simple efficient solvers for certain ill conditioned systems of linear equations including h div problems abstract simple accurate and efficient iterative methods for the solution of a nearly singular variational problem are described the systems considered arise e g when seeking to determine the flux of second order elliptic partial differential equations each outer iteration uses a robust and efficient solver which may be a direct or iterative method and only a few outer iterations are required to obtain an approximate solution reduced rank extrapolation may be applied to speed up the convergence

from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

statistical mechanics and phase transitions in clustering a new approach to clustering based on statistical physics is presented the problem is formulated as fuzzy clustering and the association probability distribution is obtained by maximizing the entropy at a given average variance the corresponding lagrange multiplier is related to the temperature and motivates a deterministic annealing process where the free energy is minimized at each temperature critical temperatures are derived for phase transitions when existing clusters split it is a hierarchical clustering estimating the most probable cluster parameters at various average variances

an on line agglomerative clustering method for nonstationary data an on line agglomerative clustering algorithm for nonstationary data is described three issues are addressed the first regards the temporal aspects of the data the clustering of stationary data by the proposed algorithm is comparable to the other popular algorithms tested batch and on line the second issue addressed is the number of clusters required to represent the data the algorithm provides an efficient framework to determine the natural number of clusters given the scale of the problem finally the proposed algorithm implicitly minimizes the local distortion a measure that takes into account clusters with relatively small mass in contrast most existing on line clustering methods assume stationarity of the data when used to cluster nonstationary data these methods fail to generate a good representation moreover most current algorithms are computationally intensive when determining the correct number of clusters these algorithms tend to neglect clusters of small mass due to their minimization of the global distortion energy

a multiscale preconditioner for stochastic mortar mixed finite elements the aim of this paper is to introduce a new approach to efficiently solve sequences of problems that typically arise when modeling flow in stochastic porous media the governing equations are based on darcy s law with a stochastic permeability field starting from a specified covariance relationship the log permeability is decomposed using a truncated karhunen loeve expansion multiscale mortar mixed finite element approximations are used in the spatial domain and a nonintrusive sampling method is used in the stochastic dimensions a multiscale mortar flux basis is computed for a single permeability called a training permeability that captures the main characteristics of the porous media and is used as a preconditioner for each stochastic realization we prove that the condition number of the preconditioned interface operator is independent of the subdomain mesh size and the mortar mesh size computational results confirm that our approach provides an efficient means to quantify the uncertainty for stochastic flow in porous media

entropy constrained vector quantization an iterative descent algorithm based on a lagrangian formulation for designing vector quantizers having minimum distortion subject to an entropy constraint is discussed these entropy constrained vector quantizers ecvqs can be used in tandem with variable rate noiseless coding systems to provide locally optimal variable rate block source coding with respect to a fidelity criterion experiments on sampled speech and on synthetic sources with memory indicate that for waveform coding at low rates about 1 bit sample under the squared error distortion measure about 1 6 db improvement in the signal to noise ratio can be expected over the best scalar and lattice quantizers when block entropy coded with block length 4 even greater gains are made over other forms of entropy coded vector quantizers for pattern recognition it is shown that the ecvq algorithm is a generalization of the k means and related algorithms for estimating cluster means in that the ecvq algorithm estimates the prior cluster probabilities as well experiments on multivariate gaussian distributions show that for clustering problems involving classes with widely different priors the ecvq outperforms the k means algorithm in both likelihood and probability of error

clustering data by melting we derive a new clustering algorithm based on information theory and statistical mechanics which is the only algorithm that incorporates scale it also introduces a new concept into clustering cluster independence the cluster centers correspond to the local minima of a thermodynamic free energy which are identified as the fixed points of a one parameter nonlinear map the algorithm works by melting the system to produce a tree of clusters in the scale space melting is also insensitive to variability in cluster densities cluster sizes and ellipsoidal shapes and orientations we tested the algorithm successfully on both simulated data and a synthetic aperture radar image of an agricultural site with 12 attributes for crop identification

on a fem bem formulation for an exterior quasilinear problem in the plane we use a version of the fem bem method introduced by costabel boundary elements ix vol 1 c a brebbia et al eds springer verlag 1987 and han j comput math 8 1990 pp 223 232 to discretize an exterior quasilinear problem we provide error estimates for the galerkin method and propose a fully discrete scheme based on simple quadrature formulas furthermore we show that these numerical integration schemes preserve the optimal rates of convergence finally we present results of numerical experiments involving our discretization method

