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

can extra updates delay mixing we consider glauber dynamics starting from an extremal configuration in a monotone spin system and show that interjecting extra updates cannot increase the expected hamming distance or the total variation distance to the stationary distribution we deduce that for monotone markov random fields when block dynamics contracts a hamming metric single site dynamics mixes in o n log n steps on an n vertex graph in particular our result completes work of kenyon mossel and peres concerning glauber dynamics for the ising model on trees our approach also shows that on bipartite graphs alternating updates systematically between odd and even vertices cannot improve the mixing time by more than a factor of log n compared to updates at uniform random locations on an n vertex graph our result is especially effective in comparing block and single site dynamics it has already been used in works of martinelli toninelli sinclair mossel sly ding lubetzky and peres in various combinations

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

least squares recursive projection twin support vector machine for classification in this paper we formulate a least squares version of the recently proposed projection twin support vector machine ptsvm for binary classification this formulation leads to extremely simple and fast algorithm called least squares projection twin support vector machine lsptsvm for generating binary classifiers different from ptsvm we add a regularization term ensuring the optimization problems in our lsptsvm are positive definite and resulting better generalization ability instead of usually solving two dual problems we solve two modified primal problems by solving two systems of linear equations whereas ptsvm need to solve two quadratic programming problems along with two systems of linear equations our experiments on publicly available datasets indicate that our lsptsvm has comparable classification accuracy to that of ptsvm but with remarkably less computational time

improved discriminate analysis for high dimensional data and its application to face recognition many pattern recognition applications involve the treatment of high dimensional data and the small sample size problem principal component analysis pca is a common used dimension reduction technique linear discriminate analysis lda is often employed for classification pca plus lda is a famous framework for discriminant analysis in high dimensional space and singular cases in this paper we examine the theory of this framework and find out that even if there is no small sample size problem the pca dimension reduction cannot guarantee the subsequent successful application of lda we thus develop an improved discriminate analysis method by introducing an inverse fisher criterion and adding a constrain in pca procedure so that the singularity phenomenon will not occur experiment results on face recognition suggest that this new approach works well and can be applied even when the number of training samples is one per class

the local discontinuous galerkin method for three dimensional shallow water flow we formulate and present a stability analysis for the local discontinuous galerkin method applied to a model of three dimensional shallow water flow this model is described by the navier stokes equations assuming hydrostatic pressure the resulting system of equations is given by momentum equations for the x and y components of velocity the continuity equation which is used to solve for the vertical component of velocity and an equation describing the motion of the free surface our analysis includes the full nonlinearities in the model with no simplifying assumptions and accounts for the movement of the mesh due to the free surface to our knowledge this is the first analysis of any numerical scheme for this complex system of equations numerical results are presented which demonstrate the accuracy of the method for a problem with a known analytical solution 2006 elsevier b v all rights reserved

generalized domino shuffling the problem of counting tilings of a plane region using specified tiles can often be recast as the problem of counting perfect matchings of some subgraph of an aztec diamond graph an or more generally calculating the sum of the weights of all the matchings where the weight of a matching is equal to the product of the pre assigned weights of the constituent edges assumed to be non negative this article presents efficient algorithms that work in this context to solve three problems finding the sum of the weights of the matchings of a weighted aztec diamond graph an computing the probability that a randomly chosen matching of an will include a particular edge where the probability of a matching is proportional to its weight and generating a matching of an at random the first of these algorithms is equivalent to a special case of mihai ciucu s cellular complementation algorithm j combin theory ser a 81 1998 34 and can be used to solve many of the same problems the second of the three algorithms is a generalization of not yet published work of alexandru ionescu and can be employed to prove an identity governing a three variable generating function whose coefficients are all the edge inclusion probabilities this formula has been used duke math j 85 1996 117 as the basis for asymptotic formulas for these probabilities but a proof of the generating function identity has not hitherto been published the third of the three algorithms is a generalization of the domino shuffling algorithm presented in j algebraic combin 1 1992 111 it enables one to generate random diabolo tilings of fortresses and thereby to make intriguing inferences about their asymptotic behavior

