geometrical phase in the cyclic evolution of non hermitian systems the authors derive by a biorthonormal state approach the analogy of berry s phase factor for open non conservative systems for both adiabatic and non adiabatic evolution in the latter case a non unitary evolution operator method is exploited an application is given to the optical supermode propagation in the free electron laser

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

estimation of false discovery rates in multiple testing application to gene microarray data testing for significance with gene expression data from dna microarray experiments involves simultaneous comparisons of hundreds or thousands of genes if r denotes the number of rejections declared significant genes and v denotes the number of false rejections then v r if r 0 is the proportion of false rejected hypotheses this paper proposes a model for the distribution of the number of rejections and the conditional distribution of v given r v r under the independence assumption the distribution of r is a convolution of two binomials and the distribution of v r has a noncentral hypergeometric distribution under an equicorrelated model the distributions are more complex and are also derived five false discovery rate probability error measures are considered fdr e v r pfdr e v r r 0 positive fdr cfdr e v r r r conditional fdr mfdr e v e r marginal fdr and efdr e v r empirical fdr the pfdr cfdr and mfdr are shown to be equivalent under the bayesian framework in which the number of true null hypotheses is modeled as a random variable we present a parametric and a bootstrap procedure to estimate the fdrs monte carlo simulations were conducted to evaluate the performance of these two methods the bootstrap procedure appears to perform reasonably well even when the alternative hypotheses are correlated rho 25 an example from a toxicogenomic microarray experiment is presented for illustration

on the benjamini hochberg method we investigate the properties of the benjamini hochberg method for multiple testing and of a variant of storey s generalization of it extending and complementing the asymptotic and exact results available in the literature results are obtained under two different sets of assumptions and include asymptotic and exact expressions and bounds for the proportion of rejections the proportion of incorrect rejections out of all rejections and two other proportions used to quantify the efficacy of the method

on the real and complex geometric phases some of the existing definitions of the real and complex geometric phases are unified and generalized the relationship of the real to the complex geometric phase is discussed it is shown why these two phases are in general completely independent in particular a simple explicit example is given which shows that the real geometric phase is not in general the real part of the complex geometric phase

non cyclic geometric phases in a proposed two photon interferometric experiment an experimental arrangement is proposed which combines the idea of two photon interferometry with that of geometric phases a pair of photons generated by parametric down conversion is fed into a pair of mach zehnder interferometers in each of which there is phase shift produced by the helically wound optical fibre in the manner of tomita and chiao 1986 if the winding angle is a multiple of 2 pi there is a closed path in parameter space in accordance with the pioneering analysis of berry 1984 more general windings are also considered in which the path in parameter space is not closed and the geometric phase for such open paths is calculated in accordance with the gauge invariant prescription of aitchison and wanelik if the proposed experiment is realized it will provide a test for the noncyclic geometric phase for photons and for the set of prescriptions equivalent to that of aitchison and wanelik 1992 furthermore the geometric phase in this arrangement will be unequivocally quantum mechanical because of the non classical character of two photon interferometry

gauge invariant reference section and geometric phase we use a gauge invariant reference section and define the geometric phase for all quantum evolutions in a closed form this geometric phase is obtained by integrating the inner product of the reference section and its path derivative along the evolution curve which is valid for non cyclic non unitary and non schrodinger evolutions of quantum systems two non trivial examples are studied to realize our new expression

quantum phase corrections from adiabatic iteration the phase change gamma acquired by a quantum state psi t rangle driven by a hamiltonian h 0 t which is taken slowly and smoothly round a cycle is given by a sequence of approximants gamma k obtained by a sequence of unitary transformations the phase sequence is not a perturbation series in the adiabatic parameter epsilon because each gamma k except gamma 0 contains epsilon to infinite order for spin frac 1 2 systems the iteration can be described in terms of the geometry of parallel transport round loops c k on the hamiltonian sphere non adiabatic effects transitions must cause the sequence of gamma k to diverge for spin systems with analytic h 0 t this happens in a universal way the loops c k are sinusoidal spirals which shrink as epsilon k until k sim epsilon 1 and then grow as k the smallest loop has a size exp 1 epsilon comparable with the non adiabaticity

