structural pursuit over multiple undirected graphs gaussian graphical models are useful to analyze and visualize conditional dependence relationships between interacting units motivated from network analysis under different experimental conditions such as gene networks for disparate cancer subtypes we model structural changes over multiple networks with possible heterogeneities in particular we estimate multiple precision matrices describing dependencies among interacting units through maximum penalized likelihood of particular interest are homogeneous groups of similar entries across and zero entries of these matrices referred to as clustering and sparseness structures respectively a nonconvex method is proposed to seek a sparse representation for each matrix and identify clusters of the entries across the matrices computationally we develop an efficient method on the basis of difference convex programming the augmented lagrangian method and the blockwise coordinate descent method which is scalable to hundreds of graphs of thousands nodes th

spatial pattern formation in external noise theory and simulation spatial pattern formation in fluctuating media is researched analytically from the point of view of the order parameters concept a reaction diffusion system with external noise is considered as a model of such media stochastic equations for unstable mode amplitudes order parameters the dispersion equation for averaged amplitudes of unstable modes and the fokker planck equation for the order parameters are obtained the theory developed makes it possible to analyze different noise induced effects including the variation of boundaries of ordering and disordering phase transitions depending on the parameters of external noise

long time behavior of solutions to a class of stochastic parabolic equations with homogeneous white noise stratonovitch s case in this article we prove new results concerning the long time behavior of random fields that are solutions in some sense to a class of semilinear parabolic equations subjected to a homogeneous and multiplicative white noise our main results state that these random fields eventually homogeneize with respect to the spatial variable and finally converge to a non random global attractor which consists of two spatially and temporally homogeneous asymptotic states more precisely we prove that the random fields either stabilize exponentially rapidly with probability one around one of the asymptotic states or that they set out to oscillate between them in the first case we can also determine exactly the corresponding lyapunov exponents in the second case we prove that the random fields are in fact recurrent in that they can reach every point between the two asymptotic states in a finite time with probability one in both cases we also interpret our results in terms of stability properties of the global attractor and we provide estimates for the average time that the random fields spend in small neighborhoods of the asymptotic states our methods of proof rest upon the use of a suitable regularization of the brownian motion along with a related wong zakai approximation procedure

statistical mechanics of neocortical interactions canonical momenta indicatorsof electroencephalography a series of papers has developed a statistical mechanics of neocortical interactions smni deriving aggregate behavior of experimentally observed columns of neurons from statistical electrical chemical properties of synaptic interactions while not useful to yield insights at the single neuron level smni has demonstrated its capability in describing large scale properties of short term memory and electroencephalographic eeg systematics the necessity of including nonlinear and stochastic structures in this development has been stressed sets of eeg and evoked potential data were fit collected to investigate genetic predispositions to alcoholism and to extract brain signatures of short term memory adaptive simulated annealing asa a global optimization algorithm was used to perform maximum likelihood fits of lagrangians defined by path integrals of multivariate conditional probabilities canonical momenta indicators cmi are thereby derived for an individual s eeg data the cmi give better signal recognition than the raw data and can be used to advantage as correlates of behavioral states these results give strong quantitative support for an accurate intuitive picture portraying neocortical interactions as having common algebraic or physics mechanisms that scale across quite disparate spatial scales and functional or behavioral phenomena i e describing interactions among neurons columns of neurons and regional masses of neurons

the joint graphical lasso for inverse covariance estimation across multiple classes we consider the problem of estimating multiple related gaussian graphical models from a high dimensional data set with observations belonging to distinct classes we propose the joint graphical lasso which borrows strength across the classes in order to estimate multiple graphical models that share certain characteristics such as the locations or weights of nonzero edges our approach is based upon maximizing a penalized log likelihood we employ generalized fused lasso or group lasso penalties and implement a fast admm algorithm to solve the corresponding convex optimization problems the performance of the proposed method is illustrated through simulated and real data examples

external fluctuations in a pattern forming instability the effect of external fluctuations on the formation of spatial patterns is analyzed by means of a stochastic swift hohenberg model with multiplicative space correlated noise numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise this shift takes place in the ordering direction i e produces patterns but its magnitude decreases with that of the noise correlation length analytical arguments are presented to explain these facts

