A permutation test for matching and its asymptotic distribution

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European Journal of Radiology 67(2008)218–229ReviewThe principles of quantiﬁcation applied toin vivo proton MR spectroscopyGunther Helms ∗MR-Research in Neurology and Psychiatry,Faculty of Medicine,University of G¨o ttingen,D-37075G¨o ttingen,GermanyReceived 27February 2008;accepted 28February 2008AbstractFollowing the identiﬁcation of metabolite signals in the in vivo MR spectrum,quantiﬁcation is the procedure to estimate numerical values oftheir concentrations.The two essential steps are discussed in detail:analysis by ﬁtting a model of prior knowledge,that is,the decomposition of the spectrum into the signals of singular metabolites;then,normalization of these signals to yield concentration estimates.Special attention is given to using the in vivo water signal as internal reference.©2008Elsevier Ireland Ltd.All rights reserved.Keywords:MRS;Brain;Quantiﬁcation;QAContents1.Introduction ............................................................................................................2192.Spectral analysis/decomposition..........................................................................................2192.1.Principles........................................................................................................2192.2.Statistical and systematic ﬁtting errors ..............................................................................2212.3.Examples of analysis software......................................................................................2212.3.1.LCModel ................................................................................................2212.3.2.jMRUI...................................................................................................2213.Signal normalization ....................................................................................................2233.1.Principles........................................................................................................2233.2.Internal referencing and metabolite ratios............................................................................2233.3.External referencing...............................................................................................2233.4.Global transmitter reference........................................................................................2233.5.Local ﬂip angle...................................................................................................2243.6.Coil impedance effects ............................................................................................2243.7.External phantom and local reference ...............................................................................2253.8.Receive only-coils ................................................................................................2253.9.Internal water reference............................................................................................2253.10.Partial volume correction.........................................................................................2264.Calibration .............................................................................................................2275.Discussion..............................................................................................................2286.Experimental ...........................................................................................................2287.Recommendations.......................................................................................................228Acknowledgements .....................................................................................................229References .............................................................................................................229∗Tel.:+495513913132;fax:+495513913243.E-mail address:ghelms@gwdg.de .0720-048X/$–see front matter ©2008Elsevier Ireland Ltd.All rights reserved.doi:10.1016/j.ejrad.2008.02.034G.Helms/European Journal of Radiology67(2008)218–2292191.IntroductionIn vivo MRS is a quantitative technique.This statement is often mentioned in the introduction to clinical MRS studies. However,the quantiﬁcation of signal produced by the MR imag-ing system is a complex and rather technical issue.Inconsistent terminology and scores of different approaches make the prob-lem appear even more complicated,especially for beginners. This article is intended to give a structured introduction to the principles of quantiﬁcation.The associated problems and pos-sible systematic errors(“bias”)are explained to encourage a critical appraisal of published results.Quantiﬁcation is essential for clinical research,less so for adding diagnostic information for which visual inspection often may sufﬁce.Subsequent to the identiﬁcation of metabolites,its foremost rationale is to provide numbers for comparison of spec-tra from different subjects and brain regions;and–ideally–different scanners and sequences.These numbers are then used for evaluation;e.g.statistical comparison of cohorts or correla-tion with clinical parameters.The problem is that the interaction of the radio-frequency(RF)hardware and the dielectric load of the subject’s body may lead to rather large signal variations(up to30%)that may blur systematic relationships to cohorts or clinical parameters.One of the purposes of quantiﬁcation is to reduce such hardware related variation in the numbers.Thus, quantiﬁcation is closely related to quality assurance(QA).In summary,quantiﬁcation is a procedure of data processing. The post-processing scheme may require additional data acqui-sitions or extraction of adjustment parameters from the scanner. The natural order of steps in the procedure is1.acquisition and pre-processing of raw data,reconstruction ofthe spectrum(e.g.averaging and FFT),2.analysis:estimation of the relative signal for each identiﬁedmetabolite(here,proton numbers and linewidth should be taken into account),3.normalization of RF-induced signal variations,4.calibration of signals by performing the quantiﬁcationscheme on a standard of known concentration.In turn,these steps yield the metabolite signals1.for visual inspection of the displayed spectrum on the ppmscale,2.in arbitrary units,from which metabolite ratios can be cal-culated,3.in institutional units(for your individual MR scanner andquantiﬁcation scheme;these numbers are proportional to the concentration),4.in absolute units of concentration(commonly inmM=mmol/l);estimated by comparison to a standard of known concentration.The term quantiﬁcation(or sometimes“quantitation”)is occasionally used to denote singular steps of this process.In this review,it will refer to the whole procedure,and further differ-entiation is made for the sake of clarity.In practice,some these steps may be performed together.Already at this stage it should be made clear that the numbers obtained by“absolute quantiﬁca-tion”are by no means“absolute”but depend on the accuracy and precision of steps1–4.Measurement and reconstruction(step1) must be performed in a consistent way lest additional errors have to be accounted for in individual experiments.Only in theory it should be possible to correct all possible sources of variation;in clinical practice it is generally is too time consum-ing.Yet the more sources of variation are cancelled(starting with the biggest effects)the smaller effects one will be able to detect.Emphasis will be put on the analysis(the models and the automated tools available),the signal normalization(and basic quality assurance issues),and the use of the localized water signal as internal reference.2.Spectral analysis/decomposition2.1.PrinciplesThe in vivo spectrum becomes more complicated with decreasing echo time(TE):next to the singlet resonances and weakly coupled multiplets,signals from strongly coupled metabolites and baseline humps from motion-restricted macro-molecules appear.Contrary to long-TE spectra short-TE spectra should not be evaluated step-by-step and line-by-line.For exam-ple,the left line of the lactate doublet is superposed onto the macromolecular signal at1.4ppm.The total signal at this fre-quency is not of interest but rather the separate contributions of lactate and macromolecules/lipids.Differences between the two whole resonance patterns can be used to separate the metabolites;e.g.the doublet of lactate versus the broad linewidth.In visual inspection,one intuitively uses such‘prior knowledge’about the expected metabolites to discern partly overlying metabolites in a qualitative way.This approach is also used to simplify the problem to automaticallyﬁnd the metabolite resonances to order to evaluate the whole spectrum“in one go”.Comparing the resonance pattern of MR spectra in vivo at highﬁeld and short TE with those of tissue extracts and sin-gle metabolites in vitro at matchedﬁeld strengths hasﬁrmly established our‘prior’knowledge about which metabolites con-tribute to the in vivo MR spectra[1].Next to TE,theﬁeld strength exerts the second biggest inﬂuence on the appearance of in vivo MR spectra.Overlap and degeneration of binomial multiplets due to strong coupling increase at the lowerﬁeld strengths of clinical MR systems(commonly3,2,or1.5T). These effects can be either measured on solutions of single metabolites[2]or simulated fromﬁrst quantum-mechanical principles,once the chemical shifts and coupling constants(J in Hz)of a certain metabolite have been determined at sufﬁ-ciently highﬁeld[3].Motion-restricted‘macromolecules’are subject to rapid relaxation that blurs the coupling pattern(if the linewidth1/πT∗2>J)and hampers the identiﬁcation of speciﬁc compounds.These usually appear as broad‘humps’that form the unresolved baseline of short-TE spectra(Fig.1).These vanish at longer TE(>135ms).The baseline underlying the metabo-220G.Helms /European Journal of Radiology 67(2008)218–229Fig.1.Including lipids/macromolecules into the basis set.Without inclusion of lipids/macromolecules in the basis set (A)the broad “humps”at 1.3and 0.9ppm are ﬁtted by the baseline.Inclusion of lipids/macromolecules (B)resulted in a better ﬁt and a lower baseline between 2.2and 0.6ppm.The SNR improved from 26to 30.The signals at 2.0ppm partly replaced the co-resonating tNAA.The 6%reduction in tNAA was larger than the ﬁtting error (3%).This may illustrate that the ﬁtting error does not account for the bias in the model.LCModel (exp.details:6.1-0;12.5ml VOI in parietal GM,3T,STEAM,TE/TM/TR/avg =20/10/6000/64).lite signals is constituted from all rapidly relaxing signals that have not decayed to zero at the chosen TE (macromolecules and lipids),the “feet”of the residual water signal,plus possible arte-facts (e.g.echo signals from moving spins that were not fully suppressed by gradient selection).The ‘prior knowledge’about which metabolites to detect and how the baseline will look like is used to construct a math-ematical model to describe the spectrum.Selecting the input signals reduces the complexity of the analysis problem.In con-trast to integrating or ﬁtting singlet lines the whole spectrum is evaluated together (“in one go”)by ﬁtting a superposition of metabolite signals and baseline signals.Thus,the in vivo spec-trum is decomposed into the constituents of the model.Without specifying the resonances this is often too complicated to be per-formed successfully,in the sense that an unaccountable number of ‘best’combinations exist.G.Helms/European Journal of Radiology67(2008)218–229221Prior knowledge may be implemented in the metabolite basis set adapting experimental data(like in LCModel[2]),theoretical patterns simulated fromﬁrst principles(QUEST[4]),or purely phenomenological functions like a superposition of Gaussians of different width to model strongly coupled signals and baseline humps alike(AMARES[5]).The least squaresﬁt may be per-formed in either time domain[6]or frequency domain or both [7].For an in-depth discussion of technical details,the reader is referred to a special issue of NMR in Biomedicine(NMR Biomed14[4];2001)dedicated to“quantitation”(in the sense of spectrum analysis)by mathematical methods.2.2.Statistical and systematicﬁtting errorsModelﬁtting yields the contribution of each input signal. Usually Cr´a mer–Rao lower bounds(CLRB)are provided as an estimate for theﬁtting error or the statistical uncertainty of the concentration estimate.These are calculated from the residual error and the Fisher matrix of the partial derivatives of the con-centrations.In the same way,correlations between the input data can be estimated.Overlapping input signals(e.g.from glutamate (Glu)and glutamine(Gln))are inversely correlated.In this case, the sum has a smaller error than the single metabolites.The uncertainties are fairly well proportional to the noise level(both must be given in the same units).The models are always an approximate,but never a com-plete description of the in vivo MR spectrum.Every model thus involves some kind of systematic error or“bias”,in the sense of deviation from the unknown“true”concentration.Contrary to the statistical uncertainty,the bias cannot be assessed within the same model.In particular,the CRLB does not account for the bias.Changes in the model(e.g.,by leaving out a minor metabo-lite)may result in systematic differences that soon become signiﬁcant(by a paired t-test).These are caused by the pro-cess of minimizing the squared residual difference whenﬁtting the same data by two different models.Spurious artefacts or“nuisance signals”that are not included in the model will results in errors that are neither statistical nor systematic.It is also useful to know,that for every non-linear function(as used in MRS)there is a critical signal-to-noise (SNR)threshold for convergence onto meaningful values.2.3.Examples of analysis softwareA number of models and algorithms have been published dur-ing the past15years.A few are available to the public and shared by a considerable number of users.These program packages are generally combined with some automated or interactive pre-processing features,such as correction of frequency offset,zero andﬁrst order,as well as eddy-current induced phase errors.We shall in brief describe the most common programs for analysis of in vivo1H MRS data.2.3.1.LCModelThe Linear Combination Model(LCModel)[2]comes as stand-alone commercial software(/ lcmodel).It comprises automated pre-processing to achieve a high degree of user-independence.An advanced regularization ensures convergence for the vast majority of in vivo spectra.It was theﬁrst program designed toﬁt a basis set(or library)of experimental single metabolite spectra to incorporate maximum information and uniqueness.This means that partly overlap-ping spectra(again such as,Glu and Gln)are discerned by their unique features,but show some residual correlation as mentioned above.Proton numbers are accounted for,even“frac-tional proton numbers”in“pseudo-singlets”(e.g.,the main resonance of mIns).Thus,the ratios provided by LCModel refer to the concentrations rather than proton numbers.The basis set of experimental spectra comprises the prior information on neurochemistry(metabolites)as well as technique(TE,ﬁeld strength,localization technique).The non-analytic line shape is constrained to unit area and capable toﬁt even distorted lines (due to motion or residual eddy currents).The number of knots of the baseline spline increases with the noise level.Thus,the LCModel is a mixture of experimental and phenomenological features.Although the basis spectra are provided in time domain, the evaluation is performed across a speciﬁed ppm interval.LCModel comes with a graphical user interface for routine application.Optionally the water signal may be used as quan-tiﬁcation reference.Recently,lipids and macromolecular signals have been included to allow evaluation of tumour and muscle spectra.An example is shown in Fig.1.LCModel comprises basic signal normalization(see below) according to the global transmitter reference[8]to achieve a consistent scaling of the basis spectra.An in-house acquired basis set can thus be used to estimate absolute concentrations. Imported basis sets are available for a wide range of scanners and measurement protocols,but require a calibration to match the individual sensitivity(signal level)of the MR system[9]. Owing to LCModel’sﬂexibility,the basis set may contain also simulated spectra or an experimentally determined baseline to account for macromolecular signals.Such advanced applica-tions require good theoretical understanding and some practical experience.Care must be taken to maintain consistent scaling when adding new metabolite spectra to an existing basis.This is easiest done by cross-evaluation,that is evaluating a reference peak(e.g.,formate)in spectrum to be included by the singlet of the original basis and correcting to the known value.Caveat:The fact that LCModel converges does not ensure reliability of the estimates;least in absolute units(see Sections 3and4).Systematic difference in SNR may translate into bias via the baseline spline(see Fig.2).The same may be due an inconsistent choice of the boundaries of the ppm interval,partic-ularly next to the water resonance.In particular,with decreasing SNR(lower than4)one may observe more often systematically low or high concentrations.This is likely due to the errors in the feet of the non-analytical line shape,as narrow lines lead to underestimation and broad lines to overestimation.The metabo-lite ratios are still valid,as all model spectra are convoluted by the same lineshape.2.3.2.jMRUIThe java-based MR user interface for the processing of in vivo MR-spectra(jMRUI)is provided without charge222G.Helms /European Journal of Radiology 67(2008)218–229Fig.2.Systematic baseline differences between low and high SNR.Single spectrum from an 1.7ml VOI in white matter of the splenium (A)and the averaged spectra of seven healthy subjects (B).Note how the straight baseline leads to a severe underestimation of all metabolites except mIns.Differences were most prominent for Glu +Gln:3.6mM (43%)in a single subject vs.6.7mM (7%)in the averaged spectrum.(http://www.mrui.uab.es/mrui/mrui Overview.shtml ).It comes with a wide range of pre-processing features and interac-tive graphical software applications,including linear prediction and a powerful water removal by Hankel–Laclosz single value decomposition (HLSVD).In contrast to LCModel,it is designed to support user interaction.Several models for analy-sis/evaluation have been implemented in jMRUI,in particular AMARES [5]and QUEST [4].These focus on time-domain analysis,including line shape conversion,time-domain ﬁlter-ing and eddy-current deconvolution.Note that in the context of jMRUI ‘quantitation’refers to spectrum analysis.The pre-processing steps may exert a systematic inﬂuence on the results of model ﬁtting.jMRUI can handle large data sets as from time-resolved MRS,two-dimensional MRS,and spatially resolved MRS,so-called MR spectroscopic imaging (MRSI)or chemical-shift imaging (CSI).G.Helms/European Journal of Radiology67(2008)218–2292233.Signal normalization3.1.PrinciplesThe signal is provided in arbitrary units of signed integer numbers,similar to MRI,and then converted toﬂoating complex numbers.In addition to scaling along the scanner’s receiver line, the proportionality between signal strength and number of spins per volume is strongly inﬂuenced by interaction of the RF hard-ware and its dielectric and conductive load,the human body.It is the correction of this interaction that forms the non-trivial part of signal normalization.Signal normalization is mainly applied to single-volume MRS,since spatially resolved MRSI poses addi-tional technical problems that are not part of this review.For sake of simplicity we assume homogeneous conditions across the whole volume-of-interest(VOI).Normalization consists of multiplications and divisions that render the signal,S,proportional to the concentration(of spins), C.Regardless whether in time domain(amplitude)or frequency domain(area),the signal is proportional to the size V of the VOI and the receiver gain R.S∼CVR or(1a) S/V/R∼C(1b) Logarithmic(decibel)units of the receiver gain must be con-verted to obtain a linear scaling factor,R.If R can be manually changed,it is advisable to check whether the characteristic of S(R)follows the assumed dependence.If a consistent(often the highest possible)gain used by default for single voxel MRS, one does not have to account for R.Correction of V for partial volume effects is discussed below.The proportionality constant will vary under the inﬂuence of the speciﬁc sample“loading”the RF coil.The properties of a loaded transmit–receive(T/R)coil are traditionally assessed by measuring the amplitude(or width)of a speciﬁc RF pulse,e.g., a180◦rectangular pulse.This strategy may also be pursued in vivo.The signal theory for T/R coils is given in concise form in [10]without use of complex numbers.Here,we develop it by presenting a chronology of strategies of increasing complexity that have been used for in vivo quantiﬁcation.3.2.Internal referencing and metabolite ratiosBy assuming a concentration C int for the signal(S int)of ref-erence substance acquired in the same VOI,one has not to care about the inﬂuence of RF or scanner parameters:SS intC int=C(2)When using the total creatine(tCr)signal,internal referencing is equivalent to converting creatine ratios to absolute units.In early quantiﬁcation work,the resonance of tCr has been assigned to 10mM determined by biochemical methods[11].However,it turned out that the MRS estimates of tCr are about25%lower and show some spatial dependence.In addition,tCr may increase in the presence of gliosis.3.3.External referencingThe most straightforward way is to acquire a reference sig-nal from an external phantom during the subject examination, with C ext being the concentration of the phantom substance [12,13].The reference signal S ext accounts for any changes in the proportionality constant.It may be normalized like the in vivo signal:S(VR)C extS ext/(V ext R ext)=C(3)If,however,the phantom is placed in the fringeﬁeld of the RF receive coil,the associated reduction in S ext will result in an overestimation of C.Care has to be taken to mount the external phantom reproducibly into the RF coil if this bias cannot be corrected otherwise.3.4.Global transmitter referenceAlready in high-ﬁeld MR spectrometers it has been noticed that by coil load the sample inﬂuences both the transmit pulse and the signal:a high load requires a longer RF pulse for a 90◦excitation,which then yields reciprocally less signal from the same number of spins.This is the principle-of-reciprocity (PoR)for transmit/receive(T/R)coils in its most rudimentary form.It has been applied to account for the coil load effect, that is,large heads giving smaller signals than small heads [8].On MRI systems,RF pulses are applied with constant duration and shape.A high load thus requires a higher volt-age U tra(or transmitter gain),as determined during pre-scan calibration.S/V/R∼Ctraor(4a) S U tra/V/R∼C(4b)Of course,U tra must always refer to a pulse of speciﬁc shape, duration andﬂip angle,as used forﬂip angle calibration.On Siemens scanners,the amplitude of a non-selective rectangu-lar pulse(rect)is used.The logarithmic transmitter gain of GE scanners is independent of the RF pulse,but has to be converted from decibel to linear units[9].Normalization by the PoR requires QA at regular intervals,as the proportionality constant in Eqs.((4a)and(4b))may change in time.This may happen gradually while the performance of the RF power ampliﬁer wears down,or suddenly after parts of the RF hardware have been replaced.For this purpose,the MRS protocol is run on a stable QA phantom of high concentration and the concentration estimate C QA(t i)obtained at time point, t i,is used to refer any concentration C back to time point zero byC→C C QA(t0)C QA(t i)(5)An example of serial QA monitoring is given in Fig.3.224G.Helms /European Journal of Radiology 67(2008)218–229Fig.3.QA measurement of temporal variation.Weekly QA performed on stable phantom of 100mM lactate and 100mM acetate from January 1996to June 1996.The standard single-volume protocol and quantiﬁcation procedure (LCModel and global reference)were applied.(A)The mean estimated concentration is shown without additional calibration.The A indicates the state after installation,B a gradual breakdown of the system;the sudden jumps were due to replacement of the pre-ampliﬁer (C and D)or head-coil (E),and retuning of the system (F).Results were used to correct proportionality to obtain longitudinally consistency.(B)The percentage deviation from the preceding measurement in Shewhart’s R-diagram indicates the weeks when quantiﬁcation may not be reliable (data courtesy of Dr.M.Dezortov´a ,IKEM,Prague,Czech Republic).3.5.Local ﬂip angleDanielsen and Hendriksen [10]noted that the PoR is a local relationship,so they used the amplitude of the water suppression pulse,U tra (x ),that had been locally adjusted on the VOI signal.S (x )U tra (x )/V/R ∼C(6)The local transmitter amplitude may also be found be ﬁtting the ﬂip angle dependence of the local signal [14].The example in Fig.4illustrates the consistency of Eq.(6)at the centre (high signal,low voltage)and outside (low signal,high voltage)the volume headcoil.Fig.4.Local veriﬁcation of the principle of reciprocity.Flip angle dependence of the STEAM signal measured at two positions along the axis of a GE birdcage head-coil by varying the transmitter gain (TG).TG was converted from logarith-mic decibel to linear units (linearized TG,corresponding to U tra ).At coil centre (×)and 5cm outside the coil (+)the received signal,S (x ),was proportional to the transmitted RF,here given by 1/lin TG(x )at the signal maximum or 90◦ﬂip angle.Like in large phantoms,there are considerable ﬂip angle devi-ations across the human head as demonstrated at 3T in Fig.5a [15].The local ﬂip angle,α(x ),may be related to the nominal value,αnom ,by α(x )=f (x )αnom(7)The spatially dependent factor is reciprocal to U tra (x ):f (x )∼1/U tra (x ).The ﬂip angle will also alter the local signal.If a local transmitter reference is used,S (x )needs to be corrected for excitation effects.For the ideal 90◦–90◦–90◦STEAM local-ization and 90◦–180◦–180◦PRESS localization in a T/R coil,the signals areS (x )STEAM ∼M tr (x )∼C2f (x )sin 3(f (x )90◦)(8a)S (x )PRESS ∼M tr (x )∼C f (x )sin 5(f (x )90◦)(8b)The dependence of S (x )was simulated for a parabolic RF proﬁle.A constant plateau is observed as the effects of transmission and reception cancel out for higher ﬂip angles in the centre of the head where the VOI is placed.This is the reason why the global ﬂip angle method works even in the presence of ﬂip angle inhomogeneities.Note that the signal drops rapidly for smaller ﬂip angles,i.e.close to the skull.3.6.Coil impedance effectsOlder quantiﬁcation studies were performed on MR systems where the coil impedance Z was matched to 50 [8,10].Since the early 1990s,most volume head coils are of the high Q design and approximately tuned and matched by the RF load of the head and the stray capacitance of the shoulders.The residual variation of the impedance Z will affect the signal by S (x )U tra (x )/V/R ∼CZ(9)G.Helms/European Journal of Radiology67(2008)218–229225Fig.5.Flip angle inhomogeneities across the human brain.(Panel A)T1-w sagittal view showing variation in the RFﬁeld.Flip angles are higher in the centre of the brain.The contours correspond to80–120◦localﬂip angle for a nominal value of90◦.(Panel B)The spatial signal dependence of STEAM and PRESS was simulated for a parabolicﬂip angle distribution with a maximum of115%relative to the global transmitter reference.This resulted in a constant signal obtained from the central regions of the brain,and a rapid decline at the edges.Reﬂection losses due to coil mismatch are symmetric in trans-mission and reception and are thus accounted for by U tra.These are likely to occur with exceptionally large or small persons (infants)or with phantoms of insufﬁcient load.3.7.External phantom and local referenceWhen the impedance is not individually matched to50 , the associated change in proportionality must be monitored by a reference signal.In aqueous phantoms,the water signal can be used as internal reference.For in vivo applications,one may resort to an extra measurement in an external phantom[14].An additionalﬂip angle calibration in the phantom will account for local differences in the RFﬁeld,especially if the phantom is placed in the fringe RFﬁeld:SU tra(x)/(VR)S ext U tra(x ext)/(V ext R ext)C ext=C(10)This is the most comprehensive signal normalization.The com-bination of external reference and localﬂip angle method corrects for all effects in T/R coils.The reference signal accounts for changes in the proportionality,while the localﬂip angle cor-rects for RF inhomogeneity.Note also that systematic errors in S,U tra and V cancel out by division.Calibration of each individual VOI may be sped up by rapid RF mapping in three dimensions.3.8.Receive only-coilsThe SNR of the MRS signal can be increased by using sur-face coils or phased arrays of surface coils.The inhomogeneous receive characteristic cannot be mapped directly.The normaliza-tions discussed above(except Section3.2)cannot be performed directly on the received signal,as the coils are not used for trans-mission.Instead,the localized water signal may be acquired with both the receive coil and the body coil to scale the low SNR metabolite signal to obey the receive characteristics of the T/R body coil[16,17]:S rec met S bodywaterS rec water=S bodymet(11)For use with phased array coils it is essential that the metabolite and water signals are combined using consistent weights,since the low SNR of the water suppressed acquisition is most likely inﬂuenced by noise.3.9.Internal water referenceThe tissue water appears to be the internal reference of choice, due to its high concentration and well established values for water content of tissues(βper volume[18]):SS waterβ55mol/litre=C(12)It should be kept in mind that in vivo water exhibits a wide range of relaxation times,with the main component relaxing consider-able faster than the main metabolites.T2-times range from much shorter(myelin-associated water in white mater T2of15ms)to much longer(CSF,2400ms in bulk down to700ms in sulci with large surface-to-volume ratio).This implies an inﬂuence of TE on the concentration estimates.In addition,relaxation time and water content are subject to change in pathologies.Since the water signal is increasing in most pathologies(by content and relaxation),water referencing tends to give lower concentration estimates in pathologies.Ideally,the water signal should be determined by a multi-componentﬁt of the T2-decay curve[12].An easy but time-consuming way is to increase TE in consecutive fully relaxed single scans.A reliable way to determine the water sig-nal is toﬁt a2nd order polynomial through theﬁrst50ms of the magnitude signal(Fig.6).Thus,determining the amplitude cancels out initial receiver instabilities and avoids lineﬁtting at an ill deﬁned phase.If care is taken to avoid partial saturation by RF leakage from the water suppression pulses,this is consistent with multi-echo measurements using a CPMG MRI sequence [18](Fig.7).。

