blind separation of positive sources by globally convergent gradient search the instantaneous noise free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix however with some prior information on the sources like positivity new analysis and perhaps simplified solution methods may yet become possible in this letter we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded which means that they have a nonzero pdf in the region of zero it can be shown that in this case the solution method is basically very simple an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources we propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint under which the separating matrix is orthogonal we further prove that in the stiefel manifold of orthogonal matrices the cost function is a lyapunov function for the matrix gradient flow implying global convergence thus this algorithm is guaranteed to find the nonnegative well grounded independent sources the analysis is complemented by a numerical simulation which illustrates the algorithm

online blind source separation using incremental nonnegative matrix factorization with volume constraint online blind source separation bss is proposed to overcome the high computational cost problem which limits the practical applications of traditional batch bss algorithms however the existing online bss methods are mainly used to separate independent or uncorrelated sources recently nonnegative matrix factorization nmf shows great potential to separate the correlative sources where some constraints are often imposed to overcome the non uniqueness of the factorization in this paper an incremental nmf with volume constraint is derived and utilized for solving online bss the volume constraint to the mixing matrix enhances the identifiability of the sources while the incremental learning mode reduces the computational cost the proposed method takes advantage of the natural gradient based multiplication updating rule and it performs especially well in the recovery of dependent sources simulations in bss for dual energy x ray images online encrypted speech signals and high correlative face images show the validity of the proposed method

exact large deviation bounds up to t c for the ising model in two dimensions we prove an upper large deviation bound for the block spin magnetization in the 2d ising model in the phase coexistence region the precise rate given by the wulff construction is shown to hold true for all c combined with the lower bounds derived in i those results yield an exact second order large deviation theory up to the critical temperature

blind spectral unmixing based on sparse nonnegative matrix factorization nonnegative matrix factorization nmf is a widely used method for blind spectral unmixing su which aims at obtaining the endmembers and corresponding fractional abundances knowing only the collected mixing spectral data it is noted that the abundance may be sparse i e the endmembers may be with sparse distributions and sparse nmf tends to lead to a unique result so it is intuitive and meaningful to constrain nmf with sparseness for solving su however due to the abundance sum to one constraint in su the traditional sparseness measured by l0 l1 norm is not an effective constraint any more a novel measure termed as s measure of sparseness using higher order norms of the signal vector is proposed in this paper it features the physical significance by using the s measure constraint smc a gradient based sparse nmf algorithm termed as nmf smc is proposed for solving the su problem where the learning rate is adaptively selected and the endmembers and abundances are simultaneously estimated in the proposed nmf smc there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior yet it does not require the preprocessing of dimension reduction in which some useful information may be lost experiments based on synthetic mixtures and real world images collected by aviris and hydice sensors are performed to evaluate the validity of the proposed method

online nonnegative matrix factorization with robust stochastic approximation nonnegative matrix factorization nmf has become a popular dimension reduction method and has been widely applied to image processing and pattern recognition problems however conventional nmf learning methods require the entire dataset to reside in the memory and thus cannot be applied to large scale or streaming datasets in this paper we propose an efficient online rsa nmf algorithm or nmf that learns nmf in an incremental fashion and thus solves this problem in particular or nmf receives one sample or a chunk of samples per step and updates the bases via robust stochastic approximation benefitting from the smartly chosen learning rate and averaging technique or nmf converges at the rate of in each update of the bases furthermore we prove that or nmf almost surely converges to a local optimal solution by using the quasi martingale by using a buffering strategy we keep both the time and space complexities of one step of the or nmf constant and make or nmf suitable for large scale or streaming datasets preliminary experimental results on real world datasets show that or nmf outperforms the existing online nmf onmf algorithms in terms of efficiency experimental results of face recognition and image annotation on public datasets confirm the effectiveness of or nmf compared with the existing onmf algorithms

harmonic crystal on the wall a microscopic approach a three dimensional winterbottom type construction in the regime of partial wetting is derived in a scaling limit of a gas of microscopic gaussian sos droplets under the fixed volume constraint the proof is based on a coarse graining of the random microscopic region wetted by the crystal random walk representations of various quantities related to free massless fields and a stability analysis of the torsional rigidity problem

tree graph inequalities and critical behavior in percolation models various inequalities are derived and used for the study of the critical behavior in independent percolation models in particular we consider the critical exponent associated with the expected cluster sizex and the structure of then site connection probabilities n x1 xn it is shown that quite generally 1 the upper critical dimension above which attains the bethe lattice value 1 is characterized both in terms of the geometry of incipient clusters and a diagramatic convergence condition for homogeneousd dimensional lattices with x y o x y d 2 atp p c our criterion shows that 1 if 6 d 3 the connectivity functions n are generally bounded by tree diagrams which involve the two point function we conjecture that above the critical dimension the asymptotic behavior of n in the critical regime is actually given by such tree diagrams modified by a nonsingular vertex factor other results deal with the exponential decay of the cluster size distribution and the function 2 x y

