a polynomial time approximation algorithm for the permanent of a matrix with nonnegative entries we present a polynomial time randomized algorithm for estimating the permanent of an arbitrary n n matrix with nonnegative entries this algorithm technically a fully polynomial randomized approximation scheme computes an approximation that is with high probability within arbitrarily small specified relative error of the true value of the permanent

stable galerkin reduced order models for linearized compressible flow the galerkin projection procedure for construction of reduced order models of compressible flow is examined as an alternative discretization of the governing differential equations the numerical stability of galerkin models is shown to depend on the choice of inner product for the projection for the linearized euler equations a symmetry transformation leads to a stable formulation for the inner product boundary conditions for compressible flow that preserve stability of the reduced order model are constructed preservation of stability for the discrete implementation of the galerkin projection is made possible using a piecewise smooth finite element basis stability of the reduced order model using this approach is demonstrated on several model problems where a suitable approximation basis is generated using proper orthogonal decomposition of a transient computational fluid dynamics simulation

a novel multiset integrated canonical correlation analysis framework and its application in feature fusion multiset canonical correlation analysis mcca is difficult to effectively express the integrated correlation among multiple feature vectors in feature fusion thus this paper firstly presents a novel multiset integrated canonical correlation analysis micca framework the micca establishes a discriminant correlation criterion function of multi group variables based on generalized correlation coefficient the criterion function can clearly depict the integrated correlation among multiple feature vectors then the paper presents a multiple feature fusion theory and algorithm using the micca method the detailed process of the algorithm is as follows firstly extract multiple feature vectors from the same patterns by using different feature extraction methods then extract multiset integrated canonical correlation features using micca finally form effective discriminant feature vectors through two given feature fusion strategies for pattern classification the multi group feature fusion method based on micca not only achieves the aim of feature fusion but also removes the redundancy between features the experiment results on cenparmi handwritten arabic numerals and uci multiple features database show that the micca method has better recognition rates and robustness than the fusion methods based on canonical correlation analysis cca and mcca

analytical level crossing rates and average fade durations for diversity techniques in nakagami fading channels the level crossing rates lcrs and average fade durations afds of a fading channel find diverse applications in the evaluation and design of wireless communication systems analytical expressions for these quantities are available in the literature for certain diversity reception techniques but are generally limited to the rayleigh fading channel with few exceptions moreover the methods employed are usually specific to a certain channel diversity pair and thus cannot be applied to all cases of interest using a unified methodology we derive analytical expressions for the lcrs and afds for three diversity reception techniques and a general nakagami 1960 fading channel we provide novel analytical expressions for selection combining sc and equal gain combining egc and rederive in a more general manner the case of maximal ratio combining mrc it is shown that our general results reduce to some specific cases previously published these results are used to examine the effects of the diversity technique the number of receiving branches and severity of the fading on the concerned quantities it is observed that as the nakagami m parameter and the diversity order increase the behavior of the combined received envelope for egc follows closely the one for mrc and distances itself from sc

zero crossing rates of mixtures and products of gaussian processes formulas for the expected zero crossing rate of non gaussian mixtures and products of gaussian processes are obtained the approach we take is to first derive the expected zero crossing rate in discrete time and then obtain the rate in continuous time by an appropriate limiting argument the processes considered which are non gaussian but derived from gaussian processes serve to illustrate the variability of the zero crossing rate in terms of the normalized autocorrelation function p t of the process for gaussian processes rice s formula gives the expected zero crossing rate in continuous time as 1 spl pi spl radic spl rho 0 we show processes exist with expected zero crossing rates given by spl kappa spl pi spl radic spl rho 0 with either spl kappa spl gt 1 or spl kappa spl lt 1 consequently such processes can have an arbitrarily large or small zero crossing rate as compared to a gaussian process with the same autocorrelation function

on the second derivative of a gaussian process envelope we explore some dynamic characteristics of the envelope of a bandpass gaussian process which are of interest in wireless fading channels specifically we show that unlike the first derivative the second derivative of the envelope which appears in a number of applications does not exist in the traditional mean square sense however we prove that the envelope is twice differentiable almost everywhere with probability one if the power spectrum of the bandpass gaussian process satisfies a certain condition we also derive an integral form for the probability density function pdf of the second derivative of the envelope assuming an arbitrary power spectrum

