non negative matrix factorization ill posedness and a geometric algorithm non negative matrix factorization nmf has been proposed as a mathematical tool for identifying the components of a dataset however popular nmf algorithms tend to operate slowly and do not always identify the components which are most representative of the data in this paper an alternative algorithm for performing nmf is developed using the geometry of the problem the computational costs of the algorithm are explored and it is shown to successfully identify the components of a simulated dataset the development of the geometric algorithm framework illustrates the ill posedness of the nmf problem and suggests that nmf is not sufficiently constrained to be applied successfully outside of a particular class of problems

using underapproximations for sparse nonnegative matrix factorization nonnegative matrix factorization consists in approximately factorizing a nonnegative data matrix by the product of two low rank nonnegative matrices it has been successfully applied as a data analysis technique in numerous domains e g text mining image processing microarray data analysis collaborative filtering etc we introduce a novel approach to solve nmf problems based on the use of an underapproximation technique and show its effectiveness to obtain sparse solutions this approach based on lagrangian relaxation allows the resolution of nmf problems in a recursive fashion we also prove that the underapproximation problem is np hard for any fixed factorization rank using a reduction of the maximum edge biclique problem in bipartite graphs we test two variants of our underapproximation approach on several standard image datasets and show that they provide sparse part based representations with low reconstruction error our results are comparable and sometimes superior to those obtained by two standard sparse nonnegative matrix factorization techniques

variational asymptotic modeling of cosserat elastic plates one of the most important branches of applied mechanics is the theory of plates defined to be plane structural elements whose thickness is very small when compared to the two planar dimensions the

an enhancement of constraint feasibility in bpn based approximate optimization back propagation neural networks bpn have been extensively used as global approximation tools in the context of approximate optimization a traditional bpn is normally trained by minimizing the absolute difference between target outputs and approximate outputs when bpn is used as a meta model for inequality constraint function approximate optimal solutions are sometimes actually infeasible in a case where they are active at the constraint boundary the paper explores the development of the efficient bpn based meta model that enhances the constraint feasibility of approximate optimal solution the bpn based meta model is optimized via exterior penalty method to optimally determine interconnection weights between layers in the network the proposed approach is verified through a simple mathematical function and a ten bar planar truss problem for constrained approximate optimization design of rotor blade is conducted to support the proposed strategies

variational asymptotic method for unit cell homogenization of periodically heterogeneous materials a new micromechanics model namely the variational asymptotic method for unit cell homogenization vamuch is developed to predict the effective properties of periodically heterogeneous materials and recover the local fields considering the periodicity as a small parameter we can formulate a variational statement of the unit cell through an asymptotic expansion of the energy functional it is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories mht can be reproduced from this variational statement in comparison to other approaches vamuch does not rely on ad hoc assumptions has the same rigor as mht has a straightforward numerical implementation and can calculate the complete set of properties simultaneously without using multiple loadings this theory is implemented using the finite element method and an engineering program vamuch is developed for micromechanical analysis of unit cells many examples of binary composites fiber reinforced composites and particle reinforced composites are used to demonstrate the application power and accuracy of the theory and the code of vamuch

on the geometric interpretation of the nonnegative rank the nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank one factors needed to reconstruct it exactly the problem of determining this rank and computing the corresponding nonnegative factors is difficult however it has many potential applications e g in data mining graph theory and computational geometry in particular it can be used to characterize the minimal size of any extended reformulation of a given combinatorial optimization program in this paper we introduce and study a related quantity called the restricted nonnegative rank we show that computing this quantity is equivalent to a problem in polyhedral combinatorics and fully characterize its computational complexity this in turn sheds new light on the nonnegative rank problem and in particular allows us to provide new improved lower bounds based on its geometric interpretation we apply these results to slack matrices and linear euclidean distance matrices and obtain counter examples to two conjectures of beasly and laffey namely we show that the nonnegative rank of linear euclidean distance matrices is not necessarily equal to their dimension and that the rank of a matrix is not always greater than the nonnegative rank of its square

nonnegative matrix factorization for spectral data analysis data analysis is pervasive throughout business engineering and science very often the data to be analyzed is nonnegative and it is often preferable to take this constraint into account in the analysis process here we are concerned with the application of analyzing data obtained using astronomical spectrometers which provide spectral data which is inherently nonnegative the identification and classification of space objects that cannot be imaged in the normal way with telescopes is an important but difficult problem for tracking thousands of objects including satellites rocket bodies debris and asteroids in orbit around the earth in this paper we develop an effective nonnegative matrix factorization algorithm with novel smoothness constraints for unmixing spectral reflectance data for space object identification and classification purposes promising numerical results are presented using laboratory and simulated datasets