blind separation of mutually correlated sources using precoders this paper studies the problem of blind source separation bss from instantaneous mixtures with the assumption that the source signals are mutually correlated we propose a novel approach to bss by using precoders in transmitters we show that if the precoders are properly designed some cross correlation coefficients of the coded signals can be forced to be zero at certain time lags then the unique correlation properties of the coded signals can be exploited in receiver to achieve source separation based on the proposed precoders a subspace based algorithm is derived for the blind separation of mutually correlated sources the effectiveness of the algorithm is illustrated by simulation examples

a convex analysis framework for blind separation of non negative sources this paper presents a new framework for blind source separation bss of non negative source signals the proposed framework referred herein to as convex analysis of mixtures of non negative sources camns is deterministic requiring no source independence assumption the entrenched premise in many existing usually statistical bss frameworks the development is based on a special assumption called local dominance it is a good assumption for source signals exhibiting sparsity or high contrast and thus is considered realistic to many real world problems such as multichannel biomedical imaging under local dominance and several standard assumptions we apply convex analysis to establish a new bss criterion which states that the source signals can be perfectly identified in a blind fashion by finding the extreme points of an observation constructed polyhedral set methods for fulfilling the camns criterion are also derived using either linear programming or simplex geometry simulation results on several data sets are presented to demonstrate the efficacy of the proposed method over several other reported bss methods

large deviations and continuum limit in the 2d ising model we study the 2d ising model in a rectangular box l of linear size o l we determine the exact asymptotic behaviour of the large deviations of the magnetization p t2 l ae t when l 1 for values of the parameters of the model corresponding to the phase coexistence region where the order parameter m is strictly positive we study in particular boundary eects due to an arbitrary real valued boundary magnetic field using the self duality of the model a large part of the analysis consists in deriving properties of the covariance function hae 0 ae t i as t 1 at dual values of the parameters of the model to do this analysis we establish new results about the high temperature representation of the model these results are valid for dimensions d 2 and up to the critical temperature they give a complete non perturbative exposition of the high temperature representation we then study the gibbs measure conditioned by p t2 l ae t im l l l ic with 0 c 1 4 and im m m we construct the continuum limit of the model and describe the limit by the solutions of a variational problem of isoperi metric type

robust independent component analysis by iterative maximization of the kurtosis contrast with algebraic optimal step size independent component analysis ica aims at decomposing an observed random vector into statistically independent variables deflation based implementations such as the popular one unit fastica algorithm and its variants extract the independent components one after another a novel method for deflationary ica referred to as robustica is put forward in this paper this simple technique consists of performing exact line search optimization of the kurtosis contrast function the step size leading to the global maximum of the contrast along the search direction is found among the roots of a fourth degree polynomial this polynomial rooting can be performed algebraically and thus at low cost at each iteration among other practical benefits robustica can avoid prewhitening and deals with real and complex valued mixtures of possibly noncircular sources alike the absence of prewhitening improves asymptotic performance the algorithm is robust to local extrema and shows a very high convergence speed in terms of the computational cost required to reach a given source extraction quality particularly for short data records these features are demonstrated by a comparative numerical analysis on synthetic data robustica s capabilities in processing real world data involving noncircular complex strongly super gaussian sources are illustrated by the biomedical problem of atrial activity aa extraction in atrial fibrillation af electrocardiograms ecgs where it outperforms an alternative ica based technique

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

adaptive method for nonsmooth nonnegative matrix factorization nonnegative matrix factorization nmf is an emerging tool for meaningful low rank matrix representation in nmf explicit constraints are usually required such that nmf generates desired products or factorizations especially when the products have significant sparseness features it is known that the ability of nmf in learning sparse representation can be improved by embedding a smoothness factor between the products motivated by this result we propose an adaptive nonsmooth nmf ans nmf method in this paper in our method the embedded factor is obtained by using a data related approach so it matches well with the underlying products implying a superior faithfulness of the representations besides due to the usage of an adaptive selection scheme to this factor the sparseness of the products can be separately constrained leading to wider applicability and interpretability furthermore since the adaptive selection scheme is processed through solving a series of typical linear programming problems it can be easily implemented simulations using computer generated data and real world data show the advantages of the proposed ans nmf method over the state of the art methods

