marcinkiewicz zygmund inequalities and interpolation by spherical harmonics abstract we find necessary density conditions for marcinkiewicz zygmund inequalities and interpolation for spaces of spherical harmonics in s d with respect to the l p norm moreover we prove that there are no complete interpolation families for p 2

divergence statistics for testing uniform association in cross classifications in this paper we consider the problem of testing uniform association in cross classifications having ordered categories taking as test statistic one in the family proposed by conde and salicru j conde m salicru uniform association in contingency tables associated to csiszar divergence statistics and probability letters 37 1998 149 154 we consider two approximations to the null distribution of the test statistics in this family an estimation of the asymptotic null distribution and a bootstrap estimator we prove that both approximations are asymptotically equivalent to study their finite sample performance we carried out two simulation experiments whose results are presented from the simulations it can be concluded that the bootstrap estimator behaves much better than the estimated asymptotic null distribution

level spacing distributions and the bessel kernel scaling models of randomn n hermitian matrices and passing to the limitn leads to integral operators whose fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order for the gaussian unitary ensemble and for many others as well the kernel one obtains by scaling in the bulk of the spectrum is the sine kernel frac sin pi x y pi x y rescaling the gue at the edge of the spectrum leads to the kernel frac ai x ai y ai x ai y x y where ai is the airy function in previous work we found several analogies between properties of this airy kernel and known properties of the sine kernel a system of partial differential equations associated with the logarithmic differential of the fredholm determinant when the underlying domain is a union of intervals a representation of the fredholm determinant in terms of a painleve transcendent in the case of a single interval and also in this case asymptotic expansions for these determinants and related quantities achieved with the help of a differential operator which commutes with the integral operator in this paper we show that there are completely analogous properties for a class of kernels which arise when one rescales the laguerre or jacobi ensembles at the edge of the spectrum namely frac j alpha sqrt x sqrt y j alpha sqrt y sqrt x j alpha sqrt x j alpha sqrt y 2 x y wherej z is the bessel function of order in the cases 1 2 these become after a variable change the kernels which arise when taking scaling limits in the bulk of the spectrum for the gaussian orthogonal and symplectic ensembles in particular an asymptotic expansion we derive will generalize ones found by dyson for the fredholm determinants of these kernels

an alternative approach to unitoidness abstract in a recent paper c r johnson s furtado a generalization of sylvester s law of inertia linear algebra appl 338 2001 287 290 sylvester s law of inertia is generalized to any matrix that is congruent to a diagonal matrix such a matrix is called unitoid in the present paper an alternative approach to the subject of unitoidness is offered specifically sylvester s law of inertia states that a hermitian n n matrix of rank r with inertia p q n r is congruent to the direct sum e i 0 i p e i i q 0 i n r it is demonstrated herein that a unitoid matrix a of rank r is congruent to a direct sum of diagonal blocks of the form e i i p e i i q together with the zero block 0in r moreover the s together with the multiplicities p and q are specified in terms of the eigenvalues and eigenvectors of a a where a is the moore penrose inverse of a

a generalization of sylvester s law of inertia abstract we introduce the class of unitoid matrices as those that are diagonalizable by congruence the nondegenerate canonical angles of a unitoid matrix a are the directions of the nonzero entries of a diagonal matrix congruent to a which are shown to be unique sylvester s law states that two hermitian matrices of the same size are congruent if and only if they have the same numbers of positive respectively negative eigenvalues two unitoid matrices are congruent if and only if they have the same nondegenerate canonical angles

landau s necessary density conditions for lca groups we derive necessary conditions for sampling and interpolation of bandlimited functions on a locally compact abelian group in line with the classical results of h landau for bandlimited functions on rd our conditions are phrased as comparison principles involving a certain canonical lattice

littlewood paley stein gk functions for fourier bessel expansions abstract g k functions related to the poisson semigroup of fourier bessel expansions are defined for each k 1 it is proved that these g k functions are calderon zygmund operators in the sense of the associated space of homogeneous type hence their mapping properties follow from the general theory

the polya information divergence extensions of sanov s theorem and the conditional limit theorem colt are established for a multicolor polya eggenberger pe urn sampling scheme giving the polya information divergence and a polya extension to the maximum relative entropy maxent method polya maxent includes the standard maxent as well as its variants used in bose einstein fermi dirac and intermediate acharya swamy statistics as special cases in the pe setting standard maxent is in general asymptotically inconsistent