高三英语学术研究方法创新不断探索单选题30题

高三英语学术研究方法创新不断探索单选题30题1. In academic research, a hypothesis is a ______ that is tested through experiments and observations.A. predictionB. conclusionC. theoryD. assumption答案：D。

本题考查学术研究中“假说”相关的基本概念。

选项A“prediction”意为“预测”，通常是基于现有信息对未来的估计；选项B“conclusion”指“结论”，是在研究后得出的最终判断；选项C“theory”是“理论”，是经过大量研究和验证形成的体系；选项D“assumption”表示“假定、设想”，更符合“假说”的含义，即在研究初期未经充分验证的设想。

2. The main purpose of conducting academic research is to ______ new knowledge and understanding.A. discoverB. createC. inventD. produce答案：A。

此题考查学术研究目的相关的词汇。

选项A“discover”意思是“发现”，强调找到原本存在但未被知晓的事物；选项B“create”意为“创造”，侧重于从无到有地造出新的东西；选项C“invent”指“发明”，通常指创造出新的工具、设备等；选项D“produce”有“生产、产生”的意思，比较宽泛。

在学术研究中，主要是“发现”新知识和理解，所以选A。

3. A reliable academic research should be based on ______ data and methods.A. accurateB. preciseC. correctD. valid答案：D。

本题关于可靠学术研究的基础。

选项A“accurate”侧重于“准确无误”，强调与事实完全相符；选项B“precise”意为“精确的、明确的”，更强调细节的清晰和明确；选项C“correct”指“正确的”；选项D“valid”表示“有效的、有根据的”，强调数据和方法具有合理性和可靠性。

高二英语数学建模方法单选题20题

高二英语数学建模方法单选题20题1.In the process of mathematical modeling, the factor that determines the outcome is called_____.A.independent variableB.dependent variableC.control variableD.extraneous variable答案：B。

本题考查数学建模中的基本术语。

独立变量（independent variable）是指在实验或研究中被研究者主动操纵的变量；因变量dependent variable）是指随着独立变量的变化而变化的变量，在数学建模中决定结果的因素通常是因变量；控制变量（control variable）是指在实验中保持不变的变量；无关变量（extraneous variable）是指与研究目的无关，但可能会影响研究结果的变量。

2.The statement “The value of y depends on the value of x” can be represented by a mathematical model where y is the_____.A.independent variableB.dependent variableC.control variableD.extraneous variable答案：B。

在“y 的值取决于x 的值”这句话中，y 是随着x 的变化而变化的变量，所以y 是因变量。

3.In a mathematical model, the variable that is held constant toobserve the effect on other variables is_____.A.independent variableB.dependent variableC.control variableD.extraneous variable答案：C。

高二英语科研项目实施单选题40题(带答案)

高二英语科研项目实施单选题40题(带答案)1.In the scientific research project, we need to collect data _____.A.accuratelyB.exactlyC.preciselyD.correctly答案：A。

“accurately”强调准确地，在科研项目中收集数据需要准确无误。

“exactly”表示确切地、完全地；“precisely”精确地，和“accurately”意思较为接近但在科研收集数据的场景下，“accurately”更常用；“correctly”正确地，通常用于方法等正确，不太符合收集数据的语境。

2.When presenting the research results, we should express our ideas _____.A.clearlyB.obviouslyC.apparentlyD.visibly答案：A。

“clearly”清晰地，在展示研究结果时要表达清晰。

“obviously”明显地；“apparently”显然地；“visibly”看得见地，后三个选项不太符合表达想法的语境。

3.The scientific research project requires ______ teamwork.A.cohesiveB.unitedC.cooperativeD.joined答案：C。

“cooperative”合作的，科研项目需要合作的团队合作。

“cohesive”有结合力的；“united”联合的；“joined”连接的，这三个选项不太符合团队合作的语境。

4.We must analyze the data ______ to draw accurate conclusions.A.thoroughlypletelyC.entirelyD.wholely答案：A。

