rough support vector regression abstract this paper describes the relationship between support vector regression svr and rough or interval patterns svr is the prediction component of the support vector techniques rough patterns are based on the notion of rough values which consist of upper and lower bounds and are used to effectively represent a range of variable values predictions of rough values in a variety of different forms within the context of interval algebra and fuzzy theory are attracting research interest an extension of svr called rough support vector regression rsvr is proposed to improve the modeling of rough patterns in particular it is argued that the upper and lower bounds should be modeled separately the proposal is shown to be a more flexible version of lower possibilistic regression model using insensitivity experimental results on the dow jones industrial average demonstrate the suggested rsvr modeling technique

note on basic features of large time behaviour of heat kernels large time behaviour of heat semigroups and more gener ally of positive selfadjoint semigroups is studied convergence of the semigroup to the ground state and of averaged logarithms of kernels to the ground state energy is shown in the general framework of positivity improving selfadjoint semigroups this framework includes laplacians on manifolds metric graphs and discrete graphs

light structures in infinite planar graphs without the strong isoperimetric property it is shown that the discharging method can be successfully applied on infinite planar graphs of subexponential growth and even on those graphs that do not satisfy the strong edge isoperimetric inequality the general outline of the method is presented and the following applications are given planar graphs with only finitely many vertices of degree 5 and with subexponential growth contain arbitrarily large finite submaps of the tessellation of the plane or of some tessellation of the cylinder by equilateral triangles every planar graph with isoperimetric number zero and with essential minimum degree 3 has infinitely many edges whose degree sum is at most 15 in particular this holds for all graphs with minimum degree 3 and with subexponential growth the cases without infinitely many edges whose degree sum is 14 or similarly 13 or 12 are also considered several further results are obtained

oversampled filter banks as error correcting codes theory and impulse noise correction oversampled filter banks ofbs provide an overcomplete representation of their input signal this paper describes how ofbs can be considered as error correcting codes acting on real or complex sequences very much like classical binary convolutional codes act on binary sequences the structured redundancy introduced by ofbs in subband signals can be used to increase robustness to noise in this paper we define the notions of code subspace syndrome and parity check polynomial matrix for ofbs furthermore we derive generic expressions for projection based decoding suitable for the case when a simple second order model completely characterizes the noise incurred by subband signals we also develop a nonlinear hypotheses test based decoding algorithm for the case when the noise in subbands is constituted by a gaussian background noise and impulsive errors a model that adequately describes the action of both quantization noise and transmission errors simulation results show that the algorithm effectively removes the effect of impulsive errors occurring with a probability of 10 sup 3

conservative and aggressive rough svr modeling support vector regression provides an alternative to the neural networks in modeling non linear real world patterns rough values with a lower and upper bound are needed whenever the variables under consideration cannot be represented by a single value this paper describes two approaches for the modeling of rough values with support vector regression svr one approach by attempting to ensure that the predicted high value is not greater than the upper bound and that the predicted low value is not less than the lower bound is conservative in nature on the contrary we also propose an aggressive approach seeking a predicted high which is not less than the upper bound and a predicted low which is not greater than the lower bound the proposal is shown to use e insensitivity to provide a more flexible version of lower and upper possibilistic regression models the usefulness of our work is realized by modeling the rough pattern of a stock market index and can be taken advantage of by conservative and aggressive traders

solving boundary value problems on networks using equilibrium measures abstract the purpose of this paper is to construct solutions of self adjoint boundary value problems on finite networks to this end we obtain explicit expressions of the green functions for all different boundary value problems the method consists of reducing each boundary value problem either to a dirichlet problem or to a poisson equation on a new network closely related with the former boundary value problem in this process we also get an explicit expression of the poisson kernel for the dirichlet problem in all cases we express the green function in terms of equilibrium measures solely which can be obtained as the unique solution of linear programming problems in particular we get analytic expressions of the green function for the following problems the poisson equation on a distance regular graph the dirichlet problem on an infinite distance regular graph and the neumann problem on a ball of an homogeneous tree

reduction to least squares estimates in multiple fuzzy regression analysis in this paper we deal with the problem of least squares multiple regression with fuzzy data the regression coefficients are assumed to be real crisp a formula for solving the regression coefficients in one variable models is derived if each independent variable is effective i e its corresponding regression coefficient is nonzero the multiple regression problem can be replaced with a 0 1 programming problem its optimal solution is easily computed finally we also propose effective algorithms to compute the regression coefficients in a general case

graphical designs and extremal combinatorics abstract a graphical design is a proper subset of vertices of a graph on which many eigenfunctions of the laplacian operator have mean value zero in this paper we show that extremal independent sets make extremal graphical designs that is a design on which the maximum possible number of eigenfunctions have mean value zero we then provide examples of such graphs and sets which arise naturally in extremal combinatorics we also show that sets which realize the isoperimetric constant of a graph make extremal graphical designs and provide examples for them as well we investigate the behavior of graphical designs under the operation of weak graph product in addition we present a family of extremal graphical designs for the hypercube graph

