zero temperature stochastic 3d ising model and dimer covering fluctuations a first step towards interface mean curvature motion we consider the glauber dynamics for the ising model with boundary conditions at zero temperature or at a temperature that goes to zero with the system size hence the quotation marks in the title in dimension d 3 we prove that an initial domain of linear size l of spins disappears within a time which is at most l2 log l c and at least l2 c log l for some c 0 the proof of the upper bound proceeds via comparison with an auxiliary dynamics which mimics the motion by mean curvature that is expected to describe on large time scales the evolution of the interface between and domains the analysis of the auxiliary dynamics requires recent results on the fluctuations of the height function associated to dimmer coverings of the infinite honeycomb lattice our result apart from the spurious logarithmic factors is the first rigorous confirmation of the lifshitz law const l2 conjectured on heuristic grounds 8 13 in dimension d 2 can be shown to be of order l2 without logarithmic corrections the upper bound was proven in 6 and here we provide the lower bound for d 2 we also prove that the spectral gap of the generator behaves like for l large as conjectured in 2 2011 wiley periodicals inc

markov processes of infinitely many nonintersecting random walks consider an n dimensional markov chain obtained from n one dimensional random walks by doob h transform with the q vandermonde determinant we prove that as n becomes large these markov chains converge to an infinite dimensional feller markov process the dynamical correlation functions of the limit process are determinantal with an explicit correlation kernel the key idea is to identify random point processes on z with q gibbs measures on gelfand tsetlin schemes and construct markov processes on the latter space independently we analyze the large time behavior of pushasep with finitely many particles and particle dependent jump rates it arises as a marginal of our dynamics on gelfand tsetlin schemes the asymptotics is given by a product of a marginal of the gue minor process and geometric distributions

a network algorithm for performing fisher s exact test in r c contingency tables abstract an exact test of significance of the hypothesis that the row and column effects are independent in an r c contingency table can be executed in principle by generalizing fisher s exact treatment of the 2 2 contingency table each table in a conditional reference set of r c tables with fixed marginal sums is assigned a generalized hypergeometric probability the significance level is then computed by summing the probabilities of all tables that are no larger on the probability scale than the observed table however the computational effort required to generate all r c contingency tables with fixed marginal sums severely limits the use of fisher s exact test a novel technique that considerably extends the bounds of computational feasibility of the exact test is proposed here the problem is transformed into one of identifying all paths through a directed acyclic network that equal or exceed a fixed length some interesting new optimization theorems are developed in the process the numer

a hierarchical bayesian model for combining multiple 2 x 2 tables using conditional likelihoods summary this paper introduces a hierarchical bayesian model for combining multiple 2 2 tables that allows the flexibility of different odds ratio estimates for different tables and at the same time allows the tables to borrow information from each other the proposed model however is different from a full bayesian model in that the nuisance parameters are eliminated by conditioning instead of integration the motivation is a more robust model and a faster and more stable gibbs algorithm we work out a gibbs scheme using the adaptive rejection sampling for log concave density and an algorithm for the mean and variance of the noncentral hypergeometric distribution the model is applied to a multicenter ulcer clinical trial

monte carlo methods for exploring sensitivity to distributional assumptions in a bayesian analysis of a series of 2 x 2 tables this paper develops monte carlo methods for a bayesian analysis of a series of 2 x 2 tables under a variety of distributional assumptions i assume that the data in each table were generated from a pair of binomial distributions and the logarithm of odds of a favourable response follows a bivariate distribution with means that are linear functions of covariates and an arbitrary covariance matrix i use gibbs and importance sampling methods to obtain various characteristics of the posterior distribution of the quantities of interest i apply the method to analyse the data from a population case control study given the size of the population at risk i also derive the posterior distribution of the risk difference defined as the difference in the probabilities of disease development in the exposed and unexposed groups

approximately exact inference for the common odds ratio in several 2 2 tables abstract the conditional maximum likelihood estimator mle of the common odds ratio in a sequence of independent 2 2 tables is known to be superior to the mantel haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known however a long standing barrier to the widespread use of this estimator has been computational intractability in particular the calculation of significance levels confidence sets and power based on the exact distribution requires fast and efficient algorithms an important class of such algorithms form the basis of statxact a software package able to solve various aspects of the exact inference problem for a sequence of several 2 2 tables in real time we provide an alternative methodology by developing several useful saddlepoint approximations to the exact distribution of the conditional mle the approximations are derived from an interesting representation for hypergeometric random variables as a sum of independent

fast computation of exact confidence limits for the common odds ratio in a series of 2 2 tables abstract the odds ratio is widely used as a measure of association in epidemiologic studies and clinical trials we consider calculation of exact confidence limits for the common odds ratio in a series of independent 2 2 tables and propose three modifications of the network algorithm of mehta patel and gray 1 formulating and dealing with the problem in algebraic instead of graph theoretic terms 2 performing convolutions on the natural scale instead of the logarithmic scale and 3 using the secant method instead of binary search to compute roots of polynomial equations enhancement of computational efficiency exceeding an order of magnitude afforded by these modifications is empirically demonstrated we also compare the modified method with one based on the fast fourier transform fft further we show that the fft method can also result in considerable loss of numerical accuracy the modifications proposed in this article yield an algorithm that is not only fast and accurate but that combine