markov chain algorithms for planar lattice structures consider the following markov chain whose states are all domino tilings of a 2n 2n chessboard starting from some arbitrary tiling pick a 2 2 window uniformly at random if the four squares appearing in this window are covered by two parallel dominoes rotate the dominoes 90 rm o in place repeat many times this process is used in practice to generate a random tiling and is a widely used tool in the study of the combinatorics of tilings and the behavior of dimer systems in statistical physics analogous markov chains are used to randomly generate other structures on various two dimensional lattices this paper presents techniques which prove for the first time that in many interesting cases a small number of random moves suffice to obtain a uniform distribution

conformal invariance of domino tiling let u be a multiply connected region in r 2 with smooth boundary let p be a polyomino in z 2 approximating u as 0 we show that for certain boundary conditions on p the height distribution on a random domino tiling dimer covering of p is conformally invariant in the limit as tends to 0 in the sense that the distribution of heights of boundary components or rather the difference of the heights from their mean values only depends on the conformal type of u the mean height is not strictly conformally invariant but transforms analytically under conformal mappings in a simple way the mean height and all the moments are explicitly evaluated

multiple time scales and pressure forcing in discontinuous galerkin approximations to layered ocean models this paper addresses some issues involving the application of discontinuous galerkin dg methods to ocean circulation models having a generalized vertical coordinate these issues include the following 1 determine the pressure forcing at cell edges where the dependent variables can be discontinuous in principle this could be accomplished by solving a riemann problem for the full system but some ideas related to barotropic baroclinic time splitting can be used to reduce the riemann problem to a much simpler system of lower dimension such splittings were originally developed in order to address the multiple time scales that are present in the system 2 adapt the general idea of barotropic baroclinic splitting to a dg implementation a significant step is enforcing consistency between the numerical solution of the layer equations and the numerical solution of the vertically integrated barotropic equations the method used here has the effect of introducing a type of time filtering into the forcing for the layer equations which are solved with a long time step 3 test these ideas in a model problem involving geostrophic adjustment in a multi layer fluid in certain situations the dg formulation can give significantly better results than those obtained with a standard finite difference formulation

how quickly can we sample a uniform domino tiling of the 2l times 2l square via glauber dynamics the prototypical problem we study here is the following given a 2l times 2l square there are approximately exp 4kl 2 pi ways to tile it with dominos i e with horizontal or vertical 2 times 1 rectangles where k approx 0 916 is catalan s constant kasteleyn in physica 27 1209 1225 1961 temperley and fisher in phil mag 6 1061 1063 1997 a conceptually simple even if computationally not the most efficient way of sampling uniformly one among so many tilings is to introduce a markov chain algorithm glauber dynamics where with rate 1 two adjacent horizontal dominos are flipped to vertical dominos or vice versa the unique invariant measure is the uniform one and a classical question levin et al in am math soc 2009 luby et al siam j comput 31 167 192 2001 wilson in ann appl probab 14 274 325 2004 is to estimate the time t mathrm mix it takes to approach equilibrium i e the running time of the algorithm luby et al in siam j comput 31 167 192 2001 and randall and tetali in j math phys 41 3 1598 1614 2000 fast mixing was proven t mathrm mix o l c for some finite c here we go much beyond and show that c l 2 le t mathrm mix le l 2 o 1 our result applies to rather general domain shapes not just the 2l times 2l square provided that the typical height function associated to the tiling is macroscopically planar in the large l limit under the uniform measure this is the case for instance for the temperley type boundary conditions considered in kenyon ann probab 28 759 795 2000 also our method extends to some other types of tilings of the plane for instance the tilings associated to dimer coverings of the hexagon or square hexagon lattices

height fluctuations in the honeycomb dimer model we study a model of random surfaces arising in the dimer model on the honeycomb lattice for a fixed wire frame boundary condition as the lattice spacing 0 cohn kenyon and propp 3 showed the almost sure convergence of a random surface to a non random limit shape 0 in 12 okounkov and the author showed how to parametrize the limit shapes in terms of analytic functions in particular constructing a natural conformal structure on them we show here that when 0 has no facets for a family of boundary conditions approximating the wire frame the large scale surface fluctuations height fluctuations about 0 converge as 0 to a gaussian free field for the above conformal structure we also show that the local statistics of the fluctuations near a given point x are as conjectured in 3 given by the unique ergodic gibbs measure on plane configurations whose slope is the slope of the tangent plane of 0 at x

