on the fiedler value of large planar graphs abstract the fiedler value 2 also known as algebraic connectivity is the second smallest laplacian eigenvalue of a graph we study the maximum fiedler value among all planar graphs g with n vertices denoted by 2 max and we show the bounds 2 1 n 2 2 max 2 o 1 n we also provide bounds on the maximum fiedler value for the following classes of planar graphs bipartite planar graphs bipartite planar graphs with minimum vertex degree 3 and outerplanar graphs furthermore we derive almost tight bounds on 2 max for two more classes of graphs those of bounded genus and k h minor free graphs

diameters and eigenvalues we derive a new upper bound for the diameter of a k regular graph g as a function of the eigenvalues of the adjacency matrix namely suppose the adjacency matrix of g has eigenvalues ai a2 a with ia i i vi21 ia i where ai k a ia21 then the diameter d g must satisfy d g we will consider families of graphs whose eigenvalues can be explicitly de termined these graphs are determined by sums or differences of vertex labels namely the pair i j being an edge depends only on the value i j or i j for directed graphs we will show that these graphs are expander graphs with small diameters by using an inequality on character sums which was recently proved by n m katz bell communications research 445 south street morristown new jersey 07960 this content downloaded from 207 46 13 111 on sat 21 may 2016 07 00 04 utc all use subject to http about jstor org terms

a separator theorem for nonplanar graphs let g be an n vertex graph with no minor isomorphic to an h vertex complete graph we prove that the vertices of g can be partitioned into three sets a b c such that no edge joins a vertex in a with a vertex in b neither a nor b contains more than 2n 3 vertices and c contains no more than h312n1 2 vertices this extends a theorem of lipton and tarjan for planar graphs we exhibit an algorithm which finds such a partition a b c in time o h l2n1 2m where m iv g je g l department of mathematics sackler faculty of exact science tel aviv university ramat aviv tel aviv 69978 israel bellcore 445 south street morristown new jersey 07960 dimacs center hill center busch campus rutgers university new brunswick new jersey 08903 school of mathematics georgia institute of technology atlanta georgia 30332 this content downloaded from 157 55 39 207 on thu 20 oct 2016 04 00 05 utc all use subject to http about jstor org terms

total variation structured total least squares method for image restoration in this paper we study the total variation structured total least squares method for image restoration in the image restoration problem the point spread function is corrupted by errors in the model we study the objective function by minimizing two variables the restored image and the estimated error of the point spread function the proposed objective function consists of the data fitting term containing these two variables the magnitude of error and the total variation regularization of the restored image by making use of the structure of the objective function an efficient alternating minimization scheme is developed to solve the proposed model numerical examples are also presented to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme

a unified convergence analysis of block successive minimization methods for nonsmooth optimization the block coordinate descent bcd method is widely used for minimizing a continuous function f of several block variables at each iteration of this method a single block of variables is optimized while the remaining variables are held fixed to ensure the convergence of the bcd method the subproblem of each block variable needs to be solved to its unique global optimal unfortunately this requirement is often too restrictive for many practical scenarios in this paper we study an alternative inexact bcd approach which updates the variable blocks by successively minimizing a sequence of approximations of f which are either locally tight upper bounds of f or strictly convex local approximations of f the main contributions of this work include the characterizations of the convergence conditions for a fairly wide class of such methods especially for the cases where the objective functions are either nondifferentiable or nonconvex our results unify and extend the existing convergence results

design and analysis of optimal controller for fuzzy systems with input constraint in this paper we present a design method of the optimal and robust controller subject to the constraint on control inputs for continuous time takagi sugeno ts fuzzy systems in order to establish this design method we consider an optimal and robust control problem for nonlinear dynamic systems for this problem we present an analytic way which can provide the optimal controller for nonlinear dynamic systems by the dynamic programming approach and the inverse optimal approach moreover we analyze the robustness property of the proposed optimal controller with respect to a class of input uncertainties by the passivity approach then based on the theoretical results presented in this paper we formulate the design problem of the optimal and robust controller with input constraint for continuous time ts fuzzy systems as the semidefinite programming problem and find the controller by solving it the usefulness of the proposed approach is illustrated by considering the three axis attitude stabilization problem of rigid spacecraft

approximation to a class of non autonomous systems by dynamic fuzzy inference marginal linearization method in this paper a dynamic fuzzy inference marginal linearization dfiml method is proposed for modeling nonlinear dynamic systems this method can transfer a group of input output data into a time variant fuzzy system with variable coefficients it is shown that solutions of time variant fuzzy systems generalized by dfiml method are universal approximators to solutions of a class of non autonomous systems also the analytical solutions of these time variant fuzzy systems can be obtained finally a simulation example is provided to illustrate the validity and potential of the developed techniques

two soft thresholding based iterative algorithms for image deblurring iterative regularization algorithms such as the conjugate gradient algorithm for least squares problems cgls and the modified residual norm steepest descent mrnsd algorithm are popular tools for solving large scale linear systems arising from image deblurring problems these algorithms however are hindered by a semi convergence behavior in that the quality of the computed solution first increases and then decreases in this paper in order to overcome the semi convergence behavior we propose two iterative algorithms based on soft thresholding for image deblurring problems one of them combines cgls with a denoising technique like soft thresholding at each iteration and another combines mrnsd with soft thresholding in a similar way we prove the convergence of mrnsd and soft thresholding based algorithm numerical results show that the proposed algorithms overcome the semi convergence behavior and the restoration results are slightly better than those of cgls and mrnsd with their optimal stopping iterations