on the critical percolation probabilities we prove that the critical probabilities of site percolation on the square lattice satisfy the relation p c p 1 furthermore we prove the continuity of the function percolation probability

constrained variational problem with applications to the ising model we continue our study of the behavior of the two dimensional nearest neighbor ferromagnetic ising model under an external magnetic fieldh initiated in our earlier work we strengthen further a result previously proven by martirosyan at low enough temperature which roughly states that for finite systems with boundary conditions under a positive external field the boundary effect dominates in the system if the linear size of the system is of orderb h withb small enough while ifb is large enough then the external field dominates in the system in our earlier work this result was extended to every subcritical value of the temperature here for every subcritical value of the temperature we show the existence of a critical valueb0 t which separates the two regimes specified above we also find the asymptotic shape of the region occupied by the phase in the second regime which turns out to be a squeezed wulff shape the main step in our study is the solution of the variational problem of finding the curve minimizing the wulff functional which curve is constrained to the unit square other tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field extended to all temperatures below the critical one

non unitary transformation of conservative to dissipative evolutions the authors briefly review in a general context the theory of non unitary transformations between conservative dynamics with internal time and dissipative evolutions developed previously in the context of statistical mechanics and apply the results to show the existence of a similarity transformation between the wave equation and the dissipative telegraphist equation

underdetermined blind source separation based on subspace representation this paper considers the problem of blindly separating sub and super gaussian sources from underdetermined mixtures the underlying sources are assumed to be composed of two orthogonal components one lying in the rowspace and the other in the nullspace of a mixing matrix the mapping from the rowspace component to the mixtures by the mixing matrix is invertible using the pseudo inverse of the mixing matrix the mapping from the nullspace component to zero by the mixing matrix is noninvertible and there are infinitely many solutions to the nullspace component the latent nullspace component which is of lower complexity than the underlying sources is estimated based on a mean square error mse criterion this leads to a source estimator that is optimal in the mse sense in order to characterize and model sub and super gaussian source distributions the parametric generalized gaussian distribution is used the distribution parameters are estimated based on the expectation maximization em algorithm when the mixing matrix is unavailable it must be estimated and a novel algorithm based on a single source detection algorithm which detects time frequency regions of single source occupancy is proposed in our simulations the proposed algorithm compared to other conventional algorithms estimated the mixing matrix with higher accuracy and separated various sources with higher signal to interference ratio

a nonnegative pca algorithm for independent component analysis we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded so that they have a nonzero probability density function pdf in the region of zero we propose the use of a nonnegative principal component analysis nonnegative pca algorithm which is a special case of the nonlinear pca algorithm but with a rectification nonlinearity and we conjecture that this algorithm will find such nonnegative well grounded independent sources under reasonable initial conditions while the algorithm has proved difficult to analyze in the general case we give some analytical results that are consistent with this conjecture and some numerical simulations that illustrate its operation

on weak mixing in lattice models for lattice models on d weak mixing is the property that the influence of the boundary condition on a finite decays exponentially with distance from that region for a wide class of models on 2 including all finite range models we show that weak mixing is a consequence of gibbs uniqueness exponential decay of an appropriate form of connectivity and a natural coupling property in particular on 2 the fortuin kasteleyn random cluster model is weak mixing whenever uniqueness holds and the connectivity decays exponentially and the q state potts model above the critical temperature is weak mixing whenever correlations decay exponentially a hypothesis satisfied if q is sufficiently large ratio weak mixing is the property that uniformly over events a and b occurring on subsets and respectively of the lattice p a b p a p b 1 decreases exponentially in the distance between and we show that under mild hypotheses for example finite range weak mixing implies ratio weak mixing

a convex geometry based blind source separation method for separating nonnegative sources this paper presents a convex geometry cg based method for blind separation of nonnegative sources first the unaccessible source matrix is normalized to be column sum to one by mapping the available observation matrix then its zero samples are found by searching the facets of the convex hull spanned by the mapped observations considering these zero samples a quadratic cost function with respect to each row of the unmixing matrix together with a linear constraint in relation to the involved variables is proposed upon which an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem unlike the traditional blind source separation bss methods the cg based method does not require the independence assumption nor the uncorrelation assumption compared with the bss methods that are specifically designed to distinguish between nonnegative sources the proposed method requires a weaker sparsity condition provided simulation results illustrate the performance of our method

on the microscopic validity of the wulff construction and of the generalized young equation for a large class of 1 1 dimensional interfaces of the solid on solid type we prove on a microscopic basis the validity of the wulff construction and of the generalized young equation which gives the contact angle of a sessile drop on a wall our proof relies on a new method to treat random walks with a finite number of global constraints