an expanded mixed finite element approach via a dual dual formulation and the minimum residual method abstract we apply an expanded mixed finite element method which introduces the gradient as a third explicit unknown to solve a linear second order elliptic equation in divergence form instead of using the standard dual form we show that the corresponding variational formulation can be written as a dual dual operator equation we establish existence and uniqueness of solution for the continuous and discrete formulations and provide the corresponding error analysis by using raviart thomas elements in addition we show that the corresponding dual dual linear system can be efficiently solved by a preconditioned minimum residual method some numerical results illustrating this fact and the rate of convergence of the mixed finite element method are also provided

deterministic annealing gustafson kessel fuzzy clustering algorithm abstract the gustafson and kessel gk fuzzy clustering algorithm proposed by gustafson and kessel in 1979 was the first important extension to the fuzzy c means fcm algorithm up to now the gk algorithm had become one of the most commonly used fuzzy clustering algorithms where the mahalanobis distance is used as a dissimilarity measure to provide more effectiveness and robustness than the fcm algorithm recently chaomurilige et al 2015 proposed a theoretical analysis on the parameter selection for the gk algorithm in which they indicated that the parameter of the fuzziness index heavily influences the performance of the gk algorithm in this paper we propose a novel gk fuzzy clustering algorithm based on the deterministic annealing approach for decreasing the effect of parameters we first consider maximizing the shannon s entropy of membership functions to the gk objective function and then use deterministic annealing to adjust the annealing parameter we also mathematically provide a theoretical initialization lower bound for the annealing parameter of the proposed deterministic annealing gk da gk algorithm comparisons between the da gk algorithm and other methods are made the computational complexity of the proposed method is also provided experimental results and comparisons actually verify theoretical results and also indicate the superiority and effectiveness of the proposed da gk algorithm

characteristic generators and dualization for tail biting trellises this paper focuses on dualizing tail biting trellises particularly kv trellises these trellises are based on characteristic generators as introduced by koetter vardy 2003 and may be regarded as a natural generalization of minimal conventional trellises even though they are not necessarily minimal two dualization techniques will be investigated the local dualization introduced by forney 2001 for general normal graphs and a linear algebra based dualization tailored to the specific class of tail biting bahl cocke jelinek raviv bcjr trellises introduced by nori shankar 2006 it turns out that in general the bcjr dual is a subtrellis of the local dual while for kv trellises these two coincide furthermore making use of both the bcjr construction and the local dualization it will be shown that for each complete set of characteristic generators of a code there exists a complete set of characteristic generators of the dual code such that their resulting kv trellises are dual to each other if paired suitably this proves a stronger version of a conjecture formulated by koetter vardy

on the coupling of boundary integral and mixed finite element methods we present a numerical method for solving an exterior dirichlet problem in the plane the technique consists in coupling boundary integral and mixed finite element methods an artificial boundary is introduced separating an interior region from an exterior one from an integral representation of the solution in the exterior domain we deduce two integral equations which relate the solution and its normal derivative over the artificial boundary these integral equations are incorporated into the so called mixed formulation of the problem in the interior region and a finite element method is used to approximate the resulting variational problem

a two grid eulerian lagrangian localized adjoint method to miscible displacement problems with dispersion term abstract in this paper we propose a novel two grid method of eulerian lagrangian localized adjoint method ellam mixed finite element method mfem solutions for nonlinear and coupled miscible displacement problems which describe complex fluid flow processes in porous media an ellam is used to solve the nonlinear convection diffusion equation for concentration and we present a mfem to compute the pressure equation for the pressure and darcy velocity a two grid scheme is investigated to linearize and decouple the mixed method equations it is illustrated that the coarse space can be selected as coarse as h o h 1 2 and the asymptotically optimal approximation as the nonlinear schemes can be still achieved as a result a large class of such nonlinear and coupled problems can be solved efficiently with large time steps