adaptive control of mimo time varying systems with indicator function based parametrization abstract this paper studies a new solution framework for adaptive control of a class of mimo time varying systems with indicator function based parametrization motivated by a general discrete time mimo takagi sugeno t s fuzzy system model in an input output form with unknown parameters an indicator membership function based parametrization has some favorable capacity to deal with certain large parameter variations a new discrete time mimo system prediction model is derived for approximating a nonlinear dynamic system and its system properties are clarified an adaptive control scheme is developed with desired controller parametrization and stable parameter estimation for control of such uncertain mimo time varying systems a control singularity problem is addressed and the closed loop stability and output tracking properties are analyzed this work provides a new method for multivariable t s fuzzy system modeling and adaptive control an illustrative example and simulation results are presented to demonstrate the proposed novel concepts and to verify the desired adaptive control system performance

on the algebraic connectivity of graphs as a function of genus abstract we find an upper bound on the algebraic connectivity of graphs of various genus we begin by showing that for fixed k 1 the graph of genus k of largest algebraic connectivity is a complete graph we then find an upper bound for noncomplete graphs of a fixed genus k 1 and we determine the values of k for which the upper bound can be attained finally we find the upper bound of the algebraic connectivity of planar graphs graphs of genus zero and determine precisely which graphs attain this upper bound

a tensor higher order singular value decomposition for prestack seismic data noise reduction and interpolation a patch of prestack data depends on four spatial dimensions x y midpoints and x y offsets and frequency the spatial data at one temporal frequency can be represented by a fourth order tensor in ideal conditions of high signal to noise ratio and complete sampling one can assume that the seismic data can be approximated via a low rank fourth order tensor missing samples were recovered by reinserting data obtained by approximating the original noisy and incomplete data volume with new observations obtained via the rank reduction process the higher order singular value decompostion was used to reduce the rank of the prestack seismic tensor synthetic data demonstrated the ability of the proposed seismic data completion algorithm to reconstruct events with curvature the synthetic example allowed to quantify the quality of the reconstruction for different levels of noise and survey sparsity we also provided a real data example from the western canadian sedimentary basin

approximation properties of piece wise parabolic functions fuzzy logic systems spline functions are widely used in the field of approximation theory and its applications in this article we propose the use of p functions which are spline functions of degree two as membership functions of the input variables at first we show by a constructive theory that multi input single output miso sugeno fuzzy logic systems with p input variables membership functions are universal approximators to every continuously differentiable function defined on a compact subset of r n moreover they are of first order approximation accuracy then we show that with appropriately chosen parameters of the p functions fuzzy logic systems with p input variables membership functions are universal approximators not only for the function itself but also for its first order derivative

eigenvalue bounds spectral partitioning and metrical deformations via flows we present a new method for upper bounding the second eigenvalue of the laplacian of graphs our approach uses multi commodity flows to deform the geometry of the graph we embed the resulting metric into euclidean space to recover a bound on the rayleigh quotient using this we show that every n vertex graph of genus g and maximum degree d satisfies 2 g eo g 1 3d n this recovers the o d n bound of spielman and teng for planar graphs and compares to kelner s bound of o g 1 poly d n but our proof does not make use of conformal mappings or circle packings we are thus able to extend this to resolve positively a conjecture of spielman and teng by proving that 2 g e o dh6log h n whenever g is kh minor free this shows in particular that spectral partitioning can be used to recover o sn sized separators in bounded degree graphs that exclude a fixed minor we extend this further by obtaining nearly optimal bounds on 2 for graphs that exclude small depth minors in the sense of plotkin rao and smith consequently we show that spectral algorithms find separators of sublinear size in a general class of geometric graphs moreover while the standard sweep algorithm applied to the second eigenvector may fail to find good quotient cuts in graphs of unbounded degree our approach produces a vector that works for arbitrary graphs this yields an alternate proof of the well known nonplanar separator theorem of alon seymour and thomas that states that every excluded minor family of graphs has o sn node balanced separators

hierarchical ts fuzzy system and its universal approximation an efficient tool to deal with the rule explosion problem is the hierarchical system by which a fuzzy system can be decomposed into a number of hierarchically connected low dimensional systems in this paper a generalized hierarehical tagaki sugeno ts system is built it is shown that the input output i o relationship of this generalized hierarehical system can be represented as one of a standard ts fuzzy system and the system approximation capability is analyzed by taking piecewise linear functions as a bridge by constructive method it is proven that the hierarchical fuzzy systems hfs s can be universal approximators for the given approximation accuracy an estimation formula about the number of the rules needed in the hfs is established finally some simulation examples confirm that the hfs s with smaller size rule base can approximate the given functions with high accuracy the results obtained here provide us with the theoretical basis for various applications of hfs s

analyses for l p μ norm approximation capability of generalized mamdani fuzzy systems abstract the connected piecewise linear functions are introduced to study the l p norm approximation capability of the generalized mamdani fuzzy system it is shown that such general fuzzy systems are the universal approximators to the p integrable functions with l p norm for the given degree of accuracy an upper bound of the fuzzy rule numbers needed in the fuzzy rule base of the system is estimated finally a simulation example is analyzed to demonstrate our conclusions

geometric separators for finite element meshes we propose a class of graphs that would occur naturally in finite element and finite difference problems and we prove a bound on separators for this class of graphs graphs in this class are embedded in d dimensional space in a certain manner for d dimensional graphs our separator bound is o n d 1 d which is the best possible bound we also propose a simple randomized algorithm to find this separator in o n time this separator algorithm can be used to partition the mesh among processors of a parallel computer and can also be used for the nested dissection sparse elimination algorithm

approximation accuracy analysis of fuzzy systems as function approximators this paper establishes the approximation error bounds for various classes of fuzzy systems i e fuzzy systems generated by different inferential and defuzzification methods based on these bounds the approximation accuracy of various classes of fuzzy systems is analyzed and compared it is seen that the class of fuzzy systems generated by the product inference and the center average defuzzifier has better approximation accuracy and properties than the class of fuzzy systems generated by the min inference and the center average defuzzifier and the class of fuzzy systems defuzzified by the mom defuzzifier in addition it is proved that fuzzy systems can represent any linear and multilinear function and explicit expressions of fuzzy systems generated by the mom defuzzified method are given