“thoroughly”彻底地，分析数据需要彻底才能得出准确结论。

Orthogonal matching pursuit recursive function approximation with

A shortcoming of the Matching Pursuit algorithm in its originally proposed form is that although asymptotic convergence is guaranteed, the resulting approximation after any nite number of iterations will in general be suboptimal in the following sense. Let N < 1,
2 Orthogonal Matching Pursuit
Assume we have the following kth-order model for f 2 H,
1 Introduction Fra biblioteknd Background
Given space H,
a collection of let us de ne
vectors
D
=
fxig
in
a
Hilbert
V = Spanfxng; and W = V? (in H):
We shall refer to D as a dictionary, and will assume the vectors xn, are normalized (kxnk = 1). In 3] Mallat and Zhang proposed an iterative algorithm that they termed Matching Pursuit (MP) to construct representations of the form
/ To appear in Proc. of the 27th Annual Asilomar Conference on Signals Systems and Computers, Nov. 1{3, 1993 /

prevision tasks for specific patterns翻译版

I. Discuss the translation technique and the ways of applying the technique to the translation of the following sentences. Complete each of the Chinese translations.1. We have come to the last and most important step of the experiment.我们的实验现在已经到了最后（一步，也就是)最重要的阶段。

2. This is extruded through minute holes in a nozzle, and the threads of filaments produced and solidified in various ways. 现将该物质从喷嘴的小孔中挤压出来，(并)将产生的纤维丝利用各种方法固化。

3. Thousands of the electric power generators, often installed on windfarms in North America and Europe, now total over 800 megawatts of rated capacity, and their numbers are continuing to grow. 数以千计的风力发电机大多安装在北美和欧洲的风力发电场，其总额定功率现已达800兆瓦，(其)数量仍在继续增加。

4. Solid silicones serve, among other things, as a kind of artificial rubber, and liquid silicones have been used as hydraulic fluids. 固体硅酮的用途很广，其中之一是用作人工橡胶，(而)液体硅酮则被用作各种液压流体。

自然语言处理及计算语言学相关术语中英对译表三_计算机英语词汇

multilingual processing system 多语讯息处理系统multilingual translation 多语翻译multimedia 多媒体multi-media communication 多媒体通讯multiple inheritance 多重继承multistate logic 多态逻辑mutation 语音转换mutual exclusion 互斥mutual information 相互讯息nativist position 语法天生假说natural language 自然语言natural language processing (nlp) 自然语言处理natural language understanding 自然语言理解negation 否定negative sentence 否定句neologism 新词语nested structure 崁套结构network 网络neural network 类神经网络neurolinguistics 神经语言学neutralization 中立化n-gram n-连词n-gram modeling n-连词模型nlp (natural language processing) 自然语言处理node 节点nominalization 名物化nonce 暂用的non-finite 非限定non-finite clause 非限定式子句non-monotonic reasoning 非单调推理normal distribution 常态分布noun 名词noun phrase 名词组np (noun phrase) completeness 名词组完全性object 宾语{语言学}/对象{信息科学}object oriented programming 对象导向程序设计[面向对向的程序设计]official language 官方语言one-place predicate 一元述语on-line dictionary 线上查询词典 [联机词点]onomatopoeia 拟声词onset 节首音ontogeny 个体发生ontology 本体论open set 开放集operand 操作数 [操作对象]optimization 最佳化 [最优化]overgeneralization 过度概化overgeneration 过度衍生paradigmatic relation 聚合关系paralanguage 附语言parallel construction 并列结构parallel corpus 平行语料库parallel distributed processing (pdp) 平行分布处理paraphrase 转述 [释意;意译;同意互训]parole 言语parser 剖析器 [句法剖析程序]parsing 剖析part of speech (pos) 词类particle 语助词part-of relation part-of 关系part-of-speech tagging 词类标注pattern recognition 型样识别p-c (predicate-complement) insertion 述补中插pdp (parallel distributed processing) 平行分布处理perception 知觉perceptron 感觉器 [感知器]perceptual strategy 感知策略performative 行为句periphrasis 用独立词表达perlocutionary 语效性的permutation 移位petri net grammar petri 网语法philology 语文学phone 语音phoneme 音素phonemic analysis 因素分析phonemic stratum 音素层phonetics 语音学phonogram 音标phonology 声韵学 [音位学;广义语音学] phonotactics 音位排列理论phrasal verb 词组动词 [短语动词]phrase 词组 [短语]phrase marker 词组标记 [短语标记]pitch 音调pitch contour 调形变化pivot grammar 枢轴语法pivotal construction 承轴结构plausibility function 可能性函数pm (phrase marker) 词组标记 [短语标记] polysemy 多义性pos-tagging 词类标记postposition 方位词pp (preposition phrase) attachment 介词依附pragmatics 语用学precedence grammar 优先级语法precision 精确度predicate 述词predicate calculus 述词计算predicate logic 述词逻辑 [谓词逻辑]predicate-argument structure 述词论元结构prefix 前缀premodification 前置修饰preposition 介词prescriptive linguistics 规定语言学 [规范语言学] presentative sentence 引介句presupposition 前提principle of compositionality 语意合成性原理privative 二元对立的probabilistic parser 概率句法剖析程序problem solving 解决问题program 程序programming language 程序设计语言 [程序设计语言] proofreading system 校对系统proper name 专有名词prosody 节律prototype 原型pseudo-cleft sentence 准分裂句psycholinguistics 心理语言学punctuation 标点符号pushdown automata 下推自动机pushdown transducer 下推转换器qualification 后置修饰quantification 量化quantifier 范域词quantitative linguistics 计量语言学question answering system 问答系统queue 队列radical 字根 [词干;词根;部首;偏旁]radix of tuple 元组数基random access 随机存取rationalism 理性论rationalist (position) 理性论立场 [唯理论观点]reading laboratory 阅读实验室real time 实时real time control 实时控制 [实时控制]recursive transition network 递归转移网络reduplication 重叠词 [重复]reference 指涉referent 指称对象referential indices 指针referring expression 指涉词 [指示短语]register 缓存器[寄存器]{信息科学}/调高{语音学}/语言的场合层级{社会语言学}regular language 正规语言 [正则语言]relational database 关系型数据库 [关系数据库]relative clause 关系子句relaxation method 松弛法relevance 相关性restricted logic grammar 受限逻辑语法resumptive pronouns 复指代词retroactive inhibition 逆抑制rewriting rule 重写规则rheme 述位rhetorical structure 修辞结构rhetorics 修辞学robust 强健性robust processing 强健性处理robustness 强健性schema 基朴school grammar 教学语法scope 范域 [作用域;范围]script 脚本search mechanism 检索机制search space 检索空间searching route 检索路径 [搜索路径]second order predicate 二阶述词segmentation 分词segmentation marker 分段标志selectional restriction 选择限制semantic field 语意场semantic frame 语意架构semantic network 语意网络semantic representation 语意表征 [语义表示] semantic representation language 语意表征语言semantic restriction 语意限制semantic structure 语意结构semantics 语意学sememe 意素semiotics 符号学sender 发送者sensorimotor stage 感觉运动期sensory information 感官讯息 [感觉信息]sentence 句子sentence generator 句子产生器 [句子生成程序]sentence pattern 句型separation of homonyms 同音词区分sequence 序列serial order learning 顺序学习serial verb construction 连动结构set oriented semantic network 集合导向型语意网络 [面向集合型语意网络]sgml (standard generalized markup language) 结构化通用标记语言shift-reduce parsing 替换简化式剖析short term memory 短程记忆sign 信号signal processing technology 信号处理技术simple word 单纯词situation 情境situation semantics 情境语意学situational type 情境类型social context 社会环境sociolinguistics 社会语言学software engineering 软件工程 [软件工程]sort 排序speaker-independent speech recognition 非特定语者语音识别spectrum 频谱speech 口语speech act assignment 言语行为指定speech continuum 言语连续体speech disorder 语言失序 [言语缺失]speech recognition 语音辨识speech retrieval 语音检索speech situation 言谈情境 [言语情境]speech synthesis 语音合成speech translation system 语音翻译系统speech understanding system 语音理解系统spreading activation model 扩散激发模型standard deviation 标准差standard generalized markup language 标准通用标示语言start-bound complement 接头词state of affairs algebra 事态代数state transition diagram 状态转移图statement kernel 句核static attribute list 静态属性表statistical analysis 统计分析statistical linguistics 统计语言学statistical significance 统计意义stem 词干stimulus-response theory 刺激反应理论stochastic approach to parsing 概率式句法剖析 [句法剖析的随机方法]stop 爆破音stratificational grammar 阶层语法 [层级语法]string 字符串[串；字符串]string manipulation language 字符串操作语言string matching 字符串匹配 [字符串]structural ambiguity 结构歧义structural linguistics 结构语言学structural relation 结构关系structural transfer 结构转换structuralism 结构主义structure 结构structure sharing representation 结构共享表征subcategorization 次类划分 [下位范畴化] subjunctive 假设的sublanguage 子语言subordinate 从属关系subordinate clause 从属子句 [从句;子句] subordination 从属substitution rule 代换规则 [置换规则] substrate 底层语言suffix 后缀superordinate 上位的superstratum 上层语言suppletion 异型[不规则词型变化] suprasegmental 超音段的syllabification 音节划分syllable 音节syllable structure constraint 音节结构限制symbolization and verbalization 符号化与字句化synchronic 同步的synonym 同义词syntactic category 句法类别syntactic constituent 句法成分syntactic rule 语法规律 [句法规则]syntactic semantics 句法语意学syntagm 句段syntagmatic 组合关系 [结构段的;组合的] syntax 句法systemic grammar 系统语法tag 标记target language 目标语言 [目标语言]task sharing 课题分享 [任务共享] tautology 套套逻辑 [恒真式;重言式;同义反复] taxonomical hierarchy 分类阶层 [分类层次] telescopic compound 套装合并template 模板temporal inference 循序推理 [时序推理] temporal logic 时间逻辑 [时序逻辑] temporal marker 时貌标记tense 时态terminology 术语text 文本text analyzing 文本分析text coherence 文本一致性text generation 文本生成 [篇章生成]text linguistics 文本语言学text planning 文本规划text proofreading 文本校对text retrieval 文本检索text structure 文本结构 [篇章结构]text summarization 文本自动摘要 [篇章摘要] text understanding 文本理解text-to-speech 文本转语音thematic role 题旨角色thematic structure 题旨结构theorem 定理thesaurus 同义词辞典theta role 题旨角色theta-grid 题旨网格token 实类 [标记项]tone 音调tone language 音调语言tone sandhi 连调变换top-down 由上而下 [自顶向下]topic 主题topicalization 主题化 [话题化]trace 痕迹trace theory 痕迹理论training 训练transaction 异动 [处理单位]transcription 转写 [抄写;速记翻译]transducer 转换器transfer 转移transfer approach 转换方法transfer framework 转换框架transformation 变形 [转换]transformational grammar 变形语法 [转换语法] transitional state term set 转移状态项集合transitivity 及物性translation 翻译translation equivalence 翻译等值性translation memory 翻译记忆transparency 透明性tree 树状结构 [树]tree adjoining grammar 树形加接语法 [树连接语法] treebank 树图数据库[语法关系树库]trigram 三连词t-score t-数turing machine 杜林机 [图灵机]turing test 杜林测试 [图灵试验]type 类型type/token node 标记类型/实类节点type-feature structure 类型特征结构typology 类型学ultimate constituent 终端成分unbounded dependency 无界限依存underlying form 基底型式underlying structure 基底结构unification 连并 [合一]unification-based grammar 连并为本的语法 [基于合一的语法] universal grammar 普遍性语法universal instantiation 普遍例式universal quantifier 全称范域词unknown word 未知词 [未定义词]unrestricted grammar 非限制型语法usage flag 使用旗标user interface 使用者界面 [用户界面]valence grammar 结合价语法valence theory 结合价理论valency 结合价variance 变异数 [方差]verb 动词verb phrase 动词组 [动词短语]verb resultative compound 动补复合词verbal association 词语联想verbal phrase 动词组verbal production 言语生成vernacular 本地话v-o construction (verb-object) 动宾结构vocabulary 字汇vocabulary entry 词条vocal track 声道vocative 呼格voice recognition 声音辨识 [语音识别]vowel 元音vowel harmony 元音和谐 [元音和谐]waveform 波形weak verb 弱化动词whorfian hypothesis whorfian 假说word 词word frequency 词频word frequency distribution 词频分布word order 词序word segmentation 分词word segmentation standard for chinese 中文分词规范word segmentation unit 分词单位 [切词单位]word set 词集working memory 工作记忆 [工作存储区]world knowledge 世界知识writing system 书写系统x-bar theory x标杠理论 ["x"阶理论]zipf's law 利夫规律 [齐普夫定律]。

检验专业英语试题及答案

检验专业英语试题及答案一、选择题（每题2分，共20分）1. Which of the following is not a routine test in clinical laboratory?A. Blood countB. Urine analysisC. Liver function testD. DNA sequencing2. The term "hemoglobin" refers to:A. A type of proteinB. A type of enzymeC. A type of hormoneD. A type of lipid3. What is the primary function of the enzyme amylase?A. To break down proteinsB. To break down carbohydratesC. To break down fatsD. To break down nucleic acids4. The process of identifying the presence of a specific microorganism in a sample is known as:A. CulturingB. IsolationC. IdentificationD. Quantification5. Which of the following is a common method for measuring the concentration of glucose in blood?A. SpectrophotometryB. ChromatographyC. ElectrophoresisD. Enzymatic assay6. The term "ELISA" stands for:A. Enzyme-Linked Immunosorbent AssayB. Electrophoresis-Linked Immunosorbent AssayC. Enzyme-Linked Immunofluorescence AssayD. Electrophoresis-Linked Immunofluorescence Assay7. In medical diagnostics, what does "PCR" refer to?A. Polymerase Chain ReactionB. Protein Chain ReactionC. Particle Count ReactionD. Pathogen Characterization Reaction8. The process of measuring the amount of a specific substance in a sample is known as:A. TitrationB. CalibrationC. QuantificationD. Qualification9. Which of the following is a common type of clinical specimen?A. BloodB. SoilC. HairD. Water10. The term "antibodies" refers to:A. Proteins that recognize and bind to specific antigensB. Substances that neutralize toxinsC. Hormones that regulate immune responseD. Cells that produce immune responses二、填空题（每空1分，共10分）1. The process of separating molecules based on their size is known as __________.2. In clinical chemistry, the term "assay" refers to a__________ method.3. The unit of measurement for pH is __________.4. A common method for detecting the presence of antibodies in a sample is the __________ test.5. The process of identifying the type of bacteria in a sample is known as __________.6. The process of separating DNA fragments based on their size is known as __________.7. The term "ELISA" is used in __________ to detect the presence of specific antibodies or antigens.8. The process of identifying the genetic makeup of an organism is known as __________.9. The process of measuring the amount of a substance in a sample using a specific wavelength of light is called__________.10. The process of identifying the presence of specific microorganisms in a sample is known as __________.三、简答题（每题5分，共20分）1. Describe the principle of the Enzyme-Linked Immunosorbent Assay (ELISA).2. Explain the importance of maintaining aseptic technique ina clinical laboratory.3. What are the steps involved in performing a blood count?4. Discuss the role of antibodies in the immune response.四、论述题（每题15分，共30分）1. Compare and contrast the methods of Chromatography and Electrophoresis in terms of their applications in clinical diagnostics.2. Discuss the ethical considerations in the use of genetic testing for medical purposes.五、翻译题（每题5分，共10分）1. 将以下句子从中文翻译成英文：在临床实验室中，酶联免疫吸附测定法是一种常用的检测特定抗体或抗原的方法。