doubly functional graphical models in high dimensions we consider estimating a functional graphical model from multivariate functional observations in functional data analysis the classical assumption is that each function has been measured over a densely sampled grid however in practice the functions have often been observed with measurement error at a relatively small number of points we propose a class of doubly functional graphical models to capture the evolving conditional dependence relationship among a large number of sparsely or densely sampled functions our approach first implements a nonparametric smoother to perform functional principal components analysis for each curve then estimates a functional covariance matrix and finally computes sparse precision matrices which in turn provide the doubly functional graphical model we derive some novel concentration bounds uniform convergence rates and model selection properties of our estimator for both sparsely and densely sampled functional data in the high dimensional large p small n regime we demonstrate via simulations that the proposed method significantly outperforms possible competitors our proposed method is applied to a brain imaging dataset

large time behavior of interface solutions to the heat equation with fisher wright white noise the one dimensional heat equation driven by fisher wright white noise is studied from initial conditions with compact support solutions retain this compact support and die out in finite time there exist interface solutions which change from the value 1 to the value 0 in a finite region the motion of the interface location is shown to approach that of a brownian motion under rescaling solutions with a finite number of interfaces are approximated by a system of annihilating brownian motions

abelian manna model in three dimensions and below the abelian manna model of self organized criticality is studied on various three dimensional and fractal lattices the exponents for avalanche size duration and area distribution of the model are obtained by using a high accuracy moment analysis together with earlier results on lower dimensional lattices the present results reinforce the notion of universality below the upper critical dimension and allow us to determine the coefficients of an e expansion by rescaling the critical exponents by the lattice dimension and incorporating the random walker dimension a remarkable relation is observed satisfied by both regular and fractal lattices

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

directed compact percolation cluster size and hyperscaling exact recurrence relations are obtained for the length and size distributions of compact directed percolation clusters on the square lattice the corresponding relation for the moment generating function of the length distribution is obtained in closed form whereas in the case of the size distribution only the first three moments are obtained the work is carried out for clusters grown from a seed of arbitrary width on an anisotropic lattice a duality property is shown to exist which relates the moment generating functions on the two sides of the critical curve the moments of both distributions have critical exponents which satisfy a constant gap hypothesis with gap exponents nu 2 and delta 3 corresponding to the scaling length and scaling size respectively the usual hyperscaling relation for directed percolation is found to be invalid for compact clusters and is replaced by delta nu d nu perpendicular to where nu perpendicular to is the exponent corresponding to the cluster width and d is the number of transverse dimensions 1 for the square lattice

mapping multiplicative to additive noise the langevin formulation of a number of well known stochastic processes involves multiplicative noise in this work we present a systematic mapping of a process with multiplicative noise to a related process with additive noise which may often be easier to analyse the mapping is easily understood in the example of the branching process in a second example we study the random neighbour or infinite range contact process which is mapped to an ornstein uhlenbeck process with absorbing wall the present work might shed some light on absorbing state phase transitions in general such as the role of conditional expectation values and finite size scaling and elucidate the meaning of the noise amplitude while we focus on the physical interpretation of the mapping we also provide a mathematical derivation

stochastic resonance between dissipative structures in a bistable noise sustained dynamics we study an extended system that without noise shows a monostable dynamics but when submitted to an adequate multiplicative noise an effective bistable dynamics arises the stochastic resonance between the attractors of the noise sustained dynamicsis investigated theoretically in terms of a two state approximation the knowledge of the exact nonequilibrium potential allows us to obtain the output signal to noise ratio its maximum is predicted in the symmetric case for which both attractors have the same nonequilibrium potential value

multivariate ornstein uhlenbeck processes with mean field dependent coefficients application to postural sway we study the transient and stationary behavior of many particle systems in terms of multivariate ornstein uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields mean field approximations of this kind of system are derived in terms of fokker planck equations in such systems multiple stationary solutions as well as bifurcations of stationary solutions may occur in addition strictly monotonically decreasing steady state autocorrelation functions that decay faster than exponential functions are found which are used to describe the erratic motion of the center of pressure during quiet standing

attractors for random dynamical systems a criterion for existence of global random attractors for rds is established existence of invariant markov measures supported by the random attractor is proved for spde this yields invariant measures for the associated markov semigroup the results are applied to reation diffusion equations with additive white noise and to navier stokes equations with multiplicative and with additive white noise

