internal diffusion limited aggregation parallel algorithms and complexity the computational complexity of internal diffusion limited aggregation dla is examined from both a theoretical and a practical point of view we show that for two or more dimensions the problem of predicting the cluster from a given set of paths is complete for the complexity class cc the subset of p characterized by circuits composed of comparator gates cc completeness is believed to imply that in the worst case growing a cluster of size n requires polynomial time in n even on a parallel computer a parallel relaxation algorithm is presented that uses the fact that clusters are nearly spherical to guess the cluster from a given set of paths and then corrects defects in the guessed cluster through a nonlocal annihilation process the parallel running time of the relaxation algorithm for two dimensional internal dla is studied by simulating it on a serial computer the numerical results are compatible with a running time that is either polylogarithmic in n or a small power of n thus the computational resources needed to grow large clusters are significantly less on average than the worst case analysis would suggest for a parallel machine with k processors we show that random clusters in d dimensions can be generated in mathcal o n k logk n 2 d steps this is a significant speedup over explicit sequential simulation which takes mathcal o n 1 2 d time on average finally we show that in one dimension internal dla can be predicted in mathcal o logn parallel time and so is in the complexity class nc

positive loadings and factor correlations from positive covariance matrices in many instances it is reasonable to assume that the population covariance matrix has positive elements this assumption implies for the single factor analysis model that the loadings and regression weights for best linear factor prediction are positive for the multiple factor analysis model where each variable loads on a single factor and a hierarchical factor model it implies that the loadings and the factor correlations are positive for the latter model it also implies that the regression weights for first and second order factor prediction are positive

bounding the bias of contrastive divergence learning optimization based on k step contrastive divergence cd has become a common way to train restricted boltzmann machines rbms the k step cd is a biased estimator of the log likelihood gradient relying on gibbs sampling we derive a new upper bound for this bias its magnitude depends on k the number of variables in the rbm and the maximum change in energy that can be produced by changing a single variable the last reflects the dependence on the absolute values of the rbm parameters the magnitude of the bias is also affected by the distance in variation between the modeled distribution and the starting distribution of the gibbs chain

on the computational complexity of ising spin glass models in a spin glass with ising spins the problems of computing the magnetic partition function and finding a ground state are studied in a finite two dimensional lattice these problems can be solved by algorithms that require a number of steps bounded by a polynomial function of the size of the lattice in contrast to this fact the same problems are shown to belong to the class of np hard problems both in the two dimensional case within a magnetic field and in the three dimensional case np hardness of a problem suggests that it is very unlikely that a polynomial algorithm could exist to solve it

asymptotics of work distributions in nonequilibrium systems the asymptotic behavior of the work distribution in driven nonequilibrium systems is determined using the method of optimal fluctuations for systems described by langevin dynamics the corresponding euler lagrange equation together with the appropriate boundary conditions and an equation for the leading pre exponential factor are derived the method is applied to three representative examples and the results are used to improve the accuracy of free energy estimates based on the application of the jarzynski equation

on the cut polytope the cut polytopep c g of a graphg v e is the convex hull of the incidence vectors of all edge sets of cuts ofg we show some classes of facet defining inequalities ofp c g we describe three methods with which new facet defining inequalities ofp c g can be constructed from known ones in particular we show that inequalities associated with chordless cycles define facets of this polytope moreover for these inequalities a polynomial algorithm to solve the separation problem is presented we characterize the facet defining inequalities ofp c g ifg is not contractible tok 5 we give a simple characterization of adjacency inp c g and prove that for complete graphs this polytope has diameter one and thatp c g has the hirsch property a relationship betweenp c g and the convex hull of incidence vectors of balancing edge sets of a signed graph is studied

justifying and generalizing contrastive divergence we study an expansion of the log likelihood in undirected graphical models such as the restricted boltzmann machine rbm where each term in the expansion is associated with a sample in a gibbs chain alternating between two random variables the visible vector and the hidden vector in rbms we are particularly interested in estimators of the gradient of the log likelihood obtained through this expansion we show that its residual term converges to zero justifying the use of a truncation running only a short gibbs chain which is the main idea behind the contrastive divergence cd estimator of the log likelihood gradient by truncating even more we obtain a stochastic reconstruction error related through a mean field approximation to the reconstruction error often used to train autoassociators and stacked autoassociators the derivation is not specific to the particular parametric forms used in rbms and requires only convergence of the gibbs chain we present theoretical and empirical evidence linking the number of gibbs steps k and the magnitude of the rbm parameters to the bias in the cd estimator these experiments also suggest that the sign of the cd estimator is correct most of the time even when the bias is large so that cd k is a good descent direction even for small k