gibbs ensembles of nonintersecting paths we consider a family of determinantal random point processes on the two dimensional lattice and prove that members of our family can be interpreted as a kind of gibbs ensembles of nonintersecting paths examples include probability measures on lozenge and domino tilings of the plane some of which are non translation invariant the correlation kernels of our processes can be viewed as extensions of the discrete sine kernel and we show that the gibbs property is a consequence of simple linear relations satisfied by these kernels the processes depend on infinitely many parameters which are closely related to parametrization of totally positive toeplitz matrices

step fluctuations for a faceted crystal a statistical mechanics model for a faceted crystal is the 3d ising model at zero temperature it is assumed that in one octant all sites are occupied by atoms the remaining ones being empty allowed atom configurations are such that they can be obtained from the filled octant through successive removals of atoms with breaking of precisely three bonds if v denotes the number of atoms removed then the grand canonical boltzmann weight is q v 0 q 1 as shown by cerf and kenyon in the limit q 1 a deterministic shape is attained which has the three facets 100 010 001 and a rounded piece interpolating between them we analyse the step statistics as q 1 in the rounded piece it is given by a determinantal process based on the discrete sine kernel exactly at the facet edge the steps have more space to meander their statistics is again determinantal but this time based on the airy kernel in particular the border step is well approximated by the airy process which has been obtained previously in the context of growth models our results are based on the asymptotic analysis for space time inhomogeneous transfer matrices

arctic boundaries of the ice model on three bundle domains in this paper we consider the six vertex model at ice point on an arbitrary three bundle domain which is a generalization of the domain wall ice model on the square or equivalently of a uniformly random alternating sign matrix we show that this model exhibits the arctic boundary phenomenon whose boundary is given by a union of explicit algebraic curves this was originally predicted by colomo and sportiello j stat phys 164 1488 1523 2016 as one of the initial applications of a general heuristic that they introduced for locating arctic boundaries called the geometric tangent method our proof uses a probabilistic analysis of non crossing directed path ensembles to provide a mathematical justification of their tangent method heuristic in this case which might be of independent interest

the arctic curve of the domain wall six vertex model the problem of the form of the arctic curve of the six vertex model with domain wall boundary conditions in its disordered regime is addressed it is well known that in the scaling limit the model exhibits phase separation with regions of order and disorder sharply separated by a smooth curve called the arctic curve to find this curve we study a multiple integral representation for the emptiness formation probability a correlation function devised to detect spatial transition from order to disorder we conjecture that the arctic curve for arbitrary choice of the vertex weights can be characterized by the condition of condensation of almost all roots of the corresponding saddle point equations at the same known value in explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle point equations the arctic curve is obtained in parametric form and appears to be a non algebraic curve in general it turns into an algebraic one in the so called root of unity cases the arctic curve is also discussed in application to the limit shape of q enumerated with 0 q 4 large alternating sign matrices in particular as q 0 the limit shape tends to a nontrivial limiting curve given by a relatively simple equation

exact versus asymptotic analysis for a matched case control study we compare exact and asymptotic methods for variable selection in matched case control studies data from a study of melanoma among the employees of the lawrence livermore national laboratory illustrate the comparisons relative to large sample methods the exact method almost always yielded larger p values the differences in p values became more pronounced with inclusion of more variables in the logistic model thus when the sample size is not large and there are many covariates under study use of the exact method tends to select more parsimonious models and avoids overfit of the data

on the deflected configuration of a slender elastic rod subject to parallel terminal forces and moments this paper investigates the three dimensional configurations of a slender elastic rod of uniform circular cross section subject to parallel terminal forces and moments the nonlinear equilibrium equations for the rod are established for a cartesian coordinate system and solved analytically without linearization consequently the results are applicable for large nonlinear elastic deformations

convexity properties of the surface tension and equilibrium crystals we study the thermodynamic limit of the orientation dependent surface tension under general conditions which we show to hold true for a large class of lattice systems we prove that the limit exists and that it satisfies some convexity properties related to the pyramidal inequality introduced by r l dobrushin and s b shlosman 1 we discuss some consequences of these results for the equilibrium crystal shape

bias corrected maximum likelihood estimator of a log common odds ratio summary a bias correction factor for the maximum likelihood estimator of the log common odds ratio for sparse data is derived which is applicable when the design is balanced and or when the number of strata is large the corrected maximum likelihood estimator is practically unbiased and its mean squared error is smaller than that of the uncorrected maximum likelihood estimator the correction factor for the maximum likelihood estimator approaches one as strata sizes increase examples demonstrate that the corrected maximum likelihood estimator and the exact conditional maximum likelihood estimator are essentially identical although the standard error of the former tends to be slightly smaller than that of the latter it is also demonstrated that a simple version of the correction factor is a satisfactory approximation the bias corrected maximum likelihood estimator proposed in this paper is the extension of breslow s 1981 and it can be useful particularly when the computational burden of the exact conditional method is excessive