partially overdetermined elliptic boundary value problems we consider semilinear elliptic dirichlet problems in bounded domains overdetermined with a neumann condition on a proper part of the boundary under different kinds of assumptions we show that these problems admit a solution only if the domain is a ball when these assumptions are not fulfilled we discuss possible counterexamples to symmetry we also consider neumann problems overdetermined with a dirichlet condition on a proper part of the boundary and the case of partially overdetermined problems on exterior domains

fuzzy nonparametric regression based on local linear smoothing technique in a great deal of literature on fuzzy regression analysis most of research has focused on some predefined parametric forms of fuzzy regression relationships especially on the fuzzy linear regression models in many practical situations it may be unrealistic to predetermine a fuzzy parametric regression relationship in this paper a fuzzy nonparametric model with crisp input and lr fuzzy output is considered and based on the distance measure for fuzzy numbers suggested by diamond p diamond fuzzy least squares information sciences 46 1988 141 157 the local linear smoothing technique in statistics with the cross validation procedure for selecting the optimal value of the smoothing parameter is fuzzified to fit this model some simulation experiments are conducted to examine the performance of the proposed method and three real world datasets are analyzed to illustrate the application of the proposed method the results demonstrate that the proposed method works quite well not only in producing satisfactory estimate of the fuzzy regression function but also in reducing the boundary effect significantly

a possibilistic regression based on gradual interval b splines application for hyperspectral imaging lake sediments abstract according to an epistemic view of intervals this paper proposes a possibilistic regression based on gradual interval b splines to represent the input output data mapping in this context an improvement of the parametric fuzzy regression through the notion of gradual interval b splines is proposed the proposed gradual regression based on b splines can be regarded as an extension of the nonparametric interval based regression where an uncertain dimension is integrated the proposed method is validated through illustrative and comparative examples moreover it is applied for modeling the input output behavior between reflectance and wavelengths in an application for hyperspectral imaging for lake sediments

serrin type overdetermined problems an alternative proof we prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations namely the hessian equations in the case of the poisson equation our proof is alternative to the proofs proposed by serrin moving planes and by weinberger moreover our proof makes no direct use of the maximum principle while it sheds light on a relation between the serrin problem and the isoperimetric inequality

a fuzzy varying coefficient model and its estimation the fuzzy linear regression model has been a useful tool for analyzing relationships between a set of variables in a fuzzy environment and has been extensively studied in the literature however this model may fail to reflect the more complicated regression relationships that are usually found in practice because of its simple and predefined linear structure in order to enhance the feasibility and adaptability of the fuzzy linear models we propose in this paper a fuzzy varying coefficient model in which the fuzzy coefficients in the fuzzy linear models are allowed to vary with a covariate a restricted weighted least squares estimation is suggested for locally fitting the model furthermore some real world datasets are analyzed in order to evaluate the performance of the proposed method and the results show that the proposed model with its estimation approach performs satisfactorily in predicting the fuzzy response even in the case where the regression relationship is complicated

hybrid fuzzy least squares regression analysis and its relibabilty measures a method for hybrid fuzzy least squares regression is developed in this paper the method uses the new definition of weighted fuzzy arithmetic and the well accepted least squares fitting criterion first a bivariate regression model using asymmetrical triangular fuzzy variables is derived three sets of normal equations are formulated to solve the three parts of hybrid regression coefficients fuzzy center left fuzzy width and right fuzzy width then the method is extended to multiple regression analysis three numerical examples are used to demonstrate the proposed method two bivariate regression examples one for symmetrical triangular fuzzy numbers and the other for asymmetrical triangular fuzzy numbers and one multiple regression example for symmetrical triangular fuzzy numbers in each example hybrid regression equation and their reliability measures are calculated the results from hybrid regression are also compared with the corresponding results from ordinary regression and other fuzzy regression methods conclusions are drawn based on the reliability evaluations furthermore hybrid fuzzy least squares regression is extended to nonlinear models issues on the calibration of nonlinear equations and their reliability measures are also discussed in conclusions the merits and limitations of the proposed method are summarized

joint source channel coding using real bch codes for robust image transmission in this paper a new still image coding scheme is presented in contrast with standard tandem coding schemes where the redundancy is introduced after source coding it is introduced before source coding using real bch codes a joint channel model is first presented the model corresponds to a memoryless mixture of gaussian and bernoulli gaussian noise it may represent the source coder the channel coder the physical channel and their corresponding decoder decoding algorithms are derived from this channel model and compared to a state of art real bch decoding scheme a further comparison with two reference tandem coding schemes and the proposed joint coding scheme for the robust transmission of still images has been presented when the tandem scheme is not accurately tuned the joint coding scheme outperforms the tandem scheme in all situations compared to a tandem scheme well tuned for a given channel situation the joint coding scheme shows an increased robustness as the channel conditions worsen the soft performance degradation observed when the channel worsens gives an additional advantage to the joint source channel coding scheme for fading channels since a reconstruction with moderate quality may be still possible even if the channel is in a deep fade