theory of a systematic computational error in free energy differences systematic inaccuracy is inherent in any computational estimate of a nonlinear average due to the availability of only a finite number of data values n free energy differences delta f between two states or systems are critically important examples of such averages previous work has demonstrated empirically that the finite sampling error can be very large many times k b t in delta f estimates for simple molecular systems here we present a theoretical description of the inaccuracy including the exact solution of a sample problem the precise asymptotic behavior in terms of 1 n for large n the identification of a universal law and numerical illustrations the theory relies on corrections to the central and other limit theorems

the geometry of algorithms using hierarchical tensors in this paper the differential geometry of the novel hierarchical tucker format for tensors is derived the set ht k of tensors with fixed tree t and hierarchical rank k is shown to be a smooth quotient manifold namely the set of orbits of a lie group action corresponding to the non unique basis representation of these hierarchical tensors explicit characterizations of the quotient manifold its tangent space and the tangent space of ht k are derived suitable for high dimensional problems the usefulness of a complete geometric description is demonstrated by two typical applications first new convergence results for the nonlinear gauss seidel method on ht k are given notably and in contrast to earlier works on this subject the task of minimizing the rayleigh quotient is also addressed second evolution equations for dynamic tensor approximation are formulated in terms of an explicit projection operator onto the tangent space of ht k in addition a numerical comparison is made between this dynamical approach and the standard one based on truncated singular value decompositions 2013 elsevier inc

identifiability of factor analysis some results and open problems abstract identifiability of the factor analysis model is discussed and some recent results and their relation to previous work are surveyed sufficient conditions for local identifiability are presented a counterexample shows that these conditions are not necessary in general a simple counting rule for local identifiability of the factor analysis model is given generically finally some open problems are formulated

might unique factors be common on the possibility of indeterminate common unique covariances the present paper shows that the usual factor analytic structured data dispersion matrix can readily arise from a set of scores y e where the common and unique e factors have nonzero covariance cove 0 implications of this finding are discussed for the indeterminacy of factor scores and for the issue of invariance of factor analytic covariance models the size of the problem is explored with numerical examples

retrieving the correlation matrix from a truncated pca solution the inverse principal component problem whenr principal components are available fork variables the correlation matrix is approximated in the least squares sense by the loading matrix times its transpose the approximation is generally not perfect unlessr k in the present paper it is shown that whenr is at or above the ledermann bound r principal components are enough to perfectly reconstruct the correlation matrix albeit in a way more involved than taking the loading matrix times its transpose in certain cases just below the ledermann bound recovery of the correlation matrix is still possible when the set of all eigenvalues of the correlation matrix is available as additional information

well posedness in critical spaces for incompressible viscoelastic fluid system abstract in this paper we study the well posedness in critical spaces of incompressible viscoelastic fluid system of oldroyd model precisely for this system with initial data in besov space of critical regularity we prove the existence and uniqueness of the local solution which is also shown to exist globally in time provided the initial data is small under certain norms

bayesian estimation of sparse dynamic factor models with order independent and ex post mode identification abstract common variation in n series is extracted into k n dynamic factors we induce sparsity by using a zero point mass normal mixture prior distribution on the loadings estimation and rotational identification are independent of variable ordering sparsity helps identifying the factor space and the factors rotational identification including factor order and sign is obtained by processing the posterior output and based on factor draws rather than factor loading draws simulating data we document sampler and estimation efficiency to illustrate we estimate the model for a large panel of swiss macroeconomic and detailed price data we identify 16 factors with a clear economic interpretation

generic global indentification in factor analysis abstract the paper proves global indentification of the unique variances in factor analysis for almost all parameter points if the number of factors is smaller than the ledermann bound it also shows how to compute using a closed form representation the second solution in the case of six variables and three factors

