finite alphabet information and multivariate blind deconvolution and identification of linear systems this article addresses the problem of estimating a multivariate linear system from its output when the input is an unobservable sequence of random vectors with finite alphabet distribution by explicitly utilizing the finite alphabet property an estimation method is proposed under the traditional inverse filtering paradigm as a generalization of a univariate method that has been studied previously identifiability of multivariate systems by the proposed method is proved mathematically under very mild conditions that can be satisfied even if the input is nonstationary and has both cross channel and serial statistical dependencies statistical super efficiency in estimating both parametric and nonparametric systems is also established for an alphabet based cost function

generalized information potential criterion for adaptive system training we have previously proposed the quadratic renyi s error entropy as an alternative cost function for supervised adaptive system training an entropy criterion instructs the minimization of the average information content of the error signal rather than merely trying to minimize its energy in this paper we propose a generalization of the error entropy criterion that enables the use of any order of renyi s entropy and any suitable kernel function in density estimation it is shown that the proposed entropy estimator preserves the global minimum of actual entropy the equivalence between global optimization by convolution smoothing and the convolution by the kernel in parzen windowing is also discussed simulation results are presented for time series prediction and classification where experimental demonstration of all the theoretical concepts is presented

smooth yamabe invariant and surgery we prove a surgery formula for the smooth yamabe invariant sigma m of a compact manifold m assume that n is obtained from m by surgery of codimension at least 3 we prove the existence of a positive number lambda n depending only on the dimension n of m such that sigma n geq min sigma m lambda n

sur quelques problemes de courbure scalaire abstract in this article we prove among other things some results about two problems which are the subject of announces these last decades 1 the compactness of the set of the solutions of the yamabe equation on a compact riemannian manifold 2 a generalization of a result of the author which is necessary to solve the yamabe problem when 2 n 6

a fast recursive total least squares algorithm for adaptive fir filtering this paper proposes a new fast recursive total least squares n rtls algorithm to recursively compute the tls solution for adaptive finite impulse response fir filtering the n rtls algorithm is based on the minimization of the constrained rayleigh quotient c rq in which the last entry of the parameter vector is constrained to the negative one as analysis results on the convergence of the proposed algorithm we study the properties of the stationary points of the c rq the high computational efficiency of the new algorithm depends on the efficient computation of the fast gain vector fgv and the adaptation of the c rq since the last entry of the parameter vector in the c rq has been fixed as the negative one a minimum point of the c rq is searched only along the input data vector and a more efficient n rtls algorithm is obtained by using the fgv as compared with davila s rtls algorithms the n rtls algorithm saves the 6m number of multiplies divides and square roots mads the global convergence of the new algorithm is studied by lasalle s invariance principle the performances of the relevant algorithms are compared via simulations and the long term numerical stability of the n rtls algorithm is verified

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

blind identification and deconvolution of linear systems driven by binary random sequences the problem of blind identification and deconvolution of linear systems with independent binary inputs is addressed to solve the problem a linear system is applied to the observed data and adjusted so as to produce binary outputs it is proved that the system coincides with the inverse of the unknown system with scale and shift ambiguities whether it is minimum or nonminimum phase these results are derived for nonstationary independent binary inputs of infinite or finite length based on these results an identification method is proposed for parametric linear systems it is shown that under some mild conditions a consistent estimator of the parameter can be obtained by minimizing a binariness criterion for the output data unlike many other blind identification and deconvolution methods this criterion handles nonstationary signals and does not utilize any moment information of the inputs three numerical examples are presented to demonstrate the effectiveness of the proposed method

convergence properties and data efficiency of the minimum error entropy criterion in adaline training recently we have proposed the minimum error entropy mee criterion as an information theoretic alternative to the widely used mean square error criterion in supervised adaptive system training for this purpose we have formulated a nonparametric estimator for renyi s entropy that employs parzen windowing mathematical investigation of the proposed entropy estimator revealed interesting insights about the process of information theoretical learning this new estimator and the associated criteria have been applied to the supervised and unsupervised training of adaptive systems in a wide range of problems successfully in this paper we analyze the structure of the mee performance surface around the optimal solution and we derive the upper bound for the step size in adaptive linear neuron adaline training with the steepest descent algorithm using mee in addition the effects of the entropy order and the kernel size in parzen windowing on the shape of the performance surface and the eigenvalues of the hessian at and around the optimal solution are investigated conclusions from the theoretical analyses are illustrated through numerical examples

minimum entropy of error estimation for discrete random variables the principle of minimum entropy of error estimation meee is formulated for discrete random variables in the case when the random variable to be estimated is binary we show that the meee is given by a neyman pearson type strictly monotonous test in addition the asymptotic behavior of the error probabilities is proved to be equivalent to that of the bayesian test

error entropy in classification problems a univariate data analysis entropy based cost functions are enjoying a growing attractiveness in unsupervised and supervised classification tasks better performances in terms both of error rate and speed of convergence have been reported in this letter we study the principle of error entropy minimization eem from a theoretical point of view we use shannon s entropy and study univariate data splitting in two class problems in this setting the error variable is a discrete random variable leading to a not too complicated mathematical analysis of the error entropy we start by showing that for uniformly distributed data there is equivalence between the eem split and the optimal classifier in a more general setting we prove the necessary conditions for this equivalence and show the existence of class configurations where the optimal classifier corresponds to maximum error entropy the presented theoretical results provide practical guidelines that are illustrated with a set of experiments with both real and simulated data sets where the effectiveness of eem is compared with the usual mean square error minimization