every covering of a compact riemann surface of genus greater than one carries a nontrivial l2 harmonic differential this paper contains the proof of the assertion in its title my motivation for considering this problem was the following let m be a compact differentiable manifold and let d be an elliptic differential operator between the spaces of c sections of two bundles on m in 4 m f atiyah proves that if index d 0 then for every galois covering at m the operator induced by d on has nontrivial l 2 solutions u 0 atiyah goes on to ask whether the same is true for coverings which are not galois his guess is that the answer is negative in general but that the counter example will be difficult to construct the simplest situation to consider in this connection is that of a surface and the operator whose index is the euler characteristic for infinite coverings since every l 2 harmonic function would be constant and nonzero constants are not in l 2 atiyah s question reduces to the question of existence of l 2 harmonic forms of degree one it is shown here that a counter example will not be found in this simple setting from now on s will denote an oriented compact surface of genus g g s l equipped with a smooth riemannian metric s s will be an arbitrary usually infinite covering of s and a a will be the laplace operator on s with respect to the pull back metric a differential exterior form of degree one on s is harmonic i e ao 0 and in l 2 if and only if cf 15 theorem 26

isoperimetric inequalities and transient random walks on graphs recurrent we show that any graph satisfying an isoperimetric inequality only slightly stronger than that of z2 is transient more precisely if f k denotes the smallest number of vertices in the boundary of a connected subgraph with k vertices then the graph is transient if the infinite sum e f k 2 converges this can be applied to parabolicity versus hyperbolicity of surfaces 1 introduction let g be a connected graph which is locally finite that is all vertices have finite degree we consider a random walk starting at a vertex v say such that at any vertex u the walk proceeds to a neighbour with probability 1 d u where d u is the degree i e the number of neighbours of u the graph g is recurrent if we revisit v with probability 1 otherwise g is transient it is well known that the three dimensional grid z3 is transient while z2 is recurrent more generally nash williams 13 see also 4 10 proved that any graph with smaller growth rate than z2 is recurrent lyons 10 showed that certain subgraphs of grids are transient provided they grow just a little faster than z2 other results in terms of isoperimetric inequalities supporting the statement that z2 is in a sense an extreme recurrent graph can be derived from work of fernandez 5 grigor yan 7 and varopoulos 15 varopoulos 16 used results of gromov 8 to characterize completely the recurrent cayley graphs we shall carry these results further if v is a vertex set in g then av will denote the boundary of v that is the set of vertices of v having neighbours outside of v let f be a nondecreasing positive real function defined on the natural numbers we say that g satisfies an f isoperimetric inequality if there exists a constant c 0 such that for each finite vertex set v of g

a variable spread fuzzy linear regression model with higher explanatory power and forecasting accuracy fuzzy regression models have been applied to operational research or applications such as forecasting some of previous studies on fuzzy regression analysis obtain crisp regression coefficients for eliminating the problem of increasing spreads for the estimated fuzzy responses as the magnitude of the independent variable increases however they still cannot cope with the situation of decreasing or variable spreads this paper proposes a three phase method to construct the fuzzy regression model with variable spreads to resolve this problem in the first phase on the basis of the extension principle the membership functions of the least squares estimates of regression coefficients are constructed to conserve completely the fuzziness of observations in the second phase then they are defuzzified by the center of gravity method to obtain crisp regression coefficients in the third phase the error terms of the proposed model are determined by setting each estimated spread equals its corresponding observed spread furthermore the mamdani fuzzy inference system is adopted for improving the accuracy of its forecasts compared to the previous studies the results from five examples and an application example of japanese house prices show that the proposed fuzzy linear regression model has higher explanatory power and forecasting performance

spectral gap of the discrete laplacian on triangulations our goal in this paper is to find an estimate for the spectral gap of the laplacian on a two simplicial complex consisting on a hypergraph of a complete graph an upper estimate is given by generalizing the cheeger constant the lower estimate is obtained from the first non zero eigenvalue of the discrete laplacian acting on the functions of certain sub graphs

correcting wavelet codes using interleaving and trapping a rate k n wavelet code a form of real convolutional code that encodes k numbers into n numerical code symbols using the present and past input numbers may be used to transport numerical data with redundancy factor rm n rm k such codes offer detection and correction within roundoff tolerances wavelet codes can be processed using two different algebraic representations vector matrix or polyphase polynomial when an interleaver intersperses the code symbols any burst of errors within the interelaver s frame length appears in only one component of the polyphase format a special extended polyphase parity check matrix exposes the error bursts directly for redundancies greater than 1 or a deconvolver operation achieves the same when the redundancy factor is 1 the trapped errors correct the symbols by subtraction simulations verify the effectiveness of this trapping technique