isoperimetric graph partitioning for image segmentation spectral graph partitioning provides a powerful approach to image segmentation we introduce an alternate idea that finds partitions with a small isoperimetric constant requiring solution to a linear system rather than an eigenvector problem this approach produces the high quality segmentations of spectral methods but with improved speed and stability

approximate counting uniform generation and rapidly mixing markov chains the paper studies effective approximate solutions to combinatorial counting and uniform generation problems using a technique based on the simulation of ergodic markov chains it is shown that for self reducible structures almost uniform generation is possible in polynomial time provided only that randomised approximate counting to within some arbitrary polynomial factor is possible in polynomial time it follows that for self reducible structures polynomial time randomised algorithms for counting to within factors of the form 1 n are available either for all fl e r or for no fi e r a substantial part of the paper is devoted to investigating the rate of convergence of finite ergodic markov chains and a simple but powerful characterisation of rapid convergence for a broad class of chains based on a structural property of the underlying graph is established finally the general techniques of the paper are used to derive an almost uniform generation procedure for labelled graphs with a given degree sequence which is valid over a much wider range of degrees than previous methods this in turn leads to randomised approximate counting algorithms for these graphs with very good

latent space regularization for recommender systems the primary latent factor model cannot effectively optimize the user item latent spaces because of the sparsity and imbalance of the rating data although existing studies have focused on exploring auxiliary information for users or items few researchers have considered users and items jointly for instance social information is incorporated into models without considering the item side in this paper we introduce latent space regularization lsr and provide a general method to improve recommender systems rss by incorporating lsr we take the assumption that users prefer items that cover one or several topics that they are interested in instead of all the topics which reflects real world situations for instance a user may focus on the humorous part of an item when he or she is at leisure time regardless of the relevance of the item to his research topics lsr operates from this assumption to account for both the user and item sides simultaneously from another point of view lsr is likely to improve the tanimoto similarity of observed user item pairs as a result lsr utilizes the number of ratings in a manner similar to weighted matrix factorization we incorporate lsr into both the traditional collaborative filtering models that use only rating information and the collaborative filtering model that uses auxiliary content information as two examples experimental results from on two real world datasets show not only the superiority of our model over other regularization models but also its effectiveness and the possibility of incorporating it into various existing latent factor models

constructing nonlinear variable gain controllers via the takagi sugeno fuzzy control we investigated the analytical structure of the takagi sugeno ts type of fuzzy controllers which was unavailable in the literature the ts fuzzy controllers we studied employ a new and simplified ts control rule scheme in which all the rule consequent use a common function and are proportional to one another greatly reducing the number of parameters needed in the rules other components of the fuzzy controllers are general arbitrary input fuzzy sets any type of fuzzy logic and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case we proved that all these ts fuzzy controllers were nonlinear variable gain controllers and characteristics of the gain variation were parametrized and governed by the rule proportionality we conducted an in depth analysis on a class of nonlinear variable gain proportional derivative pd controllers we present the results to show 1 how to analyze the characteristics of the variable gains in the context of control 2 why the nonlinear variable gain pd controllers can outperform their linear counterpart and 3 how to generate various gain variation characteristics through the manipulation of the rule proportionality

separators for sphere packings and nearest neighbor graphs a collection of n balls in d dimensions forms a k ply system if no point in the space is covered by more than k balls we show that for every k ply system there is a sphere s that intersects at most o k 1 d n 1 1 d balls of and divides the remainder of into two parts those in the interior and those in the exterior of the sphere s respectively so that the larger part contains at most 1 1 d 2 n balls this bound of o k 1 d n 1 1 d is the best possible in both n and k we also present a simple randomized algorithm to find such a sphere in o n time our result implies that every k nearest neighbor graphs of n points in d dimensions has a separator of size o k 1 d n 1 1 d in conjunction with a result of koebe that every triangulated planar graph is isomorphic to the intersection graph of a disk packing our result not only gives a new geometric proof of the planar separator theorem of lipton and tarjan but also generalizes it to higher dimensions the separator algorithm can be used for point location and geometric divide and conquer in a fixed dimensional space

the influence of miroslav fiedler on spectral graph theory abstract this note is a write up of a talk given at the ilas meeting in braunschweig 2011 at the minisymposium celebrating the 80th birthday of miroslav fiedler the purpose of the talk is to outline the impact of fiedler s work on the development of spectral graph theory fiedler is best known for putting forward the algebraic connectivity and its eigenvector these two topics were genuine gold strikes which have motivated thousands of studies in pure and applied science but there is more in fiedler s work that influences spectral graph theory and still more waiting to be discovered

random walk graph laplacian based smoothness prior for soft decoding of jpeg images given the prevalence of joint photographic experts group jpeg compressed images optimizing image reconstruction from the compressed format remains an important problem instead of simply reconstructing a pixel block from the centers of indexed discrete cosine transform dct coefficient quantization bins hard decoding soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors the challenge thus lies in how to define suitable priors and apply them effectively in this paper we combine three image priors laplacian prior for dct coefficients sparsity prior and graph signal smoothness prior for image patches to construct an efficient jpeg soft decoding algorithm specifically we first use the laplacian prior to compute a minimum mean square error initial solution for each code block next we show that while the sparsity prior can reduce block artifacts limiting the size of the overcomplete dictionary to lower computation would lead to poor recovery of high dct frequencies to alleviate this problem we design a new graph signal smoothness prior desired signal has mainly low graph frequencies based on the left eigenvectors of the random walk graph laplacian matrix lerag compared with the previous graph signal smoothness priors lerag has desirable image filtering properties with low computation overhead we demonstrate how lerag can facilitate recovery of high dct frequencies of a piecewise smooth signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering finally we construct a soft decoding algorithm using the three signal priors with appropriate prior weights experimental results show that our proposal outperforms the state of the art soft decoding algorithms in both objective and subjective evaluations noticeably