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

comprehensive study of phase transitions in relaxational systems with field dependent coefficients we present a comprehensive study of phase transitions in single field systems that relax to a nonequilibrium global steady state the mechanism we focus on is not the so called stratonovich drift combined with collective effects but is instead similar to the one associated with noise induced transitions in the manner of horsthemke lefever in zero dimensional systems as a consequence the noise interpretation e g ito vs stratonovich merely shifts the phase boundaries with the help of a mean field approximation we present a broad qualitative picture of the various phase diagrams that can be found in these systems to complement the theoretical analysis we present numerical simulations that confirm the findings of the mean field theory

joint estimation of multiple graphical models from high dimensional time series in this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions we assume that the data are collected from n subjects each of which consists of t possibly dependent observations the graphical models of subjects vary but are assumed to change smoothly corresponding to a measure of closeness between subjects we propose a kernel based method for jointly estimating all graphical models theoretically under a double asymptotic framework where both t n and the dimension d can increase we provide the explicit rate of convergence in parameter estimation it characterizes the strength one can borrow across different individuals and the impact of data dependence on parameter estimation empirically experiments on both synthetic and real resting state functional magnetic resonance imaging rs fmri data illustrate the effectiveness of the proposed method

hyperscaling in the domany kinzel cellular automaton an apparent violation of hyperscaling at the endpoint of the critical line in the domany kinzel stochastic cellular automaton finds an elementary resolution upon noting that the order parameter is discontinuous at this point we derive a hyperscaling relation for such transitions and discuss applications to related examples

nonequilibrium phase transitions induced by multiplicative noise we review a mean field analysis and give the details of a correlation function approach for spatially distributed systems subject to multiplicative noise white in space and time we confirm the existence of a pure noise induced reentrant nonequilibrium phase transition in the model introduced in c van den broeck et al phys rev lett 73 3395 1994 give an intuitive explanation of its origin and present extensive simulations in dimension d52 the observed critical properties are compatible with those of the ising universality class s1063 651x 97 08704 7

comparison methods for a class of function valued stochastic partial differential equations a comparison theorem is derived for a class of function valued stochastic partial differential equations spde s with lipschitz coefficients driven by cylindrical and regular hilbert space valued brownian motions moreover we obtain necessary and sufficient conditions for the positivity of the mild solutions of the spde s where the sufficiency follows from the comparison theorem thereby it is e g possible to identify a class of spde s which can serve as stochastic space time models for the density of particles as a consequence we can construct unique mild solutions of spde s on the cone of positive functions with non lipschitz drift parts including the case of arbitrary polynomialsr x withr o o and leading negative coefficient

stability analysis of stationary states of mean field models described by fokker planck equations abstract so far the stability of stationary solutions of mean field models described by fokker planck equations has only been determined analytically in some special cases following two earlier studies j korean phys soc 40 2002 1037 prog theoret phys suppl 150 2003 48 we discuss a stability analysis for a large class of mean field models based on fokker planck equations to this end we use linear stability analysis in addition to the well known approaches by means of transcendent equations and lyapunov s direct method we demonstrate that all three methods yield consistent results for systems that exhibit free energy functionals e g equilibrium systems we show that the simple transcendent equation analysis fails for systems that do not exhibit free energy functionals e g nonequilibrium systems and show how to solve this problem by means of a more sophisticated transcendent equation analysis furthermore we propose a norm for the perturbations of stationary states and illustrate some of our results by a model that exhibits a reentrant noise induced phase transition

