonlinearﬁlters23912.2Deterministic dynamics24012.3Local methods in phase space24112.3.1Almost model free methods24112.3.2Local linearﬁts24212.4Global nonlinear models24412.4.1Polynomials24412.4.2Radial basis functions24512.4.3Neural networks24612.4.4What to do in practice24812.5Improved cost functions24912.5.1Overﬁtting and model costs24912.5.2The errors-in-variables problem25112.5.3Modelling versus prediction25312.6Model veriﬁcation25312.7Nonlinear stochastic processes from data25612.7.1Fokker–Planck equations from data25712.7.2Markov chains in embedding space25912.7.3No embedding theorem for Markov chains26012.7.4Predictions for Markov chain data26112.7.5Modelling Markov chain data26212.7.6Choosing embedding parameters for Markov chains26312.7.7Application:prediction of surface wind velocities26412.8Predicting prediction errors26712.8.1Predictability map26712.8.2Individual error prediction26812.9Multi-step predictions versus iterated one-step predictions27113Non-stationary signals27513.1Detecting non-stationarity27613.1.1Making non-stationary data stationary27913.2Over-embedding28013.2.1Deterministic systems with parameter drift28013.2.2Markov chain with parameter drift28113.2.3Data analysis in over-embedding spaces283More informationContents ix13.2.4Application:noise reduction for human voice28613.3Parameter spaces from data28814Coupling and synchronisation of nonlinear systems29214.1Measures for interdependence29214.2Transfer entropy29714.3Synchronisation29915Chaos control30415.1Unstable periodic orbits and their invariant manifolds30615.1.1Locating periodic orbits30615.1.2Stable/unstable manifolds from data31215.2OGY-control and derivates31315.3Variants of OGY-control31615.4Delayed feedback31715.5Tracking31815.6Related aspects319A Using the TISEAN programs321A.1Information relevant to most of the routines322A.1.1Efﬁcient neighbour searching322A.1.2Re-occurring command options325A.2Second-order statistics and linear models326A.3Phase space tools327A.4Prediction and modelling329A.4.1Locally constant predictor329A.4.2Locally linear prediction329A.4.3Global nonlinear models330A.5Lyapunov exponents331A.6Dimensions and entropies331A.6.1The correlation sum331A.6.2Information dimension,ﬁxed mass algorithm332A.6.3Entropies333A.7Surrogate data and test statistics334A.8Noise reduction335A.9Finding unstable periodic orbits336A.10Multivariate data336B Description of the experimental data sets338B.1Lorenz-like chaos in an NH3laser338B.2Chaos in a periodically modulated NMR laser340B.3Vibrating string342B.4Taylor–Couetteﬂow342B.5Multichannel physiological data343More informationx ContentsB.6Heart rate during atrialﬁbrillation343B.7Human electrocardiogram(ECG)344B.8Phonation data345B.9Postural control data345B.10Autonomous CO2laser with feedback345B.11Nonlinear electric resonance circuit346B.12Frequency doubling solid state laser348B.13Surface wind velocities349References350Index365More informationPreface to theﬁrst editionThe paradigm of deterministic chaos has inﬂuenced thinking in manyﬁelds of sci-ence.As mathematical objects,chaotic systems show rich and surprising structures.Most appealing for researchers in the applied sciences is the fact that determinis-tic chaos provides a striking explanation for irregular behaviour and anomalies insystems which do not seem to be inherently stochastic.The most direct link between chaos theory and the real world is the analysis oftime series from real systems in terms of nonlinear dynamics.On the one hand,experimental technique and data analysis have seen such dramatic progress that,by now,most fundamental properties of nonlinear dynamical systems have beenobserved in the laboratory.On the other hand,great efforts are being made to exploitideas from chaos theory in cases where the system is not necessarily deterministicbut the data displays more structure than can be captured by traditional methods.Problems of this kind are typical in biology and physiology but also in geophysics,economics,and many other sciences.In all theseﬁelds,even simple models,be they microscopic or phenomenological,can create extremely complicated dynamics.How can one verify that one’s model isa good counterpart to the equally complicated signal that one receives from nature?Very often,good models are lacking and one has to study the system just from theobservations made in a single time series,which is the case for most non-laboratorysystems in particular.The theory of nonlinear dynamical systems provides new toolsand quantities for the characterisation of irregular time series data.The scope ofthese methods ranges from invariants such as Lyapunov exponents and dimensionswhich yield an accurate description of the structure of a system(provided thedata are of high quality)to statistical techniques which allow for classiﬁcation anddiagnosis even in situations where determinism is almost lacking.This book provides the experimental researcher in nonlinear dynamics with meth-ods for processing,enhancing,and analysing the measured signals.The theorist willbe offered discussions about the practical applicability of mathematical results.ThexiMore informationxii Preface to theﬁrst editiontime series analyst in economics,meteorology,and otherﬁelds willﬁnd inspira-tion for the development of new prediction algorithms.Some of the techniquespresented here have also been considered as possible diagnostic tools in clinical re-search.We will adopt a critical but constructive point of view,pointing out ways ofobtaining more meaningful results with limited data.We hope that everybody whohas a time series problem which cannot be solved by traditional,linear methodswillﬁnd inspiring material in this book.Dresden and WuppertalNovember1996More informationPreface to the second editionIn aﬁeld as dynamic as nonlinear science,new ideas,methods and experimentsemerge constantly and the focus of interest shifts accordingly.There is a continuousstream of new results,and existing knowledge is seen from a different angle aftervery few years.Five years after theﬁrst edition of“Nonlinear Time Series Analysis”we feel that theﬁeld has matured in a way that deserves being reﬂected in a secondedition.The modiﬁcation that is most immediately visible is that the program listingshave been be replaced by a thorough discussion of the publicly available softwareTISEAN.Already a few months after theﬁrst edition appeared,it became clearthat most users would need something more convenient to use than the bare libraryroutines printed in the book.Thus,together with Rainer Hegger we prepared stand-alone routines based on the book but with input/output functionality and advancedfeatures.Theﬁrst public release was made available in1998and subsequent releasesare in widespread use now.Today,TISEAN is a mature piece of software thatcovers much more than the programs we gave in theﬁrst edition.Now,readerscan immediately apply most methods studied in the book on their own data usingTISEAN programs.By replacing the somewhat terse program listings by minuteinstructions of the proper use of the TISEAN routines,the link between book andsoftware is strengthened,supposedly to the beneﬁt of the readers and users.Hencewe recommend a download and installation of the package,such that the exercisescan be readily done by help of these ready-to-use routines.The current edition has be extended in view of enlarging the class of data sets to betreated.The core idea of phase space reconstruction was inspired by the analysis ofdeterministic chaotic data.In contrast to many expectations,purely deterministicand low-dimensional data are rare,and most data fromﬁeld measurements areevidently of different nature.Hence,it was an effort of our scientiﬁc work over thepast years,and it was a guiding concept for the revision of this book,to explore thepossibilities to treat other than purely deterministic data sets.xiiiMore informationxiv Preface to the second editionThere is a whole new chapter on non-stationary time series.While detectingnon-stationarity is still brieﬂy discussed early on in the book,methods to deal withmanifestly non-stationary sequences are described in some detail in the secondpart.As an illustration,a data source of lasting interest,human speech,is used.Also,a new chapter deals with concepts of synchrony between systems,linear andnonlinear correlations,information transfer,and phase synchronisation.Recent attempts on modelling nonlinear stochastic processes are discussed inChapter12.The theoretical framework forﬁtting Fokker–Planck equations to datawill be reviewed and evaluated.While Chapter9presents some progress that hasbeen made in modelling input–output systems with stochastic but observed inputand on the embedding of time delayed feedback systems,the chapter on mod-elling considers a data driven phase space approach towards Markov chains.Windspeed measurements are used as data which are best considered to be of nonlinearstochastic nature despite the fact that a physically adequate mathematical model isthe deterministic Navier–Stokes equation.In the chapter on invariant quantities,new material on entropy has been included,mainly on the -and continuous entropies.Estimation problems for stochastic ver-sus deterministic data and data with multiple length and time scales are discussed.Since more and more experiments now yield good multivariate data,alternativesto time delay embedding using multiple probe measurements are considered at var-ious places in the text.This new development is also reﬂected in the functionalityof the TISEAN programs.A new multivariate data set from a nonlinear semicon-ductor electronic circuit is introduced and used in several places.In particular,adifferential equation has been successfully established for this system by analysingthe data set.Among other smaller rearrangements,the material from the former chapter“Other selected topics”,has been relocated to places in the text where a connectioncan be made more naturally.High dimensional and spatio-temporal data is now dis-cussed in the context of embedding.We discuss multi-scale and self-similar signalsnow in a more appropriate way right after fractal sets,and include recent techniquesto analyse power law correlations,for example detrendedﬂuctuation analysis.Of course,many new publications have appeared since1997which are potentiallyrelevant to the scope of this book.At least two new monographs are concerned withthe same topic and a number of review articles.The bibliography has been updatedbut remains a selection not unaffected by personal preferences.We hope that the extended book will prove its usefulness in many applicationsof the methods and further stimulate theﬁeld of time series analysis.DresdenDecember2002More informationAcknowledgementsIf there is any feature of this book that we are proud of,it is the fact that almost allthe methods are illustrated with real,experimental data.However,this is anythingbut our own achievement–we exploited other people’s work.Thus we are deeplyindebted to the experimental groups who supplied data sets and granted permissionto use them in this book.The production of every one of these data sets requiredskills,experience,and equipment that we ourselves do not have,not forgetting thehours and hours of work spent in the laboratory.We appreciate the generosity ofthe following experimental groups:NMR laser.Our contact persons at the Institute for Physics at Z¨u rich University were Leci Flepp and Joe Simonet;the head of the experimental group is E.Brun.(See AppendixB.2.)Vibrating string.Data were provided by Tim Molteno and Nick Tuﬁllaro,Otago University, Dunedin,New Zealand.(See Appendix B.3.)Taylor–Couetteﬂow.The experiment was carried out at the Institute for Applied Physics at Kiel University by Thorsten Buzug and Gerd Pﬁster.(See Appendix B.4.) Atrialﬁbrillation.This data set is taken from the MIT-BIH Arrhythmia Database,collected by G.B.Moody and R.Mark at Beth Israel Hospital in Boston.(See Appendix B.6.) Human ECG.The ECG recordings we used were taken by Petr Saparin at Saratov State University.(See Appendix B.7.)Foetal ECG.We used noninvasively recorded(human)foetal ECGs taken by John F.Hofmeister as the Department of Obstetrics and Gynecology,University of Colorado,Denver CO.(See Appendix B.7.)Phonation data.This data set was made available by Hanspeter Herzel at the Technical University in Berlin.(See Appendix B.8.)Human posture data.The time series was provided by Steven Boker and Bennett Bertenthal at the Department of Psychology,University of Virginia,Charlottesville V A.(SeeAppendix B.9.)xvMore informationxvi AcknowledgementsAutonomous CO2laser with feedback.The data were taken by Riccardo Meucci and Marco Cioﬁni at the INO in Firenze,Italy.(See Appendix B.10.)Nonlinear electric resonance circuit.The experiment was designed and operated by M.Diestelhorst at the University of Halle,Germany.(See Appendix B.11.)Nd:YAG laser.The data we use were recorded in the University of Oldenburg,where we wish to thank Achim Kittel,Falk Lange,Tobias Letz,and J¨u rgen Parisi.(See AppendixB.12.)We used the following data sets published for the Santa Fe Institute Time SeriesContest,which was organised by Neil Gershenfeld and Andreas Weigend in1991:NH3laser.We used data set A and its continuation,which was published after the contest was closed.The data was supplied by U.H¨u bner,N.B.Abraham,and C.O.Weiss.(SeeAppendix B.1.)Human breath rate.The data we used is part of data set B of the contest.It was submitted by Ari Goldberger and coworkers.(See Appendix B.5.)During the composition of the text we asked various people to read all or part of themanuscript.The responses ranged from general encouragement to detailed technicalcomments.In particular we thank Peter Grassberger,James Theiler,Daniel Kaplan,Ulrich Parlitz,and Martin Wiesenfeld for their helpful remarks.Members of ourresearch groups who either contributed by joint work to our experience and knowl-edge or who volunteered to check the correctness of the text are Rainer Hegger,Andreas Schmitz,Marcus Richter,Mario Ragwitz,Frank Schm¨u ser,RathinaswamyBhavanan Govindan,and Sharon Sessions.We have also considerably proﬁted fromcomments and remarks of the readers of theﬁrst edition of the book.Their effortin writing to us is gratefully appreciated.Last but not least we acknowledge the encouragement and support by SimonCapelin from Cambridge University Press and the excellent help in questions ofstyle and English grammar by Sheila Shepherd.。