estimating the asymptotics of solid partitions we study the asymptotic behavior of solid partitions using transition matrix monte carlo simulations if p 3 n denotes the number of solid partitions of an integer n we show that lim n rightarrow infty n 3 4 log p 3 n sim 1 822 pm 0 001 this shows clear deviation from the value 1 7898 attained by macmahon numbers m 3 n that was conjectured to hold for solid partitions as well in addition we find estimates for other sub leading terms in log p 3 n in a pattern deviating from the asymptotics of line and plane partitions we need to add an oscillatory term in addition to the obvious sub leading terms the period of the oscillatory term is proportional to n 1 4 the natural scale in the problem this new oscillatory term might shed some insight into why partitions in dimensions greater than two do not admit a simple generating function

stability of nonlinearly elastic rods this paper describes previously unknown stabilities and instabilities of planar equilibrium configurations of a nonlinearly elastic rod that is buckled under the action of a dead load the governing equations are derived from variational principles including ones of isoperimetric type properties of stability are accordingly determined by study of the second variation stabilities to deformations both in the plane and out of the plane are considered among the newly discovered properties are secondary bifurcation from the first buckled mode marked differences between stability to two dimensional and to three dimensional variations and the stabilizing influence of resistance to twist in the isoperimetric examples the analysis makes crucial use of a novel device to account for the dependence of the second variation on constraints

computing distributions for exact logistic regression abstract logistic regression is a commonly used technique for the analysis of retrospective and prospective epidemiological and clinical studies with binary response variables usually this analysis is performed using large sample approximations when the sample size is small or the data structure sparse the accuracy of the asymptotic approximations is in question on other occasions singularity of the covariance matrix of parameter estimates precludes asymptotic analysis under these circumstances use of exact inferential procedures would seem to be a prudent alternative cox 1970 showed that exact inference on the parameters of a logistic model with binary response requires consideration of the distribution of sufficient statistics for these parameters to date however resorting to the exact method has not been computationally feasible except in a few special situations this article presents an efficient recursive algorithm that generates the joint and conditional distributions of the sufficient

exact log rank tests for unequal follow up les tests asymptotiques du log rank et le test de wilcoxon generalise sont des procedures standards pour comparer des distributions de survie en presence de censures pour la comparaison d echantillons de tailles tres differentes un test exact base sur l ensemble des permutations du log rank ou des scores de wilcoxon est disponible alors que les tests asymptotiques ne conservent pas leur risque nominal lorsque les echantillons sont de tailles tres differentes le test exact base sur les permutations exige cependant un suivi identique dans les echantillons c est pourquoi nous avons developpe deux nouveaux tests exacts adaptes a des suivis inegaux le premier est exactement equivalent au log rank test asymptotique conditionnellement a l ensemble des risques observes alors que la deuxieme approche permute les temps de survie conditionnellement au suivi observe dans chaque groupe dans une etude empirique nous comparons ces nouvelles procedures au log rank test asymptotique au test exact de permutation complete ainsi qu a une approche proposee anterieurement qui egalise les distributions de suivi en les censurant artificiellement les resultats confirment les performances tres satisfaisantes du test exact conditionnellement au suivi observe particulierement dans le cas de suivis inegaux l avantage du nouveau test sur les autres possibilites d analyse est finalement illustre par l analyse d une etude portant sur le cancer du sein

exact inference for categorical data recent advances and continuing controversies methods for exact small sample analyses with categorical data have been increasingly well developed in recent years a variety of exact methods exist primarily using the approach that eliminates unknown parameters by conditioning on their sufficient statistics in addition a variety of algorithms now exist for implementing the methods this paper briefly summarizes the exact approaches and describes recent developments controversy continues about the appropriateness of some exact methods primarily relating to their conservative nature because of discreteness this issue is examined for two simple problems in which discreteness can be severe interval estimation of a proportion and the odds ratio in general adjusted exact methods based on the mid p value seem a reasonable way of reducing the severity of this problem

on large isolated regions in supercritical percolation we consider supercritical vertex percolation in mathbb z d d with any non degenerate uniform oriented pattern of connection in particular our results apply to the more special unoriented case we estimate the probability that a large region is isolated from in particular pancakes with a radius r and constant thickness parallel to a constant linear subspace l are isolated with probability whose logarithm grows asymptotically as rdim l if percolation is possible across l and as rdim l 1 otherwise also we estimate probabilities of large deviations in invariant measures of some cellular automata

random skew plane partitions and the pearcey process we study random skew 3d partitions weighted by qvol and specifically the q 1 asymptotics of local correlations near various points of the limit shape we obtain sine kernel asymptotics for correlations in the bulk of the disordered region airy kernel asymptotics near a general point of the frozen boundary and a pearcey kernel asymptotics near a cusp of the frozen boundary