how to center deep boltzmann machines this work analyzes centered restricted boltzmann machines rbms and centered deep boltzmann machines dbms where centering is done by subtracting offset values from visible and hidden variables we show analytically that i centered and normal boltzmann machines bms and thus rbms and dbms are different parameterizations of the same model class such that any normal bm rbm dbm can be transformed to an equivalent centered bm rbm dbm and vice versa and that this equivalence generalizes to artificial neural networks in general ii the expected performance of centered binary bms rbms dbms is invariant under simultaneous flip of data and offsets for any off set value in the range of zero to one iii centering can be reformulated as a different update rule for normal bms rbms dbms and iv using the enhanced gradient is equivalent to setting the offset values to the average over model and data mean furthermore we present numerical simulations suggesting that i optimal generative performance is achieved by subtracting mean values from visible as well as hidden variables ii centered binary rbms dbms reach significantly higher log likelihood values than normal binary rbms dbms iii centering variants whose offsets depend on the model mean like the enhanced gradient suffer from severe divergence problems iv learning is stabilized if an exponentially moving average over the batch means is used for the offset values instead of the current batch mean which also prevents the enhanced gradient from severe divergence v on a similar level of log likelihood values centered binary rbms dbms have smaller weights and bigger bias parameters than normal binary rbms dbms vi centering leads to an update direction that is closer to the natural gradient which is extremely efficient for training as we show for small binary rbms vii centering eliminates the need for greedy layer wise pre training of dbms which often even deteriorates the results independently of whether centering is used or not and ix centering is also beneficial for auto encoders

global strong solution for the density dependent incompressible viscoelastic fluids in the critical lp framework abstract in this paper we consider the cauchy problem of the density dependent incompressible viscoelastic fluids in the whole space r d d 2 with the initial data close to a stable equilibrium this work is dedicated to deriving the existence result of the global strong solution in the critical space with respect to the natural scaling of the equations in the l p framework

on products and line graphs of signed graphs their eigenvalues and energy abstract in this article we examine the adjacency and laplacian matrices and their eigenvalues and energies of the general product non complete extended p sum or neps of signed graphs we express the adjacency matrix of the product in terms of the kronecker matrix product and the eigenvalues and energy of the product in terms of those of the factor graphs for the cartesian product we characterize balance and compute expressions for the laplacian eigenvalues and laplacian energy we give exact results for those signed planar cylindrical and toroidal grids which are cartesian products of signed paths and cycles we also treat the eigenvalues and energy of the line graphs of signed graphs and the laplacian eigenvalues and laplacian energy in the regular case with application to the line graphs of signed grids that are cartesian products and to the line graphs of all positive and all negative complete graphs

theory of minimum spanning trees i mean field theory and strongly disordered spin glass model the minimum spanning tree mst is a combinatorial optimization problem given a connected graph with a real weight cost on each edge find the spanning tree that minimizes the sum of the total cost of the occupied edges we consider the random mst in which the edge costs are quenched independent random variables there is a strongly disordered spin glass model due to newman and stein phys rev lett 72 2286 1994 which maps precisely onto the random mst we study scaling properties of random msts using a relation between kruskal s greedy algorithm for finding the mst and bond percolation we solve the random mst problem on the bethe lattice bl with appropriate wired boundary conditions and calculate the fractal dimension d 6 of the connected components viewed as a mean field theory the result implies that on a lattice in euclidean space of dimension d there are of order w d ensuremath d large connected components of the random mst inside a window of size w and that d d c d 6 is a critical dimension this differs from the value 8 suggested by newman and stein we also critique the original argument for 8 and provide an improved scaling argument that again yields d c 6 the result implies that the strongly disordered spin glass model has many ground states for dg6 and only of order one below six the results for msts also apply on the poisson weighted infinite tree which is a mean field approach to the continuum model of msts in euclidean space and is a limit of the bl in a companion paper we develop an ensuremath epsilon 6 ensuremath d expansion for the random mst on critical percolation clusters

distribution of work in isothermal nonequilibrium processes diffusive motion in an externally driven potential is considered it is shown that the distribution of work required to drive the system from an initial equilibrium state to another is gaussian for slow but finite driving our result is obtained by projection method techniques exploiting a small parameter defined as the switching rate between the two states of the system the exact solution for a simple model system shows that such an expansion may fail in higher orders since the mean and the variance following from the exact distribution show nonanalytic behavior