spectral clustering with epidemic diffusion spectral clustering is widely used to partition graphs into distinct modules or communities existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph laplacian an operator that is closely associated with random walks on graphs we propose a spectral partitioning method that exploits the properties of epidemic diffusion an epidemic is a dynamic process that unlike the random walk simultaneously transitions to all the neighbors of a given node we show that the replicator an operator describing epidemic diffusion is equivalent to the symmetric normalized laplacian of a reweighted graph with edges reweighted by the eigenvector centralities of their incident nodes thus more weight is given to edges connecting more central nodes we describe a method that partitions the nodes based on the componentwise ratio of the replicator s second eigenvector to the first and compare its performance to traditional spectral clustering techniques on synthetic graphs with known community structure we demonstrate that the replicator gives preference to dense clique like structures enabling it to more effectively discover communities that may be obscured by dense intercommunity linking

direct discretization of planar div curl problems a control volume method is proposed for planar div curl systems the method is independent of potential and least squares formulations and works directly with the div curl system the novelty of the technique lies in its use of a single local vector field component and two control volumes rather than the other way round a discrete vector field theory comes quite naturally from this idea and is developed in the paper error estimates are proved for the method and other ramifications investigated

a tearing based hybrid parallel banded linear system solver a new parallel algorithm for the solution of banded linear systems is proposed the scheme tears the coefficient matrix into several overlapped independent blocks in which the size of the overlap is equal to the system s bandwidth a corresponding splitting of the right hand side is also provided the resulting independent and smaller size linear systems are solved under the constraint that the solutions corresponding to the overlap regions are identical this results in a linear system whose size is proportional to the sum of the overlap regions which we refer to as the balance system we propose a solution strategy that does not require obtaining this balance system explicitly once the balance system is solved retrieving the rest of the solution can be realized with almost perfect parallelism our proposed algorithm is a hybrid scheme that combines direct and iterative methods for solving a single banded system of linear equations on parallel architectures it has broad applications in finite element analysis particularly as a parallel solver of banded preconditioners that can be used in conjunction with outer krylov iterative schemes

image restoration using total variation with overlapping group sparsity image restoration is one of the most fundamental issues in imaging science total variation regularization is widely used in image restoration problems for its capability to preserve edges in the literature however it is also well known for producing staircase artifacts in this work we extend the total variation with overlapping group sparsity which we previously developed for one dimension signal processing to image restoration a convex cost function is given and an efficient algorithm is proposed for solving the corresponding minimization problem in the experiments we compare our method with several state of the art methods the results illustrate the efficiency and effectiveness of the proposed method in terms of psnr and computing time

ranks and representations for spectral graph bisection we investigate the minimum graph bisection size according to spectral decompositions of adjacency matrices in several representations e g laplacian 01 adjacency seidel in addition we introduce a class of adjacency matrix representations by including a multiplicative vertex degree along the diagonal of the seidel adjacency matrix the new representation denoted s c often provided smaller spectral bisections in comparison with the other representations for certain classes of graphs by adjusting the multiplicative parameter c the cut size performance varied predictably between the seidel 01 adjacency and laplacian representations for both random graphs and random geometric graphs with various edge probability parameters furthermore we analyzed the cut sizes over many representations according to each eigenvector rank for large classes of random and real world graphs to give experimental evidence that the quality of spectral bisections depends on the eigenvector rank representation and graph type ultimately we provide evidence that particular ranks and representations are predictably more appropriate for use with certain types of graphs in general the related laplacian and s 2 0 representations produced the smallest cuts for geometric graphs whereas the seidel 01 adjacency and s c with 0 leq c leq1 produced the smallest cuts for random graphs we anticipate that our results will provide motivation for a unifying theorem of spectral bisection across eigenvector ranks adjacency representations and graph types

on estimating the largest eigenvalue with the lanczos algorithm the lanczos algorithm applied to a positive definite matrix produces good approximations to the eigenvalues at the extreme ends of the spectrum after a few iterations in this note we utilize this behavior and develop a simple algorithm which computes the largest eigenvalue the algorithm is especially economical if the order of the matrix is large and the accuracy requirements are low the phenomenon of misconvergence is discussed some simple extensions of the algorithm are also indicated finally some numerical examples and a comparison with the power method are given

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

performance enhancement for t s fuzzy control using neural networks a new control scheme is proposed to improve the system performance for takagi sugeno t s fuzzy system using control grade functions tuned by neural networks first systematic modeling method is introduced to construct the exact t s fuzzy model for a nonlinear control system for the t s fuzzy model the system uncertainty affects only the membership functions to cope with this problem the grade functions resulting from the membership functions of the control rules are tuned by a back propagation network on the other hand the feedback gains of the control rules are determined by solving a set of linear matrix inequalities lmis which satisfy sufficient conditions of the closed loop stability as a result both stability guarantee and better performance are concluded the scheme is applied to a ball and beam system example verified by numerical simulations

fuzzy systems as universal approximators an additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy an additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input output state space and averaging patches that overlap the fuzzy system computes a conditional expectation e y x if we view the fuzzy sets as random sets each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state space geometry neural or statistical clustering systems can approximate the unknown fuzzy patches from training data these adaptive fuzzy systems approximate a function at two levels at the local level the neural system approximates and tunes the fuzzy rules at the global level the rules or patches approximate the function