mean field critical behaviour for correlation length for percolation in high dimensions extending the method of 27 we prove that the corrlation length of independent bond percolation models exhibits mean field type critical behaviour i e p p c p 1 2 asp p c in two situations i for nearest neighbour independent bond percolation models on ad dimensional hypercubic lattice d withd sufficiently large and ii for a class of spread out independent bond percolation models which are believed to belong to the same universality class as the nearest neighbour model in more than six dimensions the proof is based on and extends a method developed in 27 where it was used to prove the triangle condition and hence mean field behaviour of the critical exponents and 2 for the above two cases

quaternion ica from second order statistics this paper addresses the independent component analysis ica of quaternion random vectors in particular we focus on the gaussian case and therefore only consider the quaternion second order statistics sos which are given by the covariance matrix and three complementary covariance matrices first we derive the necessary and sufficient conditions for the identifiability of the quaternion ica model which are based on the definition of the properness profile of a quaternion random variable and more specifically on the concept of rotationally equivalent properness profiles second we show that the maximum likelihood ml approach to the quaternion ica problem reduces to the approximated joint diagonalization ajd of the sample mean estimates of the covariance and complementary covariance matrices unlike the complex case these four matrices cannot be simultaneously diagonalized in general and we have to resort to a particular ajd algorithm the proposed technique which can be seen as a quasi newton method is based on the local approximation of the nonconvex ml ica cost function a measure of the entropy loss due to the residual correlation among the estimated quaternion sources and it provides a satisfactory solution of the quaternion ica model the performance of the proposed quaternion ml ica algorithm as well as its relationship to the identifiability conditions are illustrated by means of several numerical examples

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

iterative gaussianization from ica to random rotations most signal processing problems involve the challenging task of multidimensional probability density function pdf estimation in this paper we propose a solution to this problem by using a family of rotation based iterative gaussianization rbig transforms the general framework consists of the sequential application of a univariate marginal gaussianization transform followed by an orthonormal transform the proposed procedure looks for differentiable transforms to a known pdf so that the unknown pdf can be estimated at any point of the original domain in particular we aim at a zero mean unit covariance gaussian for convenience rbig is formally similar to classical iterative projection pursuit algorithms however we show that unlike in pp methods the particular class of rotations used has no special qualitative relevance in this context since looking for interestingness is not a critical issue for pdf estimation the key difference is that our approach focuses on the univariate part marginal gaussianization of the problem rather than on the multivariate part rotation this difference implies that one may select the most convenient rotation suited to each practical application the differentiability invertibility and convergence of rbig are theoretically and experimentally analyzed relation to other methods such as radial gaussianization one class support vector domain description and deep neural networks is also pointed out the practical performance of rbig is successfully illustrated in a number of multidimensional problems such as image synthesis classification denoising and multi information estimation

on the 2d ising wulff crystal near criticality we study the behavior of the two dimensional ising model in a finite box at temperatures that are below but very close to the critical temperature in a regime where the temperature approaches the critical point and simultaneously the size of the box grows fast enough we establish a large deviation principle that proves the appearance of a round wulff crystal

time frequency approach to underdetermined blind source separation this paper presents a new time frequency tf underdetermined blind source separation approach based on wigner ville distribution wvd and khatri rao product to separate n non stationary sources from m m n mixtures first an improved method is proposed for estimating the mixing matrix where the negative value of the auto wvd of the sources is fully considered then after extracting all the auto term tf points the auto wvd value of the sources at every auto term tf point can be found out exactly with the proposed approach no matter how many active sources there are as long as n 2m 1 further discussion about the extraction of auto term tf points is made and finally the numerical simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing ones

group decorrelation enhanced subspace method for identifying fir mimo channels driven by unknown uncorrelated colored sources identification of finite impulse response fir and multiple input multiple output mimo channels driven by unknown uncorrelated colored sources is a challenging problem in this paper a group decorrelation enhanced subspace gdes method is presented the gdes method uses the idea of subspace decomposition and signal decorrelation more effectively than the joint diagonalization enhanced subspace jdes method previously reported in the literature the gdes method has a much better performance than the jdes method the correctness of the gdes method is proved assuming that 1 the channel matrix is irreducible and column reduced and 2 the source spectral matrix has distinct diagonal functions however the gdes method has an inherent ability to trade off between the required condition on the channel matrix and that on the source spectral matrix simulations show that the gdes method yields good results even when the channel matrix is not irreducible which is not possible at all for the jdes method