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Models and Applications, Volume 1,Second Edition61.Convergence of Probability Measures, Second Edition62.Counting Processes and Survival Analysis63.Decision Theory64.Design and Analysis of Clinical Trials: Concepts and Methodologies, SecondEdition65.Design and Analysis of Experiments: Advanced Experimental Design, Volume 266.Design and Analysis of Experiments: Introduction to Experimental Design, Volume1, Second Edition67.Design and Analysis of Experiments: Special Designs and Applications, Volume 368.Directional Statistics69.Dirichlet and Related Distributions: Theory, Methods and Applications70.Discrete Distributions: Applications in the Health Sciences71.Discriminant Analysis and Statistical Pattern Recognition72.Empirical Model Building73.Empirical Model Building: Data, Models, and Reality, Second Edition74.Environmental Statistics: Methods and Applications75.Exploration and Analysis of DNA Microarray and Protein Array Data76.Exploratory Data Mining and Data Cleaning77.Exploring Data Tables, Trends, and Shapes78.Financial Derivatives in Theory and Practice79.Finding Groups in Data: An Introduction to Cluster Analysis80.Finite Mixture Models81.Flowgraph Models for Multistate Time-to-Event Data82.Forecasting with Dynamic Regression Models83.Forecasting with Univariate Box-Jenkins Models: Concepts and Cases84.Fourier Analysis of Time Series: An Introduction, Second Edition85.Fractal-Based Point Processes86.Fractional Factorial Plans87.Fundamentals of Exploratory Analysis of Variance88.Generalized Least Squares89.Generalized Linear Models: With Applications in Engineering and the Sciences,Second Edition90.Generalized, Linear, and Mixed Models91.Geometrical Foundations of Asymptotic Inference92.Geostatistics: Modeling Spatial Uncertainty93.Geostatistics: Modeling Spatial Uncertainty, Second Edition94.High-Dimensional Covariance Estimation95.Hilbert Space Methods in Probability and Statistical Inference96.History of Probability and Statistics and Their Applications before 175097.Image Processing and Jump Regression Analysis98.Inference and Prediction in Large Dimensions99.Introduction to Nonparametric Regression100.Introduction to Statistical Time Series, Second Edition101.Introductory Stochastic Analysis for Finance and Insurancetent Class and Latent Transition Analysis: With Applications in the Social, Behavioral, and Health Sciencestent Curve Models: A Structural Equation Perspectivetent Variable Models and Factor Analysis: A Unified Approach, 3rd Edition105.Leading Personalities in Statistical Sciences: From the Seventeenth Century to the Present106.Lévy Processes in Finance: Pricing Financial Derivatives107.Linear Models: The Theory and Application of Analysis of Variance108.Linear Statistical Inference and its Applications: Second Editon109.Linear Statistical Models110.LISP-STAT: An Object-Oriented Environment for Statistical Computing and Dynamic Graphics111.Longitudinal Data Analysis112.Long-Memory Time Series: Theory and Methods113.Loss Distributions114.Loss Models: From Data to Decisions, Third Edition115.Management of Data in Clinical Trials, Second Edition116.Markov Decision Processes: Discrete Stochastic Dynamic Programming117.Markov Processes and Applications118.Markov Processes: Characterization and Convergence119.Mathematics of Chance120.Measurement Error Models121.Measurement Errors in Surveys122.Meta Analysis: A Guide to Calibrating and Combining Statistical Evidence 123.Methods and Applications of Linear Models: Regression and the Analysis of Variance124.Methods for Statistical Data Analysis of Multivariate Observations, Second Edition125.Methods of Multivariate Analysis, Second Edition126.Methods of Multivariate Analysis, Third Edition127.Mixed Models: Theory and Applications128.Mixtures: Estimation and Applications129.Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods130.Models for Investors in Real World Markets131.Models for Probability and Statistical Inference: Theory and Applications 132.Modern Applied U-Statistics133.Modern Experimental Design134.Modes of Parametric Statistical Inference135.Multilevel Statistical Models, 4th Edition136.Multiple Comparison Procedures137.Multiple Imputation for Nonresponse in Surveys138.Multiple Time Series139.Multistate Systems Reliability Theory with Applications140.Multivariable Model-Building: A pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables141.Multivariate Density Estimation: Theory, Practice, and Visualization142.Multivariate Observations143.Multivariate Statistics: High-Dimensional and Large-Sample Approximations 144.Nonlinear Regression145.Nonlinear Regression Analysis and Its Applications146.Nonlinear Statistical Models147.Nonparametric Analysis of Univariate Heavy-Tailed Data: Research and Practice148.Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed-Effects Modeling Approaches149.Nonparametric Statistics with Applications to Science and Engineering 150.Numerical Issues in Statistical Computing for the Social Scientist151.Operational Risk: Modeling Analytics152.Optimal Learning153.Order Statistics, Third Edition154.Periodically Correlated Random Sequences: Spectral Theory and Practice 155.Permutation Tests for Complex Data: Theory, Applications and Software 156.Planning and Analysis of Observational Studies157.Planning, Construction, and Statistical Analysis of Comparative Experiments158.Precedence-Type Tests and Applications159.Preparing for the Worst: Incorporating Downside Risk in Stock Market Investments160.Probability and Finance: It's Only a Game!161.Probability: A Survey of the Mathematical Theory, Second Edition162.Quantitative Methods in Population Health: Extensions of Ordinary Regression163.Random Data: Analysis and Measurement Procedures, Fourth Edition164.Random Graphs for Statistical Pattern Recognition165.Randomization in Clinical Trials: Theory and Practice166.Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment167.Records168.Regression Analysis by Example, Fourth Edition169.Regression Diagnostics: Identifying Influential Data and Sources of Collinearity170.Regression Graphics: Ideas for Studying Regressions Through Graphics171.Regression Models for Time Series Analysis172.Regression with Social Data: Modeling Continuous and Limited Response Variables173.Reliability and Risk: A Bayesian Perspective174.Reliability: Modeling, Prediction, and Optimization175.Response Surfaces, Mixtures, and Ridge Analyses, Second Edition176.Robust Estimation & Testing177.Robust Methods in Biostatistics178.Robust Regression and Outlier Detection179.Robust Statistics180.Robust Statistics, Second Edition181.Robust Statistics: Theory and Methods182.Runs and Scans with Applications183.Sampling, Third Edition184.Sensitivity Analysis in Linear Regression185.Sequential Estimation186.Shape & Shape Theory187.Simulation and the Monte Carlo Method188.Simulation and the Monte Carlo Method, Second Edition189.Simulation and the Monte Carlo Method: Solutions Manual to Accompany, Second Edition190.Simulation: A Modeler's Approach191.Smoothing and Regression: Approaches, Computation, and Application192.Smoothing of Multivariate Data: Density Estimation and Visualization193.Spatial Statistics194.Spatial Statistics and Spatio-Temporal Data: Covariance Functions and Directional Properties195.Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, Second Edition196.Stage-Wise Adaptive Designs197.Statistical Advances in the Biomedical Sciences: Clinical Trials, Epidemiology, Survival Analysis, and Bioinformatics198.Statistical Analysis of Profile Monitoring199.Statistical Design and Analysis of Experiments: With Applications to Engineering and Science, Second Edition200.Statistical Factor Analysis and Related Methods: Theory and Applications 201.Statistical Inference for Fractional Diffusion Processes202.Statistical Meta-Analysis with Applications203.Statistical Methods for Comparative Studies: Techniques for Bias Reduction 204.Statistical Methods for Forecasting205.Statistical Methods for Quality Improvement, Third Edition206.Statistical Methods for Rates and Proportions, Third Edition207.Statistical Methods for Survival Data Analysis, Third Edition208.Statistical Methods for the Analysis of Biomedical Data, Second Edition 209.Statistical Methods in Diagnostic Medicine210.Statistical Methods in Diagnostic Medicine, Second Edition211.Statistical Methods in Engineering and Quality Assurance212.Statistical Methods in Spatial Epidemiology, Second Edition213.Statistical Modeling by Wavelets214.Statistical Models and Methods for Lifetime Data, Second Edition215.Statistical Rules of Thumb, Second Edition216.Statistical Size Distributions in Economics and Actuarial Sciences217.Statistical Texts for Mixed Linear Models218.Statistical Tolerance Regions: Theory, Applications, and Computation219.Statistics for Imaging, Optics, and Photonics220.Statistics for Research, Third Edition221.Statistics of Extremes: Theory and Applications222.Statistics: A Biomedical Introduction223.Stochastic Dynamic Programming and the Control of Queueing Systems224.Stochastic Processes for Insurance & Finance225.Stochastic Simulation226.Structural Equation Modeling: A Bayesian Approach227.Subjective and Objective Bayesian Statistics: Principles, Models, and Applications, Second Edition228.Survey Errors and Survey Costs229.System Reliability Theory: Models, Statistical Methods, and Applications, Second Edition230.The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies, Second Edition231.The Construction of Optimal Stated Choice Experiments: Theory and Methods 232.The EM Algorithm and Extensions, Second Edition233.The Statistical Analysis of Failure Time Data, Second Edition234.The Subjectivity of Scientists and the Bayesian Approach235.The Theory of Measures and Integration236.The Theory of Response-Adaptive Randomization in Clinical Trials237.Theory of Preliminary Test and Stein-Type Estimation With Applications 238.Time Series Analysis and Forecasting by Example239.Time Series: Applications to Finance with R and S-Plus, Second Edition 240.Uncertainty Analysis with High Dimensional Dependence Modelling241.Univariate Discrete Distributions, Third Editioning the Weibull Distribution: Reliability, Modeling, and Inference243.Variance Components244.Variations on Split Plot and Split Block Experiment Designs245.Visual Statistics: Seeing Data with Dynamic Interactive Graphics246.Weibull Models。

罗马尼亚IMO国家队选拔考试2003

Romanian Olympiad2003IMO Team Selection Tests1st Test-April23,20031.Let(a n)n≥1be a sequence for real numbers given by a1=1/2and for each positive integer na n+1=a2na2n−a n+1.Prove that for every positive integer n we have a1+a2+···+a n<1.Titu Andreescu2.Let ABC be a triangle with∠BAC=60◦.Consider a point P inside the triangle having P A=1,P B=2and P C=3.Find the maximum possible area of the triangle ABC.3.Let n,k be positive integers such that n k>(k+1)!and consider the setM={(x1,x2,...,x n)|x i∈{1,2,...,n},i=1,k}.Prove that if A⊂M has(k+1)!+1elements,then there are two elements{α,β}⊂A,α=(α1,α2,...,αn),β=(β1,β2,...,βn)such that(k+1)!|(β1−α1)(β2−α2)···(βk−αk).Vasile ZidaruWork time:4hours.TeX(c)2003Valentin Vornicu2nd Test-April24,20034.Prove that among the elements of the sequence([n √2003])n≥1one canﬁnd a geometricprogression having any number of terms,and having the ratio bigger than k,where k can be any positive integer.Radu Gologan 5.Let f∈Z[X]be an irreducible polynomial over the ring of integer polynomials,such that|f(0)|is not a perfect square.Prove that if the leading coeﬃcient of f is1(the coeﬃcient of the term having the highest degree in f)then f(X2)is also irreducible in the ring of integer polynomials.Mihai Piticari 6.At a math contest there are2n students participating.Each of them submits a problem to the jury,which thereafter gives each students one of the2n problems submitted.One says that the contest is fair is there are n participants which receive their problems from the other n participants.Prove that the number of distributions of the problems in order to obtain a fair contest is a perfect square.Work time:4hours.TeX(c)2003Valentin Vornicu3rd Test-May24,20037.Find all integers a,b,m,n,with m>n>1,for which the polynomial f(X)=X m+aX+b divides the polynomial g(X)=X m+aX+b.Laurent¸iu Panaitopol 8.Two circlesω1andω2with radii r1and r2,r2>r1,are externally tangent.The line t1is tangent to the circlesω1andω2at points A and D respectively.The parallel line t2to the line t1is tangent to the circleω1and intersects the circleω2at points E and F.The line t3passing through D intersects the line t2and the circleω2in B and C respectively,both diﬀerent of E and F respectively.Prove that the circumcircle of the triangle ABC is tangent to the line t1.Dinu S¸erb˘a nescu 9.Let n≥3be a positive integer.Inside a n×n array there are placed n2positive numbers with sum n3.Prove that we canﬁnd a square2×2of4elements of the array,having the sides parallel with the sides of the array,and for which the sum of the elements in the square is greater than3n.Radu GologanWork time:4hours.TeX(c)2003Valentin Vornicu4th Test-April25,200310.Let P the set of all the primes and let M be a subset of P,having at least threeelements,and such that for any proper subset A of M all of the prime factors of the numberp−1+p∈Aare found in M.Prove that M=P.Valentin Vornicu 11.In a square of side6the points A,B,C,D are given such that the distance between anytwo of the four points is at least5.Prove that A,B,C,D form a convex quadrilateral and its area is greater than21.Laurent¸iu Panaitopol 12.A word consists of n letters from the alphabet{a,b,c,d}.One says that a word iscomplicated if it has two consecutive identical groups of letters(i.e.caab or cababdc are complicated words,but abcab is not a complicated word).A word that is not complicated is called a simple word.Prove that the number of simple words with n letters is greater than2n.Work time:4hours.TeX(c)2003Valentin Vornicu5th Test-June19,200313.A parliament has n senators.The senators form10parties and10committees,suchthat any senator belongs to exactly one party and one committee.Find the least possible n for which it is possible to label the parties and the committees with numbers from1to10,such that there are at least11senators for which the numbers of the corresponding party and committee are equal.Marian Andronache and Radu Gologan 14.Given is a rhombus ABCD of side1.On the sides BC and CD we are given the pointsM and N respectively,such that MC+CN+MN=2and2∠MAN=∠BAD.Find the measures of the angles of the rhombus.Cristinel Mortici 15.In a plane we choose a cartesian system of coordinates.A point A(x,y)in the planeis called an integer point if and only if both x and y are integers.An integer point A is called invisible if on the segment(OA)there is at least one integer point.Prove that for each positive integer n there exists a square of side n in which all the interior integer points are invisible.France Olympiad2003Work time:4hours.TeX(c)2003Valentin Vornicu6th Test-June20,200316.Let ABCDEF be a convex hexagon and denote by A ,B ,C ,D ,E ,F the middlepoints of the sides AB,BC,CD,DE,EF and F A respectively.Given are the areas of the triangles ABC ,BCD ,CDE ,DEF ,EF A and F AB .Find the area of the hexagon.Kvant 17.A permutationσ:{1,2,...,n}→{1,2,...,n}is called straight if and only if for eachinteger k,1≤k≤n−1the following inequality is fulﬁlled|σ(k)−σ(k+1)|≤2.Find the smallest positive integer n for which there exist at least2003straight per-mutations.Valentin Vornicu 18.For every positive integer n we denote by d(n)the sum of its digits in the decimalrepresentation.Prove that for each positive integer k there exists a positive integer m such that the equation x+d(x)=m has exactly k solutions in the set of positive integers.Polish Olympiad1999Work time:4hours.TeX(c)2003Valentin Vornicu。