Flute斯坦纳最小树构造算法

• 上述例子优化后仅有9M
HOW—最小线长计算加速
• 正常的计算POWVs线长 • 但是同一个group间的计算是有很多重复点的，
每个POWV单独计算浪费很多时间。 • POWV之间可以有依赖性的依次计算，其实这
是一个最小生长树的问题。 • 对于一个Group中q个POWVs，建立一个q+1个
节点的完全图，多出的一点对应于线长数组（HPWL），图中边权为两个相邻线长数组的边际距离。 • 从HPWL点开始宽搜建立最小生长树，叶子节点为图中的node
堆边的集合，由此线长即可以由hi,vi组成的向量表示。 • 右下图的线长可依次表示为(1, 2, 1, 1, 1, 2), (1, 1, 1, 1, 2, 3), (1, 2, 1, 1, 1, 1) • 虽然斯坦纳树数量是巨大的，但是上述的线长向量数量要小很多，并且可以略过许多一定大的向量，如a,c中a可以无视。 • 那么由此得到的最小的那些不可以被无视的向量就组成了POWVs，对于一个端点很少的线网而言，POWV是十分少的。
Chris Chu and Yiu-Chung Wong
Review By Carelife
What—FLUTE
• 基于快速查找表的矩形斯坦纳最小树构造算法 • 所有N点线网根据pin脚位置都可划分到n!个group中，每
个group中存有POWV，对于一个线网最优线长可由 POWV来获得，FLUTE算法首先会预计算这些POWV形成一个查找表。与POWV一起存储的还有POST，一个 POWV对应多个POST，一个POST只有一个POWV。 • POWV：potentially optimal wirelength vectors • POST：potentially optimal Steiner tree • 基于此，要得到一颗RSMT，只需计算线网所在组对应的POWV的线长，然后返回对应的POST即可。 • 上述查找表算法最高支持9点线网，对于9点以上的需要递归的切分线网。 • FLUTE算法的复杂度依旧是O(nlogn)

[4] H. B. Bakoglu, Circuits, Interconnections and Packaging for VLSI, Addison-Wesley, 1990,

Based Routing Constructions", in Proc. IEEE Intl. Conf. on Computer Design, Boston, October 1993, pp. 81-84. 7 B. Chandra, G. Das, G. Narasimhan and J. Soares, New Sparseness Results on Graph Spanners", Proc. 8th Ann. Symp. Computational Geometry June 1992, pp. 192-201. 8 J. Cong, A. B. Kahng, G. Robins, M. Sarrafzadeh, and C. K. Wong, Provably Good PerformanceDriven Global Routing", IEEE Trans. on CAD 116, June 1992, pp. 739-752. 9 J. Cong, K. Leung, and D. Zhou, Performance-Driven Interconnect Design Based on Distributed RC Delay Model", Proc. ACM IEEE Design Automation Conf., June 1993, pp. 606-611. 10 E. W. Dijkstra, A Note on Two Problems in Connection With Graphs", Numerische Mathematik 11959, pp. 269-271. 11 W. C. Elmore, The Transient Response of Damped Linear Network with Particular Regard to Wideband Ampli ers", J. Applied Physics 19 1948, pp. 55-63. 12 J. Ho, G. Vijayan, and C. K. Wong, New Algorithms for the Rectilinear Steiner Tree Problem", IEEE Trans. on CAD 92, Feb 1992, pp. 185-193. 13 S. Khuller, B. Raghavachari and N. Young, Balancing Minimum Spanning and Shortest Path Trees", Proc. ACM SIAM Symp. on Discrete Algorithms, January 1993, pp. 243-250. 14 S. Kim, R. M. Owens, and M. J. Irwin Experiments with a Performance Driven Module Generator", Proc. ACM IEEE Design Automation Conf., 1992, pp. 687-690. 15 E. Kuh, M. A. B. Jackson and M. Marek-Sadowska, Timing-Driven Routing for Building Block Layout", Proc. IEEE International Symposium on Circuits and Systems, pp. 518-519, 1987. 16 H.-P. Lenhof, J. S. Salowe and D. E. Wrege, New Methods to Mix Shortest-Path and Minimum Spanning Trees", manuscript, 1993. 17 S. Prastjutrakul and W. J. Kubitz, A Timing-Driven Global Router for Custom Chip Design", Proc. IEEE Intl. Conf. on Computer-Aided Design, 1990, pp. 48-51. 18 R. C. Prim, Shortest Connecting Networks and Some Generalizations", Bell System Tech. J. 36 1957, pp. 1389-1401. 19 S. K. Rao, P. Sadayappan, F. K. Hwang and P. W. Shor, The Rectilinear Steiner Arborescence Problem", Algorithmica 7 1992, pp. 277-288. 20 J. Rubinstein, P. Pen eld, and M. A. Horowitz, Signal Delay in RC Tree Networks", IEEE Trans. on CAD 23 1983, pp. 202-211. 21 J. S. Salowe, D. S. Richards and D. Wrege, Mixed Spanning Trees", Proc. Great Lakes Symp. on VLSI, March 1993, pp. 62-66. 22 S. Sutanthavibul and E. Shragowitz, Adaptive Timing-Driven Layout for High Speed VLSI", Proc. ACM IEEE Design Automation Conf., 1990, pp. 90-95.