schur complements and statistics abstract in this paper we discuss various properties of matrices of the type s h ge 1 f which we call the schur complement of e in a e f g h the matrix e is assumed to be nonsingular when e is singular or rectangular we consider the generalized schur complements s h ge f where e is a generalized inverse of e a comprehensive account of results pertaining to the determinant the rank the inverse and generalized inverses of partitioned matrices and the inertia of a matrix is given both for schur complements and for generalized schur complements we survey the known results in a historical perspective and obtain several extensions numerous applications in numerical analysis and statistics are included the paper ends with an exhaustive bibliography of books and articles related to schur complements

an eulerian description of fluids containing visco elastic particles equations governing the flow of fluid containing visco hyperelastic particles are developed in an eulerian framework the novel feature introduced here is to write an evolution equation for the strain it is envisioned that this will simplify numerical codes which typically compute the strain on lagrangian meshes moving through eulerian meshes existence results for the flow of linear visco hyperelastic particles in a newtonian fluid are established using a galerkin scheme

minimizing thermodynamic length to select intermediate states for free energy calculations and replica exchange simulations in computational thermodynamics a sequence of intermediate states is commonly introduced to connect two equilibrium states we consider two cases where the choice of intermediate states is particularly important minimizing statistical error in free energy difference calculations and maximizing average acceptance probabilities in replica exchange simulations we derive bounds for these quantities in terms of the thermodynamic distance between the intermediates and show that in both cases the intermediates should be chosen as equidistant points along a geodesic connecting the end states

equilibrium free energies from nonequilibrium measurements using maximum likelihood methods we present a maximum likelihood argument for the bennett acceptance ratio method and derive a simple formula for the variance of free energy estimates generated using this method this derivation of the acceptance ratio method using a form of logistic regression a common statistical technique allows us to shed additional light on the underlying physical and statistical properties of the method for example we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements

well posedness in critical spaces for the system of compressible navier stokes in larger spaces this paper is dedicated to the study of viscous compressible barotropic fluids in dimension n geq2 we address the question of well posedness for it large data having critical besov regularity our result improves the analysis of r danchin in cite dw of chen et al in cite c2 and of the author in cite h1 h2 inasmuch as we may take initial density in b nn p 1 with 1 leq p infty our result relies on a new a priori estimate for the velocity where we introduce a new unknown called textit effective velocity to weaken one the coupling between the density and the velocity in particular for the first time we obtain uniqueness without imposing hypothesis on the gradient of the density

bound entanglement in tree graphs in this paper we discuss the entanglement properties of graph diagonal states with particular emphasis on calculating the threshold for the transition between the presence and absence of entanglement i e the separability point special consideration is made of the thermal states of trees including the linear cluster state we characterize the type of entanglement present and describe the optimal entanglement witnesses and their implementation on a quantum computer up to an additive approximation in the case of general graphs we invoke a relation with the partition function of the classical ising model thereby intimating a connection to computational complexity theoretic tasks finally we show that the entanglement is robust to some classes of local perturbations

global solutions of the navier stokes equations for multidimensional compressible flow with discontinuous initial data abstract we prove the global existence of weak solutions of the navier stokes equations for compressible isothermal flow in two and three space dimensions when the initial density is close to a constant in l 2 and l and the initial velocity is small in l 2 and bounded in l 2 n in two dimensions the l 2 norms must be weighted slightly a great deal of qualitative information about the solution is obtained for example we show that the velocity and vorticity are relatively smooth in positive time as is the effective viscous flux f which is the divergence of the velocity minus a certain multiple of the pressure we find that f plays a crucial role in the entire analysis particularly in closing the required energy estimates understanding rates of regularization near the initial layer and most important obtaining time independent pointwise bounds for the density

j ising model on durer lattices abstract this paper tackles the problem of finding analytical expressions describing the ground state properties of durer lattices over which a generalized edwards anderson model j ising model is defined a local frustration analysis is performed based on representative cells for these lattices the concentration of ferromagnetic f bonds x is used as the independent variable in the analysis 1 x is the concentration for antiferromagnetic a bonds where x spans the range 0 00 1 00 the presence of a bonds brings frustration whose clear manifestation is when bonds around the minimum possible circuit of bonds plaquette cannot be simultaneously satisfied the distribution of curved frustrated plaquettes within the representative cell is determinant for the evaluation of the parameters of interest such as average frustration segment energy per bond and fractional content of non frustrated bonds an analytical method is developed to cope with this analysis based on the direct probability of a plaquette being curved exact numerical simulations on a large number of randomly generated samples associated to durer lattices allow to validate previously described theoretical analysis this analytical method gives an excellent description for the most of the range for x a particular discussion for the point x 0 50 belonging to spin glass phase also sheds light on the general trends of the properties described here