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

budden smith s additional memory and the geometric phase budden smith considered vector waves in a z stratified medium driven by an arbitrary matrix a x depending on parameters x z x 1 z x 2 z which characterize the medium they showed that in the short wave limit there is not only the familiar optical path phase factor but an additional memory factor m whose exponent is the line integral along the ray of a certain 1 form constructed from the eigenvectors of a their discovery anticipated the geometric phase of quantum mechanics where z is time and a is the hermitian hamiltonian operator explicit connection is made between the two formalisms if a is symmetric or can be made symmetric by multiplication by a constant matrix the 1 form is integrable and m does not represent memory because it can be expressed locally in terms of the properties of the medium at the endpoints of the ray in quantum mechanics symmetrizability is equivalent to the hamiltonian possessing antiunitary symmetry e g time reversal a non integrable real m arises when light traverses a transparent medium with variable refractive index and optical activity however the non integrability here is cancelled by an extra contribution from the ordinary optical path length arising from an additional term in the constitutive relation between electric field and displacement which is necessary in an inhomogeneous medium to ensure its transparency

plots of p values to evaluate many tests simultaneously summary when a large number of tests are made possibly on the same data it is proposed to base a simultaneous evaluation of all the tests on a plot of cumulative p values using the observed significance probabilities the points corresponding to true null hypotheses should form a straight line while those for false null hypotheses should deviate from this line the line may be used to estimate the number of true hypotheses the properties of the method are studied in some detail for the problems of comparing all pairs of means in a one way layout testing all correlation coefficients in a large correlation matrix and the evaluation of all 2 x 2 subtables in a contingency table the plot is illustrated on real data

multiple testing strategy for analyzing cdna array data on gene expression summary an objective of many functional genomics studies is to estimate treatment induced changes in gene expression cdna arrays interrogate each tissue sample for the levels of mrna for hundreds to tens of thousands of genes and the use of this technology leads to a multitude of treatment contrasts by gene hypotheses tests evaluate the evidence supporting no effect but selecting a significance level requires dealing with the multitude of comparisons the p values from these tests order the genes such that a p value cutoff divides the genes into two sets ideally one set would contain the affected genes and the other would contain the unaffected genes however the set of genes selected as affected will have false positives i e genes that are not affected by treatment likewise the other set of genes selected as unaffected will contain false negatives i e genes that are affected a plot of the observed p values 1 p versus their expectation under a uniform 0 1 distribution allows one to estimate the number of true null hypotheses with this estimate the false positive rates and false negative rates associated with any p value cutoff can be estimated when computed for a range of cutoffs these rates summarize the ability of the study to resolve effects in our work we are more interested in selecting most of the affected genes rather than protecting against a few false positives an optimum cutoff i e the best set given the data depends upon the relative cost of falsely classifying a gene as affected versus the cost of falsely classifying a gene as unaffected we select the cutoff by a decision theoretic method analogous to methods developed for receiver operating characteristic curves in addition we estimate the false discovery rate and the false nondiscovery rate associated with any cutoff value two functional genomics studies that were designed to assess a treatment effect are used to illustrate how the methods allowed the investigators to determine a cutoff to suit their research goals

hunting for significance with the false discovery rate when testing a single hypothesis it is common knowledge that increasing the sample size after nonsignificant results and repeating the hypothesis test several times at unadjusted critical levels inflates the overall type i error rate severely in contrast if a large number of hypotheses are tested controlling the false discovery rate such hunting for significance has asymptotically no impact on the error rate more specifically if the sample size is increased for all hypotheses simultaneously and only the test at the final interim analysis determines which hypotheses are rejected a data dependent increase of sample size does not affect the false discovery rate this holds asymptotically for an increasing number of hypotheses for all scenarios but the global null hypothesis where all hypotheses are true to control the false discovery rate also under the global null hypothesis we consider stopping rules where stopping before a predefined maximum sample size is reached is possible only if sufficie