large cone nonnegative matrix factorization nonnegative matrix factorization nmf has been greatly popularized by its parts based interpretation and the effective multiplicative updating rule for searching local solutions in this paper we study the problem of how to obtain an attractive local solution for nmf which not only fits the given training data well but also generalizes well on the unseen test data based on the geometric interpretation of nmf we introduce two large cone penalties for nmf and propose large cone nmf lcnmf algorithms compared with nmf lcnmf will obtain bases comprising a larger simplicial cone and therefore has three advantages 1 the empirical reconstruction error of lcnmf could mostly be smaller 2 the generalization ability of the proposed algorithm is much more powerful and 3 the obtained bases of lcnmf have a low overlapping property which enables the bases to be sparse and makes the proposed algorithms very robust experiments on synthetic and real world data sets confirm the efficiency of lcnmf

the uniqueness of the integrated density of states for the schrodinger operators with magnetic fields the integrated density of states ids for the schrodinger operators is defined in two ways by using the counting function of eigenvalues of the operator restricted to bounded regions with appropriate boundary conditions or by using the spectral projection of the whole space operator a sufficient condition for the coincidence of the two definitions above is given moreover a sufficient condition for the coincidence of the ids for the dirichlet boundary conditions and the ids for the neumann boundary conditions is given the proof is based only on the fundamental items in functional analysis such as the min max principle etc

the absolute continuity of the integrated density of states for magnetic schrodinger operators with certain unbounded random potentials the object of the present study is the integrated density of states of a quantum particle in multi dimensional euclidean space which is characterized by a schrodinger operator with magnetic field and a random potential which may be unbounded from above and below in case that the magnetic field is constant and the random potential is ergodic and admits a so called one parameter decomposition we prove the absolute continuity of the integrated density of states and provide explicit upper bounds on its derivative the density of states this local lipschitz continuity of the integrated density of states is derived by establishing a wegner estimate for finite volume schrodinger operators which holds for rather general magnetic fields and different boundary conditions examples of random potentials to which the results apply are certain alloy type and gaussian random potentials besides we show a diamagnetic inequality for schrodinger operators with neumann boundary conditions

fast and robust recursive algorithmsfor separable nonnegative matrix factorization in this paper we study the nonnegative matrix factorization problem under the separability assumption that is there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns which is equivalent to the hyperspectral unmixing problem under the linear mixing model and the pure pixel assumption we present a family of fast recursive algorithms and prove they are robust under any small perturbations of the input data matrix this family generalizes several existing hyperspectral unmixing algorithms and hence provides for the first time a theoretical justification of their better practical performance

sequential dimensionality reduction for extracting localized features abstract linear dimensionality reduction techniques are powerful tools for image analysis as they allow the identification of important features in a data set in particular nonnegative matrix factorization nmf has become very popular as it is able to extract sparse localized and easily interpretable features by imposing an additive combination of nonnegative basis elements nonnegative matrix underapproximation nmu is a closely related technique that has the advantage to identify features sequentially in this paper we propose a variant of nmu that is particularly well suited for image analysis as it incorporates the spatial information that is it takes into account the fact that neighboring pixels are more likely to be contained in the same features and favors the extraction of localized features by looking for sparse basis elements we show that our new approach competes favorably with comparable state of the art techniques on synthetic facial and hyperspectral image data sets

a bending gradient model for thick plates part i theory abstract this is the first part of a two part paper dedicated to a new plate theory for out of plane loaded thick plates where the static unknowns are those of the kirchhoff love theory 3 in plane stresses and 3 bending moments to which six components are added representing the gradient of the bending moment the new theory called the bending gradient plate theory is described in the present paper it is an extension to arbitrarily layered plates of the reissner mindlin plate theory which appears as a special case of the bending gradient plate theory when the plate is homogeneous however we demonstrate also that in the general case the bending gradient model cannot be reduced to a reissner mindlin model in part two lebee and sab 2011 the bending gradient theory is applied to multilayered plates and its predictions are compared to those of the reissner mindlin theory and to full 3d pagano s exact solutions the main conclusion of the second part is that the bending gradient gives good predictions of both deflection and shear stress distributions in any material configuration moreover under some symmetry conditions the bending gradient model coincides with the second order approximation of the exact solution as the slenderness ratio l h goes to infinity