数据结构与算法常用英语词汇

数据结构与算法常用英语词汇DataStructure基本数据结构Dictionarie字典PriorityQueue堆GraphDataStructure图SetDataStructure集合Kd-Tree线段树NumericalProblem数值问题SolvingLinearEquation线性方程组BandwidthReduction带宽压缩Matri某Multiplication矩阵乘法DeterminantandPermanent行列式ContrainedandUncontrainedOptimization最值问题LinearProgramming线性规划RandomNumberGeneration随机数生成FactoringandPrimalityTeting因子分解/质数判定ArbitraryPreciionArithmetic高精度计算KnapackProblem背包问题MedianandSelection中位数GeneratingPermutation排列生成GeneratingSubet子集生成GeneratingPartition划分生成GeneratingGraph图的生成CalendricalCalculation日期JobScheduling工程安排Satifiability 可满足性TranitiveCloureandReduction传递闭包Matching匹配EulerianCycle/ChineePotmanEuler回路/中国邮路EdgeandVerte某Connectivity割边/割点NetworkFlow网络流DrawingGraphNicely图的描绘DrawingTree树的描绘PlanarityDetectionandEmbedding平面性检测和嵌入GraphProblem--hard图论-NP问题Clique最大团IndependentSet独立集Verte某Cover点覆盖TravelingSalemanProblem旅行商问题HamiltonianCycleHamilton 回路GraphPartition图的划分Verte某Coloring点染色EdgeColoring 边染色GraphIomorphim同构SteinerTreeSteiner树Triangulation三角剖分VoronoiDiagramVoronoi图NearetNeighborSearch最近点对查询RangeSearch范围查询PointLocation位置查询InterectionDetection碰撞测试BinPacking装箱问题Medial-A某iTranformation中轴变换PolygonPartitioning多边形分割SimplifyingPolygon多边形化简ShapeSimilarity相似多边形MotionPlanning运动规划MaintainingLineArrangement平面分割MinkowkiSumMinkowki和SetandStringProblem集合与串的问题SetCover集合覆盖SetPacking集合配置StringMatching模式匹配第二部分数据结构英语词汇数据抽象dataabtraction数据元素dataelement数据对象dataobject数据项dataitem数据类型datatype抽象数据类型abtractdatatype逻辑结构logicaltructure物理结构phyicaltructure线性结构lineartructure非线性结构nonlineartructure基本数据类型atomicdatatype固定聚合数据类型fi某ed-aggregatedatatype可变聚合数据类型variable-aggregatedatatype线性表linearlit栈tack队列queue串tring数组array树tree图grabh查找，线索earching更新updating排序（分类)orting插入inertion删除deletion前趋predeceor后继ucceor直接前趋immediatepredeceor直接后继immediateucceor双端列表deque(double-endedqueue)循环队列cirularqueue指针pointer先进先出表（队列）firt-infirt-outlit后进先出表（队列）lat-infirt-outlit栈底bottom栈定top压入puh弹出pop队头front 队尾rear上溢overflow下溢underflow数组array矩阵matri某多维数组multi-dimentionalarray以行为主的顺序分配rowmajororder以列为主的顺序分配columnmajororder三角矩阵truangularmatri某对称矩阵ymmetricmatri某稀疏矩阵parematri某转置矩阵tranpoedmatri某链表linkedlit线性链表linearlinkedlit单链表inglelinkedlit多重链表multilinkedlit循环链表circularlinkedlit双向链表doublylinkedlit 十字链表orthogonallit广义表generalizedlit链link指针域pointerfield链域linkfield头结点headnode头指针headpointer尾指针tailpointer串tring空白（空格）串blanktring空串（零串）nulltring子串ubtring 树tree子树ubtree森林foret根root叶子leaf结点node深度depth层次level双亲parent孩子children兄弟brother祖先ancetor子孙decentdant二叉树binarytree平衡二叉树banlancedbinarytree满二叉树fullbinarytree双链树doublylinkedtree数字查找树digitalearchtree树的遍历traveraloftree先序遍历preordertraveral中序遍历inordertraveral后序遍历potordertraveral图graph子图ubgraph强连通图tronglyconnectedgraph弱连通图weaklyconnectedgraph 加权图weightedgraph有向无环图directedacyclicgraph稀疏图paregraph稠密图denegraph重连通图biconnectedgraph二部图bipartitegraph边edge顶点verte某弧arc路径path。

《统计词汇中英文对照》

《统计词汇中英文对照》Effect, 实验效应Eigenvalue, 特征值Eigenvector, 特征向量Ellipse, 椭圆Empirical distribution, 经验分布Empirical probability, 经验概率单位Enumeration data, 计数资料Equal sun-class number, 相等次级组含量Equally likely, 等可能Equivariance, 同变性Error, 误差/错误Error of estimate, 估计误差Error type I, 第一类错误Error type II, 第二类错误Estimand, 被估量Estimated error mean squares, 估计误差均方Estimated error sum of squares, 估计误差平方与Euclidean distance, 欧式距离Event, 事件Event, 事件Exceptional data point, 特殊数据点Expectation plane, 期望平面Expectation surface, 期望曲面Expected values, 期望值Experiment, 实验Experimental sampling, 试验抽样Experimental unit, 试验单位Explanatory variable, 说明变量Exploratory data analysis, 探索性数据分析Explore Summarize, 探索-摘要Exponential curve, 指数曲线Exponential growth, 指数式增长EXSMOOTH, 指数平滑方法Extended fit, 扩充拟合Extra parameter, 附加参数Extrapolation, 外推法Extreme observation, 末端观测值Extremes, 极端值/极值F distribution, F分布F test, F检验Factor, 因素/因子Factor analysis, 因子分析Factor Analysis, 因子分析Factor score, 因子得分Factorial, 阶乘Factorial design, 析因试验设计False negative, 假阴性False negative error, 假阴性错误Family of distributions, 分布族Family of estimators, 估计量族Fanning, 扇面Fatality rate, 病死率Field investigation, 现场调查Field survey, 现场调查Finite population, 有限总体Finite-sample, 有限样本First derivative, 一阶导数First principal component, 第一主成分First quartile, 第一四分位数Fisher information, 费雪信息量Fitted value, 拟合值Fitting a curve, 曲线拟合Fixed base, 定基Fluctuation, 随机起伏Forecast, 预测Four fold table, 四格表Fourth, 四分点Fraction blow, 左侧比率Fractional error, 相对误差Frequency, 频率Frequency polygon, 频数多边图Frontier point, 界限点Function relationship, 泛函关系Gamma distribution, 伽玛分布Gauss increment, 高斯增量Gaussian distribution, 高斯分布/正态分布Gauss-Newton increment, 高斯-牛顿增量General census, 全面普查GENLOG (Generalized liner models), 广义线性模型Geometric mean, 几何平均数Gini's mean difference, 基尼均差GLM (General liner models), 通用线性模型Goodness of fit, 拟与优度/配合度Gradient of determinant, 行列式的梯度Graeco-Latin square, 希腊拉丁方Grand mean, 总均值Gross errors, 重大错误Gross-error sensitivity, 大错敏感度Group averages, 分组平均Grouped data, 分组资料Guessed mean, 假定平均数Half-life, 半衰期Hampel M-estimators, 汉佩尔M估计量Happenstance, 偶然事件Harmonic mean, 调与均数Hazard function, 风险均数Hazard rate, 风险率Heading, 标目Heavy-tailed distribution, 重尾分布Hessian array, 海森立体阵Heterogeneity, 不一致质Heterogeneity of variance, 方差不齐Hierarchical classification, 组内分组Hierarchical clustering method, 系统聚类法High-leverage point, 高杠杆率点HILOGLINEAR, 多维列联表的层次对数线性模型Hinge, 折叶点Histogram, 直方图Historical cohort study, 历史性队列研究Holes, 空洞HOMALS, 多重响应分析Homogeneity of variance, 方差齐性Homogeneity test, 齐性检验Huber M-estimators, 休伯M估计量Hyperbola, 双曲线Hypothesis testing, 假设检验Hypothetical universe, 假设总体Impossible event, 不可能事件Independence, 独立性Independent variable, 自变量Index, 指标/指数Indirect standardization, 间接标准化法Individual, 个体Inference band, 推断带Infinite population, 无限总体Infinitely great, 无穷大Infinitely small, 无穷小Influence curve, 影响曲线Information capacity, 信息容量Initial condition, 初始条件Initial estimate, 初始估计值Initial level, 最初水平Interaction, 交互作用Interaction terms, 交互作用项Intercept, 截距Interpolation, 内插法Interquartile range, 四分位距Interval estimation, 区间估计Intervals of equal probability, 等概率区间Intrinsic curvature, 固有曲率Invariance, 不变性Inverse matrix, 逆矩阵Inverse probability, 逆概率Inverse sine transformation, 反正弦变换Iteration, 迭代Jacobian determinant, 雅可比行列式Joint distribution function, 分布函数Joint probability, 联合概率Joint probability distribution, 联合概率分布K means method, 逐步聚类法Kaplan-Meier, 评估事件的时间长度Kaplan-Merier chart, Kaplan-Merier图Kendall's rank correlation, Kendall等级有关Kinetic, 动力学Kolmogorov-Smirnove test, 柯尔莫哥洛夫-斯米尔诺夫检验Kruskal and Wallis test, Kruskal及Wallis检验/多样本的秩与检验/H 检验Kurtosis, 峰度Lack of fit, 失拟Ladder of powers, 幂阶梯Lag, 滞后Large sample, 大样本Large sample test, 大样本检验Latin square, 拉丁方Latin square design, 拉丁方设计Leakage, 泄漏Least favorable configuration, 最不利构形Least favorable distribution, 最不利分布Least significant difference, 最小显著差法Least square method, 最小二乘法Least-absolute-residuals estimates, 最小绝对残差估计Least-absolute-residuals fit, 最小绝对残差拟合Least-absolute-residuals line, 最小绝对残差线Legend, 图例L-estimator, L估计量L-estimator of location, 位置L估计量L-estimator of scale, 尺度L估计量Level, 水平Life expectance, 预期期望寿命Life table, 寿命表Life table method, 生命表法Light-tailed distribution, 轻尾分布Likelihood function, 似然函数Likelihood ratio, 似然比line graph, 线图Linear correlation, 直线有关Linear equation, 线性方程Linear programming, 线性规划Linear regression, 直线回归Linear Regression, 线性回归Linear trend, 线性趋势Loading, 载荷Location and scale equivariance, 位置尺度同变性Location equivariance, 位置同变性Location invariance, 位置不变性Location scale family, 位置尺度族Log rank test, 时序检验Logarithmic curve, 对数曲线Logarithmic normal distribution, 对数正态分布Logarithmic scale, 对数尺度Logarithmic transformation, 对数变换Logic check, 逻辑检查Logistic distribution, 逻辑斯特分布Logit transformation, Logit转换LOGLINEAR, 多维列联表通用模型Lognormal distribution, 对数正态分布Lost function, 缺失函数Low correlation, 低度有关Lower limit, 下限Lowest-attained variance, 最小可达方差LSD, 最小显著差法的简称Lurking variable, 潜在变量Main effect, 主效应Major heading, 主辞标目Marginal density function, 边缘密度函数Marginal probability, 边缘概率Marginal probability distribution, 边缘概率分布Matched data, 配对资料Matched distribution, 匹配过分布Matching of distribution, 分布的匹配Matching of transformation, 变换的匹配Mathematical expectation, 数学期望Mathematical model, 数学模型Maximum L-estimator, 极大极小L 估计量Maximum likelihood method, 最大似然法Mean, 均数Mean squares between groups, 组间均方Mean squares within group, 组内均方Means (Compare means), 均值-均值比较Median, 中位数Median effective dose, 半数效量Median lethal dose, 半数致死量Median polish, 中位数平滑Median test, 中位数检验Minimal sufficient statistic, 最小充分统计量Minimum distance estimation, 最小距离估计Minimum effective dose, 最小有效量Minimum lethal dose, 最小致死量Minimum variance estimator, 最小方差估计量MINITAB, 统计软件包Minor heading, 宾词标目Missing data, 缺失值Model specification, 模型的确定Modeling Statistics , 模型统计Models for outliers, 离群值模型Modifying the model, 模型的修正Modulus of continuity, 连续性模Morbidity, 发病率Most favorable configuration, 最有利构形Multidimensional Scaling (ASCAL), 多维尺度/多维标度Multinomial Logistic Regression , 多项逻辑斯蒂回归Multiple comparison, 多重比较Multiple correlation , 复有关Multiple covariance, 多元协方差Multiple linear regression, 多元线性回归Multiple response , 多重选项Multiple solutions, 多解Multiplication theorem, 乘法定理Multiresponse, 多元响应Multi-stage sampling, 多阶段抽样Multivariate T distribution, 多元T分布Mutual exclusive, 互不相容Mutual independence, 互相独立Natural boundary, 自然边界Natural dead, 自然死亡Natural zero, 自然零Negative correlation, 负有关Negative linear correlation, 负线性有关Negatively skewed, 负偏Newman-Keuls method, q检验NK method, q检验No statistical significance, 无统计意义Nominal variable, 名义变量Nonconstancy of variability, 变异的非定常性Nonlinear regression, 非线性有关Nonparametric statistics, 非参数统计Nonparametric test, 非参数检验Nonparametric tests, 非参数检验Normal deviate, 正态离差Normal distribution, 正态分布Normal equation, 正规方程组Normal ranges, 正常范围Normal value, 正常值Nuisance parameter, 多余参数/讨厌参数Null hypothesis, 无效假设Numerical variable, 数值变量Objective function, 目标函数Observation unit, 观察单位Observed value, 观察值One sided test, 单侧检验One-way analysis of variance, 单因素方差分析Oneway ANOVA , 单因素方差分析Open sequential trial, 开放型序贯设计Optrim, 优切尾Optrim efficiency, 优切尾效率Order statistics, 顺序统计量Ordered categories, 有序分类Ordinal logistic regression , 序数逻辑斯蒂回归Ordinal variable, 有序变量Orthogonal basis, 正交基Orthogonal design, 正交试验设计Orthogonality conditions, 正交条件ORTHOPLAN, 正交设计Outlier cutoffs, 离群值截断点Outliers, 极端值OVERALS , 多组变量的非线性正规有关Overshoot, 迭代过度Paired design, 配对设计Paired sample, 配对样本Pairwise slopes, 成对斜率Parabola, 抛物线Parallel tests, 平行试验Parameter, 参数Parametric statistics, 参数统计Parametric test, 参数检验Partial correlation, 偏有关Partial regression, 偏回归Partial sorting, 偏排序Partials residuals, 偏残差Pattern, 模式Pearson curves, 皮尔逊曲线Peeling, 退层Percent bar graph, 百分条形图Percentage, 百分比Percentile, 百分位数Percentile curves, 百分位曲线Periodicity, 周期性Permutation, 排列P-estimator, P估计量Pie graph, 饼图Pitman estimator, 皮特曼估计量Pivot, 枢轴量Planar, 平坦Planar assumption, 平面的假设PLANCARDS, 生成试验的计划卡Point estimation, 点估计Poisson distribution, 泊松分布Polishing, 平滑Polled standard deviation, 合并标准差Polled variance, 合并方差Polygon, 多边图Polynomial, 多项式Polynomial curve, 多项式曲线Population, 总体Population attributable risk, 人群归因危险度Positive correlation, 正有关Positively skewed, 正偏Posterior distribution, 后验分布Power of a test, 检验效能Precision, 精密度Predicted value, 预测值Preliminary analysis, 预备性分析Principal component analysis, 主成分分析Prior distribution, 先验分布Prior probability, 先验概率Probabilistic model, 概率模型probability, 概率Probability density, 概率密度Product moment, 乘积矩/协方差Profile trace, 截面迹图Proportion, 比/构成比Proportion allocation in stratified random sampling, 按比例分层随机抽样Proportionate, 成比例Proportionate sub-class numbers, 成比例次级组含量Prospective study, 前瞻性调查Proximities, 亲近性Pseudo F test, 近似F检验Pseudo model, 近似模型Pseudosigma, 伪标准差Purposive sampling, 有目的抽样QR decomposition, QR分解Quadratic approximation, 二次近似Qualitative classification, 属性分类Qualitative method, 定性方法Quantile-quantile plot, 分位数-分位数图/Q-Q图Quantitative analysis, 定量分析Quartile, 四分位数Quick Cluster, 快速聚类Radix sort, 基数排序Random allocation, 随机化分组Random blocks design, 随机区组设计Random event, 随机事件Randomization, 随机化Range, 极差/全距Rank correlation, 等级有关Rank sum test, 秩与检验Rank test, 秩检验Ranked data, 等级资料Rate, 比率Ratio, 比例Raw data, 原始资料Raw residual, 原始残差Rayleigh's test, 雷氏检验Rayleigh's Z, 雷氏Z值Reciprocal, 倒数Reciprocal transformation, 倒数变换Recording, 记录Redescending estimators, 回降估计量Reducing dimensions, 降维Re-expression, 重新表达Reference set, 标准组Region of acceptance, 同意域Regression coefficient, 回归系数Regression sum of square, 回归平方与Rejection point, 拒绝点Relative dispersion, 相对离散度Relative number, 相对数Reliability, 可靠性Reparametrization, 重新设置参数Replication, 重复Report Summaries, 报告摘要Residual sum of square, 剩余平方与Resistance, 耐抗性Resistant line, 耐抗线Resistant technique, 耐抗技术R-estimator of location, 位置R估计量R-estimator of scale, 尺度R估计量Retrospective study, 回顾性调查Ridge trace, 岭迹Ridit analysis, Ridit分析Rotation, 旋转Rounding, 舍入Row, 行Row effects, 行效应Row factor, 行因素RXC table, RXC表Sample, 样本Sample regression coefficient, 样本回归系数Sample size, 样本量Sample standard deviation, 样本标准差Sampling error, 抽样误差SAS(Statistical analysis system ), SAS统计软件包Scale, 尺度/量表Scatter diagram, 散点图Schematic plot, 示意图/简图Score test, 计分检验Screening, 筛检SEASON, 季节分析Second derivative, 二阶导数Second principal component, 第二主成分SEM (Structural equation modeling), 结构化方程模型Semi-logarithmic graph, 半对数图Semi-logarithmic paper, 半对数格纸Sensitivity curve, 敏感度曲线Sequential analysis, 贯序分析Sequential data set, 顺序数据集Sequential design, 贯序设计Sequential method, 贯序法Sequential test, 贯序检验法Serial tests, 系列试验Short-cut method, 简捷法Sigmoid curve, S形曲线Sign function, 正负号函数Sign test, 符号检验Signed rank, 符号秩Significance test, 显著性检验Significant figure, 有效数字Simple cluster sampling, 简单整群抽样Simple correlation, 简单有关Simple random sampling, 简单随机抽样Simple regression, 简单回归simple table, 简单表Sine estimator, 正弦估计量Single-valued estimate, 单值估计Singular matrix, 奇异矩阵Skewed distribution, 偏斜分布Skewness, 偏度Slash distribution, 斜线分布Slope, 斜率Smirnov test, 斯米尔诺夫检验Source of variation, 变异来源Spearman rank correlation, 斯皮尔曼等级有关Specific factor, 特殊因子Specific factor variance, 特殊因子方差Spectra , 频谱Spherical distribution, 球型正态分布Spread, 展布SPSS(Statistical package for the social science), SPSS统计软件包Spurious correlation, 假性有关Square root transformation, 平方根变换Stabilizing variance, 稳固方差Standard deviation, 标准差Standard error, 标准误Standard error of difference, 差别的标准误Standard error of estimate, 标准估计误差Standard error of rate, 率的标准误Standard normal distribution, 标准正态分布Standardization, 标准化Starting value, 起始值Statistic, 统计量Statistical control, 统计操纵Statistical graph, 统计图Statistical inference, 统计推断Statistical table, 统计表Steepest descent, 最速下降法Stem and leaf display, 茎叶图Step factor, 步长因子Stepwise regression, 逐步回归Storage, 存Strata, 层（复数）Stratified sampling, 分层抽样Stratified sampling, 分层抽样Strength, 强度Stringency, 严密性Structural relationship, 结构关系Studentized residual, 学生化残差/t化残差Sub-class numbers, 次级组含量Subdividing, 分割Sufficient statistic, 充分统计量Sum of products, 积与Sum of squares, 离差平方与Sum of squares about regression, 回归平方与Sum of squares between groups, 组间平方与Sum of squares of partial regression, 偏回归平方与Sure event, 必定事件Survey, 调查Survival, 生存分析Survival rate, 生存率Suspended root gram, 悬吊根图Symmetry, 对称Systematic error, 系统误差Systematic sampling, 系统抽样Tags, 标签Tail area, 尾部面积Tail length, 尾长Tail weight, 尾重Tangent line, 切线Target distribution, 目标分布Taylor series, 泰勒级数Tendency of dispersion, 离散趋势Testing of hypotheses, 假设检验Theoretical frequency, 理论频数Time series, 时间序列Tolerance interval, 容忍区间Tolerance lower limit, 容忍下限Tolerance upper limit, 容忍上限Torsion, 扰率Total sum of square, 总平方与Total variation, 总变异Transformation, 转换Treatment, 处理Trend, 趋势Trend of percentage, 百分比趋势Trial, 试验Trial and error method, 试错法Tuning constant, 细调常数Two sided test, 双向检验Two-stage least squares, 二阶最小平方Two-stage sampling, 二阶段抽样Two-tailed test, 双侧检验Two-way analysis of variance, 双因素方差分析Two-way table, 双向表Type I error, 一类错误/α错误Type II error, 二类错误/β错误UMVU, 方差一致最小无偏估计简称Unbiased estimate, 无偏估计Unconstrained nonlinear regression , 无约束非线性回归Unequal subclass number, 不等次级组含量Ungrouped data, 不分组资料Uniform coordinate, 均匀坐标Uniform distribution, 均匀分布Uniformly minimum variance unbiased estimate, 方差一致最小无偏估计Unit, 单元Unordered categories, 无序分类Upper limit, 上限Upward rank, 升秩Vague concept, 模糊概念Validity, 有效性VARCOMP (Variance component estimation), 方差元素估计Variability, 变异性Variable, 变量Variance, 方差Variation, 变异Varimax orthogonal rotation, 方差最大正交旋转Volume of distribution, 容积W test, W检验Weibull distribution, 威布尔分布Weight, 权数Weighted Chi-square test, 加权卡方检验/Cochran检验Weighted linear regression method, 加权直线回归Weighted mean, 加权平均数Weighted mean square, 加权平均方差Weighted sum of square, 加权平方与Weighting coefficient, 权重系数Weighting method, 加权法W-estimation, W估计量W-estimation of location, 位置W估计量Width, 宽度Wilcoxon paired test, 威斯康星配对法/配对符号秩与检验Wild point, 野点/狂点Wild value, 野值/狂值Winsorized mean, 缩尾均值Withdraw, 失访Youden's index, 尤登指数Z test, Z检验Zero correlation, 零有关Z-transformation, Z变换。