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

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

critical region for droplet formation in the two dimensional ising model we study the formation dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence specifically we consider the 2d ising model in volumes of size l2 inverse temperature c and overall magnetization conditioned to take the value m l2 2m vl where c 1 is the critical temperature m m is the spontaneous magnetization and vl is a sequence of positive numbers we find that the critical scaling for droplet formation dissolution is when vl3 2l 2 tends to a definite limit specifically we identify a dimensionless parameter proportional to this limit a non trivial critical value c and a function such that the following holds for c there is a single wulff shaped droplet containing a fraction c 2 3 of the magnetization deficit and there are no other droplets beyond the scale of log l moreover and are related via a universal equation that apparently is independent of the details of the system

the 2d ising model near criticality a fk percolation analysis we study the 2d ising model defined on finite boxes at temperatures that are below but very close from the critical point when the temperature approaches the critical point and the size of the box grows fast enough we establish large deviations estimates on fk percolation events that concern the phenomenon of phase coexistence

blind source separation using second order cyclostationary statistics this paper studies the blind source separation bss problem with the assumption that the source signals are cyclostationary identifiability and separability criteria based on second order cyclostationary statistics socs alone are derived the identifiability condition is used to define an appropriate contrast function an iterative algorithm ath2 is derived to minimize this contrast function this algorithm separates the sources even when they do not have distinct cycle frequencies

independent component analysis by entropy bound minimization a novel differential entropy estimator is introduced where the maximum entropy bound is used to approximate the entropy given the observations and is computed using a numerical procedure thus resulting in accurate estimates for the entropy we show that such an estimator exists for a wide class of measuring functions and provide a number of design examples to demonstrate its flexible nature we then derive a novel independent component analysis ica algorithm that uses the entropy estimate thus obtained ica by entropy bound minimization ica ebm the algorithm adopts a line search procedure and initially uses updates that constrain the demixing matrix to be orthogonal for robust performance we demonstrate the superior performance of ica ebm and its ability to match sources that come from a wide range of distributions using simulated and real world data

underdetermined blind source separation based on sparse representation this paper discusses underdetermined i e with more sources than sensors blind source separation bss using a two stage sparse representation approach the first challenging task of this approach is to estimate precisely the unknown mixing matrix in this paper an algorithm for estimating the mixing matrix that can be viewed as an extension of the duet and the tifrom methods is first developed standard clustering algorithms e g k means method also can be used for estimating the mixing matrix if the sources are sufficiently sparse compared with the duet the tifrom methods and standard clustering algorithms with the authors proposed method a broader class of problems can be solved because the required key condition on sparsity of the sources can be considerably relaxed the second task of the two stage approach is to estimate the source matrix using a standard linear programming algorithm another main contribution of the work described in this paper is the development of a recoverability analysis after extending the results in a necessary and sufficient condition for recoverability of a source vector is obtained based on this condition and various types of source sparsity several probability inequalities and probability estimates for the recoverability issue are established finally simulation results that illustrate the effectiveness of the theoretical results are presented

bernoulli percolation above threshold an invasion percolation analysis on utilise le processus de percolation d invasion pour demontrer des resultats relatifs a la percolation de bernoulli sur z d

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

on a combinatorial conjecture concerning disjoint occurrences of events recently van den berg and kesten have obtained a correlation like inequality for bernoulli sequences this inequality which goes in the opposite direction of the fkg inequality states that the probability that two monotone i e increasing or decreasing events occur disjointly is smaller than the product of the individual probabilities they conjecture that the monotonicity condition is immaterial i e that the inequality holds for all events in the present paper we try to make clear the intuitive meaning of the conjecture and prove some nontrivial special cases one of which a pure correlation inequality is an extension of harris fkg inequality

symmetric nonnegative matrix factorization algorithms and applications to probabilistic clustering nonnegative matrix factorization nmf is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents this paper focuses on symmetric nmf snmf which is a special case of nmf decomposition three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem first by minimizing the euclidean distance a multiplicative update algorithm is proposed and its convergence under mild conditions is proved based on it we further propose another two fast parallel methods snmf and snmf algorithms all of them are easy to implement these algorithms are applied to probabilistic clustering we demonstrate their effectiveness for facial image clustering document categorization and pattern clustering in gene expression