新视野大学英语第三版B4U4 TextA 课文中英对照版

unit4 TextAAchieving sustainable environmentalism完成可延续性开展的环保主义1 Environmental sensitivity is now as required an attitude in polite society as is, say, belief in democracy or disapproval of plastic surgery. But now that everyone from Ted Turner to George H. W. Bush has claimed love for Mother Earth, how are we to choose among the dozens of conflicting proposals, regulations and laws advanced by congressmen and constituents alike in the name of the environment? Clearly, not everything with an environmental claim is worth doing. How do we segregate the best options and consolidate our varying interests into a single, sound policy?在上流社会,对环境的敏感就如同信仰民主、反对整容一样,是一种不可或缺的态度。

然而,既然从泰德·特纳到乔治·W.H.布什,每个人都声称自己热爱地球母亲,那么,在由议员、选民之类的人以环境名义而提出的众多的相互矛盾的提案、规章和法规中,我们又该如何做出选择呢?显而易见,并不是每一项冠以环境爱护名义的事情都值得去做。

我们怎样才能别离出最正确选择,并且把我们各自不同的兴趣统一在同一个合理的政策当中呢?2 There is a simple way. First, differentiate between environmental luxuries and environmental necessities. Luxuries are those things that would be nice to have if costless. Necessities are those things we must have regardless. Call this distinction the definitive rule of sane environmentalism, which stipulates that combating ecological change that directly threatens the health and safety of people is an environmental necessity. All else is luxury.有一种简便的方法。

关于金刚狼的英语作文

Wolverine,a character from the Marvel Comics universe,is one of the most iconic and enduring figures in the world of comic books.With his distinct appearance, incredible abilities,and complex personality,Wolverine has captured the hearts of fans for decades.Origin and BackgroundWolverine,whose real name is James Howlett,was born in Canada in the late19th century.He is a mutant with animallike senses,enhanced physical capabilities,a regenerative healing factor,and retractable bone claws coated with the indestructible metal adamantium.His past is shrouded in mystery,with hints of a troubled and violent history that has shaped his character.Character TraitsWolverine is known for his fierce independence,quick temper,and nononsense attitude. Despite his rough exterior,he possesses a strong sense of justice and loyalty to his friends. His gruff demeanor often hides a deep emotional depth and a capacity for love and compassion,which is evident in his relationships with other characters such as Jean Grey and Rogue.Abilities and PowersWolverines most notable power is his healing factor,which allows him to recover from virtually any injury at an accelerated rate.This ability,combined with his adamantium claws,makes him a formidable opponent in combat.His heightened senses,agility,and strength are also key components of his fighting prowess.Role in the XMenAs a member of the XMen,Wolverine plays a crucial role in the teams adventures.His experience and skills often make him a leader in battles against various threats,from other mutants to powerful villains.His relationship with the XMen,particularly Professor X,showcases his growth from a lone wolf to a valued member of a family.Popularity and Cultural ImpactWolverines popularity has transcended the pages of comic books,with successful appearances in animated series,video games,and blockbuster films.Hugh Jackmans portrayal of Wolverine in the XMen film series has further cemented the characters place in popular culture,bringing his story to life for a new generation of fans.Evolution Over TimeThroughout the years,Wolverines character has evolved,exploring different aspects of his past and present.Storylines such as Old Man Logan and Wolverine:Origin havedelved into his history and the consequences of his actions,adding layers to his character and making him more relatable to readers.ConclusionWolverine stands as a testament to the power of storytelling and character development in comic books.His enduring appeal lies in his complexity,his resilience,and his ability to connect with readers on an emotional level.As a symbol of struggle and redemption, Wolverine continues to inspire fans around the world with his unwavering spirit and indomitable will.。