胡志文-20160725

error is a human action that produces an incorrect result, fault is an incorrect step, process, or data definition in a computer program and failure is the inability of a system or component to perform its required functions within specified performance requirements.
Problems of Mutation Testing and Higher Order Mutation Testing
Quang Vu Nguyen, Lech Madeyski Institute of Informatics, Wroclaw University of Technology,
Introduction
The process of MT can be explained simply in following steps: 1. Suppose we have a program P and a set of testcases T 2. Produce mutant P1 from P by inserting only one semantic fault into P 3. Execute T on P and P1 and save results as R and R1 4. Compare R1 with R: 4.1 If R1 ≠ R: T can detect the fault inserted and has killed the mutant. 4.2 If R1=R: There could be 2 reasons: + T can’t detect the fault, so have to improve T. + The mutant has the same semantic meaning as the original program. It’s equivalent mutant (an example of equivalent mutant is showed in Table 2)

十六格魔方复原方法

十六格魔方复原方法英文回答：The Rubik's Cube is a popular puzzle toy that consists of a 3x3x3 grid of small cubes. Each face of the cube is divided into nine smaller squares of different colors. The goal of the puzzle is to arrange the colors so that each face of the cube is a solid color.There are various methods to solve the Rubik's Cube, but one commonly used method is the "CFOP" method, which stands for Cross, F2L, OLL, and PLL. This method breaks down the solving process into different stages, making it easier to follow and understand.First, I start by solving the cross on one face of the cube. I look for a corner piece that has a color matching the center piece of the face I'm working on, and then I position it correctly. Then, I solve the edge pieces of the cross by aligning them with the corresponding colors on theadjacent faces.Next, I move on to the F2L stage, which stands forFirst Two Layers. In this stage, I solve the four corner-edge pairs on the first two layers of the cube. I look for a corner piece that has a color matching the center piece of the face I'm working on, and then I position it correctly. Then, I solve the edge piece by pairing it with the corresponding corner piece and inserting them together into their correct positions.After completing the F2L stage, I move on to the OLL stage, which stands for Orientation of the Last Layer. In this stage, I orient all the pieces on the last layer of the cube so that they are in their correct positions. There are 57 different OLL algorithms that can be used to solve this stage, and I choose the one that is most suitable for the current state of the cube.Finally, I move on to the PLL stage, which stands for Permutation of the Last Layer. In this stage, I permute the pieces on the last layer of the cube so that they are intheir correct positions. There are 21 different PLL algorithms that can be used to solve this stage, and I choose the one that is most suitable for the current stateof the cube.By following these steps, I am able to solve theRubik's Cube and restore it to its original state. It may take some practice and memorization of algorithms, but with time and patience, anyone can learn to solve the Rubik's Cube.中文回答：魔方是一种流行的益智玩具，由一个3x3x3的小方块网格组成。