multiclass classifiers based on dimension reduction with generalized lda linear discriminant analysis lda has been widely used for dimension reduction of data sets with multiple classes the lda has been recently extended to various generalized lda methods that are applicable regardless of the relative sizes between the data dimension and the number of data items in this paper we propose several multiclass classifiers based on generalized lda glda algorithms taking advantage of the dimension reducing transformation matrix without requiring additional training or parameter optimization a marginal linear discriminant classifier mldc a bayesian linear discriminant classifier bldc and a one dimensional bldc are introduced for multiclass classification our experimental results illustrate that these classifiers produce higher ten fold cross validation accuracy than knn and centroid based classifiers in the reduced dimensional space obtained from glda

why can lda be performed in pca transformed space abstract pca plus lda is a popular framework for linear discriminant analysis lda in high dimensional and singular case in this paper we focus on building a theoretical foundation for this framework moreover we point out the weakness of the previous lda based methods and suggest a complete pca plus lda algorithm experimental results on orl face image database indicate that the proposed method is more effective than the previous ones

analyzing glauber dynamics by comparison of markov chains a popular technique for studying random properties of a combinatorial set is to design a markov chain monte carlo algorithm for many problems there are natural markov chains connecting the set of allowable configurations which are based on local moves or glauber dynamics typically these single site update algorithms are difficult to analyze so often the markov chain is modified to update several sites simultaneously recently there has been progress in analyzing these more complicated algorithms for several important combinatorial problems in this work we use the comparison technique of diaconis and saloff coste to show that several of the natural single point update algorithms are efficient the strategy is to relate the mixing rate of these algorithms to the corresponding nonlocal algorithms which have already been analyzed this allows us to give polynomial time bounds for single point update algorithms for problems such as generating planar tilings and random triangulations of convex polygons we also survey several other comparison techniques along with specific applications which have been used in the context of estimating mixing rates of markov chains

discontinuous galerkin methods with nodal and hybrid modal nodal triangular quadrilateral and polygonal elements for nonlinear shallow water flow abstract we present a comprehensive assessment of nodal and hybrid modal nodal discontinuous galerkin dg finite element solutions on a range of unstructured meshes to nonlinear shallow water flow with smooth solutions the nodal dg methods on triangles and a tensor product nodal basis on quadrilaterals are considered the hybrid modal nodal dg methods utilize two different synergistic polynomial bases on polygons in realizing the dg discretization orthogonal basis functions constructed by the gram schmidt process are used as trial and test functions in a dg weak formulation and a nodal basis is used as an efficient means for area integration these are implemented on triangular quadrilateral and polygonal elements in addition we discuss aspects to be considered in order to achieve the so called well balanced property that preserves steady state at rest with a spatially varying bed the performance in terms of accuracy and computational cost is demonstrated using h and p convergence studies on a nonlinear problem with a manufactured solution and the nonlinear stommel problem with flat and non flat beds to assess the performance of quadrilateral and polygonal elements in comparison to triangular elements we consider a setting in which a quadrilateral mesh a mixed triangular quadrilateral mesh and polygonal mesh are derived from a given triangular mesh and vice versa the tests conducted reveal the merit of using the quadrilateral elements in terms of computational cost per accuracy and computing time more importantly the numerical results clearly show that high order schemes significantly improve the cost performance for a given level of accuracy with cubic or bi cubic interpolants particularly achieving dramatic improvements in accuracy as compared to linear and quadratic interpolants with diminishing benefit as p 3

hp discontinuous galerkin methods for the vertical extent of the water column in coastal settings part i in this article we present novel high order discontinuous galerkin dg methods for the vertical extent of the water column in coastal settings we examine the shallow water equations swe in the context of dg spatial discretizations coupled with explicit runge kutta rk time stepping all the primary variables including the free surface elevation are discretized using discontinuous polynomial spaces of arbitrary order the difficulty of mismatched lateral boundary faces that accompanies the use of a discontinuous free surface is overcome through the use of a so called sigma coordinate system in the vertical which transforms the bottom boundary and free surface into coordinate surfaces we develop high order methods for the swe that exhibit optimal orders of convergence for all the primary variables via two distinct paths the first involves the use of a convolution kernel made up of b splines to filter out errors in the dg discretization of the surface elevation and the corresponding pressure flux the second involves a method that evaluates the discrete depth integrated velocity exactly eliminating the need to solve the depth integrated momentum equation altogether the result is a simple and efficient high order scheme that can be extended to the full three dimensional swe