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

general cheeger inequalities for p laplacians on graphs abstract we prove cheeger inequalities for p laplacians on finite and infinite weighted graphs unlike in previous works we do not impose boundedness of the vertex degree nor do we restrict ourselves to the normalized laplacian and more generally we do not impose any boundedness assumption on the geometry this is achieved by a novel definition of the measure of the boundary which uses the idea of intrinsic metrics for the non normalized case our bounds on the spectral gap of p laplacians are already significantly better for finite graphs and for infinite graphs they yield non trivial bounds even in the case of unbounded vertex degree we furthermore give upper bounds by the cheeger constant and by the exponential volume growth of distance balls

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

expansion in sl d z q z q arbitrary let s be a fixed finite symmetric subset of sl d z and assume that it generates a zariski dense subgroup g we show that the cayley graphs of q g with respect to the generating set q s form a family of expanders where q is the projection map z z q z

granular box regression granular computing grc has gained increasing attention in the past decade although not uniquely defined its basic idea is to approximate detailed machine like information by a coarser presentation on a human like level within granular computing the mapping of continuous variables into intervals plays an important role these intervals are often prerequisites for the formulation of linguistic variables in this paper we suggest a piecewise interval approximation and propose granular box regression its objective is to establish relationships between independent and dependent variables by multidimensional boxes we interpret granular box regression as interval regression and show its potential for the extraction of fuzzy rules from data in two experiments we apply granular box regression to an artificial as well as to a real dataset in the field of finance and evaluate its properties

overdetermined partial boundary value problems on finite networks abstract in this study we define a class of non self adjoint boundary value problems on finite networks associated with schrodinger operators the novel feature of this study is that no data are prescribed on part of the boundary whereas both the values of the function and of its normal derivative are given on another part of the boundary we show that overdetermined partial boundary value problems are crucial for solving inverse boundary value problems on finite networks since they provide the theoretical foundations for the recovery algorithm we analyze the uniqueness and the existence of solution for overdetermined partial boundary value problems based on the nonsingularity of partial dirichlet to neumann maps these maps allow us to determine the value of the solution in the part of the boundary where no data was prescribed we also execute full conductance recovery for spider networks

from fuzzy regression to gradual regression interval based analysis and extensions abstract this paper proposes an analysis of parametric interval based regression methodologies according to ontic and epistemic visions of intervals when assuming an epistemic point of view a new interpretation of fuzzy regression through the notion of gradual intervals is developed which leads to gradual regression gradual regression is viewed as an extension of the imprecise interval based regression which is obtained by integrating an uncertain dimension gradual intervals can yield improved specificity compared to conventional intervals and jointly consider the concepts of imprecision and uncertainty through a single and coherent formalism the formulation of the gradual regression problem its resolution and the propagation of the information through the obtained regressive models are carried out via gradual interval arithmetic the proposed method allows not only the extension of the interval vision to the gradual case but also interesting interpretations according to non additive confidence measure theories possibility and belief functions

cohomology of noncompact surfaces this paper is motivated by the question of whether nonzero l2 harmonic differentials exist on coverings of a riemann surface of genus 2 our approach will be via an analogue of the de rham theorem some results concerning the invariance of l2 homology and the intersection number of lu cycles are demonstrated a growth estimate for triangulations of planar coverings of the two holed torus is derived finally the equivalence between the existence of l2 harmonic one cycles and the transience of random walks on a planar surface is shown

subspace based error and erasure correction with dft codes for wireless channels this paper deals with the decoding of lowpass discrete fourier transform dft codes in the presence of both errors and erasures we propose a subspace based approach for the error localization that is similar to the subspace approaches followed in the array signal processing for direction of arrival doa estimation the basic idea is to divide a vector space into two orthogonal subspaces of which one is spanned by the error locator vectors the locations of the errors are estimated from the spanning eigenvectors of the complement subspace however unlike the subspace approach in doa estimation which is similar to estimating the subspaces from the syndrome covariance matrix after a projection in the proposed approach the subspaces are estimated from the modified syndrome covariance matrix after a whitening transform simulation results with a gauss markov source reveal that the proposed algorithm is more efficient than the coding theoretic approach on impulsive channels as well as the subspace approach with projection on lossy channels

a sears type self adjointness result for discrete magnetic schrodinger operators abstract in the context of a weighted graph with vertex set v and bounded vertex degree we give a sufficient condition for the essential self adjointness of the operator w where is the magnetic laplacian and w v r is a function satisfying w x q x for all x v with q v 1 the condition is expressed in terms of completeness of a metric that depends on q and the weights of the graph the main result is a discrete analogue of the results of i oleinik and m a shubin in the setting of non compact riemannian manifolds