$b$-minimality

a rX iv:mat h /61183v3[mat h.LO]9M ay28Abstract .—We introduce a new notion of tame geometry for structures admit-ting an abstract notion of balls.The notion is named b -minimality and is based on deﬁnable families of points and balls.We develop a dimension theory and prove a cell decomposition theorem for b -minimal structures.We show that b -minimality ap-plies to the theory of Henselian valued ﬁelds of characteristic zero,generalizing work by Denef -Pas [25][26].Structures which are o -minimal,v -minimal,or p -minimal and which satisfy some slight extra conditions are also b -minimal,but b -minimality leaves more room for nontrivial expansions.The b -minimal setting is intended to be a natural framework for the construction of Euler characteristics and motivic or p -adic integrals.The b -minimal cell decomposition is a generalization of concepts of P.J.Co-hen [11],J.Denef [15],and the link between cell decomposition and integration was ﬁrst made by Denef [13]. 1.Introduction Originally introduced by Cohen [11]for real and p -adic ﬁelds,cell decomposition techniques were developed by Denef and Pas as a useful device for the study ofp -adic integrals [13][14][15][25][26].Roughly speaking,the basic idea is to cut a deﬁnable set into a ﬁnite number of cells each of which is like a family of balls or points.For general Henselian valued ﬁelds of residue characteristic zero,Denef and Pas proved a cell decomposition theorem where the families of balls or points are parameterized by residue ﬁeld and value group variables in a deﬁnable way.(1)An integral over the p -adic ﬁeld is then replaced by a corresponding sum over these residue ﬁeld and value group variables since the measure of a ball is clear and points have measure zero.Denef-Pas cell decomposition plays a fundamental role in our recent work [9]where we lay new general foundations for motivic integration.When we started in 2002working on the project that led to [9],we originally intended to work in the framework of an axiomatic cell decomposition of which Denef-Pas cell decomposition would be an avatar,but we ﬁnally decided to keep on the safe side by2RAF CLUCKERS&FRANC¸OIS LOESERstaying within the Denef-Pas framework and we postponed the axiomatic approach to a later occasion.The present paper is an attempt to lay the fundamentals of a tame geometry based upon a cell decomposition into basic families of points and “abstract”balls.A key point in our approach,already present in[25]and[9],is to work in a many sorted language with a unique main sort and possibly many auxiliary sorts that will parameterize the families of balls in a deﬁnable way.The theory is designed so that noﬁeld structure or topology is required.Instead,only a notion of balls is needed,whence the naming b-minimality.The collection of balls in a model is given by deﬁnition as the set ofﬁbers of a predicate B of the basic language consisting of one symbol B.The notion of b-minimality is then based on three axioms,named(b1),(b2)and(b3),where(b1)rather directly imposes the theory to allow cell decomposition and where(b2)and(b3)imply a good dimension theory and exclude pathological behavior.We show that every o-minimal structure is b-minimal,but more exotic expan-sions of o-minimal structures,like theﬁeld of real numbers with a predicate for the integer powers of2considered by van den Dries in[17],are also b-minimal,relative to the right auxiliary sorts.Also v-minimal theories of algebraically closed valued ﬁelds,deﬁned by Hrushovski and Kazhdan in[21],and p-minimal theories deﬁned by Haskell and Macpherson in[20]are b-minimal,under some slight extra conditions for the p-minimal case.Our framework is intended to be versatile enough to encom-pass promising candidate expansions,like entire analytic functions on valued and realﬁelds,but still strong enough to provide cell decomposition and a nice dimension theory.For p-minimality,for example,cell decomposition is presently missing in the theory and there seem to be few candidate expansions in sight.For C-minimality and v-minimality,expansions by nontrivial entire analytic functions are not possible since these have inﬁnitely many zeros in an algebraically closed valuedﬁeld.As already indicated,another goal of the theory is the study of Grothendieck rings and more speciﬁcally the construction of additive Euler characteristics and motivic integrals.We intend to go further into that direction in some future work.Let us brieﬂy review the content of the paper.In section2the basic axioms are introduced and discussed and in section3cell decomposition is proved.Section4 is devoted to dimension theory.In the next two sections more speciﬁc properties are considered:“preservation of balls”(which is a consequence of the Monotonicity Theorem in the o-minimal case)and b-minimality with centers(a kind of deﬁnable functions approximating the balls in the families).In section7we show that the theory of Henselian valuedﬁelds of characteristic zero is b-minimal by adapting the Cohen-Denef proof scheme.In particular we give(as far as we know)theﬁrst written instance of cell decomposition in mixed characteristic for unbounded ram-iﬁcation.Moreover,we prove that all deﬁnable functions are essentially given by terms.In section8,we compare b-minimality with p-minimality,v-minimality and C-minimality.We conclude the paper with some preliminary results on Grothendieckb-MINIMALITY3 semirings associated to b-minimal theories.2.b-minimality2.1.Preliminary conventions.—A language may have many sorts,some of which are called main sorts,the others being called auxiliary sorts.An expansion of a language may introduce new sorts.In this paper,we shall only consider languages admitting a unique main sort and a distinguished collection of auxiliary sorts.If a model is named M,then the main sort of M is denoted by M.Usually,for a predicate B of aﬁrst order language L,one has to specify that it is n-ary for some n,and one has toﬁx sorts S1,...,S n such that only for x i running over S i one is allowed to write B(x1,...,x n).We will not consider this as information of L itself,but instead this information will beﬁxed by L-theories by an axiom of the form∀x x∈B→(x∈S1×...×S n)for some n and some sorts S i.There is no harm in doing so.By deﬁnable we shall always mean deﬁnable with parameters,as opposed to L(A)-deﬁnable or A-deﬁnable,which means deﬁnable with parameters in A.By a point we mean a singleton.A deﬁnable set is called auxiliary if it is a subset of a ﬁnite Cartesian product of(the universes of)auxiliary sorts.If S is a sort,then its Cartesian power S0is considered to be a point and to be∅-deﬁnable.If S1and S2are sorts,then by convention S01is the same∅-deﬁnablepoint as S02,so in our models there is always at least one∅-deﬁnable point.Recall that o-minimality is about expansions of the language L<with one pred-icate<,with the requirement that the predicate<deﬁnes a dense linear order without endpoints.In the present setting we shall study expansions of a language L B consisting of one predicate B,which is nonempty and which hasﬁbers in the M-sort(by deﬁnition called balls).In both cases of tame geometries(o-minimal and b-minimal),the expansion has to satisfy extra properties.2.2.—Let L B be the language with one predicate B.We require that B is interpreted in any L B-model M with main sort M as a nonempty set B(M)withB(M)⊂A B×Mwhere A B is aﬁnite Cartesian product of(the universes of)some of the sorts of M.When a∈A B we write B(a)forB(a):={m∈M|(a,m)∈B(M)},and if B(a)is nonempty,we call it a ball(in the structure M),or B-ball when useful.2.2.1Deﬁnition.—Let L be any expansion of L B.We call an L-model M b-minimal when the following three conditions are satisﬁed for every set of parameters4RAF CLUCKERS&FRANC¸OIS LOESERA(the elements of A can belong to any of the sorts),for every A-deﬁnable subset X of M,and for every A-deﬁnable function F:X→M.(b1)There exists an A-deﬁnable function f:X→S with S auxiliary such that for each s∈f(X)theﬁber f−1(s)is a point or a ball.(b2)If g is a deﬁnable function from an auxiliary set to a ball,then g is not surjective. (b3)There exists an A-deﬁnable function f:X→S with S auxiliary such that for each s∈f(X)the restriction F|f−1(s)is either injective or constant.We call an L-theory b-minimal if all its models are b-minimal.We call a map f as in(b1)an A-deﬁnable b-map on X,or b-map for short,and call a map f as in(b3)compatible with F.Typically,in algebraic geometry,one studies families of varieties by means of a map from one variety X to another variety Y,and then the family consists of the ﬁbers of such a map.Such a family(ofﬁbers)is then just called a variety over Y.Likewise,in this paper,a deﬁnable set X over some other deﬁnable set Y is nothing else than a deﬁnable map from X to Y and its interest lies in the study of the family ofﬁbers of this map.Often,X will be a deﬁnable subset of M n×Y and the deﬁnable map to Y will be the coordinate projection.This terminology should not be confused with X being Y-deﬁnable meaning that X is deﬁnable using parameters from Y.By further analogy,a deﬁnable map between two deﬁnable sets X1and X2over Y is nothing else than a deﬁnable function from X1to X2making commutative diagrams with the maps from X1and X2to Y which are implicitly understood when we say that the X i are over Y.With this terminology of deﬁnable sets over deﬁnable sets,we can deﬁne a relative version of b-maps,that is,b-maps over some given deﬁnable ly,when Y and X⊂M×Y are A-deﬁnable sets,an(A-deﬁnable)b-map on X over Y is by deﬁnition a(A-deﬁnable)function f:X→S×Y which makes a commutative diagram with both projections to Y and with S auxiliary,such that for each a∈f(X)theﬁber f−1(a)is a point or a ball,where each f−1(a)is naturally considered as a subset of M(namely,by projecting on the M-coordinate).Compatibility of f with some deﬁnable function F:X⊂M×Y→M×Y over Y is deﬁned similarly.2.2.2Remark.