mathematical construction of a reissner mindlin plate theory for composite laminates abstract a reissner mindlin theory for composite laminates without invoking ad hoc kinematic assumptions is constructed using the variational asymptotic method instead of assuming a priori the distribution of three dimensional displacements in terms of two dimensional plate displacements as what is usually done in typical plate theories an exact intrinsic formulation has been achieved by introducing unknown three dimensional warping functions then the variational asymptotic method is applied to systematically decouple the original three dimensional problem into a one dimensional through the thickness analysis and a two dimensional plate analysis the resulting theory is an equivalent single layer reissner mindlin theory with an excellent accuracy comparable to that of higher order layer wise theories the present work is extended from the previous theory developed by the writer and his co workers with several sizable contributions a six more constants 33 in total are introduced to allow maximum freedom to transform the asymptotically correct energy into a reissner mindlin model b the semi definite programming technique is used to seek the optimum reissner mindlin model furthermore it is proved the first time that the recovered three dimensional quantities exactly satisfy the continuity conditions on the interface between different layers and traction boundary conditions on the bottom and top surfaces it is also shown that two of the equilibrium equations of three dimensional elasticity can be satisfied asymptotically and the third one can be satisfied approximately so that the difference between the reissner mindlin model and the second order asymptotical model can be minimized numerical examples are presented to compare with the exact solution as well as the classical lamination theory and the first order shear deformation theory demonstrating that the present theory has an excellent agreement with the exact solution

best strip beam properties derivable from classical lamination theory this paper presents a simple method to extract classical beam properties for composite strips with general anisotropy from an asymptotically correct classical lamination theory derived using the variational asymptotic method none of the ad hoc approximations common in the literature of beam theory are used rather this approach discovers the necessary and su cient engineering assumptions for obtaining the correct cross sectional constants and stress recovery relations for a strip numerical examples are provided to illustrate that the resulting theory resulting elastic constants agree well with those from well established methods of calculating cross sectional constants and the accuracy deteriorates as the strip thickness to width ratio increases

on the complexity of nonnegative matrix factorization nonnegative matrix factorization nmf has become a prominent technique for the analysis of image databases text databases and other information retrieval and clustering applications the problem is most naturally posed as continuous optimization in this report we define an exact version of nmf then we establish several results about exact nmf i that it is equivalent to a problem in polyhedral combinatorics ii that it is np hard and iii that a polynomial time local search heuristic exists

nonnegative decomposition of functional count data we present a novel decomposition of nonnegative functional count data that draws on concepts from nonnegative matrix factorization our decomposition which we refer to as narfd nonnegative and regularized function decomposition enables the study of patterns in variation across subjects in a highly interpretable manner prototypic modes of variation are estimated directly on the observed scale of the data are local and are transparently added together to reconstruct observed functions this contrasts with generalized functional principal component analysis an alternative approach that estimates functional principal components on a transformed scale produces components that typically vary across the entire functional domain and reconstructs observations using complex patterns of cancellation and multiplication of functional principal components narfd is implemented using an alternating minimization algorithm and we evaluate our approach in simulations we apply narfd to an accelerometer dataset comprising observations of physical activity for healthy older americans

asymptotic generalization of reissner mindlin theory accurate three dimensional recovery for composite shells abstract a rigorous and systematic dimensional reduction of a shell like structure is undertaken it starts with geometrically nonlinear three dimensional 3 d anisotropic elasticity theory and takes advantage of small parameters associated with the geometry this reduction is carried out using the variational asymptotic method and splits the 3 d problem into a linear one dimensional 1 d through the thickness analysis and a nonlinear two dimensional 2 d shell analysis the 2 d equations are put into the form of a nonlinear reissner mindlin shell theory details of which are dealt with in a separate paper the focus of this paper is on the through the thickness analysis which is solved by a 1 d finite element method and which provides two useful pieces of information a generalized 2 d constitutive law for the shell equations and a set of recovery relations that can be used to express the 3 d field variables through the thickness in terms of 2 d shell variables calculated in the shell analysis the resulting analysis can be incorporated into standard reissner mindlin shell finite element codes numerical results are compared with the exact solution and the excellent agreement validates the fidelity of this modeling approach

sparse and unique nonnegative matrix factorization through data preprocessing nonnegative matrix factorization nmf has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part based representation however nmf has the drawback of being highly ill posed that is there typically exist many different but equivalent factorizations in this paper we introduce a completely new way to obtaining more well posed nmf problems whose solutions are sparser our technique is based on the preprocessing of the nonnegative input data matrix and relies on the theory of m matrices and the geometric interpretation of nmf this approach provably leads to optimal and sparse solutions under the separability assumption of donoho and stodden 2003 and for rank three matrices makes the number of exact factorizations finite we illustrate the effectiveness of our technique on several image data sets