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

statistical mechanics of the maximum likelihood density estimation estimating the density of data generated by gaussian mixtures using the maximum likelihood criterion is investigated solving the statistical mechanics of this problem we evaluate the quality of the estimation as a function of the number of data points p ensuremath alpha n n being the dimensionality of the points in the limit of large n below a critical value of ensuremath alpha the estimated density consists of gaussian centers that have zero overlap with the structure of the true mixture we show numerically that estimating the centers by slowly reducing the estimated gaussian width yields a good agreement with the theory even in the presence of many local minima

on the algebraic structure of linear tail biting trellises tail biting trellises are important graphical representations of codes which can be simpler to decode than conventional trellises while conventional trellises are well understood the general theory of tail biting trellises is still under development in this paper we first develop a new algebraic framework for a systematic analysis of linear trellises which enables us to address open foundational questions in particular we present a useful and powerful characterization of linear trellis isomorphy we also obtain a new proof of the linear factorization theorem of koetter vardy and point out unnoticed problems for the group case next we apply our framework to 1 describe all the factorizations of linear trellises 2 determine and classify all the minimal linear trellises for a given linear code and 3 prove that nonmergeable one to one linear trellises are determined by the edge label sequences of certain closed paths we also provide new insight into mergeability and state how results on reduced linear trellises can be extended to nonreduced ones our classification results are relevant to iterative linear programming decoding as we show that minimal linear trellises can yield different pseudocodewords even if they have the same graph structure

local irreducibility of tail biting trellises this paper investigates tail biting trellis realizations for linear block codes intrinsic trellis properties are used to characterize irreducibility on given intervals of the time axis it proves beneficial to always consider the trellis and its dual simultaneously a major role is played by trellis properties that amount to observability and controllability of trellis fragments of various lengths for fragments of length less than the minimum span length of the code it is shown that fragment observability and fragment controllability are equivalent to irreducibility for reducible trellises a constructive reduction procedure is presented the considerations also lead to a characterization for when the dual of a trellis allows a product factorization into elementary atomic trellises

a low order mixed finite element method for a class of quasi newtonian stokes flows part i a priori error analysis abstract this is the second part of a work dealing with a low order mixed finite element method for a class of nonlinear stokes models arising in quasi newtonian fluids in the first part we showed that the resulting variational formulation is given by a twofold saddle point operator equation and that the corresponding galerkin scheme becomes well posed with piecewise constant functions and raviart thomas spaces of lowest order as the associated finite element subspaces in this paper we develop a bank weiser type a posteriori error analysis yielding a reliable estimate and propose the corresponding adaptive algorithm to compute the mixed finite element solutions several numerical results illustrating the efficiency of the method are also provided

on the coupling of mixed fem and bem for an exterior helmholtz problem in the plane this paper deals with an elliptic boundary value problem posed in the plane with variable coefficients but whose restriction to the exterior of a bounded domain reduces to a helmholtz equation we consider a mixed variational formulation in a bounded domain that contains the heterogeneous medium coupled with a boundary integral method applied to the helmholtz equation in we utilize suitable auxiliary problems duality arguments and fredholm alternative to show that the resulting formulation of the problem is well posed then we define a corresponding galerkin scheme by using rotated raviart thomas subspaces and spectral elements on the interface we show that the discrete problem is uniquely solvable and convergent and prove optimal error estimates finally we illustrate our analysis with some results from computational experiments

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

vector quantization with complexity costs vector quantization is a data compression method by which a set of data points is encoded by a reduced set of reference vectors the codebook a vector quantization strategy is discussed that jointly optimizes distortion errors and the codebook complexity thereby determining the size of the codebook a maximum entropy estimation of the cost function yields an optimal number of reference vectors their positions and their assignment probabilities the dependence of the codebook density on the data density for different complexity functions is investigated in the limit of asymptotic quantization levels how different complexity measures influence the efficiency of vector quantizers is studied for the task of image compression the wavelet coefficients of gray level images are quantized and the reconstruction error is measured the approach establishes a unifying framework for different quantization methods like k means clustering and its fuzzy version entropy constrained vector quantization or topological feature maps and competitive neural networks

nonsymmetric coupling of bem and mixed fem on polyhedral interfaces in this paper we propose and analyze some new methods for coupling mixed finite element and boundary element methods for the model problem of the laplace equation in free space or in the exterior of a bounded domain as opposed to the existing methods which use the complete matrix of operators of the calderon projector to obtain a symmetric coupled system we propose methods with only one integral equation the system can be considered as a further generalization of the johnson nedelec coupling of bem fem to the case of mixed formulations in the bounded domain using some recent analytical tools we are able to prove stability and convergence of galerkin methods with very general conditions on the discrete spaces and no restriction relating the finite and boundary element spaces this can be done for general lipschitz interfaces and in particular the coupling boundary can be taken to be a lipschitz polyhedron both the indirect and the direct approaches for the boundary integral formulation are explored