on the use of cascade structure to correct impulsive noise in multicarrier systems we propose a new decoding algorithm based on a cascade structure for impulsive noise correction in multicarrier systems such as orthogonal frequency division multiplexing ofdm based systems this new cascade structure based algorithm has the advantage to lead on one hand to a reduced complexity implementation in an ofdm demodulator and on the other hand to overcome the lacks of other algorithms dedicated for impulsive noise correction to do so we start the derivation by investigating closed form analytical expressions of the a priori probabilities used in hypotheses tests that are necessary for the different steps needed for the execution of the cascade structure based decoding algorithm such closed form expressions for the a priori probabilities result in efficient setups of the threshold values used for the execution of the decoding algorithm furthermore we show that this cascade structure can be applied to efficiently cancel the impulsive noise in ofdm systems as the clipping event present in ofdm systems can be seen as an additive impulsive noise we prove that after introducing some minor modifications we can apply the proposed cascade structure to significantly reduce the peak to average power ratio papr level in such systems simulation results are given to illustrate the usefulness of the proposed algorithm results in practical ofdm based communication systems such as hiperlan 2

new short constraint length convolutional code constructions for selected rational rates corresp new short constraint length convolutional code constructions are tabulated for rates r n k n k 1 2 cdots n 1 with n 2 3 cdots 8 and for constraint lengths k 3 4 cdots 8 these codes have been determined by iterative search based upon a criterion of optimizing the free distance profile specifically these codes maximize the free distance d f while minimizing the number of adversaries in the distance or weight spectrum in several instances we demonstrate the superiority of these codes over previously published code constructions at the same rate and constraint length these codes are expected to have a number of applications including combined source channel coding schemes as well as coding for burst or impulsive noise channels

the essential spectrum of the laplacian on rapidly branching tessellations in this paper we characterize absence of the essential spectrum of the laplacian under a hyperbolicity assumption for general graphs moreover we present a characterization for absence of the essential spectrum for planar tessellations in terms of curvature

linear and non linear fuzzy regression evolutionary algorithm solutions given some data which consists of pairs of fuzzy numbers our evolutionary algorithm searches our library of fuzzy functions which includes linear polynomial exponential and logarithmic for a fuzzy function which best fits the data tests of our fuzzy regression package are given for each of the four cases linear polynomial exponential and logarithmic for the linear model we also consider multiple independent variables in all cases we use data generated with and without noise we prove that fuzzy polynomial regression can model the extension principle extension of continuous real valued functions

impulsive noise cancellation in multicarrier transmission a parallel between reed solomon codes in the complex field and multicarrier transmission using orthogonal frequency division multiplexing ofdm is first presented this shows that when the signal is sent over some channel composed of gaussian plus impulsive noise the impulsive noise can be removed by a procedure similar to channel decoding using information carried by the syndrome this result is first derived in a simple situation oversampled discrete multitone additive channel which is merely of theoretical interest in any case consecutive zeros in the output of the ofdm modulator do not correspond to real subcarriers pilot tones are transmitted for synchronization or channel estimation purposes these pilot tones are generally scattered among the information ones our approach is to use these pilot tones as syndromes in order to correct impulsive noise we show that the correction capacity is conditioned by the position of these pilot tones in the transmitted sequence a protection subsystem based on hypotheses tests is introduced after the decoding operation in order to detect malfunctions of this decoder the efficiency of this technique is corroborated with simulations in the slightly modified hiperlan2 context other extensions are then provided in order to increase the practical usefulness of the method

a revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals conventional fuzzy regression using possibilistic concepts allows the identification of models from uncertain data sets however some limitations still exist this paper deals with a revisited approach for possibilistic fuzzy regression methods indeed a new modified fuzzy linear model form is introduced where the identified model output can envelop all the observed data and ensure a total inclusion property moreover this model output can have any kind of spread tendency in this framework the identification problem is reformulated according to a new criterion that assesses the model fuzziness independently from the collected data distribution the potential of the proposed method with regard to the conventional approach is illustrated by simulation examples

difference equations isoperimetric inequality and transience of certain random walks the difference laplacian on a square lattice in rn has been stud ied by many authors in this paper an analogous difference operator is studied for an arbitrary graph it is shown that many properties of the laplacian in the continuous setting e g the maximum principle the harnack inequality and cheeger s bound for the lowest eigenvalue hold for this difference oper ator the difference laplacian governs the random walk on a graph just as the laplace operator governs the brownian motion as an application of the theory of the difference laplacian it is shown that the random walk on a class of graphs is transient the random walks we consider are defined as follows let k be a connected graph i e a one dimensional simplicial complex for a vertex x e k let m x denote the number of edges emanating from x the probability that a particle moves from x to another vertex y e k is l m x if x and y are connected by an edge and it is zero otherwise as observed by courant friedrichs and lewy cfl for the case of a square lattice in the plane this random walk is intimately related to the difference analog of the laplacian

extended support vector interval regression networks for interval input output data in many applications it is natural to use interval data because of uncertainty existence in the measurements variability in defining terms such as the temperature during a given day description for extremely behavior such as the maximum wind speed in a given area etc in order to handle such interval data a novel approach called the interval support vector interval regression networks isvirns is proposed the isvirns is extended from our previous work the support vector interval regression networks svirns it is easy to find that svirns can handle interval output data but for input data they must be crisp in this study the hausdorff distance is employed as the distance measure of interval data and is incorporated into the kernel functions of svirns to determine the initial structure of isvirns because the proposed approach can provide a better initial structure for isvirns it can have a faster convergent speed the experimental results with real data sets show the validity of the proposed isvirns