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

analysis of sparse representation and blind source separation in this letter we analyze a two stage cluster then l1 optimization approach for sparse representation of a data matrix which is also a promising approach for blind source separation bss in which fewer sensors than sources are present first sparse representation factorization of a data matrix is discussed for a given overcomplete basis matrix the corresponding sparse solution coefficient matrix with minimum l1 norm is unique with probability one which can be obtained using a standard linear programming algorithm the equivalence of the l1 norm solution and the l0 norm solution is also analyzed according to a probabilistic framework if the obtained l1 norm solution is sufficiently sparse then it is equal to the l0 norm solution with a high probability furthermore the l1 norm solution is robust to noise but the l0 norm solution is not showing that the l1 norm is a good sparsity measure these results can be used as a recoverability analysis of bss as discussed the basis matrix in this article is estimated using a clustering algorithm followed by normalization in which the matrix columns are the cluster centers of normalized data column vectors zibulevsky pearlmutter boll and kisilev 2000 used this kind of two stage approach in underdetermined bss our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed domain and with the case in which the source number is unknown it is also robust to additive noise and estimation error in the mixing matrix finally four simulation examples and an eeg data analysis example are presented to illustrate the algorithm s utility and demonstrate its performance

large deviations and concentration properties for ϕ interface models we consider the massless field with zero boundary conditions outside d n d d n n d a suitable subset of d i e the continuous spin gibbs measure n on d n with hamiltonian given by h x y x y 1 v x y and x 0 for x d n c the interaction v is taken to be strictly convex and with bounded second derivative this is a standard effective model for a d 1 dimensional interface represents the height of the interface over the base d n due to the choice of scaling of the base we scale the height with the same factor by setting n n we study various concentration and relaxation properties of the family of random surfaces n and of the induced family of gradient fields n n as the discretization step 1 n tends to zero n in particular we prove a large deviation principle for n and show that the corresponding rate function is given by d u x dx where is the surface tension of the model this is a multidimensional version of the sample path large deviation principle we use this result to study the concentration properties of n under the volume constraint i e the constraint that 1 n d x dn n x stays in a neighborhood of a fixed volume v 0 and the hard wall constraint i e n x 0 for all x this is therefore a model for a droplet of volume v lying above a hard wall we prove that under these constraints the field n of rescaled heights concentrates around the solution of a variational problem involving the surface tension as it would be predicted by the phenomenological theory of phase boundaries our principal result however asserts local relaxation properties of the gradient field n n to the corresponding extremal gibbs states thus our approach has little in common with traditional large deviation techniques and is closer in spirit to hydrodynamic limit type of arguments the proofs have both probabilistic and analytic aspects essential analytic tools are p estimates for elliptic equations and the theory of young measures on the side of probability tools a central role is played by the helffer sjostrand 31 pde representation for continuous spin systems which we rewrite in terms of random walk in random environment and by recent results of t funaki and h spohn 25 on the structure of gradient fields

minimum volume constrained nonnegative matrix factorization enhanced ability of learning parts nonnegative matrix factorization nmf with minimum volume constraint mvc is exploited in this paper our results show that mvc can actually improve the sparseness of the results of nmf this sparseness is l0 norm oriented and can give desirable results even in very weak sparseness situations thereby leading to the significantly enhanced ability of learning parts of nmf the close relation between nmf sparse nmf and the mvc nmf is discussed first then two algorithms are proposed to solve the mvc nmf model one is called quadratic programming mvc nmf qp mvc nmf which is based on quadratic programming and the other is called negative glow mvc nmf ng mvc nmf because it uses multiplicative updates incorporating natural gradient ingeniously the qp mvc nmf algorithm is quite efficient for small scale problems and the ng mvc nmf algorithm is more suitable for large scale problems simulations show the efficiency and validity of the proposed methods in applications of blind source separation and human face images analysis

on the scaling of the chemical distance in long range percolation models we consider the unoriented long range percolation on z d in dimensions d 1 where distinct sites x y z d get connected with probability p xy 0 1 assuming p xy x y s o 1 as x y where s 0 and is a norm distance on z d and supposing that the resulting random graph contains an infinite connected component c we let d x y be the graph distance between x and y measured on c our main result is that for s d 2d d x y log x y o 1 x y c x y where 1 is the binary logarithm of 2d s and o 1 is a quantity tending to zero in probability as x y besides its interest for general percolation theory this result sheds some light on a question that has recently surfaced in the context of small world phenomena as part of the proof we also establish tight bounds on the probability that the largest connected component in a finite box contains a positive fraction of all sites in the box

lower bounds for boundary roughness for droplets in bernoulli percolation we consider boundary roughness for the droplet created when supercritical two dimensional bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l 2 for large l the maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull we show that for large l this maximum is at least of order l 1 3 logl 2 3 this complements the upper bound of order l 1 3 logl 2 3 proved in al3 for the average local roughness the exponent 1 3 on l here is in keeping with predictions from the physics literature for interfaces in two dimensions

the probability of a large finite cluster in supercritical bernoulli percolation we consider standard bernoulli site percolation on zd with probability p for each site to be occupied c denotes the occupied cluster of the origin and ici its cardinality we show that for p critical probability of the halfspacezd l x 7 one has pp ici n 0 this improves a recent result of chayes chayes and newman the proof is based on a peierls argument which shows exponential decay of the distribution of the size of an exterior boundary of c