minimal subspace rotation on the stiefel manifold for stabilization and enhancement of projection based reduced order models for the compressible navier stokes equations for a projection based reduced order model rom of a fluid flow to be stable and accurate the dynamics of the truncated subspace must be taken into account this paper proposes an approach for stabilizing and enhancing projection based fluid roms in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace attention is focused on the full non linear compressible navier stokes equations in specific volume form as a step toward a more general formulation for problems with generic non linearities unlike traditional approaches no empirical turbulence modeling terms are required and consistency between the rom and the navier stokes equation from which the rom is derived is maintained mathematically the approach is formulated as a trace minimization problem on the stiefel manifold the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems including a problem involving laminar flow over an airfoil with a high angle of attack and a channel driven cavity flow problem

zero crossing rates of functions of gaussian processes formulas for the expected zero crossing rates of random processes that are monotone transformations of gaussian processes can be obtained by using two different techniques the first technique involves derivation of the expected zero crossing rate for discrete time processes and extends the result of the continuous time case by using an appropriate limiting argument the second is a direct method that makes successive use of r price s 1958 theorem the chain rule for derivatives and s o rice s 1954 formula for the expected zero crossing rate of a gaussian process a constant which depends on the variance of the transformed process and a second moment of its derivative is derived multiplying rice s original expression by this constant yields the zero crossing formula for the transformed process the two methods can be used for the general level crossing problem of random processes that are monotone functions of a gaussian process

virtual branch analysis of symbol error probability for hybrid selection maximal ratio combining in rayleigh fading we derive analytical expressions for the symbol error probability sep for a hybrid selection maximal ratio combining h s mrc diversity system in multipath fading wireless environments with h s mrc l out of n diversity branches are selected and combined using maximal ratio combining mrc we consider coherent detection of m ary phase shift keying mpsk and quadrature amplitude modulation mqam using h s mrc for the case of independent rayleigh fading with equal signal to noise ratio averaged over the fading the proposed problem is made analytically tractable by transforming the ordered physical diversity branches which are correlated into independent and identically distributed i i d virtual branches which results in a simple derivation of the sep for arbitrary l and n we further obtain a canonical structure for the sep of h s mrc as a weighted sum of the elementary seps which are the seps using mrc with i i d diversity branches in rayleigh fading or equivalently the seps of the nondiversity single branch system in nakagami fading whose closed form expressions are well known we present numerical examples illustrating that h s mrc even with l spl lt n can achieve a performance close to that of n branch mrc

complete canonical correlation analysis with application to multi view gait recognition canonical correlation analysis cca is a well known multivariate analysis method for quantifying the correlations between two sets of multidimensional variables however for multi view gait recognition it is difficult to directly apply cca to deal with two sets of high dimensional vectors because of computational complexity moreover in such situation the eigenmatrix of cca is usually singular which makes the direct implementation of the cca algorithm almost impossible in practice pca or singular value decomposition is employed as a preprocessing step to solve these problems nevertheless this strategy may discard dimensions that contain important discriminative information and correlation information to overcome the shortcomings of cca when dealing with two sets of high dimensional vectors we develop a novel method named complete canonical correlation analysis c3a in our method we first reformulate the traditional cca so that we can avoid the computing of the inverse of a high dimensional matrix with the help of this reformulation c3a further transforms the singular generalized eigensystem computation of cca into two stable eigenvalue decomposition problems moreover a feasible and effective method is proposed to alleviate the computational burden of high dimensional matrix for typical gait image data experimental results on two benchmark gait databases casia gait database and the challenge usf gait database demonstrate the effectiveness of the proposed method highlightswe overcome the shortcomings of cca when dealing with high dimensional matrix the singularity of generalized eigenvalue problem in cca is overcome naturally the important discriminative information is preserved completely in our algorithm our scheme learns stable and complete solutions the multi view gait recognition is achieved based on our method