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

a dual dual mixed formulation for nonlinear exterior transmission problems we combine a dual mixed finite element method with a dirichletto neumann mapping derived by the boundary integral equation method to study the solvability and galerkin approximations of a class of exterior nonlinear transmission problems in the plane as a model problem we consider a nonlinear elliptic equation in divergence form coupled with the laplace equation in an unbounded region of the plane our combined approach leads to what we call a dual dual mixed variational formulation since the main operator involved has itself a dual type structure we establish existence and uniqueness of solution for the continuous and discrete formulations and provide the corresponding error analysis by using raviart thomas elements the main tool of our analysis is given by a generalization of the usual babuska brezzi theory to a class of nonlinear variational problems with constraints

regularized discriminant entropy analysis in this paper we propose the regularized discriminant entropy rde which considers both class information and scatter information on original data based on the results of maximizing the rde we develop a supervised feature extraction algorithm called regularized discriminant entropy analysis rdea rdea is quite simple and requires no approximation in theoretical derivation the experiments with several publicly available data sets show the feasibility and effectiveness of the proposed algorithm with encouraging results we propose the regularized discriminant entropy rde the rde is based on the within class entropy and robust estimation we design a supervised algorithm regularized discriminant entropy analysis rdea rdea can be regarded as a framework for supervised feature extraction

minimal realizations of linear systems the shortest basis approach given a discrete time linear system c a shortest basis for c is a set of linearly independent generators for c with the least possible lengths a basis b is a shortest basis if and only if it has the predictable span property i e has the predictable delay and degree properties and is non catastrophic or alternatively if and only if it has the subsystem basis property for any interval j the generators in b whose span is in j is a basis for the subsystem cj the dimensions of the minimal state spaces and minimal transition spaces of c are simply the numbers of generators in a shortest basis b that are active at any given state or symbol time respectively a minimal linear realization for c in controller canonical form follows directly from a shortest basis for c and a minimal linear realization for c in observer canonical form follows directly from a shortest basis for the orthogonal system c this approach seems conceptually simpler than that of classical minimal realization theory

analysis of a fem bem model posed on the conducting domain for the time dependent eddy current problem the three dimensional eddy current time dependent problem is considered we formulate it in terms of two variables one lying only on the conducting domain and the other on its boundary we combine finite elements fem and boundary elements bem to obtain a fem bem coupled variational formulation we establish the existence and uniqueness of the solution in the continuous and the fully discrete case finally we investigate the convergence order of the fully discrete scheme

an optimal iterative process for the johnson nedelec method of coupling boundary and finite elements we reformulate the discretization of the johnson nedelec method 11 of coupling boundary elements and finite elements for an exterior bidimensional laplacian this new formulation leads to optimal error estimates and allows the use of simple quadrature formulas for calculation of the boundary element matrix we show that if the parameter of discretization is sufficiently small the fully discrete scheme is well posed and the error estimates remain unaltered the rest of the paper is devoted to the study of an efficient algorithm for solving the resulting discrete linear systems

competitive algorithms for the clustering of noisy data abstract in this paper we consider the issue of clustering when outliers exist the outlier set is defined as the complement of the data set following this concept a specially designed fuzzy membership weighted objective function is proposed and the corresponding optimal membership is derived unlike the membership of fuzzy c means the derived fuzzy membership does not reduce with the increase of the cluster number with the suitable redefinition of the distance metric we demonstrate that the objective function could be used to extract c spherical shells a hard clustering algorithm alleviating the prototype under utilization problem is also derived artificially generated data are used for comparisons