sufficient conditions on general fuzzy systems as function approximators abstract in a constructive way we have found sufficient conditions under which general fuzzy systems can uniformly approximate any real continuous function on a compact domain to any degree of accuracy more importantly we have revealed the underlying mechanism of such function approximation the fuzzy systems can uniformly approximate any polynomials which according to the weierstrass approximation theorem can uniformly approximate any continuous function on a compact domain these findings lead to the following practical results 1 explicit fuzzy rules of fuzzy systems can now be easily obtained according to functions to be approximated and 2 formulas are derived which can calculate the number of input fuzzy sets output fuzzy sets and fuzzy rules needed in order to satisfy any given approximation accuracy the number increases as required approximation error decreases and as approximation error approaches zero the number approaches these formulas also reveal that the number is minimal when the maximum number of intersection between adjacent input fuzzy sets is one practical implications of these results will be discussed especially in the context of fuzzy control and fuzzy modeling two examples are provided to demonstrate how to design fuzzy systems to approximate given functions with required approximation accuracy

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

sufficient conditions for the stability of linear takagi sugeno free fuzzy systems in this paper we will study the stability issues of the linear takagi sugeno t s free fuzzy systems based on matrix norm we propose a new sufficient condition for the linear t s free fuzzy system to be globally asymptotically stable we then study the stability analysis in the case of systems with consequent parameter uncertainty based on mayer s convergent theorem we propose a sufficient condition which is easily implemented for the systems with consequent parameter uncertainty to be globally asymptotically stable

technical communique extending the domain of definition of functional series for nonlinear systems functional series are the basis of much of existing nonlinear system theory the present note extends the well known local series beyond its radius of convergence to describe the entire system trajectory for as long as it exists first steps towards a generalization to systems defined on analytic manifolds are made

sugeno type controllers are universal controllers abstract we show that given any continuous real valued function on a compact set there is a sugeno type controller that will approximate this function to any degree of accuracy an application of this result to fuzzy control is presented which shows that this type of sugeno controller is a universal controller

approximation of stochastic processes by t s fuzzy systems fuzzy systems can provide us with universal approximation models of deterministic input output relationships but in the stochastic environment few achievements related to the subject have so far achieved in the paper a novel stochastic takagi sugeno t s fuzzy system is introduced to represent approximately existing randomness in many real world systems by recapitulating the general architecture of the stochastic t s fuzzy rule based system we analyze systematically approximating capability of the stochastic system to a class of stochastic processes by the canonical representation of the stochastic processes the stochastic fuzzy system is capable of with arbitrary accuracy providing the approximation to the stochastic processes in mean square sense finally an efficient algorithm for the stochastic t s fuzzy system is developed a simulation example demonstrates how a stochastic t s fuzzy system can be constructed to realize the given stochastic process approximately

support vector learning for fuzzy rule based classification systems to design a fuzzy rule based classification system fuzzy classifier with good generalization ability in a high dimensional feature space has been an active research topic for a long time as a powerful machine learning approach for pattern recognition problems the support vector machine svm is known to have good generalization ability more importantly an svm can work very well on a high or even infinite dimensional feature space this paper investigates the connection between fuzzy classifiers and kernel machines establishes a link between fuzzy rules and kernels and proposes a learning algorithm for fuzzy classifiers we first show that a fuzzy classifier implicitly defines a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function fuzzy inference on the if part of a fuzzy rule can be viewed as evaluating the kernel function the kernel function is then proven to be a mercer kernel if the reference functions meet a certain spectral requirement the corresponding fuzzy classifier is named positive definite fuzzy classifier pdfc a pdfc can be built from the given training samples based on a support vector learning approach with the if part fuzzy rules given by the support vectors since the learning process minimizes an upper bound on the expected risk expected prediction error instead of the empirical risk training error the resulting pdfc usually has good generalization moreover because of the sparsity properties of the svms the number of fuzzy rules is irrelevant to the dimension of input space in this sense we avoid the curse of dimensionality finally pdfcs with different reference functions are constructed using the support vector learning approach the performance of the pdfcs is illustrated by extensive experimental results comparisons with other methods are also provided

provably good partitioning and load balancing algorithms for parallel adaptive n body simulation we present an efficient and provably good partitioning and load balancing algorithm for parallel adaptive n body simulation the main ingredient of our method is a novel geometric characterization of a class of communication graphs that can be used to support hierarchical n body methods such as the fast multipole method fmm and the barnes hut method bh we show that communication graphs of these methods have a good partition that can be found efficiently sequentially and in parallel in particular we show that an n body communication graph either for bh or for fmm can be partitioned into two subgraphs with equal computation load by removing only o sqrt n log n and o n2 3 log n 1 3 number of nodes respectively for two and three dimensions these bounds on node partition imply bounds on edge partition of o sqrt n log n 3 2 and o n2 3 log n 4 3 respectively for two and three dimensions to the best of our knowledge this is the first theoretical result on the quality of partitioning n body communication graphs for nonuniformly distributed particles our results imply that parallel adaptive n body simulation can be made as scalable as computation on regular grids and as efficient as parallel n body simulation on uniformly distributed particles

commute times for a directed graph using an asymmetric laplacian the expected commute times for a strongly connected directed graph are related to an asymmetric laplacian matrix as a direct extension to similar well known formulas for undirected graphs we show the close relationships between the asymmetric laplacian and the so called fundamental matrix we give bounds for the commute times in terms of the stationary probabilities for a random walk over the graph together with the asymmetric laplacian and show how this can be approximated by a symmetrized laplacian derived from a related weighted undirected graph