accelerating simulated annealing for the permanent and combinatorial counting problems we present an improved cooling schedule for simulated annealing algorithms for combinatorial counting problems under our new schedule the rate of cooling accelerates as the temperature decreases thus fewer intermediate temperatures are needed as the simulated annealing algorithm moves from the high temperature easy region to the low temperature difficult region we present applications of our technique to colorings and the permanent perfect matchings of bipartite graphs moreover for the permanent we improve the analysis of the markov chain underlying the simulated annealing algorithm this improved analysis combined with the faster cooling schedule results in an o n 7 log 4 n time algorithm for approximating the permanent of a 0 1 matrix

stabilization of projection based reduced order models summary a rigorous method for stabilizing projection based linear reduced order models without significantly affecting their accuracy is proposed unlike alternative approaches this method is computationally efficient it requires primarily the solution of a small scale convex optimization problem furthermore it is nonintrusive in the sense that it operates directly on readily available reduced order operators these can be precomputed using any data compression technique including balanced truncation balanced proper orthogonal decomposition proper orthogonal decomposition or moment matching the proposed method is illustrated with three applications the stabilization of the reduction of the computational fluid dynamics based model of a linearized unsteady supersonic flow the reduction of a computational structural dynamics system and the stabilization of the reduction of a coupled computational fluid dynamics computational structural dynamics model of a linearized aeroelastic system in the transonic flow regime copyright 2012 john wiley sons ltd

expected number of maxima in the envelope of a spherically invariant random process in many engineering applications specially in communication engineering one encounters a bandpass non gaussian random process with a slowly varying envelope among the available models for non gaussian random processes spherically invariant random processes sirps play an important role these processes are of interest mainly due to the fact that they allow one to relax the assumption of gaussianity while keeping many of its useful characteristics in this paper we have derived a simple and closed form formula for the expected number of maxima of a sirp envelope since gaussian random processes are special cases of sirps this formula holds for gaussian random processes as well in contrast with the available complicated expression for the expected number of maxima in the envelope of a gaussian random process our simple result holds for an arbitrary power spectrum the key idea in deriving this result is the application of the characteristic function rather than the probability density function for calculating the expected level crossing rate of a random process

approximating the permanent a randomised approximation scheme for the permanent of a 0 1s presented the task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph the latter is accomplished by simulating a markov chain whose states are the matchings in the graph for a wide class of 0 1 matrices the approximation scheme is fully polynomial i e runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output this class includes all dense matrices those that contain sufficiently many 1 s and almost all sparse matrices in some reasonable probabilistic model for 0 1 matrices of given density for the approach sketched above to be computationally efficient the markov chain must be rapidly mixing informally it must converge in a short time to its stationary distribution a major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing apparently the first such result for a markov chain with genuinely c

level crossing rate in terms of the characteristic function a new approach for calculating the fading rate in diversity systems the level crossing rate lcr of a random process conveys useful information about the underlying process and is of interest in diverse engineering fields in wireless communications it is related to the system characteristics such as handoff outage probability fading rate average duration of fades velocity or maximum doppler shift of the mobile and the effect of diversity on fading the lcr formula was originally derived by rice in terms of the joint probability density function pdf of the underlying process and its time derivative in this letter we express the lcr in terms of the joint characteristic function cf this new formula is useful for many cases where the joint cf is simpler to derive than the associated joint pdf as an application and for a direct sequence code division multiple access system the fading rate at the output of a rake receiver with either maximal ratio combiner or postdetection equal gain combiner operating over a frequency selective fading channel with different path statistics is easily calculated using the new cf based lcr formula