airy distribution function from the area under a brownian excursion to the maximal height of fluctuating interfaces the airy distribution function describes the probability distribution of the area under a brownian excursion over a unit interval surprisingly this function has appeared in a number of seemingly unrelated problems mostly in computer science and graph theory in this paper we show that this distribution function also appears in a rather well studied physical system namely the fluctuating interfaces we present an exact solution for the distribution p h m l of the maximal height h m measured with respect to the average spatial height in the steady state of a fluctuating interface in a one dimensional system of size l with both periodic and free boundary conditions for the periodic case we show that p h m l l 1 2f h m l 1 2 for all l 0 where the function f x is the airy distribution function this result is valid for both the edwards wilkinson ew and the kardar parisi zhang interfaces for the free boundary case the same scaling holds p h m l l 1 2f h m l 1 2 but the scaling function f x is different from that of the periodic case we compute this scaling function explicitly for the ew interface and call it the f airy distribution function numerical simulations are in excellent agreement with our analytical results our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables some of these results were announced in a recent letter s n majumdar and a comtet phys rev lett 92 225501 2004

mean field limit of systems with multiplicative noise a detailed study of the mean field solution of langevin equations with multiplicative noise is presented three different regimes depending on noise intensity weak intermediate and strong noise are identified by performing a self consistent calculation on a fully connected lattice the most interesting strong noise regime is shown to be intrinsically unstable with respect to the inclusion of fluctuations as a ginzburg criterion shows on the other hand the self consistent approach is shown to be valid only in the thermodynamic limit while for finite systems the critical behavior is found to be different in this last case the self consistent field itself is broadly distributed rather than taking a well defined mean value its fluctuations described by an effective zero dimensional multiplicative noise equation govern the critical properties these findings are obtained analytically for a fully connected graph and verified numerically both on fully connected graphs and on random regular networks the results presented here shed some doubt on what is the validity and meaning of a standard mean field approach in systems with multiplicative noise in finite dimensions where each site does not see an infinite number of neighbors but a finite one the implications of all this on the existence of a finite upper critical dimension for multiplicative noise and kardar parisi zhang problems are briefly discussed

pathwise mild solutions for quasilinear stochastic partial differential equations abstract stochastic partial differential equations spdes have become a key modeling tool in applications yet there are many classes of spdes where the existence and regularity theory for solutions is not completely developed here we contribute to this aspect and prove the existence of mild solutions for a broad class of quasilinear cauchy problems including among others cross diffusion systems as a key application our solutions are local in time and are derived via a fixed point argument in suitable function spaces the key idea is to combine in a suitable way the classical theory of deterministic quasilinear parabolic partial differential equations pdes with recent theory of evolution semigroups we also show how to apply our theory to the shigesada kawasaki teramoto skt model furthermore we provide examples of blow up and ill posed operators which can occur after finite time showing that solutions can only be local in time for general quasilinear spdes while they might be global in time for special subclasses of problems

phase separation in binary systems with internal multiplicative noise abstract a study of a phase separation process in stochastic systems with a field dependent kinetic coefficient and an internal multiplicative noise is presented dynamics of spinodal decomposition at early and late stages is investigated by computer simulations where the domain growth law is generalized a mean field approach was carried out in order to obtain the stationary probability bifurcation and phase diagrams displaying reentrant phase transitions we relate our approach to entropy driven phase transitions theory

the stampacchia maximum principle for stochastic partial differential equations and applications abstract stochastic partial differential equations spdes are considered linear and nonlinear for which we establish comparison theorems for the solutions or positivity results a e and a s for suitable data comparison theorems for spdes are available in the literature the originality of our approach is that it is based on the use of truncations following the stampacchia approach to maximum principle we believe that our method which does not rely too much on probability considerations is simpler than the existing approaches and to a certain extent more directly applicable to concrete situations among the applications boundedness results and positivity results are respectively proved for the solutions of a stochastic boussinesq temperature equation and of reaction diffusion equations perturbed by a non lipschitz nonlinear noise stabilization results to a chafee infante equation perturbed by a nonlinear noise are also derived

noise induced phase separation mean field results we present a study of a phase separation process induced by the presence of spatially correlated multiplicative noise we develop a mean field approach suitable for conserved order parameter systems and use it to obtain the phase diagram of the model mean field results are compared with numerical simulations of the complete model in two dimensions additionally a comparison between the noise driven dynamics of conserved and nonconserved systems is made at the level of the mean field approximation