asymptotic expansion for the density of states of the magnetic schrodinger operator with a random potential we study the asymptotics for the density of states of the magnetic schrodinger operator with a random potential by using the methods of effective hamiltonian complex dilation and complex translation we obtain in the large magnetic field limit the asymptotic expansion for the density of states measure considered as a distribution

variational asymptotic micromechanics modeling of heterogeneous porous materials abstract this paper presents a numerical technique to predict the effective elastic properties of heterogeneous fluid filled porous media where the heterogeneity may result from dissimilar solid and fluid phase properties or due to mismatch in porous microstructure the technique is based on the variational asymptotic method of homogenization where finite element method is employed for discretization biot s theory of poroelasticity is used to describe porous media where both solid and fluid phase motions u u formulation are considered with associated strain measures the method estimates the poroelastic constitutive law in single analysis which makes it very efficient compared to other finite element based homogenization techniques the method is also general enough to compute all 28 elements of an anisotropic constitutive matrix other than estimating the effective properties the micro stress strain distribution is also obtained at no additional cost the method is successfully applied for homogenization of porous media fluid filled cavity and finally for effective property estimation of bone lamella in absence of any other direct method of porous media homogenization the present technique is compared with classical homogenization methods with fluid approximated as solid of very high poisson s ratio the suitability of this approximation and various other alternatives are also discussed it is shown that the present homogenization method can be an efficient tool for bone property estimation where fluid filled porous hierarchical micro nanostructure must be respected at all steps

enhanced first order theory based on mixed formulation and transverse normal effect abstract an accurate prediction of displacements and stresses for laminated and sandwich plates is presented using an enhanced first order plate theory based on the mixed variational theorem efsdtm developed in this paper in the mixed formulation transverse shear stresses based on an efficient higher order plate theory ehopt developed by cho and parmerter cho m parmerter r r 1993 efficient higher order composite plate theory for general lamination configurations aiaa journal 31 1299 1306 are utilized and modified to satisfy prescribed lateral conditions and displacements are assumed to be those of a first order shear deformation theory fsdt relationships between the modified ehopt and the fsdt are systematically derived via both the mixed variational theorem and the least square approximation of difference between in plane stresses including the transverse normal stress effect it is shown that the transverse normal stress effect should be considered in predicting the in plane stresses when the poisson effect is dominant the developed efsdtm preserves the computational advantage of the classical fsdt while allowing for important local through the thickness variations of displacements and stresses through the recovery procedure the accuracy and efficiency of the present theory are assessed by comparing its results with various plate models as well as the three dimensional exact solutions for thick laminated and sandwich plates

variational asymptotic analysis for plates of variable thickness abstract it is a common assumption in plate theory that the effect of varying thickness on plate elastic constants can be simply accounted for by incorporating the thickness distribution in the formulae obtained for a plate of uniform thickness for plates whose thickness varies linearly in the global directions the variation described by a set of taper parameters a plate theory has been developed using the variational asymptotic method in a first of its kind development both the 8 8 stiffness matrix and the 3d stress and strain recovery are shown to contain these taper parameters explicitly as opposed to their merely being present by virtue of the varying plate thickness furthermore terms such as bending shear and twist shear coupling are shown to be present which are typically disregarded in published works on tapered plates it is later clearly demonstrated using the full 3d finite element solutions from a test case that an analysis of this kind is needed to accurately determine the complete stress distribution in conclusion merely changing the thickness distributions in results for uniform plates may work for some problems but it is clearly not sufficient in general nor can it guarantee good agreement with all aspects of plate analysis this is because these kinds of approximations are not in tune with the mechanics of such a problem as they disregard the tilt of the outward directed normals in the boundary conditions for top and bottom surfaces furthermore as always a theory developed using the variational asymptotic method does not make any assumptions regarding the deformation and is generally well suited for capturing such effects without fundamental changes in the procedure