regular paper the takagi sugeno fuzzy controllers using the simplified linear control rules are nonlinear variable gain controllers takagi sugeno ts for short fuzzy controllers have been used and treated as black box controllers and there exists no explicit structure of any ts fuzzy controller in the literature in this paper we investigate the analytical structure of the ts fuzzy controllers that use our newly introduced simplified ts control rule scheme our scheme requires that all the rule consequent employ a common linear function and be proportional to one another the scheme drastically reduces the number of adjustable parameters required by the original ts rule scheme product fuzzy logic and was employed in the rule antecedents we theoretically proved that the ts controllers using the simplified rule scheme were nonlinear variable gain controllers the proportionality of the rule consequent parameterized the gain variation characteristics as special cases the ts controllers with three or two input variables and the simplified linear rule consequent were nonlinear variable gain pid pi or pd controllers as an illustration we mathematically analyzed the nonlinear variable gain pi controllers and revealed that the gain variation empowered the controllers to outperform their linear counterparts stability of the nonlinear pi control systems was also addressed a practical example is given to show how to achieve the desired characteristics of the gain variation by properly designing the simplified rules

topic tensor factorization for recommender system reviews are collaboratively generated by users on items and generally contain rich information than ratings in a recommender system scenario ratings are modeled successfully with latent space models by capturing interaction between users and items however only a few models collaboratively deal with documents such as reviews in this study by modeling reviews as a three order tensor we propose a refined tensor topic model ttm for text tensors inspired by tucker decomposition user and item dimensions are co reduced with vocabulary space and interactions between users and items are captured using a core tensor in dimension reduced form ttm is proposed to obtain low rank representations of words as well as of users and items furthermore general rules are developed to transform a decomposition model into a probabilistic model ttm is augmented further to predict ratings with the assistance of a low dimensional representation of users and items obtained by ttm this augmented model is called matrix factorization by learning a bilinear map a core regularized version is further developed to incorporate additional information from the ttm encouraging experimental results not only show that the ttm outperforms existing topic models in modeling texts with a user item word structure but also show that our proposed rating prediction models outperform state of the art approaches

a note on fiedler value of classes with sublinear separators abstract the n th fiedler value of a class of graphs c is the maximum second eigenvalue 2 g of a graph g c with n vertices in this note we relate this value to shallow minors and as a corollary we determine the right order of the n th fiedler value for some minor closed classes of graphs including the class of planar graphs

kernel shapes of fuzzy sets in fuzzy systems for function approximation the shapes of if part fuzzy sets affect the approximating capability of fuzzy systems in this paper the fuzzy systems with the kernel shaped if part fuzzy sets are built directly from the training data it is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single input single output siso case on the basis of these rates the relationships between the approximating capability and the shapes of if part fuzzy sets are developed for the fuzzy systems furthermore the sinc functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions the theoretical results are confirmed from the simulation data in addition the estimations of the uniform approximation rates are extended to the multi input single output miso case

spectral partitioning eigenvalue bounds and circle packings for graphs of bounded genus in this paper we address two long standing questions about finding good separators in graphs of bounded genus and degree 1 it is a classical result of gilbert hutchinson and tarjan j algorithms 5 1984 pp 391 407 that one can find asymptotically optimal separators on these graphs if given both the graph and an embedding of it onto a low genus surface does there exist a simple efficient algorithm to find these separators given only the graph and not the embedding 2 in practice spectral partitioning heuristics work extremely well on these graphs is there a theoretical reason why this should be the case we resolve these two questions by showing that a simple spectral algorithm finds separators of cut ratio o sqrt smash b g n and vertex bisectors of size o sqrt gn in these graphs both of which are optimal as our main technical lemma we prove an o g n bound on the second smallest eigenvalue of the laplacian of such graphs and show that this is tight thereby resolving a conjecture of spielman and teng while this lemma is essentially combinatorial in nature its proof comes from continuous mathematics drawing on the theory of circle packings and the geometry of compact riemann surfaces

a vibrational approach to node centrality and vulnerability in complex networks we propose a new measure of vulnerability of a node in a complex network the measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs we define the measure as the node displacement or the amplitude of vibration of each node under fluctuation due to the thermal bath in which the network is supposed to be submerged we prove exact relations among the thus defined node displacement the information centrality and the kirchhoff index the relation between the first two suggests that the node displacement has a better resolution of the vulnerability than the information centrality because the latter is the sum of the local node displacement and the node displacement averaged over the entire network

a generalized grid connectivity based parameterization for subsurface flow model calibration 1 we develop a novel method of parameterization for spatial hydraulic property characterization to mitigate the challenges associated with the nonlinear inverse problem of subsurface flow model calibration the parameterization is performed by the projection of the estimable hydraulic property field onto an orthonormal basis derived from the grid connectivity structure the basis functions represent the modal shapes or harmonics of the grid are defined by a modal frequency and converge to special cases of the discrete fourier series under certain grid geometries and boundary assumptions therefore hydraulic property updates are performed in the spectral domain and merge with fourier analysis in ideal cases dependence on the grid alone implies that the basis may characterize any grid geometry including corner point and unstructured is model independent and is constructed off line and only once prior to flow data assimilation we apply the parameterization in an adaptive multiscale model calibration workflow for three subsurface flow models several different grid geometries are considered in each case the prior hydraulic property model is updated using a parameterized multiplier field that is superimposed onto the grid and assigned an initial value of unity at each cell the special case corresponding to a constant multiplier is always applied through the constant basis function higher modes are adaptively employed during minimization of data misfit to resolve multiscale heterogeneity in the geomodel the parameterization demonstrates selective updating of heterogeneity at locations and spatial scales sensitive to the available data otherwise leaving the prior model unchanged as desired