δ entropy definition properties and applications in system identification with quantized data recently the minimum error entropy criterion an information theoretic alternative to the traditional mean square error criterion has been successfully used in the contexts of machine learning and signal processing for system identification however the mee criterion will be no longer suitable if the training data are discrete valued since minimizing error s discrete entropy cannot constrain error s dispersion in this paper to make the mee criterion suitable for the discrete valued data cases we give a new entropy definition for the discrete random variables i e the d entropy based on riemann sums for finite size partitions a probability weighted formula is established to calculate the average partition this new entropy retains some important properties of the differential entropy and reduces to discrete entropy under certain conditions unlike discrete entropy the d entropy is sensitive to the dynamic range of the data and can be used as a superior optimality criterion in system identification problems also we present a plug in estimate of d entropy analyze its asymptotic behavior and explore the links to the kernel based and m spacing based estimates for differential entropy finally the d entropy criterion is applied in system identification with coarsely quantized input output data to search for the optimum parameter set monte carlo simulations demonstrate the performance improvement that may be achieved with the d entropy criterion

q prolate spheroidal wave functions and q sampling theorem in this paper we introduce a q version of the prolate spheroidal wave functions which is the eigenfunction of the concentration problem related to sampling and interpolation of q hankel bandlimited functions as application we give a q sampling theorem which extrapolates functions in l 2 space with q n email protected z as sampling points

mean and weak convergence of fourier bessel series abstract we study the uniform boundedness on some weighted lp spaces of the partial sum operators associated to fourier bessel series obtaining necessary and sufficient conditions for this boundedness in terms of the weights on the other hand we study the weak and restricted weak type of the partial sum operators in the end points of the interval of strong boundedness

transplantation and multiplier theorems for fourier bessel expansions proved are weighted transplantation inequalities for fourier bessel expansions these extend known results on this subject by considering the largest possible range of parameters allowing more weights and admitting a shift the results are then used to produce a fairly general multiplier theorem with power weights for considered expansions also fractional integral results and conjugate function norm inequalities for these expansions are proved

general statistical inference for discrete and mixed spaces by an approximate application of the maximum entropy principle we propose a method for learning a general statistical inference engine operating on discrete and mixed discrete continuous feature spaces such a model allows inference on any of the discrete features given values for the remaining features applications are e g to medical diagnosis with multiple possible diseases fault diagnosis information retrieval and imputation in databases bayesian networks bns are versatile tools that possess this inference capability however bns require explicit specification of conditional independencies which may be difficult to assess given limited data alternatively cheeseman 1983 proposed finding the maximum entropy me joint probability mass function pmf consistent with arbitrary lower order probability constraints this approach is in principle powerful and does not require explicit expression of conditional independence however until now the huge learning complexity has severely limited the use of this approach here we propose an approximate me method which also encodes arbitrary low order constraints but while retaining quite tractable learning our method uses a restriction of joint pmf support during learning to a subset of the feature space results on the university of california irvine repository reveal performance gains over several bn approaches and over multilayer perceptrons

univariate marginal distribution algorithm dynamics for a class of parametric functions with unitation constraints in this paper we introduce a mathematical model for analyzing the dynamics of the univariate marginal distribution algorithm umda for a class of parametric functions with isolated global optima we prove a number of results that are used to model the evolution of umda probability distributions for this class of functions we show that a theoretical analysis can assess the effect of the function parameters on the convergence and rate of convergence of umda we also introduce for the first time a long string limit analysis of umda finally we relate the results to ongoing research on the application of the estimation of distribution algorithms for problems with unitation constraints