—Axiom(b2)expresses in a strong way that the auxiliary sorts are diﬀerent from the main sort.In particular,the main sort is not interpretable in the auxiliary sorts by a deﬁnable function,in the sense of model theory.It follows from(b2)that if f:X→S is a b-map and X is a ball,then at least oneﬁber of f is not a point,and hence,no ball is a point.2.2.3Remark.—Most of the theory can be developed with the slightly weaker axiom(b3′)instead of axiom(b3):(b3′)There exists aﬁnite partition X i of X into A-deﬁnable parts and A-deﬁnable functions f i:X i→S i with S i auxiliary such that for each i and s∈f i(X i)therestriction F|f−1i (s)is either injective or constant.b-MINIMALITY5 As soon as there are at least two∅-deﬁnable auxiliary points,(b3)and(b3′)become equivalent.Another variant with a similar theory would be to allow for more than one pred-icate B to deﬁne the balls,for example,predicates B i⊂A Bi ×M and a ball beingaﬁber B i(a)⊂M for a∈A Bi.We don’t pursue this variant here.2.2.4Remark.—Unlike many other notions of minimality or of tame geometries, the notion of b-minimality does not require the theory to be complete.2.3.Reﬁnements.—As explained after Deﬁnition2.2.1,a deﬁnable function f can be seen as the family of itsﬁbers.The following notion of reﬁnement captures the idea that each of theﬁbers of f gets partitioned intoﬁbers of another function f′,where the images of f and of f′are supposed to be auxiliary sets.This last condition is assumed in order to exclude trivial maps like X→X.Let f:X→S be a deﬁnable function on X⊂M,with S auxiliary.By a reﬁnement of f we mean a pair(f′,g)with f′:X→S′and g:f′(X)→S deﬁnable functions and S′auxiliary,such that g◦f′=f.Since g is uniquely determined by f′,we shall write f′instead of(f′,g)for a reﬁnement of f and f≥f′if f′is a reﬁnement of f.This induces a structure of partially ordered set on the set of all deﬁnable functions on X of the form X→S with S auxiliary.In the relative setting,let f:X→S×Y be a deﬁnable function on X⊂M×Y over Y(the terminology over Y means that f makes a commutative diagram with the projections to Y,see the discussion below Deﬁnition2.2.1),with S auxiliary. By a reﬁnement of f(over Y)we mean a pair(f′,g)with f′:X→S′×Y a deﬁnable function on X over Y,g:f′(X)→S×Y a deﬁnable function over Y and S′auxiliary,such that g◦f′=f.Since g is uniquely determined by f′,we call f′a reﬁnement of f and write f≥f′.2.3.1Lemma.—Let M be a model of a b-minimal theory.Let F:X→X′be a deﬁnable function over Y for some subsets X and X′of M×Y(that F is over Y means that F commutes with the projections to Y).Then any two deﬁnable functions f:X→S×Y and f′:X→S′×Y over Y with S and S′auxiliary admit a common reﬁnement f′′:X→S′′×Y over Y,such that f′′is moreover a b-map over Y and compatible with F.(In particular,the opposite category of the category associated to the partially ordered set of such maps on X over Y is ﬁltering.)If moreover F,f,and f′are A-deﬁnable for some A,then f′′can be taken A-deﬁnable.Proof.—For each y∈Y there exists a map as in(b3)on theﬁberπ−1(y),with π:X→Y the projection,and similarly in all models of the theory.By compactness, oneﬁnds a deﬁnable f0:X→S0×Y over Y,with S0auxiliary,which is compatible with F.Now deﬁnef1:X→S×S′×S0×Ybyx→p(f(x),f′(x),f0(x))6RAF CLUCKERS&FRANC¸OIS LOESERwithp:S×S′×S0×Y3→S×S′×S0×Ythe projection.For each s∈S×S′×S0×Y there exists a b-map on f−11(s)by (b1),and this holds in all models of the theory.By compactness,oneﬁnds a b-map f′′:X→S×S′×S0×S′′×Y on X over Y,for some auxiliary S′′,whose composition with the projection to S×S′×S0×Y equals f1.We obtain this way a map f′′as required.2.4.Some Criteria.—The following two criteria are consequences of the lemmas and their corollary below.2.4.1Proposition.—Let T be an L-theory with all its models satisfying(b1) and(b2).Suppose that there are at least two∅-deﬁnable auxiliary points.Then T is b-minimal if and only if for all models M the following statement(∗)holds in M:(∗)if F:X⊂M→Y is a deﬁnable surjection with Y a ball,then not allﬁbers of F contain balls.2.4.2Proposition.—Let T be an L-theory with all its models satisfying(b1). Suppose that there are at least two∅-deﬁnable auxiliary points.Then T is b-minimal if and only if for all models M the following statement(†)holds in M:(†)If F:X⊂S×M→Y is a deﬁnable surjection with S auxiliary and Y a ball, then there exists y∈F(X)such that p(F−1(y))does not contain a ball,with p the projection X→M.2.4.3Lemma.—Let T be an L-theory with all its models satisfying(b2)and (b3).Then conditions(∗)and(†)are satisﬁed for each model M of T. Proof.—Weﬁrst prove(∗).Let Y be a ball and let F:X⊂M→Y be a deﬁnable surjection.Consider a map g:X→S such that,for every s in g(X),the restriction F|g−1(s)is either injective or constant,given by(b3).Consider the deﬁnable subset S1of S consisting of all points s such that F|g−1(s)is injective and set X1:=g−1(S1),S2:=g(X)\S1and X2:=g−1(S2).Suppose that for some y∈Y the set F−1|X1(y)contains a ball T.Then the restriction of g to T is injective,which contradicts(b2).Hence,no set of the form F−1|X1(y)contains a ball.Now,for every s in S2,g−1(s)iscontained in a(unique)ﬁber of F|X2.It follows that F induces a deﬁnable surjection S2→F(X2).If Y=F(X2),then we get a contradiction to(b2).If Y=F(X2) then there exists a point y∈Y with F−1(y)=F|X1−1(y)which does not contain a ball as shown above.We now prove(†),in a similar way.Let Y be a ball and let F:X⊂S×M→Y be a deﬁnable surjection with S auxiliary.By(b3)and by compactness(as in the proof of Lemma2.3.1)we can consider a map g:X→S×S′over S such that, for every t in g(X),the restriction F|g−1(t)is either injective or constant.For s in S,set X s=X∩({s}×M).Consider the deﬁnable subset S1of g(X)consisting of all points t such that F|g−1(t)is injective and set X1:=g−1(S1),S2:=g(X)\S1b-MINIMALITY7and X2:=g−1(S2).Suppose that for some y∈Y the set p(F−1|X1(y))contains a ballT0,with p the projection to M.Of course we can identify any subset of X s with a subset of M by projecting on the M-coordinate.When we do so we have the following helpful claim.Claim.The set X s∩F−1|X1(y)contains a ball T for some s(after identiﬁ-cation with a subset of M by projecting on the M-coordinate).Weﬁrst prove the claim.Denote by C s the set X s∩F−1|X1(y).Suppose by contradictionthat,for all s,the set C s contains no ball.Apply(b1)to the sets C s for all s.Since C s contains no balls,weﬁnd b-maps f s:C s→S s for some auxiliary sets S s such that the nonemptyﬁbers of the f s are points.But then by compactness weﬁnd a single b-map f′:p(F−1|X1(y))→S′for some auxiliary S′such that all nonemptyﬁbersof f′are points.Since we have supposed that p(F−1|X1(y))contains the ball T0,therestriction of f′to T0gives a deﬁnable bijection between T0and an auxiliary set. This is a contradiction to(b2)and the claim is proven.By the claim g is injective on T,which again gives a contradiction to(b2).Hence,no set of the form p(F−1|X1(y)) contains a ball.Now,for every t in S2,g−1(t)is contained in a(unique)ﬁber of F|X2.It follows that F induces a deﬁnable surjection S2→F(X2).If Y=F(X2), then we have a contradiction to(b2).If Y=F(X2)then there exists a point y∈Y with F−1(y)=F|X1−1(y)which does not contain a ball as shown above.2.4.4Lemma.—Let T be an L-theory with all its models satisfying(b1),(b2) and condition(∗).Suppose that there are at least two∅-deﬁnable auxiliary points. Then T satisﬁes(b3).Proof.—Let M be a model of T and let F:X→Y be A-deﬁnable with X,Y subsets of M.We may work piecewise on A-deﬁnable sets since there are at least two∅-deﬁnable auxiliary points.Let Y1be the deﬁnable subset of Y consisting of thosey∈Y such that F−1(y)contains a ball.Let f1:Y1→S1be a b-map on Y1.By(∗), allﬁbers of f1are points.Taking X1:=F−11(Y1)and f′1:X1→S1:x→f1(F(x)), we see that f′1is compatible with F|X1.Hence we may suppose that Y1is empty. LetΓF be the graph of F.Take a b-map f2:ΓF→Y×S ofΓF over Y(thus not over X).Deﬁnef:X→S:x→p S◦f2(x,F(x)),with p S the projection Y×S→S.Then clearly f is compatible with F|X.Indeed,all ﬁbers of f2are points,thus for x1=x2in X either f(x1)=f(x2),or F(x1)=F(x2).The functions f i and f can clearly be taken A-deﬁnable so(b3)follows.2.4.5Lemma.—Let T be any L-theory with all its models satisfying condition (†).Then all models of T satisfy(b2).Proof.—Suppose by contradiction to(b2)that Y is a ball and thatg:S→Y8RAF CLUCKERS&FRANC¸OIS LOESERis deﬁnable and surjective,with S auxiliary.Let T be a ball.Then the mapF:X→Y:(s,t)→g(s)with X=S×T contradicts(†).2.4.6Corollary.—Let T be any L-theory which satisﬁes(b1)and condition(†) for all its models M.Suppose that there are at least two∅-deﬁnable auxiliary points. Then T satisﬁes(b3)for all its models.Proof.—Follows by Lemmas2.4.4and2.4.5by noticing that M satisﬁes(∗)when-ever it satisﬁes(†).3.Cell decompositionLet L be any expansion of L B,as before,and let M be an L-model.Cells are deﬁned by induction on the number of variables.3.1.Cells.—Let X⊂M be deﬁnable and f:X→S a deﬁnable function with S auxiliary.If allﬁbers of f are balls,then we call(X,f)a(1)-cell with presentation f.If allﬁbers of f are points,then we call(X,f)a(0)-cell with presentation f. For short,we call such X a cell and f its presentation.Let X⊂M n be deﬁnable and let(j1,...,j n)be in{0,1}n.Let p:X→M n−1 be a coordinate projection.We call X a(j1,...,j n)-cell with presentationf:X→Sfor some auxiliary S,if for eachˆx:=(x1,...,x n−1)∈p(X),the set p−1(ˆx)⊂{ˆx}×M,identiﬁed with a subset of M via the projection{ˆx}×M→M,is a (j n)-cell with presentationp−1(ˆx)→S:x n→f(ˆx,x n)and p(X)is a(j1,...,j n−1)-cell with some presentationf′:p(X)→S′satisfying f′◦p=p′◦f for some deﬁnable p′:S→S′.