improved exact inference about conditional association in three way contingency tables abstract we propose modified exact inferential methods for contingency tables ordinary exact inference is conservative because of the discreteness for estimating a common odds ratio in several 2 2 tables two modifications of the ordinary exact confidence interval maintain at least a fixed confidence level but tend to be much narrower one approach inverts results of a test with a modified p value utilizing the test statistic and table probabilities the second approach inverts one two sided test rather than two one sided tests this approach is much less conservative when the true odds ratio is relatively small or large we also generalize results of cohen and sackrowitz and relate modified p values to construction of exact unbiased and admissible tests for an ordinal alternative to conditional independence

surface order large deviations for high density percolation we derive surface order large deviation estimates for the volume of the largest cluster and for the volume of the largest region surrounded by a cluster of a bernoulli percolation process restricted to a big finite box with sufficiently large parameter we also establish a useful version of the isoperimetric inequality which is the main tool of our proofs

testing conditional independence via empirical likelihood we construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter one class is based on the cdf another is based on smoother functions we show that the test statistics are asymptotically normal under the null hypothesis and a sequence of pitman local alternatives we also show that the tests possess an asymptotic optimality property in terms of average power simulations suggest that the tests are well behaved in finite samples applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear granger causality test fails to detect

the low temperature expansion of the wulff crystal in the 3d ising model we compute the expansion of the surface tension of the 3d random cluster model for q 1 in the limit where p goes to 1 we also compute the asymptotic shape of a plane partition of n as n goes to this same shape determines the wulff crystal to order o in the 3d ising model and more generally in the 3d random cluster model for q 1 at temperature

rigidity of the interface in percolation and random cluster models we study conditioned random cluster measures with edge parameter p and cluster weighting factor q satisfying q 1 the conditioning corresponds to mixed boundary conditions for a spin model interfaces may be defined in the sense of dobrushin and these are proved to be rigid in the thermodynamic limit in three dimensions and for sufficiently large values of p this implies the existence of non translation invariant conditioned random cluster measures in three dimensions the results are valid in the special case q 1 thus indicating a property of three dimensional percolation not previously noted

on a sharp transition from area law to perimeter law in a system of random surfaces we introduce and study a phase transition which is associated with the spontaneous formation of infinite surface sheets in a bernoulli system of random plaquettes the transition is manifested by a change in the asymptotic behavior of the probability of the formation of a surface spanning a prescribed loop as such this transition offers a generalization of the bond percolation phenomenon at low plaquette densities the probability for large loops is shown to decay exponentially with the loops area whereas for high densities the decay is by a perimeter law furthermore we show that the two phases of the three dimensional plaquette system are in a precise correspondence with the two phases of the dual system of random bonds thus if a natural conjecture about the phase structure of the bond percolation model is true then there is a sharp transition in the asymptotic behavior of the surface events our analysis incorporates block variables in terms of which a non critical system is transformed into one which is close to a trivial high or low density fixed point stochastic geometric effects like those discussed here play an important role in lattice gauge theories

on the wulff crystal in the ising model we study the phase separation phenomenon in the ising model in dimensions d 3 to this end we work in a large box with plus boundary conditions and we condition the system to have an excess amount of negative spins so that the empirical magnetization is smaller than the spontaneous magnetization m we confirm the prediction of the phenomenological theory by proving that with high probability a single droplet of the minus phase emerges surrounded by the plus phase moreover the rescaled droplet is asymptotically close to a definite deterministic shape the wulff crystal which minimizes the surface free energy in the course of the proof we establish a surface order large deviation principle for the magnetization our results are valid for temperatures t below a limit of slab thresholds t c conjectured to agree with the critical point t c moreover t should be such that there exist only two extremal translation invariant gibbs states at that temperature a property which can fail for at most countably many values and which is conjectured to be true for every t the proofs are based on the fortuin kasteleyn representation of the ising model along with coarse graining techniques to handle the emerging macroscopic objects we employ tools from geometric measure theory which provide an adequate framework for the large deviation analysis finally we propose a heuristic picture that for subcritical temperatures close enough to t c the dominant minus spin cluster of the wulff droplet permeates the entire box and has a strictly positive local density everywhere

testing logistic regression coefficients with clustered data and few positive outcomes applications frequently involve logistic regression analysis with clustered data where there are few positive outcomes in some of the independent variable categories for example an application is given here that analyzes the association of asthma with various demographic variables and risk factors using data from the third national health and nutrition examination survey a weighted multi stage cluster sample although there are 742 asthma cases in all out of 18 395 individuals for one of the categories of one of the independent variables there are only 25 asthma cases out of 695 individuals generalized wald and score hypothesis tests which use appropriate cluster level variance estimators and a bootstrap hypothesis test have been proposed for testing logistic regression coefficients with cluster samples when there are few positive outcomes simulations presented in this paper show that these tests can sometimes have either inflated or very conservative levels a simulation based method is proposed for testing logistic regression coefficients with cluster samples when there are few positive outcomes this testing methodology is shown to compare favorably with the generalized wald and score tests and the bootstrap hypothesis test in terms of maintaining nominal levels the proposed method is also useful when testing goodness of fit of logistic regression models using deciles of risk tables published in 2007 by john wiley sons ltd