generalized framework for the level crossing analysis of ordered random processes this paper investigates the following general problem relating to ordered random processes given n independent but not necessarily identical random processes how frequently on average does any given process become one of the pth p 1 2 n 1 largest processes this is a fundamental problem arising in the design and analysis of contemporary multidimensional wireless communication systems e g multiantenna multiuser employing opportunistic selection we formulate this problem as one involving the level crossing rate lcr of a carefully defined ordered random process across the zero threshold which we solve by developing a new mathematical framework based on the theory of permanents for the case where the processes correspond to time varying rayleigh fading channels we present exact closed form formulas for the lcr simplified tight upper bounds as well as asymptotic results for n and p approaching infinity but with fixed ratio these results reveal interesting fundamental limits for the lcr and are shown to given meaningful insight even for small values of n and p we further use our mathematical framework to characterize the required per branch and overall switching rate of a generalized selection combining diversity receiver allowing for different average powers for each branch with the aid of majorization theory we demonstrate that the overall switching rate is maximized when the power delay profile is uniform

approximating the α permanent summary the standard matrix permanent is the solution to a number of combinatorial and graph theoretic problems and the weighted permanent is the density function for a class of cox processes called boson processes the exact computation of the ordinary permanent is known to be p complete and the same appears to be the case for the permanent for most values of at present the lack of a satisfactory algorithm for approximating the permanent is a formidable obstacle to the use of boson processes in applied work this paper proposes an importance sampling estimator using nonuniform random permutations generated in a cycle format empirical investigation reveals that the estimator works well for the sorts of matrices that arise in point process applications involving up to a few hundred points we conclude with a numerical illustration of the bayes estimate of the intensity function of a boson point process which is a ratio of permanents

origin of rice s formula the origin of s o rice s formula for the average rate of level crossings of a rather general random process is traced to his 1936 private notes entitled singing transmission lines the notes formulate an engineering problem in terms of the probability distribution of the absolute maximum of an envelope process in a closed interval rice showed that if the envelope of the reflected wave on a loaded transmission line were to equal or exceed the maximum value in the closed interval then singing or oscillation could be expected to occur and the analog transmission system would become unstable and useless for the transmission of information the formula and its generalizations are now basic for the analysis of level crossings and first and second passage times of random processes

canonical correlation analysis for multilabel classification a least squares formulation extensions and analysis canonical correlation analysis cca is a well known technique for finding the correlations between two sets of multidimensional variables it projects both sets of variables onto a lower dimensional space in which they are maximally correlated cca is commonly applied for supervised dimensionality reduction in which the two sets of variables are derived from the data and the class labels respectively it is well known that cca can be formulated as a least squares problem in the binary class case however the extension to the more general setting remains unclear in this paper we show that under a mild condition which tends to hold for high dimensional data cca in the multilabel case can be formulated as a least squares problem based on this equivalence relationship efficient algorithms for solving least squares problems can be applied to scale cca to very large data sets in addition we propose several cca extensions including the sparse cca formulation based on the 1 norm regularization we further extend the least squares formulation to partial least squares in addition we show that the cca projection for one set of variables is independent of the regularization on the other set of multidimensional variables providing new insights on the effect of regularization on cca we have conducted experiments using benchmark data sets experiments on multilabel data sets confirm the established equivalence relationships results also demonstrate the effectiveness and efficiency of the proposed cca extensions

switching rates of dual selection diversity and dual switch and stay diversity the switching rates of dual selection combining diversity and dual switch and stay combining diversity in rayleigh rician and nakagami m m half integer or integer fading are derived closed form or single integral expressions are obtained for both the cases of balanced channels and unbalanced channels

facial expression recognition using kernel canonical correlation analysis kcca in this correspondence we address the facial expression recognition problem using kernel canonical correlation analysis kcca following the method proposed by lyons et al and zhang et al we manually locate 34 landmark points from each facial image and then convert these geometric points into a labeled graph lg vector using the gabor wavelet transformation method to represent the facial features on the other hand for each training facial image the semantic ratings describing the basic expressions are combined into a six dimensional semantic expression vector learning the correlation between the lg vector and the semantic expression vector is performed by kcca according to this correlation we estimate the associated semantic expression vector of a given test image and then perform the expression classification according to this estimated semantic expression vector moreover we also propose an improved kcca algorithm to tackle the singularity problem of the gram matrix the experimental results on the japanese female facial expression database and the ekman s pictures of facial affect database illustrate the effectiveness of the proposed method