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

maximal clusters in non critical percolation and related models we investigate the maximal non critical cluster in a big box in various percolation type models we investigate its typical size and the fluctuations around this typical size the limit law of these fluctuations is related to maxima of independent random variables with law described by a single cluster

projection pursuit based method for blind separation of nonnegative sources this paper presents a projection pursuit pp based method for blind separation of nonnegative sources first the available observation matrix is mapped to construct a new mixing model in which the inaccessible source matrix is normalized to be column sum to 1 then the pp method is proposed to solve this new model where the mixing matrix is estimated column by column through tracing the projections to the mapped observations in specified directions which leads to the recovery of the sources the proposed method is much faster than chan s method which has similar assumptions to ours due to the usage of optimal projection it is also more advantageous in separating cross correlated sources than the independence and uncorrelation based methods as it does not employ any statistical information of the sources furthermore the new method does not require the mixing matrix to be nonnegative simulation results demonstrate the superior performance of our method

a simple geometric blind source separation method for bounded magnitude sources a novel blind source separation approach and the corresponding adaptive algorithm is presented it is assumed that the observation mixture is obtained through an unknown memoryless linear mapping of independent and bounded magnitude sources we further assume an initial adaptive prewhitening of the original observation vector which transforms it into a white vector with the same dimension as the original source vector our approach is centered around the basic geometric fact that under a certain boundedness assumption the unitary mapping which transforms the whitening output vector into an independent vector has the minimum value of maximum real component magnitude output over the ensemble of all output components therefore the related criterion is the minimization of the infinity norm of the real component of the unitary separator s output over all possible output combinations for the minimization of the corresponding nondifferentiable cost function we propose the use of subgradient optimization methods to obtain a low complexity iterative adaptive solution the resulting algorithm is fairly intuitive and simple and provides a low complexity solution especially to a class of multiuser digital communications problems we provide examples at the end of this paper to illustrate the performance of our algorithm

equilibrium shapes of crystals in a gravitational field crystals on a table we consider the variational problem associated with the equilibrium shape of crystals resting on a table in a gravitational field for two dimensional crystals the shape can be calculated explicitly i e reduced to quadrature in three dimensions only qualitative results are available the most interesting new result is that for large crystals under suitable conditions the top may be a corrugated facet or curved surface the motivation for this work comes from lowtemperature experiments on helium crystals in equilibrium with the superfluid

nonnegative least correlated component analysis for separation of dependent sources by volume maximization although significant efforts have been made in developing nonnegative blind source separation techniques accurate separation of positive yet dependent sources remains a challenging task in this paper a joint correlation function of multiple signals is proposed to reveal and confirm that the observations after nonnegative mixing would have higher joint correlation than the original unknown sources accordingly a new nonnegative least correlated component analysis nlca method is proposed to design the unmixing matrix by minimizing the joint correlation function among the estimated nonnegative sources in addition to a closed form solution for unmixing two mixtures of two sources the general algorithm of nlca for the multisource case is developed based on an iterative volume maximization ivm principle and linear programming the source identifiability and required conditions are discussed and proven the proposed nlca algorithm denoted by nlca ivm is evaluated with both simulation data and real biomedical data to demonstrate its superior performance over several existing benchmark methods

analyticity properties and power law estimates of functions in percolation theory we consider percolation on the sites of a graphg e g a regulard dimensional lattice all sites ofg are occupied vacant with probabilityp respectively q 1 p independently of each other w denotes the cluster of occupied sites containing a fixed site which will usually be taken to be the origin andw the cardinality ofw the percolation probability is the probability that w i e p pp w some critical values ofp ph andpt are defined respectively as the smallest value ofp for which p 0 and for which the expectation of w is infinite formally ph inf p p 0 andpt inf p ep w we show for fairly general graphsgthat ifp pt thenpp w n decreases exponentially inn for the special casesg g0 the simple quadratic lattice andg1 the graph which corresponds to bond percolation on 2 we obtain upper and lower bounds for p of the formc p ph and bounds forep w of the formc p ph we also investigate smoothness properties of p ep number of clusters per site ep w 1 w 1 this function was introduced by sykes and essam who assumed that has exactly one singularity namely atp ph for the graphsg0 andg1 i e site or bond percolation on 2 we show that p is analytic atp ph and has two continuous derivatives atp ph the emphasis is on rigorous proofs