convergence of estimates of unique variances in factor analysis based on the inverse sample covariance matrix if the ratio m p tends to zero where m is the number of factors m and p the number of observable variables then the inverse diagonal element of the inverted observable covariance matrix pjj 1 tends to the corresponding unique variance jj for almost all of these guttman 1956 if the smallest singular value of the loadings matrix from common factor analysis tends to infinity as p increases then m p tends to zero the same condition is necessary and sufficient for pjj 1 to tend to jj for all of these several related conditions are discussed psycinfo database record c 2009 apa all rights reserved journal abstract

algorithms for estimating the partition function of restricted boltzmann machines abstract accurate estimates of the normalization constants partition functions of energy based probabilistic models markov random fields are highly important for example for assessing the performance of models monitoring training progress and conducting likelihood ratio tests several algorithms for estimating the partition function in relation to a reference distribution have been introduced including annealed importance sampling ais and bennett s acceptance ratio method bar however their conceptual similarities and differences have not been worked out so far and systematic comparisons of their behavior in practice have been missing we devise a unifying theoretical framework for these algorithms which comprises existing variants and suggests new approaches it is based on a generalized form of crooks equality linking the expectation over a distribution of samples generated by a transition operator to the expectation over the distribution induced by the reversed operator the framework covers different ways of generating samples such as parallel tempering and path sampling an empirical comparison revealed the differences between the methods when estimating the partition function of restricted boltzmann machines and ising models in our experiments bar using parallel tempering worked well with a small number of bridging distributions while path sampling based ais performed best when many bridging distributions were available because bar gave the overall best results we favor it over ais furthermore the experiments showed the importance of choosing a proper reference distribution

bayesian exploratory factor analysis this paper develops and applies a bayesian approach to exploratory factor analysis that improves on ad hoc classical approaches our framework relies on dedicated factor models and simultaneously determines the number of factors the allocation of each measurement to a unique factor and the corresponding factor loadings classical identification criteria are applied and integrated into our bayesian procedure to generate models that are stable and clearly interpretable a monte carlo study confirms the validity of the approach the method is used to produce interpretable low dimensional aggregates from a high dimensional set of psychological measurements

a global existence result for the compressible navier stokes equations in the critical l p framework the present paper is dedicated to the global well posedness issue for the barotropic compressible navier stokes system in the whole space mathbb r d with d 2 we aim at extending the work by danchin inventiones mathematicae 141 3 579 614 2000 to a critical framework which is not related to the energy space for small perturbations of a stable equilibrium state in the sense of suitable lp type besov norms we establish the global existence as a consequence like for incompressible flows one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true in passing we obtain new estimates for the linearized and the paralinearized systems which may be of interest for future works on compressible flows

global solutions for incompressible viscoelastic fluids we prove the existence of both local and global smooth solutions to the cauchy problem in the whole space and the periodic problem in the n dimensional torus for the incompressible viscoelastic system of oldroyd b type in the case of near equilibrium initial data the results hold in both two and three dimensional spaces the results and methods presented in this paper are also valid for a wide range of elastic complex fluids such as magnetohydrodynamics liquid crystals and mixture problems

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

training products of experts by minimizing contrastive divergence it is possible to combine multiple latent variable models of the same data by multiplying their probability distributions together and then renormalizing this way of combining individual expert models makes it hard to generate samples from the combined model but easy to infer the values of the latent variables of each expert because the combination rule ensures that the latent variables of different experts are conditionally independent when given the data a product of experts poe is therefore an interesting candidate for a perceptual system in which rapid inference is vital and generation is unnecessary training a poe by maximizing the likelihood of the data is difficult because it is hard even to approximate the derivatives of the renormalization term in the combination rule fortunately a poe can be trained using a different objective function called contrastive divergence whose derivatives with regard to the parameters can be approximated accurately and efficiently examples are presented of contrastive divergence learning using several types of expert on several types of data