(2)b-MINIMALITY9 3.2.Relative cells.—In the relative setting,when Y and X⊂M n×Y are deﬁnable sets,we say that X together with a deﬁnable function f:X→S×Y commuting with the projectionsπ:X→Y and S×Y→Y and with S auxiliary is a(j1,...,j n)-cell over Y with presentationf:X→S×Yif the following holds with p:M n×Y→M n−1×Y a coordinate projection.For each(ˆx,y):=(x1,...,x n−1,y)∈p(X),the set p−1(ˆx,y)⊂{ˆx}×M×{y},identiﬁed with a subset of M via the projection{ˆx}×M×{y}→M,is a(j n)-cell with presentationp−1(ˆx,y)→S:x n→f(ˆx,x n,y)and p(X)is a(j1,...,j n−1)-cell over Y with some presentationf′:p(X)→S′×Ysatisfying f′◦p=p′◦f for some p′:S×Y→S′×Y.3.3.b-maps.—Let X⊂M n and f:X→S be deﬁnable with S auxiliary.By induction on the variables,with p:X→M n−1the coordinate projection on theﬁrst n−1variables,f is called a b-map on X when for eachˆx:=(x1,...,x n−1)∈p(X), the functionp−1(ˆx)→S:x n→f(ˆx,x n)is a b-map on p−1(ˆx)as in section2.2,and there exists some b-mapf′:p(X)→S′satisfying f′◦p=p′◦f for some p′:S→S′.Working relatively,for X⊂M n×Y a deﬁnable set,we say that a deﬁnable function f:X→S×Y over Y is a b-map on X over Y if there is a projection p:X→M n−1×Y such that for every(ˆx,y)∈p(X)the restriction of f to p−1(ˆx,y) (also here identiﬁed with a subset of M)is a b-map on p−1(ˆx,y)and there is a b-map f′:p(X)→S′×Y on p(X)over Y and a deﬁnable function p′:S×Y→S′×Y satisfying f′◦p=p′◦f.3.4Remark.—The ordering of coordinates on M n used for cells and b-maps,is usually implicitly chosen.Such a choice appears also in the deﬁnitions of o-minimal and p-adic cells.3.5Lemma-Deﬁnition(types of cells).—Let M be a model of a b-minimal theory.Let Y and X⊂M n×Y be deﬁnable sets.If X is a(i1,...,i n)-cell over Y, then X is not a(i′1,...,i′n)-cell over Y(for the same ordering of the factors of M n) for any tuple(i′1,...,i′n)diﬀerent from(i1,...,i n).We call(i1,...,i n)the type of the cell X.Proof.—By induction on n.For n=1,this follows from(b2),cf.Remark2.2.2. The image X′of X under the projection p n:M n×Y→M n−1×Y is a(i1,...,i n−1)-cell over Y and by induction this type is unique.Assume now X is at the same time a(i1,...,i n−1,0)-cell over Y and a(i1,...,i n−1,1)-cell over Y.This means that X10RAF CLUCKERS&FRANC¸OIS LOESERis at the same time a(1)-cell and a(0)-cell over M n−1×Y which is impossible again by(b2).3.6Lemma-Deﬁnition(Reﬁnements).—Let M be a model of a b-minimal theory.Let Y and X⊂M n×Y be deﬁnable.Then there exists a b-map on X over Y.Moreover,any two b-maps f:X→S×Y,f′:X→S′×Y over Y have a common reﬁnement,namely,a b-map f′′:X→S′′×Y over Y with(automatically unique)deﬁnable mapsλ:f′′(X)→S×Y andµ:f′′(X)→S′×Y such that λ◦f′′=f andµ◦f′′=f′.Proof.—By compactness(as in the proof of Lemma2.3.1)and induction on n(as in the proof of Lemma3.5).Indeed,for n=1,the existence of a b-map on X over Y follows clearly by compactness.For n>1,let f0:X→S0×M n−1×Y be a b-map over M n−1×Y which exists by the result for n=1.Next,write p(X)for the image of X under the coordinate projection p:M n×Y→M n−1×Y.By induction,there exists a b-map f′:p(X)→S′×Y over Y.Now let f:X→S′×S0×Y be the deﬁnable function x∈X→(π′f′(p(x)),f0(x))withπ′:S′×Y→S′the coordinate projection.Then f is a b-map over Y as desired since clearly f′◦p=p′◦f with p′:S′×S0×Y→S′×Y the coordinate projection.This proves the existence of b-maps on X over Y.The construction of the reﬁnements is done as in the proof of Lemma2.3.1.3.7Theorem(Cell decomposition).—Let M be a model of a b-minimal the-ory.Let Y and X⊂M n×Y be deﬁnable sets.Then there exists aﬁnite partition of X into cells over Y.Proof.—Same proof as for Lemma3.6.3.8Deﬁnition(Reﬁnements of cell decompositions)Let Y and X⊂M n×Y be deﬁnable sets.Let P and P′be twoﬁnite partitions of X into cells(X i,f i),resp.(X′j,f′j),over Y.We call P′a reﬁnement of P when for each j there exists i such thatX′j⊂X iand such that f′j is a reﬁnement of f i|X′j in the sense of Lemma-Deﬁnition3.6,or inother words,for each b∈f′j(X′j),there exists a(necessarily unique)a∈f i|X′j (X′j)such thatf′j−1(b)⊂f−1i(a).3.9Lemma.—Let M be a model of a b-minimal theory.Let Y and X⊂M n×Y be deﬁnable sets.Then any two cell decompositions of X over Y admit a common reﬁnement.Proof.—As for Lemma2.3.1.3.10Remark.—In fact,the results of this section on cell decomposition already hold for a theory satisfying only(b1)and(b2)for all its models.b-MINIMALITY114.Dimension theoryWe now develop a dimension theory for b-minimal structures along similar lines as what is done for o-minimal theories,cf.[18].In what follows L is any expansion of L B as before and M is an L-model.4.1Deﬁnition.—The dimension of a nonempty deﬁnable set X⊂M n is deﬁned as the maximum of all sumsi1+...+i nwhere(i1,...,i n)runs over the types of all cells contained in X,for all orderings of the n factors of M n.To the empty set we assign the dimension−∞.If X⊂S×M n is deﬁnable with S auxiliary,the dimension of X is deﬁned as the dimension of p(X)with p:S×M n→M n the projection.When F:X→Y is an L-deﬁnable function,the dimension of X over Y is deﬁned as the maximum of the dimensions of theﬁbers F−1(y)over all y∈Y.(Of course,the dimension of X over Y depends on F.)We write dim(X/Y)for the dimension of X over Y,and dim(X)for the dimension of X.The dimension of X over Y is also called the relative dimension of X over Y (along F).Usually,F is implicit and X is just called a deﬁnable set over Y,see the discussion below Deﬁnition2.2.1.4.2Proposition.—Let M be a model of a b-minimal theory.Let Y,W,Z be deﬁnable sets,let X be a(i1,...,i n)-cell over Y,and let A,B,C be deﬁnable sets over Y with A,B⊂C.Then(0)dim(X/Y)=i1+...+i n,(1)dim(A∪B/Y)=max(dim(A/Y),dim(B/Y)),(2)dim(W×Z)=dim(W)+dim(Z).Proof.—Let us prove(0).First we notice that for any deﬁnable subset E⊂Xwhich is a(i E1,...,i En)-cell over Y,with the same ordering of coordinates,one hasi Ej ≤i j for j=1,...,n.For n=1,this follows from(b2),and for n>1this isproven by induction on n similarly as in the proof of Lemma-Deﬁnition3.5.Next we show that for any deﬁnable subset E⊂X which is a(i E1,...,i En)-cell over Y with respect to a diﬀerent order of the coordinates on M n,one hasi E1+...+i En≤i1+...+i n.This is clear for n=1,so let us consider the casen=2.We may assume Y is a point.Assumeﬁrst that i E1=i E2=1.We wantto prove that i1=i2=1.By(b2),or rather by Remark2.2.2,oneﬁnds i1=1. Denote by p2X:M2→M and p1X:M→M0the projections corresponding to the order of coordinates for the cell X,and by p2E:M2→M and p1E:M→M0the projections corresponding to the order of coordinates for the cell E.We may assume that the image of E by p2E is a ball T and that allﬁbers of the restriction of p2E to E contain a ball,since E is a(1,1)-cell.Assume now that i2=0.This means that X is a0-cell over M with respect to the projection p2X,thus,there exists an injective map g:X→S×M over M,with S auxiliary.Hence,the mapF:=p2E◦g|E−1:g(E)→M12RAF CLUCKERS&FRANC¸OIS LOESERgives a surjection from g(E)to the ball T.Moreover,pF−1(t)contains a ball for each t∈T with p:S×M→M the projection,which contradicts condition(†)of Lemma2.4.2.To conclude the case n=2,it is enough to prove that if i1=i2=0,theni E1=i E2=0.But if i1=i2=0,then X is deﬁnably isomorphic to a deﬁn-able subset of some auxiliary sorts,which makes it impossible for E to contain aball by(b2),hence forces i E1=i E2=0.Now for general n,it is enough to con-sider a transposition((x1,...,x j,x j+1),...,x n)→((x1,...,x j+1,x j),...,x n)of two adjacent coordinates.By induction on n and by projecting onto theﬁrst j+1coor-dinates,x1,...,x j+1,one may suppose that j+1=n and one reduces to the cases already considered.Statement(0)follows.Proving(1)amounts to showing that if X is a(i1,...,i n)-cell over Y and X j is aﬁnite partition of X into(i j1,...,i jn)-cells with respect to the same ordering of the coordinates,then max j(i j1+...+i jn)=dim X,which is clear when n=1 and follows by induction on n when n>1.Property(2)is clear by the previous properties since partitions of W and Z into cells induce a partition of W×Z into cells.Recall that,in our terminology,a deﬁnable set over another deﬁnable set has the meaning as explained after Deﬁnition2.2.1.4.3Proposition.—Let M be a model of a b-minimal theory.Let Y be a deﬁnable set,let X and X′be deﬁnable sets over Y,and let f:X→X′be a deﬁnable function over Y,that is,compatible with the maps to Y.Then(3)dim(X)≥dim(f(X)),hence also dim(X/Y)≥dim(f(X)/Y).(4)For each integer d≥0the set S f(d):={x′∈X′|dim(f−1(x′)/Y)=d}isdeﬁnable anddim(f−1(S f(d))/Y)=dim(S f(d)/Y)+d,with the convention−∞+d=−∞.(5)If Y is auxiliary,then dim(X/Y)=dim(X).Proof.—Weﬁrst prove(5).We reduce to the case that X is a deﬁnable subset of M n×Y,as follows.By the deﬁnition of relative dimensions we may replace X be the graph of X→Y so that X becomes a deﬁnable subset of M n×S×Y for some auxiliary S and some n≥0.Again by the deﬁnition of relative dimensions,we may replace Y by S×Y to conclude our reduction to the case that X is a deﬁnable subset of M n×Y.By property(1)of Proposition4.2and Theorem3.7we may then suppose that X is a(i1,...,i n)-cell over Y.Now(5)follows similarly to the way that(0)of Proposition4.2is ly,if n=1,(5)follows from(b2), for n=2it follows from property(†),and for n>2one uses induction.For(3)and(4),we may suppose that Y is a point,since relative dimension over Y is deﬁned as the maximum of the dimensions of theﬁbers of y∈Y.For(4),letΓf⊂X′×X be the graph of f(more precisely,the transpose of the graph).We have X⊂M n×S and X′⊂M m×S′for some auxiliary sets S and。