a dual dual formulation for the coupling of mixed fem and bem in hyperelasticity we combine a dual mixed finite element method with the boundary integral equation method to study the solvability and galerkin approximations of a linear nonlinear transmission problem arising in plane elastostatics our approach is based on the introduction of the strain tensor as an auxiliary unknown in the finite element domain and it leads to what we call a dual dual mixed formulation since the corresponding operator equation becomes of a twofold saddle point structure we derive existence and uniqueness of solution for the continuous and discrete formulations and provide the associated error analysis in particular we extend the finite element space for plane elasticity given by the peers element and define an explicit finite element boundary element subspace satisfying all the required compatibility conditions most of our analysis makes use of an extension of the classical babuska brezzi theory to a class of nonlinear saddle point problems

least squares methods for the coupling of fem and bem in the present paper we propose least squares formulations for the numerical solution of exterior boundary value problems the partial differential equation is a first order system in a bounded subdomain and the unbounded subdomain is treated by means of boundary integral equations the first order system is derived from a strongly elliptic second order system the analysis of the present least squares formulations is reduced to the analysis of the galerkin method for the coupling of finite element and boundary element methods fem and bem of the second order problem the least squares approach requires no stability condition however it requires the computation of negative as well as of half integer sobolev norms the arising linear systems can be preconditioned to have condition numbers sim 1 the present methods benefit strongly from the use of biorthogonal wavelets on the coupling boundary and the computation of corresponding equivalent norms in sobolev spaces in particular the application of green s formula leads to an efficient discretization of least squares formulations

an error control scheme for transmission of vector quantization data over noisy channels this paper presents an error control scheme for transmitting vector quantized data over noisy channels first we review a self organizing feature map sofm based approach to construct the mapping from the codebook of the quantizer to the channel signal set of the communication system this approach is robust with respect to channel noise even if we do not use any error control scheme in the communication system afterwards a new trellis type quantizer namely the trellis coded kohonen 1984 map tckm is presented the design process of the tckm which is based on the neighborhood structure of sofms is simpler than that of conventional trellis coded vector quantizers tcvqs simulation results show that the performance of tckms is comparable with that of tcvqs last we introduce the error control scheme based on the concepts of the above two applications of sofms simulation results show that the proposed error control scheme is more robust with respect to channel noise the advantage of our approaches mentioned above is that the design processes of transmission systems are predefined before the construction of the codebook thus different codebooks with the same neighborhood structure can share the same design

the dynamics of group codes state spaces trellis diagrams and canonical encoders a group code c over a group g is a set of sequences of group elements that itself forms a group under a component wise group operation a group code has a well defined state space sigma sub k at each time k each code sequence passes through a well defined state sequence the set of all state sequences is also a group code the state code of c the state code defines an essentially unique minimal realization of c the trellis diagram of c is defined by the state code of c and by labels associated with each state transition the set of all label sequences forms a group code the label code of c which is isomorphic to the state code of c if c is complete and strongly controllable then a minimal encoder in controller canonical feedbackfree form may be constructed from certain sets of shortest possible code sequences called granules the size of the state space sigma sub k is equal to the size of the state space of this canonical encoder which is given by a decomposition of the input groups of c at each time k if c is time invariant and nu controllable then mod sigma sub k mod pi sub 1

a primal mixed formulation for exterior transmission problems in bf r 2 we combine a primal mixed finite element approach with a dirichlet to neumann mapping arising from the boundary integral equation method to study the weak solvability and galerkin approximations of a class of linear exterior transmission problems in potential theory our results are mainly based on the babuska brezzi theory for variational problems with constraints we establish the uniqueness of solution for the continuous and discrete formulations and show that finite element subspac es of lagrange type satisfy the discrete compatibility conditions in addition we provide the error analysis including polygonal approximations of the domain and prove strong convergence of the galerkin solutions moreover under additional regularity assumptions on the solution of the continuous formulation we obtain the asymptotic rate of convergence o h