rank reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis one of the intriguing questions of factor analysis is the extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries we show in this paper that the set of matrices which can be reduced to rankr has positive lebesgue measure if and only ifr is greater or equal to the ledermann bound in other words the ledermann bound is shown to bealmost surely the greatest lower bound to a reduced rank of the sample covariance matrix afterwards an asymptotic sampling theory of so called minimum trace factor analysis mtfa is proposed the theory is based on continuous and differential properties of functions involved in the mtfa convex analysis techniques are utilized to obtain conditions for differentiability of these functions

dispersive effect and global well posedness of the compressible viscoelastic fluids abstract this paper is concerned with the global well posedness issue of the compressible viscoelastic fluids in the whole space r n n 2 the proof relies on the dispersive estimates to the linearized hyperbolic system combined with energy estimates to the hyperbolic parabolic system by exploiting the intrinsic structure of the system under some physical restrictions we find that the compressible viscoelastic fluids admits a unique global solution with a class of large initial data in the sense of critical l 2 framework

global well posedness for compressible viscoelastic fluids near equilibrium in this paper we prove local well posedness for compressible viscoelastic fluids of the oldroyd model under the assumption that the initial density is bounded away from zero and global well posedness near equilibrium the proof of global well posedness relies on some intrinsic properties of viscoelastic fluids and on a uniform estimate for a linearized hyperbolic parabolic system with convection terms

exact ground states of large two dimensional planar ising spin glasses studying spin glass physics through analyzing their ground state properties has a long history although there exist polynomial time algorithms for the two dimensional planar case where the problem of finding ground states is transformed to a minimum weight perfect matching problem the reachable system sizes have been limited both by the needed cpu time and by memory requirements in this work we present an algorithm for the calculation of exact ground states for two dimensional ising spin glasses with free boundary conditions in at least one direction the algorithmic foundations of the method date back to the work of kasteleyn from the 1960s for computing the complete partition function of the ising model using kasteleyn cities we calculate exact ground states for huge two dimensional planar ising spin glass lattices up to 3000 2 spins within reasonable time according to our knowledge these are the largest sizes currently available kasteleyn cities were recently also used by thomas and middleton in the context of extended ground states on the torus moreover they show that the method can also be used for computing ground states of planar graphs furthermore we point out that the correctness of heuristically computed ground states can easily be verified finally we evaluate the solution quality of heuristic variants of the l bieche et al approach

fast computing global structural balance in signed networks based on memetic algorithm abstract structural balance is a large area of study in signed networks and it is intrinsically a global property of the whole network computing global structural balance in signed networks which has attracted some attention in recent years is to measure how unbalanced a signed network is and it is a nondeterministic polynomial time hard problem many approaches are developed to compute global balance however the results obtained by them are partial and unsatisfactory in this study the computation of global structural balance is solved as an optimization problem by using the memetic algorithm the optimization algorithm named meme sb is proposed to optimize an evaluation function energy function which is used to compute a distance to exact balance our proposed algorithm combines genetic algorithm and a greedy strategy as the local search procedure experiments on social and biological networks show the excellent effectiveness and efficiency of the proposed method

a numerical approach to the approximate and the exact minimum rank of a covariance matrix a concept of approximate minimum rank for a covariance matrix is defined which contains the exact minimum rank as a special case a computational procedure to evaluate the approximate minimum rank is offered the procedure yields those proper communalities for which the unexplained common variance ignored in low rank factor analysis is minimized the procedure also permits a numerical determination of the exact minimum rank of a covariance matrix within limits of computational accuracy a set of 180 covariance matrices with known or bounded minimum rank was analyzed the procedure was successful throughout in recovering the desired rank

on hydrodynamics of viscoelastic fluids in this paper we study a hydrodynamic system describing fluids with viscoelastic properties after a brief examination of the relations between several models we shall concentrate on a few analytical issues concerning them in particular we establish local existence and global existence with small initial data of classical solutions for an oldroyd system without an artificially postulated damping mechanism