post hoc power estimation for topological inference in fmri when analyzing functional mri data several thresholding procedures are available to account for the huge number of volume units or features that are tested simultaneously the main focus of these methods is to prevent an inflation of false positives however this comes with a serious decrease in power and leads to a problematic imbalance between type i and type ii errors in this paper we show how estimating the number of activated peaks or clusters enables one to estimate post hoc how powerful the selection procedure performs this procedure can be used in real studies as a diagnostics tool and raises awareness on how much activation is potentially missed the method is evaluated and illustrated using simulations and a real data example our real data example illustrates the lack of power in current fmri research

nonexistence of solutions to hele shaw equations abstract we study nonexistence of the solutions to quasilinear elliptic differential equations arising from nonisothermal non newtonian hele shaw flows the proof is based on the trial function method developed by pohozaev without recourse to comparison theorems and to the maximum principle

the stationary thermistor problem with a current limiting device the electrical heating of a conductor connected with a current limiting device of total resistance r is studied under mixed boundary conditions a theorem of existence is given using a transformation which permits the reduction of the nonlinear system governing the problem to the classical mixed boundary value problem for the laplace equation

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

quantal phase factors accompanying adiabatic changes a quantal system in an eigenstate slowly transported round a circuit c by varying parameters r in its hamiltonian r will acquire a geometrical phase factor exp i c in addition to the familiar dynamical phase factor an explicit general formula for c is derived in terms of the spectrum and eigenstates of r over a surface spanning c if c lies near a degeneracy of c takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy as an illustration c is calculated for spinning particles in slowly changing magnetic fields although the sign reversal of spinors on rotation is a special case the effect is predicted to occur for bosons as well as fermions and a method for observing it is proposed it is shown that the aharonov bohm effect can be interpreted as a geometrical phase factor

asymptotic analysis of a non newtonian fluid in a thin domain with tresca law abstract in this paper we prove first the existence and uniqueness results for the weak solution to the stationary equations for non newtonian and incompressible fluid in a three dimensional bounded domain with tresca fluid solid interface on one part of the boundary and dirichlet one on the other part then we study the asymptotic analysis when one dimension of the fluid domain tend to zero the strong convergence of the velocity is proved a specific reynolds limit equation and the limit of tresca free boundary conditions are obtained the uniqueness of the velocity limit and the pressure limit are also proved

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

mixed variational formulation and numerical analysis of thermally coupled nonlinear darcy flows a mixed variational formulation and its finite element approximate procedure combined with a fixed point algorithm is presented for solving a thermally coupled nonlinear darcy flow problem existence and uniqueness of the solution to the nonlinear mixed variational formulation are established a more general result on uniqueness of the continuous problem is presented numerical analysis of the finite element approximation with the corresponding error estimates is given numerical results are presented confirming the expected rates of convergence and illustrating the influence of the exponent of the nonlinear power law constitutive equation

thermally coupled quasi newtonian flows analysis and computation in this paper we consider an incompressible quasi newtonian flow with a temperature dependent viscosity obeying a power law and the thermal balance includes viscous heating some mathematical results such as the existence and uniqueness are established finite element approximation based on an iterative solution scheme is proposed and convergence analysis is presented

mixed discontinuous galerkin analysis of thermally nonlinear coupled problem abstract a stabilized mixed discontinuous galerkin smdg method based on brezzi hughes marini masud f brezzi t j r hughes l d marini a masud mixed discontnuous galerkin methods for darcy flow j sci comput 22 2005 119 145 is proposed to solve a thermally coupled nonlinear elliptic system modeling a large class of engineering problems a fixed point algorithm is adopted to solve the nonlinear systems convergence analysis and error estimates are presented for equal order linear or bilinear discontinuous lagrangian finite element interpolations for all fields numerical results are presented confirming the predicted convergence rates and illustrating the performance of the proposed formulation solving problems with globally stable and blowing up solutions