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

online nonnegative matrix factorization with outliers we propose a unified and systematic framework for performing online nonnegative matrix factorization in the presence of outliers our framework is particularly suited to large scale data we propose two solvers based on projected gradient descent and the alternating direction method of multipliers we prove that the sequence of objective values converges almost surely by appealing to the quasi martingale convergence theorem we also show the sequence of learned dictionaries converges to the set of stationary points of the expected loss function almost surely in addition we extend our basic problem formulation to various settings with different constraints and regularizers we also adapt the solvers and analyses to each setting we perform extensive experiments on both synthetic and real datasets these experiments demonstrate the computational efficiency and efficacy of our algorithms on tasks such as parts based basis learning image denoising shadow removal and foreground background separation

non negative matrix factorization revisited uniqueness and algorithm for symmetric decomposition non negative matrix factorization nmf has found numerous applications due to its ability to provide interpretable decompositions perhaps surprisingly existing results regarding its uniqueness properties are rather limited and there is much room for improvement in terms of algorithms as well uniqueness aspects of nmf are revisited here from a geometrical point of view both symmetric and asymmetric nmf are considered the former being tantamount to element wise non negative square root factorization of positive semidefinite matrices new uniqueness results are derived e g it is shown that a sufficient condition for uniqueness is that the conic hull of the latent factors is a superset of a particular second order cone checking this condition is shown to be np complete yet this and other results offer insights on the role of latent sparsity in this context on the computational side a new algorithm for symmetric nmf is proposed which is very different from existing ones it alternates between procrustes rotation and projection onto the non negative orthant to find a non negative matrix close to the span of the dominant subspace simulation results show promising performance with respect to the state of art finally the new algorithm is applied to a clustering problem for co authorship data yielding meaningful and interpretable results

semidefinite programming based preconditioning for more robust near separable nonnegative matrix factorization nonnegative matrix factorization nmf under the separability assumption can provably be solved efficiently even in the presence of noise and has been shown to be a powerful technique in document classification and hyperspectral unmixing this problem is referred to as near separable nmf and requires that there exists a cone spanned by a small subset of the columns of the input nonnegative matrix approximately containing all columns in this paper we propose a preconditioning based on the minimum volume ellipsoid and semidefinite programming making the input matrix well conditioned this in turn can improve significantly the performance of near separable nmf algorithms which is illustrated on the popular successive projection algorithm spa the new preconditioned spa is provably more robust to noise and outperforms spa on several synthetic data sets we also show how an active set method allows us to apply the preconditioning on large scale real world hyperspectral images

computing symmetric nonnegative rank factorizations an algorithm is described for the nonnegative rank factorization nrf of some completely positive cp matrices whose rank is equal to their cp rank the algorithm can compute the symmetric nrf of any nonnegative symmetric rank r matrix that contains a diagonal principal submatrix of that rank and size with leading cost o rm2 operations in the dense case the algorithm is based on geometric considerations and is easy to implement the implications for matrix graphs are also discussed

nonlinear bending analysis of radial stiffened annular laminated sector plates with dynamic relaxation method in this paper the nonlinear bending of laminated stiffened annular sector plates under mechanical loading with various boundary conditions is investigated the plates are made of layers with orthotropic properties and different fiber orientations which the aforementioned fibers are placed in a cartesian coordinate system based on first order shear deformation plate theory fsdt and von karman relations for large deflection nonlinear equilibrium equations are developed dynamic relaxation dr numerical method combined with the finite difference discretization technique is used to solve the plate nonlinear partial differential equations and fortran program is developed to generate the numerical results effects of the plate thickness to radius ratio boundary condition stiffener depth plate lay ups and the sector angle are discussed

on asymptotically correct linear laminated plate theory abstract the focus of this paper is the development of asymptotically correct theories for laminated plates the material properties of which vary through the thickness and for which each lamina is orthotropic this work is based on the variational asymptotical method a mathematical technique by which the three dimensional analysis of plate deformation can be split into two separate analyses a one dimensional through the thickness analysis and a two dimensional plate analysis the through the thickness analysis includes elastic constants for use in the plate theory and approximate closed form recovering relations for all three dimensional field variables expressed in terms of plate variables in general the specific type of plate theory that results from this procedure is determined by the procedure itself however in this paper only reissner like plate theories are considered often called first order shear deformation theories this paper makes three main contributions first it is shown that construction of an asymptotically correct reissner like theory for laminated plates of the type considered is not possible in general second a new point of view on the variational asymptotical method is presented leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible third numerical results from such an optimum reissner like theory are presented these results include comparisons of plate displacement as well as of three dimensional field variables and are the best of all extant reissner like theories indeed they even surpass results from theories that carry many more generalized displacement variables