rare events and the convergence of exponentially averaged work values equilibrium free energy differences are given by exponential averages of nonequilibrium work values such averages however often converge poorly as they are dominated by rare realizations i show that there is a simple and intuitively appealing description of these rare but dominant realizations this description is expressed as a duality between forward and reverse processes and provides both heuristic insights and quantitative estimates regarding the number of realizations needed for convergence of the exponential average analogous results apply to the equilibrium perturbation method of estimating free energy differences the pedagogical example of a piston and gas r c lua and a y grosberg j phys chem b 109 6805 2005 is used to illustrate the general discussion

on the initial boundary value problem of the incompressible viscoelastic fluid system in this paper we shall establish the local well posedness of the initial boundary value problem of the viscoelastic fluid system of the oldroyd model we shall also prove that the local solutions can be extended globally and that the global solutions decay exponentially fast as time goes to infinity provided that the initial data are sufficiently close to the equilibrium state c 2007 wiley periodicals inc

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

free energy reconstruction from steered dynamics without post processing various methods achieving importance sampling in ensembles of nonequilibrium trajectories enable one to estimate free energy differences and by maximum likelihood post processing to reconstruct free energy landscapes here based on bayes theorem we propose a more direct method in which a posterior likelihood function is used both to construct the steered dynamics and to infer the contribution to equilibrium of all the sampled states the method is implemented with two steering schedules first using non autonomous steering we calculate the migration barrier of the vacancy in email protected second using an autonomous scheduling related to metadynamics and equivalent to temperature accelerated molecular dynamics we accurately reconstruct the two dimensional free energy landscape of the 38 atom lennard jones cluster as a function of an orientational bond order parameter and energy down to the solid solid structural transition temperature of the cluster and without maximum likelihood post processing

global well posedness for compressible navier stokes equations with highly oscillating initial velocity in this paper we prove global well posedness for compressible navier stokes equations in the critical functional framework with the initial data close to a stable equilibrium this result allows us to construct global solutions for the highly oscillating initial velocity the proof relies on a new estimate for the hyperbolic parabolic system with convection terms 2010 wiley periodicals inc

the rank of reduced dispersion matrices psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements psychometricians concentrate on cases in which low rank can be attained preferably rank one the spearman case econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one the frisch case in this paper we give an extensive historial discussion of both fields we prove the two key results in a more satisfactory and uniform way we point out various small errors and misunderstandings and we present a methodological comparison of factor analysis and regression on the basis of our results

linear models based on noisy data and the frisch scheme we address the problem of identifying linear relations among variables based on noisy measurements this is a central question in the search for structure in large data sets often a key assumption is that measurement errors in each variable are independent this basic formulation has its roots in the work of charles spearman in 1904 and of ragnar frisch in the 1930s various topics such as errors in variables factor analysis and instrumental variables all refer to alternative viewpoints on this problem and on ways to account for the anticipated way that noise enters the data in the present paper we begin by describing certain fundamental contributions by the founders of the field and provide alternative modern proofs to certain key results we then go on to consider a modern viewpoint and novel numerical techniques to the problem the central theme is expressed by the frisch kalman dictum which calls for identifying a noise contribution that allows a maximal number of simultaneous linear relations a

making classical ground state spin computing fault tolerant we examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation this model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions in its most primitive form systems constructed in this model cannot compute in an error free manner when working at nonzero temperature however by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error free we achieve this by using techniques in fault tolerant classical computing and the result is that the system can compute effectively error free if the temperature is below a critical temperature we further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class merlin arthur this provides an interesting connection between the physical behavior of certain many body spin systems and computational complexity

a bound for the convergence rate of parallel tempering for sampling restricted boltzmann machines sampling from restricted boltzmann machines rbms is done by markov chain monte carlo mcmc methods the faster the convergence of the markov chain the more efficiently can high quality samples be obtained this is also important for robust training of rbms which usually relies on sampling parallel tempering pt an mcmc method that maintains several replicas of the original chain at higher temperatures has been successfully applied for rbm training we present the first analysis of the convergence rate of pt for sampling from binary rbms the resulting bound on the rate of convergence of the pt markov chain shows an exponential dependency on the size of one layer and the absolute values of the rbm parameters it is minimized by a uniform spacing of the inverse temperatures which is often used in practice similarly as in the derivation of bounds on the approximation error for contrastive divergence learning our bound on the mixing time implies an upper bound on the error of the gradient approximation when the method is used for rbm training