testing the expansion of a graph we study the problem of testing the expansion of graphs with bounded degree d in sublinear time a graph is said to be an a expander if every vertex set u v of size at most 12 v has a neighborhood of size at least a u we show that the algorithm proposed by goldreich and ron 9 eccc 2000 for testing the expansion of a graph distinguishes with high probability between a expanders of degree bound d and graphs which are far from having expansion at least w a 2 this improves a recent result of czumaj and sohler 3 focs 07 who showed that this algorithm can distinguish between a expanders of degree bound d and graphs which are far from having expansion at least w a 2 logn it also improves a recent result of kale and seshadhri 12 eccc 2007 who showed that this algorithm can distinguish between a expanders and graphs which are far from having expansion at least w a 2 with twice the maximum degree our methods combine the techniques of 3 9 and 12

multiple regression with fuzzy data in this paper we propose an iterative algorithm for multiple regression with fuzzy variables while using the standard least squares criterion as a performance index we pose the regression problem as a gradient descent optimisation the separation of the evaluation of the gradient and the update of the regression variables makes it possible to avoid undue complication of analytical formulae for multiple regression with fuzzy data the origins of fuzzy input data are traced back to the fundamental concept of information granulation and an example fcm based granulation method is proposed and illustrated by some numerical examples the proposed multiple regression algorithm is applied to one three and nine dimensional synthetic data sets as well as the 13 dimensional boston housing dataset from the machine learning repository the algorithm s performance is illustrated by the corresponding plots of convergence of regression parameters and the values of the prediction error of the resulting regression model general comments on the numerical complexity of the proposed algorithm are also provided

instantaneous erasures in oversampled filter banks conditions for output perfect reconstruction in this paper we aim at finding the conditions that an oversampled filter bank ofb should satisfy in order to maintain its perfect reconstruction property when erasures happen in the subband domain this problem has been addressed before mainly from frame theoretic point of view and only for the case of what we call in this paper classic erasure in the frame theoretic approach the stable filter banks are associated with frames in l2 bbz and a subband erasure is defined as the deletion of the frame expansion coefficients corresponding to the frame vectors resulting from each filter and all its translated versions this is equivalent to assuming that all the samples of a subband have been completely lost classic erasure and this is why in this approach it is always assumed that each channel is either working perfectly or not at all in this paper we extend this notion of erasure to a situation where subband channels are allowed to be on or off arbitrarily in each time instance and we define a new type of erasure called instantaneous erasure using an approach based on the time domain analysis of perfect reconstruction property we introduce general conditions for perfect reconstruction of the output and also the sufficient conditions for two classes of filter banks causal ofbs with causal inverse and ofbs with maximum robustness against classic erasure

the heat flow on metric random walk spaces abstract in this paper we study the heat flow on metric random walk spaces which unifies into a broad framework the heat flow on locally finite weighted connected graphs the heat flow determined by finite markov chains and some nonlocal evolution problems we give different characterizations of the ergodicity and prove that a metric random walk space with positive ollivier ricci curvature is ergodic furthermore we prove a cheeger inequality and as a consequence we show that a poincare inequality holds if and only if an isoperimetric inequality holds we also study the bakry emery curvature dimension condition and its relation with functional inequalities like the poincare inequality and the transport information inequalities

asymptotic properties of least squares estimation with fuzzy observations this paper deals with the asymptotic properties of the least squares estimators for fuzzy linear regression models with fuzzy triangular input output and random error terms the asymptotic normality and strong consistency of the fuzzy least squares estimator flse are investigated a confidence region based on a class of flses is proposed the asymptotic relative efficiency of flses with respect to the crisp least squares estimators is also provided and a numerical example is given some simulation results are also presented to illustrate the behavior of flses

wavelet codes detection and correction using kalman estimation wavelet codes encoded by uniform oversampled filter banks where the wavelet coefficients represent code symbols are decoded employing kalman fixed lag estimation procedures the code symbol error estimates are based on the mean squared error mse criterion and are first used to detect the presence of large numerical errors then the correction of symbols uses these kalman estimators directly the wavelet code symbols are corrupted by low levels of processing noise continuously and occasionally by large disruptive errors e g impulsive noise the modeling variables have time varying statistics allowing both types of errors to be handled naturally kalman time varying tracking filters which use wavelet syndromes as their measurement inputs develop the fixed lag smoothed estimates for the larger errors the syndromes are also modeled as corrupted by processing noise modeling computational failure errors large and small hypothesis detection methods are used to locate large errors and their statistics must include kalman mismatch characteristics to be valid estimators from several adjacent lag positions assist in the detection procedures simulation results show correction accuracy in the time domain as well as on a mse basis large classes of wavelet codes are designed using binary convolutional codes as starting points from which the proper filter weights for encoding and syndrome evaluating are determined