nonnegative matrix factorization with the itakura saito divergence with application to music analysis this letter presents theoretical algorithmic and experimental results about nonnegative matrix factorization nmf with the itakura saito is divergence we describe how is nmf is underlaid by a well defined statistical model of superimposed gaussian components and is equivalent to maximum likelihood estimation of variance parameters this setting can accommodate regularization constraints on the factors through bayesian priors in particular inverse gamma and gamma markov chain priors are considered in this work estimation can be carried out using a space alternating generalized expectation maximization sage algorithm this leads to a novel type of nmf algorithm whose convergence to a stationary point of the is cost function is guaranteed we also discuss the links between the is divergence and other cost functions used in nmf in particular the euclidean distance and the generalized kullback leibler kl divergence as such we describe how is nmf can also be performed using a gradient multiplicative algorithm a standard algorithm structure in nmf whose convergence is observed in practice though not proven finally we report a furnished experimental comparative study of euclidean nmf kl nmf and is nmf algorithms applied to the power spectrogram of a short piano sequence recorded in real conditions with various initializations and model orders then we show how is nmf can successfully be employed for denoising and upmix mono to stereo conversion of an original piece of early jazz music these experiments indicate that is nmf correctly captures the semantics of audio and is better suited to the representation of music signals than nmf with the usual euclidean and kl costs

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

non negative blind source separation algorithm based on minimum aperture simplicial cone we address the problem of blind source separation bss when the hidden sources are nonnegative n bss in this case the scatter plot of the mixed data is contained within the simplicial cone generated by the columns of the mixing matrix the proposed method termed scsa uns for simplicial cone shrinking algorithm for unmixing non negative sources aims at estimating the mixing matrix and the sources by fitting a minimum aperture simplicial cone masc to the cloud of mixed data points scsa uns is evaluated on both independent and correlated synthetic data and compared to other n bss methods simulations are also performed on real liquid chromatography mass spectrum lc ms data for the metabolomic analysis of a chemical sample and on real dynamic positron emission tomography pet images in order to study the pharmacokinetics of the 18f fdg fluorodeoxyglucose tracer in the brain

asymptotic construction of reissner like composite plate theory with accurate strain recovery abstract the focus of this paper is to develop an asymptotically correct theory for composite laminated plates when each lamina exhibits monoclinic material symmetry the development starts with formulation of the three dimensional 3 d anisotropic elasticity problem in which the deformation of the reference surface is expressed in terms of intrinsic two dimensional 2 d variables the variational asymptotic method is then used to rigorously split this 3 d problem into a linear one dimensional normal line analysis and a nonlinear 2 d plate analysis accounting for classical as well as transverse shear deformation the normal line analysis provides a constitutive law between the generalized 2 d strains and stress resultants as well as recovering relations to approximately but accurately express the 3 d displacement strain and stress fields in terms of plate variables calculated in the plate analysis it is known that more than one theory may exist that is asymptotically correct to a given order this nonuniqueness is used to cast a strain energy functional that is asymptotically correct through the second order into a simple reissner like plate theory although it is not possible in general to construct an asymptotically correct reissner like composite plate theory an optimization procedure is used to drive the present theory as close to being asymptotically correct as possible while maintaining the beauty of the reissner like formulation numerical results are presented to compare with the exact solution as well as a previous similar yet very different theory the present theory has excellent agreement with the previous theory and exact results

finding minimal convex nested polygons abstract we consider the problem of finding a polygon nested between two given convex polygons that has a minimal number of vertices our main result is an o n log k algorithm for solving the problem where n is the total number of vertices of the given polygons and k is the number of vertices of a minimal nested polygon we also present an o n sub optimal algorithm and a simple o nk optimal algorithm

accelerated multiplicative updates and hierarchical als algorithms for nonnegative matrix factorization nonnegative matrix factorization nmf is a data analysis technique used in a great variety of applications such as text mining image processing hyperspectral data analysis computational biology and clustering in this letter we consider two well known algorithms designed to solve nmf problems the multiplicative updates of lee and seung and the hierarchical alternating least squares of cichocki et al we propose a simple way to significantly accelerate these schemes based on a careful analysis of the computational cost needed at each iteration while preserving their convergence properties this acceleration technique can also be applied to other algorithms which we illustrate on the projected gradient method of lin the efficiency of the accelerated algorithms is empirically demonstrated on image and text data sets and compares favorably with a state of the art alternating nonnegative least squares algorithm

low dimensional polytope approximation and its applications to nonnegative matrix factorization in this study nonnegative matrix factorization is recast as the problem of approximating a polytope on the probability simplex by another polytope with fewer facets working on the probability simplex has the advantage that data are limited to a compact set with a known boundary making it easier to trace the approximation procedure in particular the supporting hyperplane that separates a point from a disjoint polytope a fact asserted by the hahn banach theorem can be calculated in finitely many steps this approach leads to a convenient way of computing the proximity map which in contrast to most existing algorithms where only an approximate map is used finds the unique and global minimum per iteration this paper sets up a theoretical framework outlines a numerical algorithm and suggests an effective implementation testing results strongly evidence that this approach obtains a better low rank nonnegative matrix approximation in fewer steps than conventional methods