PCGSE包（Principal Component Gene Set Enrichment）版本0

Package‘PCGSE’August20,2023Type PackageTitle Principal Component Gene Set EnrichmentVersion0.5.0Date2023-08-20Author H.Robert FrostMaintainer H.Robert Frost<***********************>Description Contains logic for computing the statistical association of vari-able groups,i.e.,gene sets,with respect to the principal components of genomic data. Depends R(>=2.15.0),RMTstat,MASS,methodsLicense GPL(>=2)Copyright Dartmouth CollegeNeedsCompilation noRepository CRANDate/Publication2023-08-2015:42:38UTCR topics documented:PCGSE-package (1)pcgse (3)sgse (7)Index11 PCGSE-package Implementation of the Principal Component Gene Set Enrichment(PCGSE)and Spectral Gene Set Enrichment(SGSE)algorithmsDescriptionContains logic to compute the statistical association between gene sets and the principal components of experimental data.12PCGSE-package DetailsPackage:PCGSEType:PackageVersion:0.4.1Date:2023-08License:GPL-3Principal component gene set enrichment is performed using the function pcgse.Spectral gene set enrichment is performed using the function sgse.NoteThis work was supported by the National Institutes of Health R01grants LM010098,LM011360, EY022300,GM103506and GM103534.Author(s)H.Robert FrostReferences•Frost,H.R.,Li,Z.,and Moore,J.H.(2014).Principal component gene set enrichment (PCGSE).ArXiv e-prints.arXiv:1403.5148.•Frost,H.R.,Li,Z.,and Moore,J.H.(2014).Spectral gene set enrichment(SGSE).ArXiv e-prints.pcgse Principal component gene set enrichment(PCGSE)algorithmDescriptionImplementation of the PCGSE putes the statistical association between gene sets and the principal components of experimental data using a two-stage competitive test.Supported gene-level test statistics include the PC loadings for each genomic variable,the Pearson correlation coefﬁcients between each genomic variable and each PC and the Fisher-transformed correlation coefﬁcients.The input data is centered and scaled so that eigendecomposition is computed on the sample correlation matrix rather than the sample covariance matrix.Because the PC loadings for PCA on a correlation matrix are proportional to the Pearson correlation coefﬁcients between each PC and each variable,all supported gene-level statistics provide a measure of correlation between genomic variables and PCs.Each gene set is quantiﬁed using either a standardized mean difference statistic or a standardized rank sum statistic.The statistical signiﬁcance of each gene set test statistic is computed according to a competitive null hypothesis using either a parametric test,a correlation-adjusted parametric test or a permutation test.Usagepcgse(data,prcomp.output,pc.indexes=1,gene.sets,gene.statistic="z", transformation="none",gene.set.statistic="mean.diff",gene.set.test="cor.adj.parametric",nperm=9999)Argumentsdata Empirical data matrix,observations-by-variables.Must be speciﬁed.Cannot contain missing values.prcomp.output Output of prcomp(data,center=T,scale=T).If not speciﬁed,it will be computed.pc.indexes Indices of the PCs for which enrichment should be computed.Defaults to1.gene.sets Data structure that holds gene set membership information.Must be either a binary membership matrix or a list of gene set member indexes.For the membermatrix,rows are gene sets,columns are genes,elements are binary membershipvalues.For the membership index list,each element of the list represents a geneset and holds a vector of indexes of genes that are members.Must be a matrix ifgene.set.test is set to"permutation".gene.statistic The gene-level statistic used to quantify the association between each genomic variable and each PC.Must be one of the following(default is"z"):•"loading":PC loading associated with the genomic variable.•"cor":Pearson correlation coefﬁcient between the PC and the genomic vari-able.•"z":Fisher-transformed Pearson correlation coefﬁcient.transformation Optional transformation to apply to the gene-level statistics.Must be one of the following(default is"none"):•"none":No transformations are applied to the gene-level statistics.•"abs.value":The absolute value of the gene-level statistics is used.gene.set.statisticThe gene set statisic computed from the gene-level statistics.Must be one of thefollowing(default is"mean.diff"):•"mean.diff":The standardized difference between the mean of the gene-level statistics for members of the gene set and the mean of the gene-levelstatistics for genomic variables not in the gene set.Equivalent to the U_Dstatistic from Barry et al.•"rank.sum":The standardized Wilcoxon rank sum statistic computed fromthe gene-level statistics for members of the gene set.Equivalent to the U_Wstatistic from Barry et al.gene.set.test The statistical test used to compute the signiﬁcance of the gene set statistics under a competitive null hypothesis.The"parametric"test is in the"class1"testcategory according to Barry et al.,the"cor.adj.parametric"and"permutation"tests are in the"class2"test category according to Barry et al.Must be one ofthe following(default is"cor.adj.parametric"):•"parametric":If the mean difference is being used as the gene set statis-tic,corresponds to a two-sided,two-sample t-test with equal variances.Ifthe rank sum is being used as the gene set statistic,this corresponds to atwo-sided,two-sample z-test based on the standardized rank sum statistic.NOTE:both of these tests incorrectly assume the gene-level statistics arei.i.d.and should therefore only be used for comparative purposes.•"cor.adj.parametric":Tests statistical signiﬁcance of the standardized andcorrelation-adjusted gene set statistic using a two-sided t-test or z-test.Sim-ilar to the CAMERA method by Wu et al.,standardization of either themean different statistic or rank sum statistic is performed using a varia-tion inﬂation factor based on the average pair-wise correlation between thegene-level statistics for members of the gene set.Per Barry et al.,this isapproximated by the average correlation between the genomic variables.Per Wu et al.,the signiﬁcance of the correlation-adjusted t-statistic is testedusing a two-sided t-test with n-2df and the signiﬁcance of the correlation-adjusted rank sum z-statistic is tested using a two-sided z-test.•"permutation":Tests gene set enrichment via the permutation distributionof the gene set statistic.The permutation distribution is computed via per-mutation of the sample labels,which,in this case,is equivalent to permu-tation of the elements of the target PC.This test is realized using the safe()function from the R safe package.The number of permutations is con-trolled by the"nperm"parameter.The gene.statistic cannot be set to"load-ings"with this option.Per Barry et al.,this correlation is approximated bythe average correlation between the genomic variables.This option can beextremely computationally expensive so should not be used for most appli-cations.nperm Number of permutations to perform.Only relevant if gene.set.test is set to"per-mutation".ValueList with the following elements:•p.values:Matrix with one row per gene set and one column for each tested PC.Elements are the two-sided competitive enrichment p-values.Multiple hypothesis correction is NOT applied to these p-values.•statistics:Matrix with one row per gene set and one column for each tested PC.Elements are the gene set test statistics for each gene set.Exampleslibrary(MASS)p=200##number of genomic variablesn=50##number of observationsf=20##number of gene sets##Create annotation matrix with disjoint gene setsgene.sets=matrix(0,nrow=f,ncol=p)for(i in1:f){gene.sets[i,((i-1)*p/f+1):(i*p/f)]=1}##Simulate MVN data with two population PCs whose loadings are##associated with the first and second gene sets,respectively.var1=2##variance of first population PCvar2=1##variance of second population PCdefault.var=.1##background variance of population PCsload=sqrt(.1)##value of population loading vector for gene set1on PC1and set2on PC2##Creates a first PC with loadings for just the first20genes and a##second PC with loadings for just the second20genesloadings1=c(rep(load,p/f),rep(0,p-p/f))loadings2=c(rep(0,p/f),rep(load,p/f),rep(0,p-2*p/f))##Create the population covariance matrixsigma=var1*loadings1%*%t(loadings1)+var2*loadings2%*%t(loadings2)+diag(rep(default.var,p))##Simulate MVN datadata=mvrnorm(n=n,mu=rep(0,p),Sigma=sigma)##Perform PCA on the standardized dataprcomp.output=prcomp(data,center=TRUE,scale=TRUE)##Execute PCGSE using Fisher-transformed correlation coefficients as the gene-level statistics, ##the standardized mean difference as the gene set statistic and an unadjusted two-sided,##two-sample t-test for the determination of statistical significance.pcgse.results=pcgse(data=data,prcomp.output=prcomp.output,pc.indexes=1:2,gene.sets=gene.sets,gene.statistic="z",transformation="none",gene.set.statistic="mean.diff",gene.set.test="parametric")##Apply Bonferroni correction to p-valuesfor(i in1:2){pcgse.results$p.values[,i]=p.adjust(pcgse.results$p.values[,i],method="bonferroni")}##Display the p-values for the first5gene sets for PCs1and2pcgse.results$p.values[1:5,]##Execute PCGSE again but using a correlation-adjusted t-testpcgse.results=pcgse(data=data,prcomp.output=prcomp.output,pc.indexes=1:2,gene.sets=gene.sets,gene.statistic="z",transformation="none",gene.set.statistic="mean.diff",sgse7gene.set.test="cor.adj.parametric")##Apply Bonferroni correction to p-valuesfor(i in1:2){pcgse.results$p.values[,i]=p.adjust(pcgse.results$p.values[,i],method="bonferroni") }##Display the p-values for the first5gene sets for PCs1and2pcgse.results$p.values[1:5,]sgse Spectral gene set enrichment(SGSE)algorithmDescriptionImplementation of the SGSE putes the statistical association between gene sets and the spectra of the speciﬁed data set.The association between each gene set and each PC is ﬁrst computed using the pcgse function.The PC-speciﬁc p-values are then combined using the weighted Z-method with weights set to either the PC variance or the PC variance scaled by the lower-tailed p-value calculated for the variance according to the Tracey-Widom distribution. Usagesgse(data,prcomp.output,gene.sets,gene.statistic="z",transformation="none",gene.set.statistic="mean.diff",gene.set.test="cor.adj.parametric",nperm=999,pc.selection.method="all",pc.indexes=NA,rmt.alpha=.05,pcgse.weight="rmt.scaled.var")Argumentsdata Empirical data matrix,observations-by-variables.Must be speciﬁed.Cannot contain missing values.prcomp.output Output of prcomp(data,center=T,scale=T).If not speciﬁed,it will be computed.gene.sets See documentation for gene.sets argument for pcgse function.gene.statistic See documentation for gene.statistic argument for pcgse function.transformation See documentation for transformation argument for pcgse function.gene.set.statisticSee documentation for gene.set.statistic argument for pcgse function.gene.set.test See documentation for gene.set.test argument for pcgse function.nperm See documentation for nperm argument for pcgse function.pc.selection.methodMethod used to determine the PCs for which enrichment will be computed.Mustbe one of the following:•"all":All PCs with non-zero variance will be used.8sgse•"speciﬁc":The set of PCs speciﬁed by pc.indexes will be used.•"rmt":The set of PCs with signiﬁcant eigenvalues according to the Tracy-Widom distribution for a white Wishart at the alpha speciﬁed by the"rmt.alpha"parameter.pc.indexes Indices of the PCs for which enrichment should be computed.Must be speciﬁedif pc.selection.method is"speciﬁc".rmt.alpha Signiﬁcance level for selection of PCs according to the Tracy-Widom distribu-tion.Must be speciﬁed if pc.selection.method is"rmt".pcgse.weight Type of weight to use with the weighted Z-method to combine the p-valuesfrom the PCGSE tests on all PCs selected according to the pc.selection.methodparameter value.Must be one of the following:•"variance":The PC variance is used as the weight.NOTE:this should onlybe used for evaluation and testing.•"rmt.scaled.var":The product of the PC variance and the Tracey-Widomlower-tailed p-value for the eigenvalue associated with the PC is used asthe weight.ValueList with the following elements:•"pc.indexes":Indices of the PCs on which enrichment was performed.•"pcgse":Output from pcgse function on the PCs identiﬁed by pc.indexes.•"sgse":Vector of combined p-values for all PCs identiﬁed by pc.indexes.•"weights":Vector of PC-speciﬁc weights for the PCs identiﬁed by pc.indexes.See AlsopcgseExampleslibrary(MASS)p=200##number of genomic variablesn=50##number of observationsf=20##number of gene sets##Create annotation matrix with disjoint gene setsgene.sets=matrix(0,nrow=f,ncol=p)for(i in1:f){gene.sets[i,((i-1)*p/f+1):(i*p/f)]=1}##Simulate MVN data where the##first population PC loadings are##associated with the first gene set.sgse9 var=2##variance of first population PCdefault.var=.1##background variance of population PCsload=sqrt(.1)##value of population loading vector for gene set1on PC1##Creates a first PC with loadings for just the first20genes and aloadings=c(rep(load,p/f),rep(0,p-p/f))##Create the population covariance matrixsigma=var*loadings%*%t(loadings)+diag(rep(default.var,p))##Simulate MVN datadata=mvrnorm(n=n,mu=rep(0,p),Sigma=sigma)##Perform PCA on the standardized dataprcomp.output=prcomp(data,center=TRUE,scale=TRUE)##Execute SGSE using Fisher-transformed correlation coefficients as##the gene-level statistics,the standardized mean difference as the##gene set statistic and a correlation adjusted two-sided,##two-sample t-test for the determination of statistical significance,##all PCs with non-zero eigenvalues for spectral enrichment and##variance weightssgse.results=sgse(data=data,prcomp.output=prcomp.output,gene.sets=gene.sets,gene.statistic="z",transformation="none",gene.set.statistic="mean.diff",gene.set.test="cor.adj.parametric",pc.selection.method="all",pcgse.weight="variance")##Display the PCGSE p-values for the first5gene sets for PC1sgse.results$pcgse$p.values[1:5,1]##Display the SGSE weights for the first5PCssgse.results$weights[1:5]##Display the SGSE p-values for the first5gene setssgse.results$sgse[1:5]##Execute SGSE again but using RMT scaled variance weightssgse.results=sgse(data=data,prcomp.output=prcomp.output,gene.sets=gene.sets,gene.statistic="z",transformation="none",gene.set.statistic="mean.diff",gene.set.test="cor.adj.parametric",pc.selection.method="all",pcgse.weight="rmt.scaled.var")##Display the SGSE weights for the first5PCs10sgse sgse.results$weights[1:5]##Display the SGSE p-values for the first5gene setssgse.results$sgse[1:5]##Execute SGSE again using RMT scaled variance weights and##all RMT-significant PCs at alpha=.05sgse.results=sgse(data=data,prcomp.output=prcomp.output,gene.sets=gene.sets,gene.statistic="z",transformation="none",gene.set.statistic="mean.diff",gene.set.test="cor.adj.parametric",pc.selection.method="rmt",rmt.alpha=.05,pcgse.weight="rmt.scaled.var")##Display the indexes of the RMT-significant PCssgse.results$pc.indexes##Display the SGSE p-values for the first5gene setssgse.results$sgse[1:5]Index∗ﬁlepcgse,3sgse,7∗packagePCGSE-package,1pcgse,3,8PCGSE-package,1sgse,711。