computing an exact confidence interval for the common odds ratio in several 2 2 contingency tables abstract a quadratic time network algorithm is provided for computing an exact confidence interval for the common odds ratio in several 2 2 independent contingency tables the algorithm is shown to be a considerable improvement on an existing algorithm developed by thomas 1975 which relies on exhaustive enumeration problems that would formerly have consumed several cpu hours can now be solved in a few cpu seconds the algorithm can easily handle sparse data sets where asymptotic results are suspect the network approach on which the algorithm is based is also a powerful tool for exact statistical inference in other settings

an algorithm for exact logistic regression abstract an efficient algorithm is given for the exact logistic analysis of a single parameter hypothesis tests and confidence intervals for a logistic regression parameter are obtained the method provides for the control of the effect of a stratification factor when making inferences concerning the regression parameter

eulerian formulation of elastic rods in numerous biological medical and engineering applications elastic rods are constrained to deform inside or around tube like surfaces to solve efficiently this class of problems the equations governing the deflection of elastic rods are reformulated within the eulerian framework of this generic tubular constraint defined as a perfectly stiff normal ringed surface this reformulation hinges on describing the rod deformed configuration by means of its relative position with respect to a reference curve defined as the axis or spine curve of the constraint and on restating the rod local equilibrium in terms of the curvilinear coordinate parametrizing this curve associated with a segmentation strategy which partitions the global problem into a sequence of rod segments either in continuous contact with the constraint or free of contact except for their extremities this re parametrization not only trivializes the detection of new contacts but also transforms these free boundary problems into classic two points boundary value problems and suppresses the isoperimetric constraints resulting from the imposition of the rod position at the extremities of each rod segment

exact solutions for kpz type growth processes random matrices and equilibrium shapes of crystals abstract three models from statistical physics can be analyzed by employing space time determinantal processes 1 crystal facets in particular the statistical properties of the facet edge and equivalently tilings of the plane 2 one dimensional growth processes in the kardar parisi zhang universality class and directed last passage percolation 3 random matrices multi matrix models and dyson s brownian motion we explain the method and survey results of physical interest

the wulff theorem revisited the parametrized indicator measures and the brunn minkowski inequality are used to prove that the wulff set w is a minimizer for the surface energy where the density is the support function of w the support of the indicator measures associated to minimizing sequences is characterized it is shown that if w is polyhedral then minimizing sequences cannot oscillate

a variational principle for domino tilings 1 1 description of results a domino is a 1 x 2 or 2 x 1 rectangle and a tiling of a region by dominos is a way of covering that region with dominos so that there are no gaps or overlaps in 1961 kasteleyn kal found a formula for the number of domino tilings of an m x n rectangle with mn even as shown in figure 1 for rm n 68 temperley and fisher tf used a differenit method and arrived at the same result at almost exactly the same time both lines of calculation showed that the logarithm of number of tilings divided by the number of dominos in a tiling that is mn 2 converges to 2g 7r 0 58 here g is catalan s constant on the other hand in 1992 elkies et al eklp studied domino tilings of regions they called aztec diamonds figure 2 shows an aztec diamond of order 48 and showed that the logarithm of the number of tilings divided by the number of dominos converges to the smaller number log 2 2 0 35 thus even though the region in figure 1 has slightly smaller area than the region in figure 2 the former has far more domino tilings for regions with other shapes neither of these asymptotic formulas may apply in the present paper we consider simply connected regions of arbitrary shape we give an exact formula for the limiting value of the logarithm of the number of tilings per unit area as a function of the shape of the boundary of the region as the size of the region goes to infinity in particular we show that computation of this limit is intimately linked with an understanding of long range variations in the local statistics of random domino tilings such variations can be seen by comparing figures 1 and 2 each of the two tilings is random in the sense that the algorithm pwi that was used to create it generates each of the possible tilings of the region being tiled with the same probability hence one can expect each tiling to be qualitatively typical of the overwhelming majority of tilings of the region in

exact significance testing to establish treatment equivalence with ordered categorical data this communication concerns the problem of establishing the therapeutic equivalence of two treatments that are being compared on the basis of ordered categorical data the problem is formulated as a significance test in which the null hypothesis specifies a treatment difference an efficient numerical algorithm for computing the exact significance level is provided along with a simple method for obtaining the asymptotic significance level both methods are applied to a clinical trial of a new agent versus an active control guidelines for when to use the exact procedure and when to rely on asymptotic theory are provided