a study of vector quantization for noisy channels several issues related to vector quantization for noisy channels are discussed an algorithm based on simulated annealing is developed for assigning binary codewords to the vector quantizer code vectors it is shown that this algorithm could result in dramatic performance improvements as compared to randomly selected codewords a modification of the simulated annealing algorithm for binary codeword assignment is developed for the case where the bits in the codeword are subjected to unequal error probabilities resulting from unequal levels of error protection an algorithm for the design of an optimal vector quantizer for a noisy channel is briefly discussed and its robustness under channel mismatch conditions is studied numerical results for a stationary first order gauss markov source and a binary symmetric channel are provided it is concluded that the channel optimized vector quantizer design algorithm if used carefully can result in a fairly robust system with no additional delay the case in which the communication channel is nonstationary as in mobile radio channels is studied and some preliminary ideas for quantizer design are presented

minimal state space realization in linear system theory an overview we give a survey of the results in connection with the minimal state space realization problem for linear time invariant systems we start with a brief historical overview and a short introduction to linear system theory next we present some of the basic algorithms for the reduction of nonminimal state space realizations and for the minimal state space realization of infinite or finite sequences of markov parameters of linear time invariant systems finally we discuss some extensions of this problem to other classes of systems and point out some related problems

complexity optimized data clustering by competitive neural networks data clustering is a complex optimization problem with applications ranging from vision and speech processing to data transmission and data storage in technical as well as in biological systems we discuss a clustering strategy that explicitly reflects the tradeoff between simplicity and precision of a data representation the resulting clustering algorithm jointly optimizes distortion errors and complexity costs a maximum entropy estimation of the clustering cost function yields an optimal number of clusters their positions and their cluster probabilities our approach establishes a unifying framework for different clustering methods like k means clustering fuzzy clustering entropy constrained vector quantization or topological feature maps and competitive neural networks

a theory of proximity based clustering structure detection by optimization abstract in this paper a systematic optimization approach for clustering proximity or similarity data is developed starting from fundamental invariance and robustness properties a set of axioms is proposed and discussed to distinguish different cluster compactness and separation criteria the approach covers the case of sparse proximity matrices and is extended to nested partitionings for hierarchical data clustering to solve the associated optimization problems a rigorous mathematical framework for deterministic annealing and mean field approximation is presented efficient optimization heuristics are derived in a canonical way which also clarifies the relation to stochastic optimization by gibbs sampling similarity based clustering techniques have a broad range of possible applications in computer vision pattern recognition and data analysis as a major practical application we present a novel approach to the problem of unsupervised texture segmentation which relies on statistical tests as a measure of homogeneity the quality of the algorithms is empirically evaluated on a large collection of brodatz like micro texture mondrians and on a set of real word images to demonstrate the broad usefulness of the theory of proximity based clustering the performances of different criteria and algorithms are compared on an information retrieval task for a document database the superiority of optimization algorithms for clustering is supported by extensive experiments

grid modification for the wave equation with attenuation the wave equation with attenuation due to a linear friction is approximated by a new mixed finite element method which allows one to use different grids and basis functions at different times when necessary this method enables one to track sharp moving wave fronts more efficiently and accurately error estimates with optimal convergent rates are established unconditional stability is also proved for this method

variational formulations of transmission problems via fem bem and dtn mappings the purpose of this work is to review some of the main results on the weak solvability and galerkin approximations of interior and exterior transmission problems arising in potential theory and elastostatics both linear and nonlinear model problems are included in our presentation we consider variational formulations based on the combination of mixed finite elements with either boundary integral equations or dirichlet to neumann dtn mappings we provide existence and uniqueness of solution for the continuous formulations and give general approximation estimates for the associated galerkin schemes some open questions are also mentioned

optimal unsupervised learning we introduce an inferential approach to unsupervised learning which allows us to define an optimal learning strategy applying these ideas to a simple previously studied model we show that it is impossible to detect structure in data until a critical number of examples have been presented an effect which will be observed in all problems with certain underlying symmetries thereafter the advantage of optimal learning over previously studied learning algorithms depends critically upon the distribution of patterns optimal learning may be exponentially faster models with more subtle correlations are harder to analyse but in a simple limit of one such problem we calculate exactly the efficacy of an algorithm similar to some used in practice and compare it to that of the optimal prescription