general siso takagi sugeno fuzzy systems with linear rule consequent are universal approximators takagi sugeno ts fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice virtually all the ts fuzzy systems use linear rule consequent at present there exist no results qualitative or quantitative to answer the fundamentally important question that is especially critical to ts fuzzy systems as fuzzy controllers and models are ts fuzzy systems with linear rule consequent universal approximators if the answer is yes then how can they be constructed to achieve prespecified approximation accuracy and what are the sufficient renditions on systems configuration in this paper we provide answers to these questions for a general class of single input single output siso fuzzy systems that use any type of continuous input fuzzy sets ts fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifier as a special case we first constructively prove that this general class of siso ts fuzzy systems can uniformly approximate any polynomial arbitrarily well and then prove by utilizing the weierstrass approximation theorem that the general ts fuzzy systems can uniformly approximate any continuous function with arbitrarily high precision furthermore we have derived a formula as part of sufficient conditions for the fuzzy approximation that can compute the minimal upper bound on the number of input fuzzy sets and rules needed for any given continuous function and prespecified approximation error bound an illustrative numerical example is provided

a hierarchical o n force calculation algorithm a novel code for the approximate computation of long range forces between n mutually interacting bodies is presented the code is based on a hierarchical tree of cubic cells and features mutual cell cell interactions which are calculated via a cartesian taylor expansion in a symmetric way such that total momentum is conserved the code benefits from an improved and simple multipole acceptance criterion that reduces the force error and the computational effort for n 104 the computational costs are found empirically to rise sublinearly with n for applications in stellar dynamics this is the first competitive code with complexity o n it is faster than the standard tree code by a factor of 10 or more

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

asymptotic theory of eigenvectors for random matrices with diverging spikes characterizing the asymptotic distributions of eigenvectors for large random matrices poses important challenges yet can provide useful insights into a range of statistical applications to this en

spectral clustering and the high dimensional stochastic blockmodel networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors social ne tworks representing people who communicate with each other are one example communities or clusters of highly connected actors form an essential feature in the structure of several empirical networks spectral clustering is a popular and computationally feasi ble method to discover these communities the stochastic block model holland et al 1983 is a social network model with well defined communities each node is a member of one community for a network generated from the stochastic block model we bound the number of nodes misclus tered by spectral clustering the asymptotic results in th is paper are the first clustering results that allow the number of clusters in the model to grow with the number of nodes hence the name high dimensional in order to study spectral clustering under the stochastic block model we first show that under the more general latent space model the eigenvectors of the normalized graph laplacian asymptotically converge to the eigenvectors of a population normal ized graph laplacian aside from the implication for spectral clustering this provides insight into a graph visualization technique our method of studying the eigenvectors of random matrices is original ams 2000 subject classifications primary 62h30 62h25 secondary 60b20

ordering trees and graphs with few cycles by algebraic connectivity abstract several approaches for ordering graphs by spectral parameters are presented in the literature we can find graph orderings either by the greatest eigenvalue spectral radius or index or by the sum of the absolute values of the eigenvalues the energy of a graph or by the second smallest eigenvalue of the laplacian matrix the algebraic connectivity among others by considering the fact that the algebraic connectivity is related to the connectivity and shape of the graphs several structural properties of graphs relative to this parameter have been studied hence a large number of papers about ordering graphs by algebraic connectivity mainly about trees and graphs with few cycles have been published this paper surveys the significant results concerning these topics trying to focus on possible points to be investigated in order to understand the difficulties to obtain partial orderings via algebraic connectivity

stable indirect adaptive control based on discrete time t s fuzzy model this paper presents an indirect adaptive fuzzy control scheme for uncertain nonlinear asymptotically stable plants a discrete time t s fuzzy input output model is employed to approximate the unknown plant dynamics the t s fuzzy model is fed with its own states which are indeed its past outputs rather than the measurements from the plants entirely based on this model a feedback linearization control law is designed by using the model structure model parameters and model states and then applied to control the model and the plant premise and consequent parameters of the model are updated on line by gradient descent algorithm and recursive least square estimation method using plant output measurements stability analysis shows that if there the model structure is accurate the adaptive controller achieves the bounded tracking error and boundedness of all the closed loop signals in the ideal case where the signals are persistently exciting during the model parameter adaptation a perfect asymptotic tracking is ensured the effectiveness of the method is verified by simulation application to siso and mimo example plants

a unified definition and computation of laplacian spectral distances abstract laplacian spectral kernels and distances e g biharmonic heat diffusion wave kernel distances are easily defined through a filtering of the laplacian eigenpairs they play a central role in several applications such as dimensionality reduction with spectral embeddings diffusion geometry image smoothing geometric characterisations and embeddings of graphs extending the results recently derived in the discrete setting 38 39 to the continuous case we propose a novel definition of the laplacian spectral kernels and distances whose approximation requires the solution of a set of inhomogeneous laplace equations their discrete counterparts are equivalent to a set of sparse symmetric and well conditioned linear systems which are efficiently solved with iterative methods finally we discuss the optimality of the laplacian spectrum for the approximation of the spectral kernels the relation between the spectral and green kernels and the stability of the spectral distances with respect to the evaluation of the laplacian spectrum and to multiple laplacian eigenvalues

a partial k arboretum of graphs with bounded treewidth the notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies this survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class also some mutual relations between such classes are discussed

tensor completion using total variation and low rank matrix factorization in this paper we study the problem of recovering a tensor with missing data we propose a new model combining the total variation regularization and low rank matrix factorization a block coordinate decent bcd algorithm is developed to efficiently solve the proposed optimization model we theoretically show that under some mild conditions the algorithm converges to the coordinatewise minimizers experimental results are reported to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme

spectral partitioning works planar graphs and finite element meshes abstract spectral partitioning methods use the fiedler vector the eigenvector of the second smallest eigenvalue of the laplacian matrix to find a small separator of a graph these methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well in this paper we show that spectral partitioning methods work well on bounded degree planar graphs and finite element meshes the classes of graphs to which they are usually applied while naive spectral bisection does not necessarily work we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is o n for bounded degree planar graphs and two dimensional meshes and o n1 d for well shaped d dimensional meshes the heart of our analysis is an upper bound on the second smallest eigenvalues of the laplacian matrices of these graphs we prove a bound of o 1 n for bounded degree planar graphs and o 1 n2 d for well shaped d dimensional meshes

necessary conditions for some typical fuzzy systems as universal approximators abstract we investigate necessary conditions for general single input single output fuzzy systems and a class of typical multiple input single output fuzzy systems as universal approximators for continuous functions defined on compact domains with arbitrarily small uniform approximation error bounds considering the case where the only available data about the continuous function to be approximated are a finite set of its extrema we have established some necessary conditions for the fuzzy systems to be universal approximators of the function the conditions can be used practically to determine input fuzzy sets output fuzzy sets and fuzzy rules of the fuzzy systems furthermore these necessary conditions provide a basis for insightful analysis of the strengths as well as the limitations of the fuzzy systems the main strength is that only a small number of fuzzy rules may be needed to uniformly approximate continuous functions that have a complicated formulation but a relatively small number of extrema the limitation is that in order to approximate highly oscillatory continuous functions the number of fuzzy rules must be large 1997 elsevier science ltd

fuzzy control as a universal control tool abstract it is known that fuzzy control is a universal control tool because an arbitrary control strategy in particular a control strategy that is in some sense optimal can be obtained in principle by applying a fuzzy control methodology to some set of rules this result has already been proved e g 2 7 20 21 for the case when a plant is described by finitely many parameters and a special type of fuzzy control methodology is used in this paper we prove it for arbitrary plants including plants that are distributed systems i e plants whose state requires infinitely many parameters to describe and arbitrary fuzzy control methodologies we also prove that there exists a universal fuzzy controller that generates an appropriate control from an input description of a plant and the desired objective mathematically we prove that fuzzy systems can approximate arbitrary continuous functionals thus generalizing a known result about continuous functions

an experimental study on nonlinear function computation for neural fuzzy hardware design an experimental study on the influence of the computation of basic nodal nonlinear functions on the performance of nfss is described in this paper systems architecture size their approximation capability and the smoothness of provided mappings are used as performance indexes for this comparative paper two widely used kernel functions the sigmoid logistic function and the gaussian function are analyzed by their computation through an accuracy controllable approximation algorithm designed for hardware implementation two artificial neural network ann paradigms are selected for the analysis backpropagation neural networks bpnns with one hidden layer and radial basis function rbf networks extensive simulation of simple benchmark approximation problems is used in order to achieve generalizable conclusions for the performance analysis of fuzzy systems a functional equivalence theorem is used to extend obtained results to fuzzy inference systems fiss finally the adaptive neurofuzzy inference system anfis paradigm is used to observe the behavior of neurofuzzy systems with learning capabilities

dynamic output feedback control for continuous time t s fuzzy systems using fuzzy lyapunov functions a novel relaxation approach is proposed for the analysis and dynamic output feedback control of continuous time takagi sugeno t s fuzzy systems using fuzzy lyapunov functions previous relaxation methods for t s fuzzy systems have some drawbacks in relaxing quadratic functions depending on normalized fuzzy weighting functions they often introduce conservatism or lead to computational difficulty in analysis and control synthesis different from previous works the proposed approach employs linear fractional transformation mechanism and full block s procedure to reduce the conservatism in analysis furthermore the relaxation technique proposed in this paper can be used in solving the controller synthesis problem effectively as a result a design procedure of a nonparallel distributed compensation output feedback controller which ensures asymptotic stability and optimizes mathcal l 2 gain performance of the closed loop systems is provided several examples have been used to illustrate the advantages and efficiency of the proposed method extensively

a comparative study on sufficient conditions for takagi sugeno fuzzy systems as universal approximators universal approximation is the basis of theoretical research and practical applications of fuzzy systems studies on the universal approximation capability of fuzzy systems have achieved great progress in recent years in this paper linear takagi sugeno ts fuzzy systems that use linear functions of input variables as rule consequent and their special case named simplified fuzzy systems that use fuzzy singletons as rule consequent are investigated on condition that overlapped fuzzy sets are employed new sufficient conditions for simplified fuzzy systems and linear ts fuzzy systems as universal approximators are given respectively then a comparative study on existing sufficient conditions is carried out with numeric examples

approximation theory of fuzzy systems spl minus siso case in this paper the approximation properties of mimo fuzzy systems generated by the product inference are discussed we first give an analysis of fuzzy basic functions fbf s and present several properties of fbf s based on these properties of fbf s we obtain several basic approximation properties of fuzzy systems 1 basic approximation property which reveals the basic approximation mechanism of fuzzy systems 2 uniform approximation bounds which give the uniform approximation bounds between the desired control or decision functions and fuzzy systems 3 uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions and 4 universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect the similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds

analysis and design of time variant fuzzy systems based on dynamic fuzzy inference in this paper a class of time variant fuzzy systems is designed and analyzed firstly a novel model of dynamic fuzzy inference dfi is proposed and the corresponding dfi method is obtained then the response abilities of time variant fuzzy systems constructed by the dfi method are analyzed some sufficient conditions for time variant fuzzy systems as step functions fitted functions and interpolation functions are derived furthermore a sufficient and necessary condition for time variant fuzzy systems as interpolation functions is also deduced in addition the approximation problem of time variant fuzzy systems is discussed it is proved that time variant fuzzy systems constructed by the dfi method are universal approximators to a class of nonlinear systems in addition the approximation accuracy of the corresponding time variant fuzzy systems is investigated finally a simulation experiment is provided to demonstrate how to design a time variant fuzzy system in order to approximate a given nonlinear system to a desired accuracy