informedSen包的说明文档说明书

Package‘informedSen’October13,2022Type PackageTitle Sensitivity Analysis Informed by a Test for BiasVersion1.0.7Author Paul R RosenbaumMaintainer Paul R Rosenbaum<***********************.edu>Description After testing for biased treatment assignment in an observational study using an unaf-fected outcome,the sensitivity analysis is constrained to be compatible with that test.The pack-age uses the optimization software gurobi obtainable from<https:///>,to-gether with its associated R package,also called gurobi;see:<https:///documentation/7.0/refman/installing_the_r_package.html>.The method is a substan-tial computational and practical enhancement of a concept introduced in Rosenbaum(1992)De-tecting bias with conﬁdence in observational studies Biometrika,79(2),367-374<doi:10.1093/biomet/79.2.367>.License GPL-2Encoding UTF-8LazyData trueImports sensitivitymult,statsEnhances gurobiDepends R(>=3.5.0)NeedsCompilation noRepository CRANDate/Publication2021-08-0409:50:05UTCR topics documented:informedSen-package (2)HDL (4)informedsen (5)senmscores (7)Index91informedSen-package Sensitivity Analysis Informed by a Test for BiasDescriptionAfter testing for biased treatment assignment in an observational study using an unaffected outcome,the sensitivity analysis is constrained to be compatible with that test.The package uses the optimiza-tion software gurobi obtainable from<https:///>,together with its associated Rpackage,also called gurobi;see:<https:///documentation/7.0/refman/installing_the_r_package.html>.The method is a substantial computational and practical enhancement of a concept introduced inRosenbaum(1992)Detecting bias with conﬁdence in observational studies Biometrika,79(2),367-374<doi:10.1093/biomet/79.2.367>.DetailsThe DESCRIPTIONﬁle:Package:informedSenType:PackageTitle:Sensitivity Analysis Informed by a Test for BiasVersion: 1.0.7Author:Paul R RosenbaumMaintainer:Paul R Rosenbaum<***********************.edu>Description:After testing for biased treatment assignment in an observational study using an unaffected outcome,the sensiti License:GPL-2Encoding:UTF-8LazyData:trueImports:sensitivitymult,statsEnhances:gurobiDepends:R(>=3.5.0)Index of help topics:HDL Light Daily Alcohol and HDL Cholesterol LevelsinformedSen-package Sensitivity Analysis Informed by a Test forBiasinformedsen Sensitivity Analysis Informed by a Test forUnmeasured Biassenmscores Computes M-scores for M-tests.The package performs a sensitivity analysis within a conﬁdence set provided by a test for unmea-sured bias.The method is a substantial computational and practical enhancement of a concept intro-duced in Rosenbaum(1992)Detecting bias with conﬁdence in observational studies.Biometrika,79(2),367-374.<doi:10.1093/biomet/79.2.367>The main function in the package is informedsen.The package uses the optimization software gurobi obtainable from<https:///>,to-gether with its associated R package,also called gurobi;see:<https:///documentation/7.0/refman/installing_See the example in informedsen for discussion about obtaining gurobi and its associated local R-package.Author(s)Paul R RosenbaumMaintainer:Paul R Rosenbaum<***********************.edu>ReferencesRosenbaum,P.R.(1984).From association to causation in observational studies:The role of tests of strongly ignorable treatment assignment.Journal of the American Statistical Association79, 41-48.<doi:10.1080/01621459.1984.10477060>Rosenbaum,P.R.(1989a).On permutation tests for hidden biases in observational studies.The Annals of Statistics17,643-653.<doi:10.1214/aos/1176347131>Rosenbaum,P.R.(1989b).The role of known effects in observational studies.Biometrics45, 557-569.<doi:10.2307/2531497>Rosenbaum,P.R.(1992).Detecting bias with conﬁdence in observational studies.Biometrika, 79(2),367-374.<doi:10.1093/biomet/79.2.367>Rosenbaum,P.R.(2007)Sensitivity analysis for m-estimates,tests and conﬁdence intervals in matched observational studies.Biometrics,2007,63,456-464.<doi:10.1111/j.1541-0420.2006.00717.x> Rosenbaum,P.R.(2021).Sensitivity analyses informed by tests for bias in observational stud-ies.Manuscript.This manuscript describes and illustrates the new computational tools that make feasible the method in Rosenbaum(1992).The example in the package is the example in this manuscript.Examples##Not run:#To run these examples,you MUST have gurobi installed.#The makers of gurobi provide free access to academics.#Additionally,you must install the local R package gurobi#that is provided by installing gurobi.#The examples are from Rosenbaum(2021)data(HDL)shdl<-senmscores(HDL$hdl,HDL$z,HDL$mset)smmerc<-senmscores(HDL$mmercury,HDL$z,HDL$mset)sc<-cbind(shdl,smmerc)informedsen(3.5,sc,HDL$z,HDL$mset,alpha=0.05)informedsen(3.4,sc,HDL$z,HDL$mset,alpha=c(0.04,0.01))##End(Not run)4HDL HDL Light Daily Alcohol and HDL Cholesterol LevelsDescriptionAn observational study of light daily alcohol consumption(1-3drinks per day)versus little or no alcohol,and its possible effects on HDL cholesterol levels.The level of methylmercury is viewed as an unaffected outcome and used to test for biased treatment assignment.Data is from NHANES 2013/2014and2015/2016.Usagedata("HDL")FormatA data frame with800observations on the following9variables.SEQN NHANES sequence numbernh Either1314for NHANES2013/2014or1516for NHANES2015/2016z Treatment indicator,z=1for light daily alcohol or z=0for little or no alcohol.mset Matched set indicator,1to200,for200matched sets,each containing one treated and three controls.age Age in ed in matching.female1for female,0for ed in matching.education NHANES1-5education scale.1is<9th grade,3is high school,5is at least a BA degree.hdl HDL cholesterol levelmmercury Methylmercury levelSourceUS National Health and Nutrition Examination Survey.Publicly available on-line.ReferencesLoConte,N.K.,Brewster,A.M.,Kaur,J.S.,Merrill,J.K.,and Alberg,A.J.(2018).Alcohol and cancer:a statement of the American Society of Clinical Oncology.Journal of Clinical Oncology 36,83-93.Rosenbaum,P.R.(2021).Sensitivity analyses informed by tests for bias in observational studies.Manuscript.See its data appendix.Suh,I.,Shaten,B.J.,Cutler,J.A.,and Kuller,L.H.(1992).Alcohol use and mortality from coronary heart disease:the role of high-density lipoprotein cholesterol.Annals of Internal Medicine 116,881-887.Examplesdata(HDL)boxplot(HDL$age~HDL$z)#ages are similarboxplot(HDL$hdl~HDL$z)#hdl is higherboxplot(HDL$mmercury~HDL$z,log="y")#methylmercury is higherinformedsen Sensitivity Analysis Informed by a Test for Unmeasured BiasDescriptionThe function does a a sensitivity analysis for one outcome informed or constrained by the results ofa test for unmeasured bias based on another outcome known to be unaffected by the treatment.Thepackage uses gurobi to solve a quadratically constrained quadratic program.To use the package, the gurobi solver must be installed.See the discussion about installing gurobi in the example below.Usageinformedsen(gamma,sc,z,mset,alpha=0.05)Argumentsgamma The sensitivity parameter.A number greater than or equal to1.sc A matrix with N rows and at least two columns.Theﬁrst column is the primary outcome,typically after scoring using senmscores.The remaining columns areunaffected outcomes used to test for bias,typically after scoring using senm-scores.z A vector of length N whose N coordinates are1for treated,0for control.mset A vector of length N indicating the matched set.Each matched set contains one treated individual and the sameﬁxed number of controls.alpha A vector with length equal to the number of columns of sc.The jth coordinate of alpha is the level of the test applied to the jth column of sc.If alpha is a scalar,it is repeated for every column of sc.Valueresult Text indicating whether or not the test for bias rejects all biases of magnitude Gamma or less.If yes,then the conclusion is that you must increase Gamma tocontinue.If no,then the test on the promary outcome is conducted inside theconﬁdence set deﬁned by a test for bias.The text begins after gurobi prints itsstandard output for the underlying optimization problem.optimization.problemReiterates the result above,where the word yes means the optimization problemis infeasible,and the word no means it is feasible.See the conclusion for ascientiﬁc interpretation of this aspect of the output.conclusion Text indicating the result of the test for effect on the primary outcome.deviates A vector of standardized deviates that might be compared with the standard Nor-mal distribution.There is one deviate for each column of sc.If sc has columnnames,then the column names label the deviates.The deviates are computedat the treatment assignment probabilities,theta,that solve the constrained opti-mization problem.alphas A vector of two-sided levels used for the deviates,together with their total.Thetotal is relevant if the Bonferroni inequality is used to ensure joint level of allthe tests.The absolute deviates might be compared with qnorm(1-alphas/2)fora two-sided test.NoteWhen gurobi is called,it produces extensive output.The output for informedsen appears at the end,after gurobi has produced its output.Most users will wish to skip to the end,for the output frominformedsen,returning to the gurobi output only if needed.informedsen checks that your input has the required form,and it will stop if there is a problem withyour input.For instance,informedsen will stop if you supply a value of gamma that is less than one.Author(s)Paul R.RosenbaumReferencesBerger,R.L.and Boos,D.D.(1994).P-values maximized over a conﬁdence set for the nuisance pa-rameter.Journal of the American Statistical Association,89,1012-1016.<doi:10.1080/01621459.1994.10476836> Rosenbaum,P.R.(1984).From association to causation in observational studies:The role of testsof strongly ignorable treatment assignment.Journal of the American Statistical Association79,41-48.<doi:10.1080/01621459.1984.10477060>Rosenbaum,P.R.(1989a).On permutation tests for hidden biases in observational studies.TheAnnals of Statistics17,643-653.<doi:10.1214/aos/1176347131>Rosenbaum,P.R.(1989b).The role of known effects in observational studies.Biometrics45,557-569.<doi:10.2307/2531497>Rosenbaum,P.R.(1992).Detecting bias with conﬁdence in observational studies.Biometrika,79(2),367-374.<doi:10.1093/biomet/79.2.367>Rosenbaum,P.R.(2007)Sensitivity analysis for m-estimates,tests and conﬁdence intervals inmatched observational studies.Biometrics,2007,63,456-464.<doi:10.1111/j.1541-0420.2006.00717.x>Rosenbaum,P.R.(2021).Sensitivity analyses informed by tests for bias in observational studies.Manuscript.Examples##Not run:#To run these examples,you MUST have gurobi installed.#gurobi is available for free to academic faculty#Search for the gurobi web page,and click the menu for Academia#Search for"gurobi and R"to find gurobi s local R package#connecting gurobi and R.You must install both gurobi#and its local R package to run informedsen.##The examples are from Rosenbaum(2021)##gurobi generates output before the output from informedsen#appears.In a first use,you might skip to the output#from informedsen,which begins with text labeled result.#data(HDL)shdl<-senmscores(HDL$hdl,HDL$z,HDL$mset)smmerc<-senmscores(HDL$mmercury,HDL$z,HDL$mset)sc<-cbind(shdl,smmerc)#A test within the confidence setinformedsen(3.5,sc,HDL$z,HDL$mset,alpha=0.05)#A test within the confidence set using#the method of Berger and Boos(1994)informedsen(3.4,sc,HDL$z,HDL$mset,alpha=c(0.04,0.01))#An example in which the confidence set is emptyinformedsen(1.25,sc,HDL$z,HDL$mset,alpha=.05)##End(Not run)senmscores Computes M-scores for M-tests.DescriptionComputes M-scores for an M-test with one outcome in1-to-k matched sets,forﬁxed k>=1.For the one-sample problem or matched pairs,Maritz(1979)proposed robust tests and conﬁdence intervals based on Huber’s(1981)M-estimates.These tests are extended to matching with several controls in Rosenbaum(2007).Usagesenmscores(y,z,mset,inner=0,trim=3,lambda=1/2)Argumentsy A vector of length N for one outcome.z A vector whose N coordinates are1for treated,0for control.mset A vector of length N giving the matched set.inner See trim.trim The two values,inner and trim,deﬁne the M-statistic’s psi-function.The psi-function is an odd function,psi(y)=-psi(-y),so it sufﬁces to deﬁne it for non-negative y.For nonnegative y,psi(y)equals0for y between0and inner,riseslinearly from0to1for y between inner and trim,and equals1for y greater thantrim.There are two requirements:inner must be nonnegative,and trim must belarger than inner.lambda A number strictly between0and1.The M-scores are psi(y/s)where s is thelambda quantile of the within-set absolute pair differences.DetailsThe choice of psi-function to increase insensitivity to unmeasured bias is discussed in Rosenbaum (2013),where the parameter inner is proposed.ValueA vector of length N containing the M-scores.NoteThe function is essentially a wrapper for the mscoresv function in the sensitivitymult package.It is easier to use senmscores when using the informedSen package.Author(s)Paul R.RosenbaumReferencesHuber,P.(1981).Robust Statistics.NY:Wiley.Maritz,J.S.(1979).A note on exact robust condence intervals for location.Biometrika66,163-170.Rosenbaum,P.R.(2007)Sensitivity analysis for m-estimates,tests and conﬁdence intervals in matched observational studies.Biometrics,2007,63,456-464.<doi:10.1111/j.1541-0420.2006.00717.x> Rosenbaum,P.R.(2013).Impact of multiple matched controls on design sensitivity in observational studies.Biometrics69118-127.(Introduces inner trimming.)<doi:10.1111/j.1541-0420.2012.01821.x> Rosenbaum,P.R.(2015).Two R packages for sensitivity analysis in observational studies.Obser-vational Studies,v.1.(Free on-line.)Examplesdata(HDL)shdl<-senmscores(HDL$hdl,HDL$z,HDL$mset)plot(HDL$hdl,shdl)Index∗Causal inferenceinformedsen,5informedSen-package,2∗Control outcomeinformedsen,5informedSen-package,2∗Known effectinformedsen,5informedSen-package,2∗Observational studyinformedsen,5informedSen-package,2∗Placebo testinformedsen,5informedSen-package,2∗Sensitivity analysisinformedsen,5informedSen-package,2∗Test for biasinformedsen,5informedSen-package,2∗Unaffected outcomeinformedsen,5informedSen-package,2∗datasetsHDL,4∗designinformedsen,5∗htestinformedsen,5senmscores,7∗packageinformedSen-package,2HDL,4informedSen(informedSen-package),2 informedsen,5informedSen-package,2senmscores,79。

Bootstrap和Permutation方法在样本率多重比较中的应用

Bootstrap和Permutati on方法在样本率多重比较中的应用钱　俊　陈平雁【摘要】　目的　介绍Bootstrap和Per mutati on方法在样本率多重比较中的应用。

方法调用S AS中的MULTTEST 过程,编写程序实现样本率的两两比较和与控制组比较,并通过实例说明效果。

结果运用Bootstrap和Per mutati on方法能较好解决样本率的多重比较问题。

结论使用Bootstrap和Per mutati on方法的S AS程序,简单明了,结果准确,使用方便。

【关键词】　Bootstrap　Per mutati on　样本率　多重比较中图分类号:R195.1　文献标识码:A　文章编号:100625253(2008)0120043203Appli ca ti on s of bootstrap and per m ut a ti on on m ulti ple co m par ison s i n proporti on s　Q I AN Jun,CHEN P ing2yan.Southern M edical U niversity,Guangzhou510515,China【Abstract】　O bjecti ve　To exp l ore the app lying of bootstrap and per mutati on on multi p le comparis ons in p r oporti ons. M ethods　Comp leted pair wise comparis ons and multi p le comparis ons with the contr ol in p ractical app licati ons using S AS lan2 guage and the MULTTEST p r ocedures.Results　Achieved multi p le comparis ons in p r oporti ons by bootstrap and per mutati on methods.Conclusi on　The S AS p r ogram for bootstrap and per mutati on is useful,exp licit,and p r ovided with perfect results.【Key words】　Bootstrap　Per mutati on　Pr oporti on　M ulti p le comparis ons 样本率多重比较常用的方法有Scheffe可信区间法、S NK法、B runden法、杜养志法等[123]。

2024年考研英语1试卷

1、Which of the following strategies is NOT typically recommended for improving reading comprehension in an academic context?A. Actively summarizing paragraphs as you readB. Skimming the text for main ideas before deep readingC. Underlining every unfamiliar word for later reviewD. Making connections between the text and prior knowledge (答案：C)2、In a research paper, the abstract serves as a:A. Detailed explanation of the methodology usedB. Concise summary of the entire study's findingsC. List of all references cited in the documentD. Discussion of future research directions (答案：B)3、Which of these phrases is correctly punctuated?A. The report, which was due last Friday, is still not finished.B. The report which was due last Friday, is still not finished.C. The report which was due, last Friday is still not finished.D. The report, which was due last Friday is still, not finished. (答案：A)4、When writing a thesis statement for an argumentative essay, it should:A. Present a fact without offering an opinionB. Be vague and open-ended to avoid controversyC. Clearly state the author's position on the topicD. Focus on multiple unrelated ideas (答案：C)5、In the context of academic writing, which of the following is considered plagiarism?A. Paraphrasing a source without proper citationB. Using direct quotes with correct attributionC. Summarizing a complex idea in simpler termsD. Acknowledging limitations in your own research (答案：A)6、Which of the following is NOT a common type of paragraph structure in academic writing?A. Topic sentence followed by supporting detailsB. Chronological order of eventsC. Problem-solution formatD. Random assortment of unrelated ideas (答案：D)7、When analyzing a pie chart in a research report, the reader should expect to find:A. A detailed narrative of the research processB. A list of raw data used to create the chartC. A visual representation of quantitative data along with brief explanationsD. An extensive history of chart design methodologies (答案：C)8、In a compare-and-contrast essay, the primary purpose is to:A. Argue for one side of an issueB. Describe the similarities between two subjectsC. Highlight both similarities and differences between two or more subjectsD. Provide a step-by-step guide on how to perform a task (答案：C)。

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1 Introduction
The work in this paper was motivated by examples such as the following. Example 1. Schiffman et. al (1978), with statistical assistance by one of the authors† , studied the inﬂuence of a doctor’s prior probabilities of diseases on diagnosis. Statistical thinking, which can be formalized in Bayesian terms, suggests that given a set of symptoms, a doctor’s diagnosis or ranking of possible diagnoses should be inﬂuenced not only by the symptoms, but also by the disease prevalence at the time of diagnosis. Doctors’ information on prevalence may come, for example, from textbooks, articles, and personal experience. The goal of the study was to verify the inﬂuence of personal prior information or opinion on disease prevalence (henceforth referred to as “personal prior”) on diagnosis and help determine whether doctors need to be better educated to take prevalence into account, or if providing them with information on prevalence at the time of diagnosis is useful. In this study each doctor in a sample produced ﬁrst a ranking X of the prevalence, or of the probability of various diseases from a given list; such a ranking represents the doctor’s personal prior. A compatible medical scenario was then presented to all doctors, and each one of them produced a ranked list Y of possible diagnoses from the same given list. Rank correlations between X and Y for each doctor were then computed. To test the hypotheses that a doctor’s personal prior does not inﬂuence his diagnostic rankings, a null hypotheses of zero correlation between each doctor’s X and Y is not appropriate. Even with no such inﬂuence, one
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Received September 2003 and revised November 2003
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would expect that pairs of rankings would have some nonzero baseline correlation due to the inﬂuence of other factors like common medical knowledge. The null hypothesis of interest that there is no inﬂuence of personal prior is complex since the baseline correlation is unknown. The presence of an unknown baseline correlation raises the question of how high the within-doctor rank correlations need to be to reject the null hypothesis and assert the claim that there is inﬂuence of personal prior on diagnostic rankings. Correlations are used here as a measure of similarity between ranked lists. Henceforth we will talk about similarity in general, and the approach applies to any measure of similarity or proximity deﬁned on the sample space. The main focus of this paper is on examples of the following kind: Example 2. This example is somewhat artiﬁcial, but it is simpler and can clarify the issue; it will also help in explaining the example that follows it which is rather similar. Consider an instructor who wants to know if students are copying from their neighbors in a class where students take an exam while seated in pairs. Given a measure of similarity between exams, we expect any two exams to be similar even in the absence of copying. Common knowledge that all students hopefully have would make their exams similar to a certain, unknown degree. Therefore, we want to test if the similarity between seated pairs is unusual (due to copying) relative to some unknown baseline similarity. This example is different from the ﬁrst in that here a similarity score can be computed for any pair of exams Xi , Xj , whereas in the ﬁrst example the correlations of interest are those between X and Y. Example 3. Situations similar to Example 2 arise naturally in environmental and medical studies, where subjects in a given study group are matched (paired) by certain common background of interest, such as having lived in the same neighborhood during a given period, having certain common medical conditions or having certain variables in common (e.g., gender, age, weight, etc.). In order to assess the inﬂuence of the background in question on a given set of certain medical conditions (denoted by Xi for subject i), one should test whether matched pairs are more similar than unmatched ones relative to the medical condition being studied. The baseline similarity between unmatched pairs is again unknown, but a certain degree of similarity must certainly exist due to common factors that all subject in the particular study might have. More speciﬁcally, suppose we have an even number n of subjects and those indexed by 2i − 1 and 2i form the matched pairs for i = 1, . . . , n/2, and let Xi measure subject i’s medical condition. Our goal is to test whether all X2i−1 and Xi , which arise from the matched pairs, exhibit more similarity then Xi and Xj from unmatched pairs. 2