systems with multiplicative noise critical behavior from kpz equation and numerics we show that certain critical exponents of systems with multiplicative noise can be obtained from exponents of the kpz equation numerical simulations in 1d confirm this prediction and yield other exponents of the multiplicative noise problem the numerics also verify an earlier prediction of the divergence of the susceptibility over an entire range of control parameter values and show that the exponent governing the divergence in this range varies continuously with control parameter

regularized matrix regression modern technologies are producing a wealth of data with complex structures for instance in two dimensional digital imaging flow cytometry and electroencephalography matrix type covariates frequently arise when measurements are obtained for each combination of two underlying variables to address scientific questions arising from those data new regression methods that take matrices as covariates are needed and sparsity or other forms of regularization are crucial owing to the ultrahigh dimensionality and complex structure of the matrix data the popular lasso and related regularization methods hinge on the sparsity of the true signal in terms of the number of its non zero coefficients however for the matrix data the true signal is often of or can be well approximated by a low rank structure as such the sparsity is frequently in the form of low rank of the matrix parameters which may seriously violate the assumption of the classical lasso we propose a class of regularized matrix regression methods based on spectral regularization a highly efficient and scalable estimation algorithm is developed and a degrees of freedom formula is derived to facilitate model selection along the regularization path superior performance of the method proposed is demonstrated on both synthetic and real examples

effect of noise on front propagation in reaction diffusion equations of kpp type we consider reaction diffusion equations of kpp type in one spatial dimension perturbed by a fisher wright white noise under the assumption of uniqueness in distribution examples include the randomly perturbed fisher kpp equations partial tu partial x 2u u 1 u epsilon sqrt u 1 u dot w and partial tu partial x 2u u 1 u epsilon sqrt u dot w where dot w dot w t x is a space time white noise we prove the brunet derrida conjecture that the speed of traveling fronts for small e is 2 pi 2 log epsilon 2 2 o log log epsilon log epsilon 3

bounded solutions to singularly perturbed systems of o d e abstract we consider existence and stability properties of bounded solutions to singular systems of o d e the method we suggest considers the concept of singular maps between scales of banach spaces and their properties this theory is then applied to obtain existence and transversality of bounded solutions to singular systems of o d e

sparse precision matrix estimation via lasso penalized d trace loss we introduce a constrained empirical loss minimization framework for estimating high dimensional sparse precision matrices and propose a new loss function called the d trace loss for that purpose a novel sparse precision matrix estimator is defined as the minimizer of the lasso penalized d trace loss under a positive definiteness constraint under a new irrepresentability condition the lasso penalized d trace estimator is shown to have the sparse recovery property examples demonstrate that the new condition can hold in situations where the irrepresentability condition for the lasso penalized gaussian likelihood estimator fails we establish rates of convergence for the new estimator in the elementwise maximum frobenius and operator norms we develop a very efficient algorithm based on alternating direction methods for computing the proposed estimator simulated and real data are used to demonstrate the computational efficiency of our algorithm and the finite sample performance of the new estimator the lasso penalized d trace estimator is found to compare favourably with the lasso penalized gaussian likelihood estimator

noise driven mechanism for pattern formation tion we modify the coupling term of the model in such a way that a morphological instability can appear we will show by means of numerical simulations and analytic calculations that an increasingly ordered spatial structure develops as the intensity of the fluctuation increases beyond a critical value moreover we show that for sufficiently high noise intensity there is nonmonotonic behavior as a function of the coupling that is there exists an optimal value of the coupling for which the ordered structure exhibits maximum coherence the paper is organized as follows we introduce the model in sec ii and explicitly show that no short time instability can drive pattern formation in this system in sec iii and the appendix we present a modulated mean field theory and the phase diagram of the model obtained from this theory numerical simulations that confirm the qualitative validity of the theoretical results are presented in sec iv finally we summarize our main conclusions in sec v