multi step transversal and tangential linearization methods applied to a class of nonlinear beam equations a novel and continuously parameterized form of multi step transversal linearization mtrl method is developed and numerically explored for solving nonlinear ordinary differential equations governing a class of boundary value problems bvps of relevance in structural mechanics a similar family of multi step tangential linearization mtnl methods is also developed and applied to such bvp s within the framework of mtrl and mtnl a bvp is treated as a constrained dynamical system i e a constrained initial value problem ivp while the mtrl requires the linearized solution manifold to transversally intersect the nonlinear solution manifold at a chosen set of points across the axis of the independent variable the essential difference of the present mtrl method from its previous version roy d kumar r 2005 a multistep transversal linearization mtl method in nonlinear structural dynamics j sound vib 17 829 852 is that it has the flexibility of treating nonlinear damping and stiffness terms as time variant damping and stiffness terms in the linearized system the resulting time variant linearized system is then solved using magnus characterization magnus w 1954 on the exponential solution of differential equations for a linear operator commun pure appl math 7 649 673 towards numerical illustrations response of a tip loaded cantilever beam elastica is first obtained next the response of a simply supported nonlinear timoshenko beam is obtained using a variationally correct vc model for the beam marur s prathap g 2005 nonlinear beam vibration problems and simplification in finite element model comput mech 35 5 352 360 the new model does not involve any simplifications commonly employed in the finite element formulations in order to ease the computation of nonlinear stiffness terms from nonlinear strain energy terms a comparison of results through mtrl and mtnl techniques consistently indicate a superior quality of approximations via the transversal linearization technique while the usage of tangential system matrices is common in nonlinear finite element practices it is demonstrated that the transversal version of linearization offers an easier and more general implementation requires no computations of directional derivatives and leads to a consistently higher level of numerical accuracy it is also observed that higher order versions of mtrl mtnl with lagrangian interpolations may not work satisfactorily and hence spline interpolations are suggested to overcome this problem

surface order large deviations for ising potts and percolation models we derive uniform surface order large deviation estimates for the block magnetization in finite volume ising or potts models with plus or free or a combination of both boundary conditions in the phase coexistence regime ford 3 the results are valid up to a limit of slab thresholds conjectured to agree with the critical temperature our arguments are based on the renormalization of the random cluster model withq 1 andd 3 and on corresponding large deviation estimates for the occurrence in a box of a largest cluster with density close to the percolation probability the results are new even for the case of independent percolation q 1 as a byproduct of our methods we obtain further results in the fk model concerning semicontinuity inp andq of the percolation probability the second largest cluster in a box and the tail of the finite cluster size distribution

dynamics of an unbounded interface between ordered phases we investigate the evolution of a single unbounded interface between ordered phases in two dimensional ising ferromagnets that are endowed with single spin flip zero temperature glauber dynamics we examine specifically the cases where the interface initially has either one or two corners in both examples the interface evolves to a limiting self similar form we apply the continuum time dependent ginzburg landau equation and a microscopic approach to calculate the interface shape for the single corner system we also discuss a correspondence between the interface and the young diagram that represents the partition of the integers

on small sample confidence intervals for parameters in discrete distributions summary the traditional definition of a confidence interval requires the coverage probability at any value of the parameter to be at least the nominal confidence level in constructing such intervals for parameters in discrete distributions less conservative behavior results from inverting a single two sided test than inverting two separate one sided tests of half the nominal level each we illustrate for a variety of discrete problems including interval estimation of a binomial parameter the difference and the ratio of two binomial parameters for independent samples and the odds ratio

a uniqueness proof for the wulff theorem the wulff problem is a generalisation of the isoperimetric problem and is relevant for the equilibrium of small elastic crystals it consists in minimising the generally anisotropic surface energy among sets of given volume a solution of this problem is given by a geometric construction due to wulff in the class of sets of finite perimeter this was first shown by j e taylor who using methods of geometric measure theory also proved uniqueness here a more analytic uniqueness proof is presented the main ingredient is a sharpened version of the brunn minkowski inequality

methods of estimation in log odds ratio regression models mccullagh s 1984 journal of the royal statistical society series b 46 250 256 approximation to the conditional maximum likelihood estimator in log odds ratio regression models is shown to have negligible asymptotic bias unless the odds ratios are large and the sample sizes in individual 2 x 2 tables are very small in application to two sets of case control data it yields results virtually indistinguishable from those of the conditional analysis a generalization of the mantel haenszel estimator proposed by davis 1985 biometrics 41 487 495 does not approximate the conditional results nearly as well

arctic curves of the six vertex model on generic domains the tangent method we revisit the problem of determining the arctic curve in the six vertex model with domain wall boundary conditions we describe an alternative method by which we recover the previously conjectured analytic expression in the square domain we adapt the method to work for a large class of domains and for other models exhibiting limit shape phenomena we study in detail some examples and derive in particular the arctic curve of the six vertex model in a triangoloid domain at the ice point