uniform spanning forests we study uniform spanning forest measures on infinite graphs which are weak limits of uniform spanning tree measures from finite subgraphs these limits can be taken with free fsf or wired wsf boundary conditions pemantle proved that the free and wired spanning forests coincide in z d and that they give a single tree iff d 4 in the present work we extend pemantle s alternative to general graphs and exhibit further connections of uniform spanning forests to random walks potential theory invariant percolation and amenability the uniform spanning forest model is related to random cluster models in statistical physics but because of the preceding connections its analysis can be carried further among our results are the following the fsf and wsf in a graph g coincide iff all harmonic dirichlet functions on g are constant the tail fields of the wsf and the fsf are trivial on any graph on any cayley graph that is not a finite extension of z all component trees of the wsf have one end this is new in z d for d 5 on any tree as well as on any graph with spectral radius less than 1 a s all components of the wsf are recurrent the basic topology of the free and the wired uniform spanning forest measures on lattices in hyperbolic space h d is analyzed a cayley graph is amenable iff for all e 0 the union of the wsf and bernoulli percolation with parameter e is connected harmonic measure from infinity is shown to exist on any recurrent proper planar graph with finite codegrees we also present numerous open problems and conjectures

fuzzy regression methods a comparative assessment abstract the fundamental differences between fuzzy regression and ordinary regression are identified in this paper fuzzy regression can be used to fit fuzzy data and crisp data into a regression model whereas ordinary regression can only fit crisp data through a comprehensive literature review three approaches of fuzzy regression are summarized the first approach of fuzzy regression is based on minimizing fuzziness as an optimal criterion the second approach uses least squares of errors as a fitting criterion and two methods are summarized in this paper the third approach can be described as an interval regression analysis for each fuzzy regression method numerical examples and graphical presentations are used to evaluate their characteristic and differences with ordinary least squares regression based on the comparative assessment the fundamental differences between ordinary least squares regression and conventional fuzzy regression are concluded that is ordinary least squares regression modeling data with randomness type of uncertainty and conventional fuzzy regression modeling data with fuzziness type of uncertainty in order to integrate both randomness and fuzziness types of uncertainty into one regression model the concept of hybrid fuzzy least squares regression analysis is proposed in this paper and the details of its method are derived in the accompanying paper

robust support vector regression for uncertain input and output data in this paper a robust support vector regression rsvr method with uncertain input and output data is studied first the data uncertainties are investigated under a stochastic framework and two linear robust formulations are derived linear formulations robust to ellipsoidal uncertainties are also considered from a geometric perspective second kernelized rsvr formulations are established for nonlinear regression problems both linear and nonlinear formulations are converted to second order cone programming problems which can be solved efficiently by the interior point method simulation demonstrates that the proposed method outperforms existing rsvrs in the presence of both input and output data uncertainties

distributed source channel coding based on real field bch codes we use real number codes to compress statistically dependent sources and establish a new framework for distributed lossy source coding in which we compress sources before rather than after quantization this change in the order of binning and quantization blocks makes it possible to model the correlation between continuous valued sources more realistically and compensate for the quantization error partially we then focus on the asymmetric case i e lossy source coding with side information at the decoder the encoding and decoding procedures are described in detail for a class of real number codes called discrete fourier transform dft codes both for the syndrome and parity based approaches we leverage subspace based decoding to improve the decoding and by extending it we are able to perform distributed source coding in a rate adaptive fashion to further improve the decoding performance when the statistical dependency between sources is unknown we also extend the parity based approach to the case where the transmission channel is noisy and thus we perform distributed joint source channel coding in this context the proposed system is well suited for low delay communications as the mean squared reconstruction error mse is shown to be reasonably low for very short block length

fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks in this paper first we explain several versions of fuzzy regression methods based on linear fuzzy models with symmetric triangular fuzzy coefficients next we point out some limitations of such fuzzy regression methods then we extend the symmetric triangular fuzzy coefficients to asymmetric triangular and trapezoidal fuzzy numbers we show that the limitations of the fuzzy regression methods with the symmetric triangular fuzzy coefficients are remedied by such extension several formulations of linear programming problems are proposed for determining asymmetric fuzzy coefficients from numerical data finally we show how fuzzified neural networks can be utilized as nonlinear fuzzy models in fuzzy regression in the fuzzified neural networks asymmetric fuzzy numbers are used as connection weights the fuzzy connection weights of the fuzzified neural networks correspond to the fuzzy coefficients of the linear fuzzy models nonlinear fuzzy regression based on the fuzzified neural networks is illustrated by computer simulations where type i and type ii membership functions are determined from numerical data

redundancy the discrete fourier transform and impulse noise cancellation the relationship between the discrete fourier transform and error control codes is examined under certain conditions we show that discrete time sequences carry redundant information which then allow for the detection and correction of errors an application of this technique to impulse noise cancellation for pulse amplitude modulation transmission is described