model selection and estimation in the gaussian graphical model summary we propose penalized likelihood methods for estimating the concentration matrix in the gaussian graphical model the methods lead to a sparse and shrinkage estimator of the concentration matrix that is positive definite and thus conduct model selection and estimation simultaneously the implementation of the methods is nontrivial because of the positive definite constraint on the concentration matrix but we show that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization we propose a bic type criterion for the selection of the tuning parameter in the penalized likelihood methods the connection between our methods and existing methods is illustrated simulations and real examples demonstrate the competitive performance of the new methods

local martingale and pathwise solutions for an abstract fluids model we establish the existence and uniqueness of both local martingale and local pathwise solutions of an abstract nonlinear stochastic evolution system the primary application of this abstract framework is to infer the local existence of strong pathwise solutions to the 3d primitive equations of the oceans and atmosphere forced by a nonlinear multiplicative white noise instead of developing our results specifically for the 3d primitive equations we choose to develop them in a slightly abstract framework which covers many related forms of these equations atmosphere oceans coupled atmosphere ocean on the sphere on the beta plane approximation etc and the incompressible navier stokes equations in applications all of the details are given for the beta plane approximation of the oceans equations

phase ordering dynamics with an order parameter dependent mobility the large n limit the effect of an order parameter dependent mobility or kinetic coefficient on the phase ordering dynamics of a system described by an n component vector order parameter is addressed at zero temperature in the large n limit we consider cases in which the mobility or kinetic coefficient vanishes when the magnitude of the order parameter takes its equilibrium value in the large n limit the system is exactly soluble for both conserved and non conserved order parameter in the non conserved case the scaling form for the correlation function and it s fourier transform the structure factor is established with the characteristic length growing as a power of time in the conserved case the structure factor is evaluated and found to exhibit a multi scaling behaviour with two growing length scales differing by a logarithmic factor in both cases the rate of growth of the length scales depends on the manner in which the mobility or kinetic coefficient vanishes as the magnitude of the order parameter approaches its equilibrium value

on population resilience to external perturbations we study a spatially explicit harvesting model in periodic or bounded environments the model is governed by a parabolic equation with a spatially dependent nonlinearity of kolmogorov petrovsky piskunov type and a negative external forcing term delta using sub and supersolution methods and the characterization of the first eigenvalue of some linear elliptic operators we obtain existence and nonexistence results as well as results on the number of stationary solutions we also characterize the asymptotic behavior of the evolution equation as a function of the forcing term amplitude in particular we define two critical values delta and delta 2 such that if delta is smaller than delta the population density converges to a significant state which is everywhere above a certain small threshold whereas if delta is larger than delta 2 the population density converges to a remnant state everywhere below this small threshold our results are shown to be useful for studying

a constrained l1 minimization approach to sparse precision matrix estimation this article proposes a constrained l1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p variate random variables the resulting estimator is shown to have a number of desirable properties in particular the rate of convergence between the estimator and the true s sparse precision matrix under the spectral norm is when the population distribution has either exponential type tails or polynomial type tails we present convergence rates under the elementwise l norm and frobenius norm in addition we consider graphical model selection the procedure is easily implemented by linear programming numerical performance of the estimator is investigated using both simulated and real data in particular the procedure is applied to analyze a breast cancer dataset and is found to perform favorably compared with existing methods

on dimension folding of matrix or array valued statistical objects we consider dimension reduction for regression or classification in which the predictors are matrix or array valued this type of predictor arises when measurements are obtained for each combination of two or more underlying variables for example the voltage measured at different channels and times in electroencephalography data for these applications it is desirable to preserve the array structure of the reduced predictor e g time versus channel but this cannot be achieved within the conventional dimension reduction formulation in this paper we introduce a dimension reduction method to be called dimension folding for matrix and array valued predictors that preserves the array structure in an application of dimension folding to an electroencephalography data set we correctly classify 97 out of 122 subjects as alcoholic or nonalcoholic based on their electroencephalography in a cross validation sample