the correlation length for the high density phase of bernoulli percolation l auteur examine 2 types standards de fonctions de connectivite dans la phase de densite elevee de filtration de bernoulli du plus proche voisin il demontre que les 2 quantites decroissent exponentiellement avec le meme taux constant la reciproque de cette constante definit donc une longueur de correlation pour laquelle on n arrive pas a montrer qu elle est finie au dessus d une densite critique associee a la transition de phases des proprietes de semicontinuite et de convexite sont montrees pour cette longueur de correlation et on obtient des resultats analogues a ceux concernant le modele d ising en deux dimensions

alternative formulation of classical and quantum dynamics for non integrable systems we continue our work on large poincare systems lps characterized by a continuous spectrum and a continuous set of resonances poincare s theorem prevents the existence of solutions of the eigenvalue problem associated with the hamiltonian as well as the liouville operator which would be analytic in the coupling constant in simple cases such as the friedrichs model studied in a recent paper poincare s divergences can be avoided using a natural time ordering of the dynamical states in the hilbert space however in general the time ordering has to be performed in the liouville space of density matrices

a proof of the gibbs thomson formula in the droplet formation regime we study equilibrium droplets in two phase systems at parameter values corresponding to phase coexistence specifically we give a self contained microscopic derivation of the gibbs thomson formula for the deviation of the pressure and the density away from their equilibrium values which according to the interpretation of the classical thermodynamics appears due to the presence of a curved interface the general albeit heuristic reasoning is corroborated by a rigorous proof in the case of the two dimensional ising lattice gas

finite clusters in high density continuous percolation compression and sphericality a percolation process inrd is considered in which the sites are a poisson process with intensity and the bond between each pair of sites is open if and only if the sites are within a fixed distancer of each other the distribution of the number of sites in the clusterc of the origin is examined and related to the geometry ofc it is shown that when andk are large there is a characteristic radius such that conditionally on c k the convex hull ofc closely approximates a ball of radius with high probability when the normal volumek thatk points would occupy is small the cluster is compressed in that the number of points per unit volume in this ball is much greater than the ambient density for larger normal volumes there is less compression this can be compared to bernoulli bond percolation on the square lattice in two dimensions where an analog of this compression is known not to occur

smoothing neural network for constrained non lipschitz optimization with applications in this paper a smoothing neural network snn is proposed for a class of constrained non lipschitz optimization problems where the objective function is the sum of a nonsmooth nonconvex function and a non lipschitz function and the feasible set is a closed convex subset of using the smoothing approximate techniques the proposed neural network is modeled by a differential equation which can be implemented easily under the level bounded condition on the objective function in the feasible set we prove the global existence and uniform boundedness of the solutions of the snn with any initial point in the feasible set the uniqueness of the solution of the snn is provided under the lipschitz property of smoothing functions we show that any accumulation point of the solutions of the snn is a stationary point of the optimization problem numerical results including image restoration blind source separation variable selection and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the snn comparisons with some existing algorithms show the advantages of the snn

lie admissible perturbation methods for open quantum systems abstract we consider open quantum systems described by a hamiltonian of the type h0 v where is a small parameter for such systems we develop perturbative methods of solution of the corresponding liouville von neumann and schrodinger equations by introducing dissipation operators which connect conservative to dissipative systems in the case of the density matrix the corresponding operator is nothing but the non unitary transformation of misra prigogine and courbage our perturbative approach possesses a lie admissible structure since the dissipation operators obey time evolution equations whose brackets are the product of a lie admissible algebra explicit solutions for such operators are found in the form of series expansions in the matrix formulation of the above results is also given

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

algebraic structure of linear and non linear models of open quantum systems abstract we show that all the linear and nonlinear evolution equations proposed so far for the density operator of open quantum systems admit a common algebraic structure in the form of a generalized commutator which is the nonassociative product of a lie admissible algebra

nonnegative blind source separation by sparse component analysis based on determinant measure the problem of nonnegative blind source separation nbss is addressed in this paper where both the sources and the mixing matrix are nonnegative because many real world signals are sparse we deal with nbss by sparse component analysis first a determinant based sparseness measure named d measure is introduced to gauge the temporal and spatial sparseness of signals based on this measure a new nbss model is derived and an iterative sparseness maximization ism approach is proposed to solve this model in the ism approach the nbss problem can be cast into row to row optimizations with respect to the unmixing matrix and then the quadratic programming qp technique is used to optimize each row furthermore we analyze the source identifiability and the computational complexity of the proposed ism qp method the new method requires relatively weak conditions on the sources and the mixing matrix has high computational efficiency and is easy to implement simulation results demonstrate the effectiveness of our method