small sample confidence regions in exponential families this article presents an algorithm for small sample conditional confidence regions for two or more parameters for any discrete regression model in the generalized linear interactive model family regions are constructed by careful inversion of conditional hypothesis tests this method presupposes the use of approximate or exact techniques for enumerating the sample space for some components of the vector of sufficient statistics conditional on other components such enumeration may be performed exactly or by exact or approximate monte carlo including the algorithms of kolassa and tanner 1994 journal of the american statistical association 89 697 702 1999 biometrics 55 246 251 this method also assumes that one can compute certain conditional probabilities for a fixed value of the parameter vector because of a property of exponential families one can use this set of conditional probabilities to directly compute the conditional probabilities associated with any other value of the vector of the parameters of interest this observation dramatically reduces the computational effort required to invert the hypothesis test to obtain the confidence region to construct a region with confidence level 1 alpha the algorithm begins with a grid of values for the parameters of interest for each parameter vector on the grid corresponding to the current null hypothesis one transforms the initial set of conditional probabilities using exponential tilting and then calculates the p value for this current null hypothesis the confidence region is the set of parameter values for which the p value is at least alpha

fluctuations of an atomic ledge bordering a crystalline facet when a high symmetry facet joins the rounded part of a crystal the step line density vanishes as square root of r with r denoting the distance from the facet edge this means that the ledge bordering the facet has a lot of space to meander as caused by thermal activation we investigate the statistical properties of the border ledge fluctuations in the scaling regime they turn out to be non gaussian and related to the edge statistics of gaussian unitary ensemble multimatrix models

an exact analysis of conditional independence in several 2 x 2 contingency tables summary this paper proposes an exact test of conditional independence and an efficient algorithm for several 2 x 2 contingency tables simulations compare it with a commonly used exact test for null interaction and common odds ratio

exact inference for proportions from a stratified finite population abstract auditors and others often encounter finite populations with a dichotomous characteristic from which they draw stratified samples in auditing the dichotomy arises when a population item is classified as either in error or in compliance with some rule or regulation usually the proportion of errors is small the auditing objective may require calculation of a p value for the sample outcome relative to a hypothesis or a confidence bound for the proportion or total number of errors in the population in sampling from l strata with hypotheses concerning the total number of errors in the population the calculation of p values is not straightforward the complication arises because the parameter of the null hypothesis does not completely specify the distribution of the test statistic this distribution depends on an l 1 dimensional nuisance parameter consisting of the number of errors in each stratum because confidence bounds can be obtained by inverting the hypothesis test the same difficulty

critical resonance in the non intersecting lattice path model we study the phase transition in the honeycomb dimer model equivalently monotone non intersecting lattice path model at the critical point the system has a strong long range dependence in particular periodic boundary conditions give rise to a resonance phenomenon where the partition function and other properties of the system depend sensitively on the shape of the domain

combining independent studies of a diagnostic test into a summary roc curve data analytic approaches and some additional considerations we consider how to combine several independent studies of the same diagnostic test where each study reports an estimated false positive rate fpr and an estimated true positive rate tpr we propose constructing a summary receiver operating characteristic roc curve by the following steps i convert each fpr to its logistic transform u and each tpr to its logistic transform v after increasing each observed frequency by adding 1 2 ii for each study calculate d v u which is the log odds ratio of tpr and fpr and s v u an implied function of test threshold then plot each study s point si di iii fit a robust resistant regression line to these points or an equally weighted least squares regression line with v u as the dependent variable iv back transform the line to roc space to avoid model dependent extrapolation from irrelevant regions of roc space we propose defining a priori a value of fpr so large that the test simply would not be used at that fpr and a value of tpr so low that the test would not be used at that tpr then a only data points lying in the thus defined north west rectangle of the unit square are used in the data analysis and b the estimated summary roc is depicted only within that subregion of the unit square we illustrate the methods using simulated and real data sets and we point to ways of comparing different tests and of taking into account the effects of covariates

analysis of binary data from a multicentre clinical trial summary we develop several methods for estimating the treatment effect difference defined as the overall log odds ratio of favourable response in a multicentre clinical trial comparing two treatments with binary response a simulation study compares the bias and mean squared error of the point estimates and the exact coverage probabilities of confidence intervals obtained distributions multicentre randomized clinical trials are frequently used to test the efficacy of new medical regimens these trials are attractive due to the ease of getting the desired sample size in a short period of time and the broad coverage of the patient population and medical practitioners the analysis of data from such trials requires combining information from the centres in a way that properly accounts for the variation due to the centres and the differential efficacy of treatments between the centres in this paper we investigate several approaches to pooling the data across centres and for handling the effects associated with the centres chakravarthi grizzle 1975 and beitler landis 1985 argue for treating these effects as random and fleiss 1986 argues against because the centres are seldom chosen at random from a well defined population of clinics and therefore the effects cannot be associated with any population we prefer the random effect model approach for the following reasons the goal of a trial is to extend the results of the study to the general population duly accounting for variation in the patient population and the medical skills of practitioners hence if we believe that the variability between centres as estimated by the data is typical of the variability in the population of centres then the inference based on the random effects model is more appropriate than the one based on the fixed effects model furthermore the variation among the centres may be more than that predicted from samples from a binomial distribution treating the centre effects as random introduces this intra class correlation into our model assumptions let the outcome variable from each centre be a pair of binomial random variables xaj