simple unified view of branching process statistics random walks in balanced logarithmic potentials we revisit the problem of deriving the mean field values of avalanche exponents in systems with absorbing states these are well known to coincide with those of unbiased branching processes here we show that for at least four different universality classes directed percolation dynamical percolation the voter model or compact directed percolation class and the manna class of stochastic sandpiles this common result can be obtained by mapping the corresponding langevin equations describing each of them into a random walker confined to the origin by a logarithmic potential we report on the emergence of nonuniversal continuously varying exponent values stemming from the presence of small external driving that might induce avalanche merging that to the best of our knowledge has not been noticed in the past many of the other results derived here appear in the literature as independently derived for individual universality classes or for the branching process itself still we believe that a simple and unified perspective as the one presented here can help 1 clarify the overall picture 2 underline the superuniversality of the behavior as well as the dependence on external driving and 3 avoid the common existing confusion between unbiased branching processes equivalent to a random walker in a balanced logarithmic potential and standard unconfined random walkers

functional graphical models graphical models have attracted increasing attention in recent years especially in settings involving high dimensional data in particular gaussian graphical models are used to model the conditio

local and global existence of smooth solutions for the stochastic euler equations with multiplicative noise we establish the local existence of pathwise solutions for the stochastic euler equations in a three dimensional bounded domain with slip boundary conditions and a suitable nonlinear multiplicative noise in the two dimensional case we obtain the global existence of these solutions with additive or linear multiplicative noise finally we show that in the three dimensional case the addition of linear multiplicative noise provides a regularizing effect the global existence of solutions occurs with high probability if the initial data is sufficiently small or if the noise coefficient is sufficiently large

partial correlation estimation by joint sparse regression models this article features online supplementary material in this article we propose a computationally efficient approach space sparse partial correlation estimation for selecting nonzero partial correlations under the high dimension low sample size setting this method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting we illustrate the performance of space by extensive simulation studies it is shown that space performs well in both nonzero partial correlation selection and the identification of hub variables and also outperforms two existing methods we then apply space to a microarray breast cancer dataset and identify a set of hub genes that may provide important insights on genetic regulatory networks finally we prove that under a set of suitable assumptions the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation

sparsistency and rates of convergence in large covariance matrix estimation this paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions here sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one depending on the case of applications sparsity priori may occur on the covariance matrix its inverse or its cholesky decomposition we study these three sparsity exploration problems under a unified framework with a general penalty function we show that the rates of convergence for these problems under the frobenius norm are of order s n log p n n 1 2 where s n is the number of nonzero elements p n is the size of the covariance matrix and n is the sample size this explicitly spells out the contribution of high dimensionality is merely of a logarithmic factor the conditions on the rate with which the tuning parameter n goes to 0 have been made explicit and compared under different penalties as a result for the l 1 penalty to guarantee the sparsistency and optimal rate of convergence the number of nonzero elements should be small sn o pn at most among o pn2 parameters for estimating sparse covariance or correlation matrix sparse precision or inverse correlation matrix or sparse cholesky factor where sn is the number of the nonzero elements on the off diagonal entries on the other hand using the scad or hard thresholding penalty functions there is no such a restriction

on quasi linear stochastic partial differential equations we prove existence and uniqueness of the solution of a parabolic spde in one space dimension driven by space time white noise in the case of a measurable drift and a constant diffusion coefficient as well as a comparison theorem

on the regularization effect of space time white noise on quasi linear parabolic partial differential equations we show that an existence and uniqueness and a comparison theorem hold if we add a space time white noise to a quasi linear parabolic equation in one space dimension even if the nonlinearity is only measurable and not even locally bounded

stick slip chaos detection in coupled oscillators with friction abstract we consider two coupled oscillators with negative duffing type stiffness which are self due to friction and externally harmonically excited the fundamental solutions of the homoclinic orbit are constructed then the melnikov gruendler approach is used to define the melnikov s function including smooth and stick slip chaotic behaviour theoretical considerations are supported by numerical examples