analysis of adaptive mesh refinement for imex discontinuous galerkin solutions of the compressible euler equations with application to atmospheric simulations the resolutions of interests in atmospheric simulations require prohibitively large computational resources adaptive mesh refinement amr tries to mitigate this problem by putting high resolution in crucial areas of the domain we investigate the performance of a tree based amr algorithm for the high order discontinuous galerkin method on quadrilateral grids with non conforming elements we perform a detailed analysis of the cost of amr by comparing this to uniform reference simulations of two standard atmospheric test cases density current and rising thermal bubble the analysis shows up to 15 times speed up of the amr simulations with the cost of mesh adaptation below 1 of the total runtime we pay particular attention to the implicit explicit imex time integration methods and show that the ark2 method is more robust with respect to dynamically adapting meshes than bdf2 preliminary analysis of preconditioning reveals that it can be an important factor in the amr overhead the compiler optimizations provide significant runtime reduction and positively affect the effectiveness of amr allowing for speed ups greater than it would follow from the simple performance model

an efficient approach for face recognition based on common eigenvalues in this paper a simple technique is proposed for face recognition among many human faces it is based on the polynomial coefficients covariance matrix and algorithm on common eigenvalues the main advantage of the proposed approach is that the identification of similarity between human faces is carried out without computing actual eigenvalues and eigenvectors a symmetric matrix is calculated using the polynomial coefficients based companion matrices of two compared images the nullity of a calculated symmetric matrix is used as similarity measure for face recognition the value of nullity is very small for dissimilar images and distinctly large for similar face images the feasibility of the propose approach is demonstrated on three face databases i e the orl database the yale database b and the feret database experimental results have shown the effectiveness of the proposed approach for feature extraction and classification of the face images having large variation in pose and illumination

decay of correlations in surface models a convergent low temperature expansion for a variety of models of twodimensional surfaces is presented it yields existence of the thermodynamic limit for the pressure and correlation functions as well as analyticity inz e in addition the estimates give exponential decay of truncated correlations which proves the existence of a gap in the spectrum of the transfer matrix below the ground state eigenvalue two particular examples included in the general framework are the solid on solid and discrete gaussian models

hyperplane navigation a method to set individual scores in fmri group datasets abstract recent studies have demonstrated that spatial patterns of fmri bold activity distribution over the brain may be used to classify different groups or mental states these studies are based on the application of advanced pattern recognition approaches and multivariate statistical classifiers most published articles in this field are focused on improving the accuracy rates and many approaches have been proposed to accomplish this task nevertheless a point inherent to most machine learning methods and still relatively unexplored in neuroimaging is how the discriminative information can be used to characterize groups and their differences in this work we introduce the maximum uncertainty linear discrimination analysis mlda and show how it can be applied to infer groups patterns by discriminant hyperplane navigation in addition we show that it naturally defines a behavioral score i e an index quantifying the distance between the states of a subject from predefined groups we validate and illustrate this approach using a motor block design fmri experiment data with 35 subjects

dimers and amoebae we study random surfaces which arise as height functions of random perfect matchings a k a dimer configurations on a weighted bipartite doubly periodic graph g embedded in the plane we derive explicit formulas for the surface tension and local gibbs measure probabilities of these models the answers involve a certain plane algebraic curve which is the spectral curve of the kasteleyn operator of the graph for example the surface tension is the legendre dual of the ronkin function of the spectral curve the amoeba of the spectral curve represents the phase diagram of the dimer model further we prove that the spectral curve of a dimer model is always a real curve of special type namely it is a harnack curve this implies many qualitative and quantitative statement about the behavior of the dimer model such as existence of smooth phases decay rate of correlations growth rate of height function fluctuations etc

mixing times of monotone surfaces and sos interfaces a mean curvature approach we consider stochastic spin flip dynamics for i monotone discrete surfaces in mathbb z 3 with planar boundary height and ii the one dimensional discrete solid on solid sos model confined to a box in both cases we show almost optimal bounds o l2polylog l for the mixing time of the chain where l is the natural size of the system the dynamics at a macroscopic scale should be described by a deterministic mean curvature motion such that each point of the surface feels a drift which tends to minimize the local surface tension spohn in j stat phys 71 1081 1132 1993 inspired by this heuristics our approach consists in bounding the dynamics with an auxiliary one which with very high probability follows quite closely the deterministic mean curvature evolution key technical ingredients are monotonicity coupling and an argument due to wilson ann appl probab 14 274 325 2004 in the framework of lozenge tiling markov chains our approach works equally well for both models despite the fact that their equilibrium maximal height fluctuations occur on very different scales log l for monotone surfaces and sqrt l for the sos model finally combining techniques from kinetically constrained spin systems cancrini et al in probab th rel fields 140 459 504 2008 together with the above mixing time result we prove an almost diffusive lower bound of order 1 l2polylog l for the spectral gap of the sos model with horizontal size l and unbounded heights