On a Conjecture of EM Stein on the Hilbert Transform on Vector Fields

v
Preface
This memoir is devoted to a question in planar Harmonic Analysis, a subject which is a circle of problems all related to the Besicovitch set. This anomalous set has zero Lebesgue measure, yet contains a line segment of unit length in each direction of the plane. It is a known, since the 1970’s, that such sets must necessarily have full Hausdorﬀ dimension. The existence of these sets, and the full Hausdorﬀ dimension, are intimately related to other, independently interesting issues [26]. An important tool to study these questions is the so-called Kakeya Maximal Function, in which one computes the maximal average of a function over rectangles of a ﬁxed eccentricity and arbitrary orientation. Most famously, Charles Feﬀerman showed [10] that the Besicovitch set is the obstacle to the boundedness of the disc multiplier in the plane. But as well, this set is intimately related to ﬁner questions of Bochner-Riesz summability of Fourier series in higher dimensions and space-time regularity of solutions of the wave equation. This memoir concerns one of the ﬁner questions which center around the Besicovitch set in the plane. (There are not so many of these questions, but our purpose here is not to catalog them!) It concerns a certain degenerate Radon transform. Given a vector ﬁeld v on R2 , one considers a Hilbert transform computed in the one dimensional line segment determined by v , namely the Hilbert transform of a function on the plane computed on the line segment {x + tv (x) | |t| ≤ 1}. The Besicovitch set itself says that choice of v cannot be just measurable, for you can choose the vector ﬁeld to always point into the set. Finer constructions show that one cannot take it to be H¨ older continuous of any index strictly less than one. Is the sharp condition of H¨ older continuity of index one enough? This is the question of E. M. Stein, motivated by an earlier question of A. Zygmund, who asked the same for the question of diﬀerentiation of integrals. The answer is not known under any condition of just smoothness of the vector ﬁeld. Indeed, as is known, and we explain, a positive answer would necessarily imply Carleson’s famous theorem on the convergence of Fourier series, [6]. This memoir is concerned with reversing

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Nobel laureates in the center
Nobel Prize in physiology or medicine (1990)
Nobel Prize in physiology or medicine (2004)
Nobel Prize in physiology or medicine (2001)
The Fred Hutchinson Cancer Research Center
The Fred Hutchinson Cancer Research Center is a world leader in research to understand, treat and prevent cancer and other life-threatening diseases.
The Cancer Killer
Yao Qiang Renal Division, Renji Hospital, SSMU 2005.5
Words in the short
Treatment with drugs that kill cancer cells. Chemotherapy The use of high-energy radiation from x-rays, gamma rays, neutrons, and other sources to kill cancer cells and shrink tumors . Radiotherapy Radiation may come from a machine outside the body (externalbeam radiation therapy), or it may come from radioactive material placed in the body near cancer cells (internal radiation therapy, implant radiation, or brachytherapy). Systemic radiotherapy uses a radioactive substance, such as a radiolabeled monoclonal antibody, that circulates throughout the body. Also called radiation therapy. Treatment using more than one anticancer drug. Chemical combination (combination chemotherapy)