a nonparametric graphical model for functional data with application to brain networks based on fmri abstractwe introduce a nonparametric graphical model whose observations on vertices are functions many modern applications such as electroencephalogram and functional magnetic resonance imaging fmri produce data are of this type the model is based on additive conditional independence aci a statistical relation that captures the spirit of conditional independence without resorting to multi dimensional kernels the random functions are assumed to reside in a hilbert space no distributional assumption is imposed on the random functions instead their statistical relations are characterized nonparametrically by a second hilbert space which is a reproducing kernel hilbert space whose kernel is determined by the inner product of the first hilbert space a precision operator is then constructed based on the second space which characterizes aci and hence also the graph the resulting estimator is relatively easy to compute requiring no iterative optimization or inversion of large matrices we estab

nonequilibrium transitions induced by multiplicative noise it is well established that the effects of noise in stochastic equations can be rather surprising and counterintuitive the presence of a noisy term can modify in quite an unexpected way the behavior of the corresponding deterministic noiseless equation a well known example of this is the stochastic resonance in which the response to an external periodically oscillating field of a stochastic system is enhanced by increasing its internal noise amplitude 1 other examples are the resonant activation 2 noise induced spatial patterns 3 the noise induced ordering transition niot 4 6 and the noise induced disordering transition nidt 4 these last two transitions were first analyzed together in an interesting work to the best of our knowledge by van den broeck parrondo and toral 4 vpt hereafter they considered a langevin equation with a monostable deterministic term to which a nontrivial noise is added owing to the combined effect of the noise and the spatial coupling two real phase transitions were shown to appear for small noise amplitudes the system is disordered while by increasing the noise amplitude the system gets ordered in a symmetrybreaking state exhibiting therefore a niot if the noise is increased further the ordered state is destroyed and therefore there is a nidt afterwards different works on niot and nidt appearing in different models and systems have been proposed in the literature 7 9 in particular in 7 a noiseinduced reentrant transition is reported for a time dependent ginzburg landau model with both additive and multiplicative noise in 8 9 first order transitions are shown to be induced by the presence of nontrivial noises an interesting task is that of understanding the nature of this striking phenomena in the simplest possible model understanding whether it comes from an interplay between additive and multiplicative noises or not and determining whether the critical behavior of these transitions can be described by any standard universality class in this direction the following langevin equation has been proposed by vpt as a possible simplest model exhibiting these two noiseinduced transitions

distribution of the first return time in fractional brownian motion and its application to the study of on off intermittency herein the term fractional brownian motion is used to refer to a class of random walks with long range correlated steps where the mean square displacement of the walker at large time t is proportional to mathit t 2 mathit h with 0h1 for ordinary brownian motion we obtain h 1 2 let t denote the time at which the random walker starting at the origin first returns to the origin the purpose of this paper is to show that the probability distribution of t scales with t as p t ensuremath sim mathit t mathit h mathrm ensuremath 2 theoretical arguments and numerical simulations are presented to support the result additional issues explored include modification to the power law distribution when the random walk is biased and the application of the result to the characterization of on off intermittency a recently proposed mechanism for bursting

stability of strong solutions for a model of incompressible two phase flow under thermal fluctuations abstract we consider a model of a two phase flow based on the phase field approach where the fluid bulk velocity obeys the standard navier stokes system while the concentration difference of the two fluids plays a role of order parameter governed by the allen cahn equations possible thermal fluctuations are incorporated through a random forcing term in the allen cahn equation we show that suitable dissipative martingale solutions satisfy a stochastic version of the relative energy inequality this fact is used for showing the weak strong uniqueness principle both pathwise and in law

martingale and stationary solutions for stochastic navier stokes equations we prove the existence of martingale solutions and of stationary solutions of stochastic navier stokes equations under very general hypotheses on the diffusion term the stationary martingale solutions yield the existence of invariant measures when the transition semigroup is well defined the results are obtained by a new method of compactness

boundary layer analysis for the stochastic nonlinear reaction diffusion equations abstract singularly perturbed stochastic and deterministic nonlinear reaction diffusion equations are considered we first study the governing problem posed in the channel domain with lateral periodicity and extend the results to general smooth domains introducing corrector functions which correct the boundary values discrepancies we are able to develop the convergence analysis for the analysis we make use of the maximum principle to estimate the corrector functions the stochastic problems also rely on the deterministic corrector functions which lead to simpler computations than those of the stochastic version of the correctors