landauʼs necessary density conditions for the hankel transform abstract we will prove an analogue of landau s necessary conditions h j landau necessary density conditions for sampling and interpolation of certain entire functions acta math 117 1967 37 52 for spaces of functions whose hankel transform is supported in a measurable subset s of the positive semi axis as a special case necessary density conditions for the existence of fourier bessel frames are obtained

adaptive estimated maximum entropy distribution model the estimation of distribution algorithm eda model is an optimization procedure through learning and sampling a conditional probabilistic function the use of conditional density function permits multivariate dependency modelling which is not captured in a population based representation like the classical genetic algorithms the gaussian model is a simple and widely used model for density estimation however an assumption of normality is not realistic for many real life problems alternatively the maximum entropy model can be used which makes no assumption of a normal distribution one disadvantage of the maximum entropy model is the learning cost of its parameters this paper proposes an adaptive estimated maximum entropy distribution adaptive meed model which aims to reduce learning complexity of building a model adaptive meed exploits the fact that samples have a low average fitness in the early stage but they gradually converge to an optima towards the end of the search hence it is not necessary to inference the model with a full account of observed constraints in the early stage of the search the proposed model attempts to estimate the density function with a dynamic set of samples and active constraints in addition the proposed model includes a global sampling function to address the issue of a missing mutation operator the ergodic convergence properties of the proposed model are discussed with the markov chain analysis the preliminary experimental evaluation shows that the proposed model performs well against genetic algorithms on several clustering problems

gakrem a novel hybrid clustering algorithm we introduce a novel clustering algorithm named gakrem genetic algorithm k means logarithmic regression expectation maximization that combines the best characteristics of the k means and em algorithms but avoids their weaknesses such as the need to specify a priori the number of clusters termination in local optima and lengthy computations to achieve these goals genetic algorithms for estimating parameters and initializing starting points for the em are used first second the log likelihood of each configuration of parameters and the number of clusters resulting from the em is used as the fitness value for each chromosome in the population the novelty of gakrem is that in each evolving generation it efficiently approximates the log likelihood for each chromosome using logarithmic regression instead of running the conventional em algorithm until its convergence another novelty is the use of k means to initially assign data points to clusters the algorithm is evaluated by comparing its performance with the conventional em algorithm the k means algorithm and the likelihood cross validation technique on several datasets

inexact graph matching by means of estimation of distribution algorithms abstract estimation of distribution algorithms edas are a quite recent topic in optimization techniques they combine two technical disciplines of soft computing methodologies probabilistic reasoning and evolutionary computing several algorithms and approaches have already been proposed by different authors but up to now there are very few papers showing their potential and comparing them to other evolutionary computational methods and algorithms such as genetic algorithms gas this paper focuses on the problem of inexact graph matching which is np hard and requires techniques to find an approximate acceptable solution this problem arises when a nonbijective correspondence is searched between two graphs a typical instance of this problem corresponds to the case where graphs are used for structural pattern recognition in images eda algorithms are well suited for this type of problems this paper proposes to use eda algorithms as a new approach for inexact graph matching also two adaptations of the eda approach to problems with constraints are described as two techniques to control the generation of individuals and the performance of edas for inexact graph matching is compared with the one of gas

on nonuniform sampling expansions using entire interpolating functions and on the stability of bessel type sampling expansions the author has extended the work of n levinson 1940 to derive nonuniform sampling expansions that are stable in the sense of k yao and j b thomas ieee trans circuit theory vol ct 14 p 404 8 1967 and reduce to bessel type sampling expansions for a particular choice of the sampling sequence

mse estimates for multitaper spectral estimation and off grid compressive sensing we obtain estimates for the mean squared error mse for the multitaper spectral estimator and certain compressive acquisition methods for multi band signals we confirm a fact discovered by thomson spectrum estimation and harmonic analysis proc ieee 1982 assuming bandwidth w and n time domain observations the average of the square of the first k lfloor 2nw rfloor slepian functions approaches as k grows an ideal bandpass kernel for the interval w w we provide an analytic proof of this fact and measure the corresponding rate of convergence in l 1 norm this validates a heuristic approximation used to control the mse of the multitaper estimator the estimates have also consequences for the method of compressive acquisition of multi band signals introduced by davenport and wakin giving mse approximation bounds for the dictionary formed by modulation of the critical number of prolates