hierarchical unsupervised learning with growing via phase transitions we address unsupervised learning subject to structural constraints with particular emphasis placed on clustering with an imposed decision tree structure most known methods are greedy optimizing one node of the tree at a time to minimize a local cost by constrast we develop a joint optimization method derived based on information theoretic principles and closely related to known methods in statistical physics the approach is inspired by the deterministic annealing algorithm for unstructured data clustering which was based on maximum entropy inference the new approach is founded on the principle of minimum cross entropy using informative priors to approximate the unstructured clustering solution while imposing the structural constraint the resulting method incorporates supervised learning principles applied in an unsupervised problem setting in our approach the tree grows by a sequence of bifurcations that occur while optimizing an effective free energy cost at decreasing temperature scales thus estimates of the tree size and structure are naturally obtained at each temperature in the process examples demonstrate considerable improvement over known methods

coupling of raviart thomas and hybridizable discontinuous galerkin methods with bem we present new a priori error analyses of the coupling of the raviart thomas rt method and bem as well as of the coupling of the hybridizable discontinuous galerkin hdg method with bem the novel features of the analysis of the rt bem coupling are the superconvergence estimates for the scalar approximation of the interior problem and new bounds in weak and strong norms for the boundary variables the analysis of the hdg bem coupling is the first analysis of this coupling and shows that the coupling provides approximations with the same convergence properties as those of the rt bem coupling

linear tail biting trellises characteristic generators and the bcjr construction this paper investigates the constructions of tail biting trellises for linear block codes as introduced by koetter and vardy 2003 and nori and shankar 2006 for a given code the sets of characteristic generators are defined slightly more generally than by koetter and vardy in particular they are not uniquely determined by the code the effect of the choice of characteristic generators on the resulting product trellises called kv trellises is discussed in detail it is shown that each kv trellis is a span based bcjr trellis and that the latter are always nonmergeable finally a duality conjecture posed by koetter and vardy is addressed by making use of a dualization technique of bcjr trellises the conjecture is proven for minimal trellises

hierarchical high order finite element spaces in h div ω h1 ω for a stabilized mixed formulation of darcy problem abstract the classical dual mixed finite element method for flow simulations is based on h div conforming approximation spaces for the flux which guarantees continuous normal components on element interfaces and discontinuous approximations in l 2 for the pressure however stability and convergence can only be obtained for compatible approximation spaces stabilized finite element methods may provide an alternative stable procedure to avoid this kind of delicate balance the main purpose of this paper is to present a high order finite element methodology to solve the darcy problem based on the combination of an unconditionally stable mixed finite element method with a hierarchical methodology for the construction of finite dimensional subspaces of h div and h 1 the chosen stabilized method is free of mesh dependent stabilization parameters and allows for the use of different high order finite element approximations for the flux and the pressure variables without requiring any compatibility constraint as required in mixed methods for these problems convergence studies are presented comparing the numerical solutions obtained for different approximation orders on quadrilateral elements with the ones given by classical mixed formulation with raviart thomas elements

shifts on compact and discrete lie groups algebraic topological invariants and classification problems abstract this paper is devoted to an investigation of various dynamical concepts for group shift systems which are invariant by algebraic conjugacy i e topological conjugacy preserving the group structure the concept of controllability which is stronger than topological transitivity and the concept of limit dimension which is analogous to topological entropy are discussed at length particular attention is dedicated to the abelian case for which duality results are also established

a mixed finite element method for a strongly nonlinear second order elliptic problem the approximation of the solution of the first boundary value problem for a strongly nonlinear second order elliptic problem in divergence form by the mixed finite element method is considered existence and uniqueness of the approximation are proved and optimal error estimates in l 2 are established for both the scalar and vector functions approximated by the method error estimates are also derived in l q 2 q

codes on graphs observability controllability and local reducibility this paper investigates properties of realizations of linear or group codes on general graphs that lead to local reducibility trimness and properness are dual properties of constraint codes a linear or group realization with a constraint code that is not both trim and proper is locally reducible a linear or group realization on a finite cycle free graph is minimal if and only if every local constraint code is trim and proper a realization is called observable if there is a one to one correspondence between codewords and configurations and controllable if it has independent constraints a linear or group realization is observable if and only if its dual is controllable a simple counting test for controllability is given an unobservable or uncontrollable realization is locally reducible parity check realizations are controllable if and only if they have independent parity checks in an uncontrollable tail biting trellis realization the behavior partitions into disconnected sub behaviors but this property does not hold for nontrellis realizations on a general graph the support of an unobservable configuration is a generalized cycle