研究生英语提高级 A Beautiful Mind课文翻译

A Beautiful MindSylvia Nasar[1] John Forbes Nash, Jr.— mathematical genius, inventor of a theory of rational behavior, visionary of the thinking machine—had been sitting with his visitor, also a mathematician, for nearly half an hour. It was late on a weekday afternoon in the spring of 1959, and, though it was only May, uncomfortably warm. Nash was slumped in an armchair in one corner of the hospital lounge, carelessly dressed in a nylon shirt that hung limply over his unbelted trousers. His powerful frame was slack as a rag doll's, his finely molded features expressionless. He had been staring dully at a spot immediately in front of the left footof Harvard professor George Mackey, hardly moving except to brush his long dark hair away from his forehead in a fitful, repetitive motion. His visitor sat upright, oppressed by the silence, acutely conscious that the doors to the room were locked. Mackey finally could contain himself no longer. His voice was slightly querulous, but he strained to be gentle. "How could you," began Mackey, "how could you, a mathematician, a man devoted to reason and logical proof...how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you...?"[2] Nash looked up at last and fixed Mackey with an unblinking stare as cooland dispassionate as that of any bird or snake. "Because," Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, "the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously."[3] The young genius from Bluefield, West Virginia—handsome, arrogant, and highly eccentric—burst onto the mathematical scene in 1948. Over the next decade, a decade as notable for its supreme faith in human rationality as for its dark anxieties about mankind's survival, Nash proved himself, in the words of the eminent geometer Mikhail Gromov, "the most remarkable mathematician of the second half of the century." Games of strategy, economic rivalry, computer architecture, the shape of the universe, the geometry of imaginary spaces, the mystery of prime numbers—all engaged his wide-ranging imagination. His ideas were of the deep and wholly unanticipated kind that pushes scientific thinking in new directions.[4] Geniuses, the mathematician Paul Halmos wrote, "are of two kinds: the ones who are just like all of us, but very much more so, and the ones who, apparently, have an extra human spark. We can all run, and some of us can run the mile in less than 4 minutes; but there is nothing that most of us can do that compares with the creation of the Great G-minor Fugue ." Nash's genius was of that mysterious variety more often associated with music and art than with the oldest of all sciences: It wasn't merely that his mind worked faster, that his memory was more retentive, or that his power of concentration was greater. The flashes of intuition were nonrational. Like other great mathematical intuitionists—Georg Friedrich Bernhard Riemann, Jules Henri Poincaré, Srinivasa Ramanujan—Nash saw the vision first; constructing the laborious proofs long afterward. But even after he'd try to explain some astonishing result, the actual route he had taken remained a mystery to others who tried to follow his reasoning. Donald Newman, a mathematician who knew Nash at MIT in the 1950s, used to say about him that "everyone else would climb a peak by looking for a path somewhere on the mountain. Nash would climb anothermountain altogether and from that distant peak would shine a searchlight back onto the first peak".[5] No one was more obsessed with originality, more disdainful of authority, or more jealous of his independence. As a young man he was surrounded by the high priests of twentieth-century science—Albert Einstein, John von Neumann, and Norbert Wiener—but he joined no school, became no one's disciple, got along: largely without guides or followers. In almost everything he did—from game theory to geometry—he thumbed his nose at the received wisdom, current fashions, established methods. He almost always worked alone, in his head, usually walking, often whistling Bach. Nash acquired his knowledge of mathematics not mainly from studying what other mathematicians had discovered, but by rediscovering their truths for himself. Eager to astound, he was always on the lookout for the really big problems. When he focused on some new puzzle, he saw dimensions that people who really knew the subject (he never did) initially dismissed as naive or wrong-headed. Even as a student, his indifference to others' skepticism, doubt, and ridicule was awesome.[6] Nash's faith in rationality and the power of pure thought was extreme, even for a very young mathematician and even for the new age of computers, space travel, and nuclear weapons. Einstein once chided him for wishing to amend relativity theory without studying physics. His heroes were solitary thinkers and supermen like Newton and Nietzsche. Computers and science fiction were his passions. He considered "thinking machines", as he called them, superior in some ways to human beings. At one point, he became fascinated by the possibility that drugs could heighten physical and intellectual performance. He was beguiled by the idea of alien races of hyper-rational beings who had taught themselves to disregard allemotion. Compulsively rational, he wished to turn life's decisions—whether to take the first elevator or wait for the next one, where to bank his money, what job to accept, whether to marry—into calculations of advantage and disadvantage, algorithms or mathematical rules divorced from emotion, convention, and tradition. Even the small act of saying an automatic hello to Nash in a hallway could elicit a furious "Why are you saying hello to me?"[7] His contemporaries, on the whole, found him immensely strange. They described him as "aloof", "haughty", "without affect", "detached", "spooky", "isolated", and "queer". Nash mingled rather than mixed with his peers. Preoccupied with his own private reality, he seemed not to share their mundane concerns. His manner—slightly cold, a bit superior, somewhat secretive—suggested something "mysterious and unnatural". His remoteness was punctuated by flights of garrulousness about outer space and geopolitical trends, childish pranks, and unpredictable eruptions of anger. But these outbursts were, more often than not, as enigmatic as his silences. "He is not one of us" was a constant refrain. A mathematician at the Institute for Advanced Study remembers meeting Nash for the first time at a crowded student party at Princeton:I noticed him very definitely among a lot of other people who were there. He was sitting on the floor in a half-circle discussing something. He made me feel uneasy. He gave me a peculiar feeling. I had a feeling of a certain strangeness. He was different in some way. I was not aware of the extent of his talent. I had no idea he would contribute as much as he really did.[8] But he did contribute, in a big way. The marvelous paradox was that the ideas themselves were not obscure. In 1958, Fortune singled Nash out for his achievements in game theory, algebraic geometry, and nonlinear theory, calling him the most brilliant of the younger generation of new ambidextrous mathematicians who worked in both pure and applied mathematics. Nash's insight into the dynamics of human rivalry—his theory of rational conflict and cooperation—was to become one of the most influential ideas of the twentieth century, transforming the young science of economics the way that Mendel's ideas of genetic transmission, Darwin's model of natural selection, and Newton's celestial mechanics reshaped biology and physics in their day.第六课美丽心灵西尔维亚•纳萨尔[1]小约翰•福布斯•纳什，数学天才、理性行为理论创立者、预见会思考的机器出现的预言者，已经和他的同样是数学家的来访者一起坐了差不多半个小时。

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A New Heuristic for Rectilinear Steiner Trees
Ion I. Mandoiu Vijay V. Vazirani Joseph L. Ganleyy
1 Introduction
The Steiner tree problem is that of nding a minimum-length interconnection of a set of points in the plane, and has long been one of the fundamental problems in the eld of electronic design automation. Although recent advances of integrated circuit technology into the deep-submicron realm have introduced additional routing objective functions, the Steiner tree problem retains its importance: For non-critical nets, or in physically small instances, minimum length is still frequently a good objective function, since a minimumlength interconnection has minimum overall capacitance and occupies a minimum amount of area. Furthermore, the development of good algorithms for the Steiner tree problem often lays a foundation for expanding these algorithms to accommodate objective functions other than purely minimizing length. The rectilinear Steiner tree (RST) problem|in which the terminals are points in the plane and distances between them are measured in the L1 metric|has been the most-examined variant in electronic design automation, since IC fabrication technology typically mandates the use of only horizontal and vertical interconnect. The RST problem is NP-hard 8], and much e ort has been devoted to designing heuristic and approximation algorithms 1, 2, 5, 11, 13, 15, 16, 18, 24, 25, 26]. In an extensive survey of RST heuristics up to 1992 14], the Batched Iterated 1-Steiner (BI1S) heuristic of Kahng and Robins 15] emerged as the clear winner with an average improvement over the MST on terminals of almost 11%. Subsequently, two other heuristics 2, 16] have been reported to match the same performance. After a steady, but relatively slow progress 4, 6, 21], exact RST algorithms have recently witnessed spectacular progress 22]. The new release 23] of the GeoSteiner code by Warme, Winter, and Zachariasen has average running time comparable to the fast BI1S implementation of Robins 19] on random instances. We are thus faced with the paradoxical situation that an exact algorithm for an NP-hard problem has the same average running time as a state-of-the art heuristic for the problem. We try to remedy this situation by proposing a new RST heuristic. Our experiments show that the new heuristic has better average running time than both Robins' implementation of BI1S and the GeoSteiner code. Moreover, the new heuristic gives higher-quality solutions than BI1S on the average; of course, it cannot beat GeoSteiner in solution quality. Our results are obtained by exploiting a number of recent
fmandoiu,vaziranig@
y Cadence
College of Computing, Georgia Institute of Technology, Design Systems, ganley@
algorithmic and implementation ideas. On the algorithmic side, we build on the recent 3=2 approximation algorithm of Rajagopalan and Vazirani 17] for the metric Steiner tree problem on quasi-bipartite graphs; these are graphs that do not contain edges connecting pairs of Steiner vertices. This algorithm is based on the linear programming relaxation of a sophisticated integer formulation of the metric Steiner tree problem, called the bidirected cut formulation. It is well known that the RST problem can be reduced to the metric Steiner tree problem on graphs 10]; however, the graphs obtained from the reduction are not quasi-bipartite. We give an RV-based heuristic for nding Steiner trees in arbitrary (non quasi-bipartite) metric graphs. The heuristic, called Iterated RV (IRV), computes a Steiner tree of a quasi-bipartite subgraph of the original graph using the RV algorithm, in order to select a set of candidate Steiner vertices. The process is repeated with the selected Steiner vertices treated as terminals|thereby allowing the algorithm to pick larger quasi-bipartite subgraphs, and seek additional Steiner vertices for inclusion in the tree|until no further improvement is possible. The speed of our heuristic depends critically on the size of the quasi-bipartite subgraphs cohe size of the graphs that correspond to RST instances by applying reductions|deletion of edges and vertices that do not a ect the quality of the result. Our key edge reduction is based on Robins and Salowe's result that bounds the maximum degree of a rectilinear MST 20], and allows us to retain in the graph at most 4 edges incident to each Steiner vertex. Notably, this observation also formed the basis of a signi cant speed-up in the running time of BI1S 9], and is currently used in the implementation 19]. Our vertex reduction is based on the empty rectangle test that has its roots in the work of Berman and Ramaiyer 1] (see also 5, 25]). We ran experiments to compare our implementation of IRV against Robins' implementation of BI1S 19] and against the GeoSteiner code of Warme, Winter, and Zachariasen 23]. The results reported in Section 4 show that, on both random and real VLSI instances, our new heuristic produces on the average higher-quality solutions than BI1S. The quality improvement is not spectacular, around 0.03% from the cost of the MST on the average, but we should note that solutions produced by BI1S are themselves less than 0.5% away from optimum on the average|this leaves little space for improvement. More importantly, IRV's improvement in solution quality is achieved with an excellent running time. Our IRV code runs 4{8 times faster than GeoSteiner, and 2{8 times faster than Robins' implementation of BI1S on random instances 1