zeroth order shear deformation micro mechanical model for composite plates with in plane heterogeneity abstract this article introduces a new model for investigating the mechanical behavior of heterogeneous plates which are composed of periodically repeated microstructures along the in plane directions we first formulate the original three dimensional problem in an intrinsic form for implementation into a single unified formulation and application to geometrically nonlinear problem taking advantage of smallness of the plate thickness to length parameter and heterogeneity and performing homogenization along dimensional reduction simultaneously the variational asymptotic method is used to rigorously construct an effective zeroth order plate model which is similar to a generalized reissner mindlin model the first order shear deformation model capable of capturing the transverse shear deformations but still carries out the zeroth order approximation which can maximize simplicity and promote efficiency this present approach is incorporated into a commercial analysis package for the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level a few examples available in literature are used to demonstrate the consistence and efficiency of this new model especially for the structures in which the effects of transverse shear deformations are significant

underdetermined sparse blind source separation of nonnegative and partially overlapped data we study the solvability of sparse blind separation of n nonnegative sources from m linear mixtures in the underdetermined regime m n the geometric properties of the mixture matrix and the sparseness structure of the source matrix are closely related to the identification of the mixing matrix we first illustrate and establish necessary and sufficient conditions for the unique separation for the case of m mixtures and m 1 sources and develop a novel algorithm based on data geometry source sparseness and ell 1 minimization then we extend the results to any order m times n 3 leq m n based on the degree of degeneracy of the columns of the mixing matrix numerical results substantiate the proposed solvability conditions and show satisfactory performance of our approach

an asymptotic method based composite plate model considering imperfect interfaces abstract this paper presents an asymptotic method based analysis of composite laminates having interfacial imperfections in general imperfect interfaces are simply modeled by introducing a linear spring layer model which empirically assumes that the displacement jumps that occur at the weakened interface are proportional to the transverse shear stresses of interface positions in this study we propose a composite plate model derived by using asymptotic expansion that does not make any assumptions other than the scaling of coordinate systems within the framework of the asymptotic analysis the spring layer model is introduced to describe the effect of weakened interfaces which is realized by the separation of domains in the through the thickness direction and the integration of piecewise continuous warping functions as a result we newly define a spring parameter that is exactly the same as the stiffness of a spring therefore a set of spring elements are added to the through the thickness modeling of the microscopic analysis and the plate equations derived in the macroscopic problem are the same as those of the perfectly bonded laminates as a consequence we also derive the proposed plate model with the mathematical rigor that the previous asymptotic models contain we provide some numerical results verifying that the proposed method shows good agreement with the elasticity and 3d fem solutions

compressed nonnegative matrix factorization is fast and accurate nonnegative matrix factorization nmf has an established reputation as a useful data analysis technique in numerous applications however its usage in practical situations is undergoing challenges in recent years the fundamental factor to this is the increasingly growing size of the datasets available and needed in the information sciences to address this in this work we propose to use structured random compression that is random projections that exploit the data structure for two nmf variants classical and separable in separable nmf snmf the left factors are a subset of the columns of the input matrix we present suitable formulations for each problem dealing with different representative algorithms within each one we show that the resulting compressed techniques are faster than their uncompressed variants vastly reduce memory demands and do not encompass any significant deterioration in performance the proposed structured random projections for snmf allow to deal with arbitrarily shaped large matrices beyond the standard limit of tall and skinny matrices granting access to very efficient computations in this general setting we accompany the algorithmic presentation with theoretical foundations and numerous and diverse examples showing the suitability of the proposed approaches our implementations are publicly available

a nonconvex splitting method for symmetric nonnegative matrix factorization convergence analysis and optimality symmetric nonnegative matrix factorization symnmf has important applications in data analytics problems such as document clustering community detection and image segmentation in this paper we propose a novel nonconvex variable splitting method for solving symnmf the proposed algorithm is guaranteed to converge to the set of karush kuhn tucker kkt points of the nonconvex symnmf problem furthermore it achieves a global sublinear convergence rate we also show that the algorithm can be efficiently implemented in parallel further sufficient conditions are provided that guarantee the global and local optimality of the obtained solutions extensive numerical results performed on both synthetic and real datasets suggest that the proposed algorithm converges quickly to a local minimum solution