asymptotic behavior of the transition probability of a random walk on an infinite graph ideas cultivated in spectral geometry are applied to obtain an asymptotic property of a reversible random walk on an infinite graph satisfying a certain periodic condition in the course of our argument we employ perturbation theory for the maximal eigenvalues of twisted transition operator as a result an asymptotic of the probabilityp n x y that a particle starting atxreachesyat timenasngoes to infinity is established

isoperimetric inequalities and random walks on quotients of graphs and buildings let be a euclidean or hyperbolic building and let g aut be a locally compact unimodular group which acts strongly transitively on we use graphs quasi isometric to to study asymptotic properties of quotients where is a discrete subgroup of g if g has kazhdan s property t we show that such quotients satisfy strong isoperimetric inequalities this yields new examples of graphs with positive cheeger constant such graphs cannot be bi lipschitz embedded into hilbert space moreover simple random walks on such quotients are shown to be recurrent if and only if is a uniform lattice in g

extended fuzzy regression models using regularization method regularization approach to regression can be easily found in statistics and information science literatures the technique of regularization was introduced as a way of controlling the smoothness properties of regression function the main purpose of this paper is to extend the models of diamond inform sci 46 1988 141 to fuzzy multiple linear regression models and to extend the model f3 with numerical input of diamond inform sci 46 1988 141 to fuzzy nonlinear model here all extensions are based on regularization technique

discrete serrin s problem we consider here the discrete analogue of serrin s problem if the equilibrium measure of a network with boundary satisfies that its normal derivative is constant what can be said about the structure of the network and the symmetry of the equilibrium measure in the original serrin s problem the conclusion is that the domain is a ball and the solution is radial to study the discrete serrin s problem we first introduce the notion of radial function and then prove a generalization of the minimum principle which is one of the main tools in the continuous case moreover we obtain similar results to those of the continuous case for some families of networks with a ball like structure which include spider networks with radial conductances distance regular graphs or more generally regular layered networks

improved coding theoretic and subspace based decoding algorithms for a wider class of dct and dst codes the decoding of a class of discrete cosine transform dct and discrete sine transform dst codes that are maximum distance separable codes mds is considered in this paper these class of codes are considered for error correction over real fields all the existing algebraic decoding algorithms are capable of decoding only a subclass of these codes which can be characterized into the bose chaudhuri hocquenghem bch form and fails to decode the remaining even though they are mds in this paper we propose a new generic algorithm along the lines of coding theoretic and subspace methods to decode the entire class of mds dct and dst codes the proposed subspace approaches are similar to popular esprit and music algorithms the proposed algorithms also perform significantly better than the existing algorithms on the bch like subclass a perturbation analysis is also presented to study the effect of various parameters on the error localization due to the quantization noise simulation results are presented to demonstrate the capability of proposed algorithms to decode the entire class and to perform significantly better on the bch like subclass than the existing algorithm under the influence of quantization noise

transient random walks on graphs and metric spaces with applications to hyperbolic surfaces we introduce an r net 0 2r r of a metric space m as a maximal graph whose vertices are elements in m of pairwise distance at least r such that any two vertices of distance at most r are adjacent we show that for a large class of metric spaces including many riemannian manifolds the property of transience of a net and the property of the net carrying a non constant harmonic function of bounded energy is independent of the choice of the net we give a new necessary and sufficient condition for a graph with bounded degrees and satisfying an isoperimetric inequality to have no non constant harmonic functions for this purpose we develop equivalent analytic conditions for graphs satisfying an isoperimetric inequality some of these results have been discovered recently by others in more general settings but our treatment here is specific and self contained we use graph transience to prove that scherk s surface is hyperbolic a problem posed by osserman in 1965

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

overdetermined partial resolvent kernels for finite networks abstract in 2 a study of the existence and uniqueness of solution of partial overdetermined boundary value problems for finite networks was performed these problems involve schrodinger operators and the novel feature is that no data are prescribed on part of the boundary whereas both the values of the function and of its normal derivative are given on another part of the boundary in the present work we study the resolvent kernels associated with overdetermined partial boundary value problems on finite network and we express them in terms of the well known green operator and the dirichlet to robin map moreover we analyze their main properties and we compute them in the case of a generalized cylinder the obtained expression involve polynomials that can be seen as a generalization of chebyshev polynomials and indeed when the conductances along axes are constant the expressions for the overdetermined partial resolvent kernels are given in terms of second kind chebyshev polynomials

analysis of the physical laplacian and the heat flow on a locally finite graph we study the physical laplacian and the corresponding heat flow on an infinite locally finite graph with possibly unbounded valence

multi way dual cheeger constants and spectral bounds of graphs we introduce a set of multi way dual cheeger constants and prove universal higher order dual cheeger inequalities for eigenvalues of normalized laplace operators on weighted finite graphs our proof proposes a new spectral clustering phenomenon deduced from metrics on real projective spaces we further extend those results to a general reversible markov operator and find applications in characterizing its essential spectrum