generalized sampling theorems for bessel type transforms of bandlimited functions and distributions this paper adapts the ideas of helms and thomas proc ire 50 1962 pp 179 184 and jerri applicable anal 14 1982 pp 11 25 to derive bessel type sampling expansions and determine upper bounds on the truncation errors in deriving these expansions it is shown that the fourier transform property of additivity of supports under convolution also holds for h 0 hankel transforms under certain conditions

canonical forms for complex matrix congruence and congruence abstract canonical forms for congruence and congruence of square complex matrices were given by horn and sergeichuk in linear algebra appl 389 2004 347 353 based on sergeichuk s paper math ussr izvestiya 31 3 1988 481 501 which employed the theory of representations of quivers with involution we use standard methods of matrix analysis to prove directly that these forms are canonical our proof provides explicit algorithms to compute all the blocks and parameters in the canonical forms we use these forms to derive canonical pairs for simultaneous congruence of pairs of complex symmetric and skew symmetric matrices as well as canonical forms for simultaneous congruence of pairs of complex hermitian matrices

a stable nonuniform sampling expansion involving derivatives the work of d a linden and n m abramson inf control vol 3 p 26 31 1960 and vol 4 p 95 6 1961 is completed in the sense that a full investigation of the convergence properties of the expansion is made by adapting the work of n levinson am math soc colloq pub vol 26 1940 on nonharmonic fourier series and general results from the theory of b splines the author extends the result to the case of sampling with uniformly spaced samples a stability property is proved

estimation of particle swarm distribution algorithms combining the benefits of pso and edas this paper presents a novel framework of the estimation of particle swarm distribution algorithms epsdas the aim is to effectively combine particle swarm optimization pso with the estimation of distribution algorithms edas without losing their unique features this aim is achieved by incorporating the following mechanisms 1 selection is applied to the local best solutions in order to obtain more promising individuals for model building 2 a probabilistic model of the problem is built from the selected solutions and 3 new individuals are generated by a stochastic combination of the eda s model sampling method and the pso s particle moving mechanism to exhibit the utility of the epsda framework an extended compact particle swarm optimization ecpso is developed by combining the strengths of the extended compact genetic algorithm ecga with binary pso bpso along the lines of the suggested framework due to its effective nature of harmonizing the global search of ecga with the local search of bpso ecpso is able to discover the optimal solution in a fast and reliable manner experimental results on artificial to real world problems have adduced grounds for the effectiveness of the proposed approach

mining maximal hyperclique pattern a hybrid search strategy a hyperclique pattern is a new type of association pattern that contains items which are highly affiliated with each other specifically the presence of an item in one transaction strongly implies the presence of every other item that belongs to the same hyperclique pattern in this paper we present an algorithm for mining maximal hyperclique patterns which specifies a more compact representation of hyperclique patterns and are desirable for many applications such as pattern based clustering our algorithm exploits key advantages of both the depth first search dfs strategy and the breadth first search bfs strategy indeed we adapt the equivalence pruning method one of the most efficient pruning methods of the dfs strategy into the process of the bfs strategy our experimental results show that the performance of our algorithm can be orders of magnitude faster than standard maximal frequent pattern mining algorithms particularly at low levels of support

convergence analysis of canonical genetic algorithms this paper analyzes the convergence properties of the canonical genetic algorithm cga with mutation crossover and proportional reproduction applied to static optimization problems it is proved by means of homogeneous finite markov chain analysis that a cga will never converge to the global optimum regardless of the initialization crossover operator and objective function but variants of cga s that always maintain the best solution in the population either before or after selection are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent cga these results are discussed with respect to the schema theorem