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

tiling with dominoes pictures of plane figures without holes graphic basis of the thurston algorithm parallelization uniqueness and decomposition resume le desormais classique algorithme de thurston 1990 pour le pavage des figures planes finies et sans trous par des dominos peut etre retrouve par la condition de hall sur les couplages dans les graphes bipartis et la consideration de plus courts chemins dans un graphe associe a la figure a paver ce point de vue nouveau permet une parallelisation en temps o log n avec n 3 processeurs sur un modele pram c est a dire de facon efficace classe nc ce meme algorithme resout la question de l unicite d un pavage et de facon plus generale donne une decomposition canonique de la figure

dominos and the gaussian free field we define a scaling limit of the height function on the domino tiling model dimer model on simply connected regions in z 2 and show that it is the massless free field a gaussian process with independent coefficients when expanded in the eigenbasis of the laplacian

rapid and brief communication generalizing relevance weighted lda in this paper a new variant on linear discriminant analysis lda that we refer to as generalizing relevance weighted lda or grw lda is proposed grw lda extends the applicability to cases that lda cannot handle by combining the advantages of two recent lda enhancements namely generalized singular value decomposition based lda and relevance weighted lda experimental results on feret face database demonstrate the effectiveness of the proposed method

a parallel local timestepping runge kutta discontinuous galerkin method with applications to coastal ocean modeling abstract geophysical flows over complex domains often encompass both coarse and highly resolved regions approximating these flows using shock capturing methods with explicit timestepping gives rise to a courant friedrichs lewy cfl timestep constraint this approach can result in small global timesteps often dictated by flows in small regions vastly increasing computational effort over the whole domain one approach for coping with this problem is to use locally varying timesteps in previous work we formulated a local timestepping lts method within a runge kutta discontinuous galerkin framework and demonstrated the accuracy and efficiency of this method on serial machines for relatively small scale shallow water applications for more realistic models involving large domains and highly complex physics the lts method must be parallelized for multi core parallel computers furthermore additional physics such as strong wind forcing can effect the choice of local timesteps in this paper we describe a parallel lts method parallelized using domain decomposition and mpi we demonstrate the method on tidal flows and hurricane storm surge applications in the coastal regions of the western north atlantic ocean

pressure forcing and dispersion analysis for discontinuous galerkin approximations to oceanic fluid flows this paper is part of an effort to examine the application of discontinuous galerkin dg methods to the numerical modeling of the general circulation of the ocean one step performed here is to develop an integral weak formulation of the lateral pressure forcing that is suitable for usage with a dg method and with a generalized vertical coordinate that includes level terrain fitted isopycnic and hybrid coordinates as examples this formulation is then tested in special cases with analyses of dispersion relations and numerical stability and with some computational experiments these results suggest that the advantages of dg methods may significantly outweigh their disadvantages in the settings tested here this paper also outlines some other issues that need to be addressed in future work

dynamics of 2 1 dimensional sos surfaces above a wall slow mixing induced by entropic repulsion we study the glauber dynamics for the 2 1 d solid on solid model above a hard wall and below a far away ceiling on an l times l box of z 2 with zero boundary conditions at large inverse temperature beta it was shown by bricmont el mellouki and frohlich 1986 that the floor constraint induces an entropic repulsion effect which lifts the surface to an average height h asymp 1 beta log l as an essential step in understanding the effect of entropic repulsion on the glauber dynamics we determine the equilibrium height h to within an additive constant h 1 4 beta log l o 1 we then show that starting from zero initial conditions the surface rises to its final height h through a sequence of metastable transitions between consecutive levels the time for a transition from height h ah a in 0 1 to height h 1 is roughly exp c l a for some constant c 0 in particular the mixing time of the dynamics is exponentially large in l i e t mix geq e c l we also provide the matching upper bound t mix leq e c l requiring a challenging analysis of the statistics of height contours at low temperature and new coupling ideas and techniques finally to emphasize the role of entropic repulsion we show that without a floor constraint at height zero the mixing time is no longer exponentially large in l