efficient power computation for exact and mid p tests for the common odds ratio in several 2 2 tables when designing a study that may generate a set of sparse 2 x 2 tables or when confronted with negative results upon exact analysis of such tables we need to compute the power of exact tests in this paper we provide an efficient approach for computing exact unconditional power for four exact tests on the common odds ratio in a series of 2 x 2 tables these tests are the traditional exact test a test based on a probability ordering of the sample space and two tests based on ordering the sample space according to distance from the mean or median for each test we consider both a conservative version and a mid p adjusted version we explore three computational options for power determination exact power computation calculation of exact upper and lower bounds for power and monte carlo confidence bounds for power we present an interactive program implementing these options for study design the program may be run several times to arrive at a sample configuration with adequate power

fluctuations of the maximal particle energy of the quantum ideal gas and random partitions we investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics we show that for a big family of gibbs measures on partitions so called generalized bose einstein statistics this distribution is the well known gumbel distribution which usually appears in the context of indepedent random variables in particular it means that the properly rescaled maximal energy of an individual particle in the grand canonical ensemble of the d dimensional quantum ideal gas has the gumbel distribution in the limit

random tilings of high symmetry i mean field theory we study random tiling models in the limit of high rotational symmetry in this limit a mean field theory yields reasonable predictions for the configurational entropy of free boundary rhombus tilings in two dimensions we base our mean field theory on an iterative tiling construction inspired by the work of de bruijn in addition to the entropy we consider correlation functions phason elasticity and the thermodynamic limit tilings of dimension other than two are considered briefly

an empirical assessment of saddlepoint approximations for testing a logistic regression parameter saddlepoint methods provide quick and easy approximations to significance levels for conditional tests of logistic regression parameters we evaluate the accuracies of saddlepoint approximations for three well known conditional tests bartlett s test for no three factor interaction in a 2 x 2 x 2 table the test for trend in a series of probabilities and the exact test of no association in stratified 2 x 2 tables with a common odds ratio general recommendations are suggested regarding the use of saddlepoint approximations for exact conditional significance levels

saddlepoint approximations for small sample logistic regression problems double saddlepoint approximations provide quick and accurate approximations to exact conditional tail probabilities in a variety of situations this paper describes the use of these approximations in two logistic regression problems an investigation of regression analysis of the log odds ratio in a sequence or set of 2 2 tables via simulation studies shows that in practical settings the saddlepoint methods closely approximate exact conditional inference the double saddlepoint approximation in the test for trend in a sequence of binomial random variates is also shown via simulation studies to be an effective approximation to exact conditional inference copyright 2000 john wiley sons ltd

the wulff construction and asymptotics of the finite cluster distribution for two dimensional bernoulli percolation we consider two dimensional bernoulli percolation at densityp p c and establish the following results

the stochastic random cluster process and the uniqueness of random cluster measures the random cluster model is a generalization of percolation and ferromagnetic potts models due to fortuin and kasteleyn not only is the random cluster model a worthwhile topic for study in its own right but also it provides much information about phase transitions in the associated physical models this paper serves two functions first we introduce and survey random cluster measures from the probabilist s point of view giving clear statements of some of the many open problems second we present new results for such measures as follows we discuss the relationship between weak limits of random cluster measures and measures satisfying a suitable dlr condition using an argument based on the convexity of pressure we prove the uniqueness of random cluster measures for all but at most countably many values of the parameter p related results concerning phase transition in two or more dimensions are included together with various stimulating conjectures the uniqueness of the infinite cluster is employed in an intrinsic way in part of these arguments in the second part of this paper is constructed a markov process whose level sets are reversible markov processes with random cluster measures as unique equilibrium measures this construction enables a coupling of random cluster measures for all values of p furthermore it leads to a proof of the semicontinuity of the percolation probability and provides a heuristic probabilistic justification for the widely held belief that there is a first order phase transition if and only if the cluster weighting factor q is sufficiently large

geometric variational problems of statistical mechanics and of combinatorics we present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics together with the wulff construction which predicts the shape of the crystals we discuss the construction which exhibits the shape of a typical young diagram and of a typical skyscraper

strings rods vortices and wave equations the hasimoto type theory of vortex filament motion is reviewed by replacing the first order law of motion velocity given with a second order law acceleration given dynamics of e g flexible and rigid elastic strings is described in a similar manner a system of nine coupled partial differential equations results but on eliminating longitudinal motion a smaller system is obtained classic vibration equations are recovered as special cases the dynamic and static equations may be applied to problems concerning cables textile fibres molecules and other objects