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

geometrically exact intrinsic theory for dynamics of moving composite plates a geometrically exact and fully intrinsic theory is presented for dynamics of composite plates undergoing large deformation to say that the formulation is intrinsic means that it is without displacement and rotation variables although the equations are geometrically exact the highest degree nonlinearities are quadratic there are no singularities associated with finite rotation methods for posing problems in this framework along with advantages of the formulation are discussed

homogenization and dimensional reduction of composite plates with in plane heterogeneity the variational asymptotic method is used to construct a new model for composite plates which could have in plane heterogeneity due to both geometry and material we first formulate the original three dimensional problem in an intrinsic form which is suitable for geometrically nonlinear analysis taking advantage of smallness of the plate thickness and heterogeneity we use the variational asymptotic method to rigorously construct an effective plate model unifying a homogenization process and a dimensional reduction process this approach is implemented in the computer code vapas using the finite element technique for the purpose of dealing with realistic heterogeneous plates a few examples are used to demonstrate the capability of this new model

lower bounds on nonnegative rank via nonnegative nuclear norms the nonnegative rank of an entrywise nonnegative matrix a in mathbb r m times n a r m n is the smallest integer r r such that a a can be written as a uv a uv where u in mathbb r m times r u r m r and v in mathbb r r times n v r r n are both nonnegative the nonnegative rank arises in different areas such as combinatorial optimization and communication complexity computing this quantity is np hard in general and it is thus important to find efficient bounding techniques especially in the context of the aforementioned applications in this paper we propose a new lower bound on the nonnegative rank which unlike most existing lower bounds does not solely rely on the matrix sparsity pattern and applies to nonnegative matrices with arbitrary support the idea involves computing a certain nuclear norm with nonnegativity constraints which allows to lower bound the nonnegative rank in the same way the standard nuclear norm gives lower bounds on the standard rank our lower bound is expressed as the solution of a copositive programming problem and can be relaxed to obtain polynomial time computable lower bounds using semidefinite programming we compare our lower bound with existing ones and we show examples of matrices where our lower bound performs better than currently known ones

reconstruction of first order shear deformation shell theory for laminated and sandwich shells a first order shear deformation shell theory fsdt based on general curvilinear coordinates has been reconstructed through a strain energy transformation based on the definition of the mean displacements the transverse shear strains that are constant through the thickness are improved to vary through the thickness it is assumed that the displacements and in surface strains of three dimensional theory are approximated by those of fsdt relationship between fsdt and three dimensional theory has been systematically established in the averaged least square sense this relationship provides the closed form recovering relations for three dimensional variables expressed in terms of fsdt relations the present approach has been applied to a higher order zigzag shell theory comparisons of displacements and stresses of laminated and sandwich shells using the present theory are made with the original fsdt and three dimensional exact solutions

lifshitz tails for random schrodinger operators with negative singular poisson potential we develop a method of asymptotic study of the integrated density of states ids n e of a random schrodinger operator with a non positive attractive poisson potential the method is based on the periodic approximations of the potential instead of the dirichlet neumann bracketing used before this allows us to derive more precise bounds for the rate of approximations of the ids by the ids of respective periodic operators and to obtain rigorously for the first time the leading term of log n e as e for the poisson random potential with a singular single site impurity potential in particular for the screened coulomb impurities dislocations etc

the integrated density of states in strong magnetic fields we consider three dimensional schrodinger operators with constant magnetic fields and ergodic electric potentials we study the strong magnetic field asymptotic behaviour of the integrated density of states distinguishing between the asymptotics far from the landau levels and the asymptotics near a given landau level

invariant finite element model for composite structures the generalized unified formulation the generalized unified formulation presented here is a modern approach for the finite element analysis of sandwich plates and in general multilayered structures a large variety of types of theories with any combination of orders of expansion for the different displacement variables can be obtained from the expansion of six 1 x 1 arrays the kernels or fundamental nuclei of the generalized unified formulation each of the displacement variables is independently treated and different orders of expansions for the different unknowns can be chosen because infinite combinations can be freely chosen for the displacements the generalized unified formulation allows the user to write 3 higher order shear deformation theories 3 zig zag theories and 3 layerwise theories with a single invariant formulation implemented in a single finite element method code the six independent fundamental nuclei are formally invariant with respect to the order used for the expansion or with respect to the type of theory the generalized unified formulation can be also adopted for mixed variational statements in such cases the number of independent kernels would be different but their size would still be 1 x 1 arrays this paper assesses bending of sandwich structures analytical and elasticity solution are compared the effect of the zig zag form of the displacement is discussed