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

maximum entropy membership functions for discrete fuzzy variables due to the deficiency of information the membership function of a fuzzy variable cannot be obtained explicitly it is a challenging work to find an appropriate membership function when certain partial information about a fuzzy variable is given such as expected value or moments this paper solves such problems for discrete fuzzy variables via maximum entropy principle and proves some maximum entropy theorems with certain constraints a genetic algorithm is designed to solve the general maximum entropy model for discrete fuzzy variables which is illustrated by some numerical experiments

minimum entropy of error principle in estimation abstract the principle of minimum error entropy estimation as found in the work of weidemann and stear is reformulated as a problem of finding optimum locations of probability densities in a given mixture such that the resulting differential entropy is minimized new results concerning the entropy lower bound are derived continuity of the entropy and attaining the minimum entropy are proved in the case where the mixture is finite some other examples and situations in particular that of symmetric unimodal densities are studied in more detail

a presentation for j4 let g g j 4 be the rank 4 p geometry with janko s fourth group j 4 as a flag transitive automorphism group let a be the amalgam of maximal parabolics corresponding to the action of j 4 on g we prove that g is simply connected i e that it has no proper coverings this result is equivalent to the fact that j 4 coincides with the universal closure of the amalgam a so any presentation for a is a presentation for j 4 this implies in particular that a nice set of generators and relations given by g stroth and r weiss is a presentation for j 4 in addition we obtain a uniqueness proof for j 4

solution complete de la c0 compacite de l ensemble des solutions de l equation de yamabe abstract on a compact riemannian manifold v n g n 2 a long standing question is does the set of the solutions of the yamabe equation compact in c 0 there are three cases in the yamabe problem see aubin t aubin some nonlinear problems in riemannian geometry springer verlag new york 1998 according to the sign of the inf of the yamabe functional we prove the c 0 compactness of the set of the solutions of the yamabe equation except on the sphere in the positive case the only case which makes difficulties

continuously differentiable sample spacing entropy estimation the insufficiency of using only second order statistics and premise of exploiting higher order statistics of the data has been well understood and more advanced objectives including higher order statistics especially those stemming from information theory such as error entropy minimization are now being studied and applied in many contexts of machine learning and signal processing in the adaptive system training context the main drawback of utilizing output error entropy as compared to correlation estimation based second order statistics is the computational load of the entropy estimation which is usually obtained via a plug in kernel estimator sample spacing estimates offer computationally inexpensive entropy estimators however resulting estimates are not differentiable hence not suitable for gradient based adaptation in this brief paper we propose a nonparametric entropy estimator that captures the desirable properties of both approaches the resulting estimator yields continuously differentiable estimates with a computational complexity at the order of those of the sample spacing techniques the proposed estimator is compared with the kernel density estimation kde based entropy estimator in the supervised neural network training framework with computation time and performance comparisons

identification of noisy linear systems with discrete random input we propose a new method for the blind deconvolution of a discrete linear system perturbed with additive noise the method comes from a characterization of discrete variables when perturbed with additive noise with unknown variance together with a characterization of this variance through hankel matrix based on this probabilistic description an estimator is proposed for the inverse system and the variance of the noise these estimators are shown to be consistent under weak assumptions whatever the signal to noise ratio is in particular the input signal needs not be independently distributed numerical examples demonstrate the effectiveness of the method even when nonstationary signals are used as inputs

error whitening criterion for adaptive filtering theory and algorithms mean squared error mse has been the dominant criterion in adaptive filter theory a major drawback of the mse criterion in linear filter adaptation is the parameter bias in the wiener solution when the input data are contaminated with noise we propose and analyze a new augmented mse criterion called the error whitening criterion ewc ewc is able to eliminate this bias when the noise is white we will determine the analytical solution of the ewc discuss some interesting properties and develop stochastic gradient and other fast algorithms to calculate the ewc solution in an online fashion the stochastic algorithms are locally computable and have structures and complexities similar to their mse based counterparts lms and nlms convergence of the stochastic gradient algorithm is established with mild assumptions and upper bounds on the step sizes are deduced for guaranteed convergence we will briefly discuss an rls like recursive error whitening rew algorithm and a minor components analysis mca based ewc total least squares tls algorithm and further draw parallels between the rew algorithm and the instrumental variables iv method for system identification finally we will demonstrate the noise rejection capability of the ewc by comparing the performance with mse criterion and tls

equivariant yamabe problem and hebey vaugon conjecture abstract in their study of the yamabe problem in the presence of isometry groups e hebey and m vaugon announced a conjecture this conjecture generalizes t aubin s conjecture which has already been proven and is sufficient to solve the yamabe problem in this paper we generalize aubin s theorem and we prove the hebey vaugon conjecture in dimensions less or equal to 37

new property of a generalized holder s inequality and its applications in this paper we present a new property of a generalized holder s inequality and then we obtain a new refinement of the generalized holder s inequality as applications we give a generalization and refinement of the opial beesack inequality by using the obtained result moreover as an application in information theory we give a refinement of singh s inequality which is a generalized shannon s inequality

identification input design for consistent parameter estimation of linear systems with binary valued output observations input design is of essential importance in system identification for providing sufficient probing capabilities to guarantee convergence of parameter estimates to their true values this paper presents conditions on input signals that characterize their probing richness for strongly consistent parameter estimation of linear systems with binary valued output observations necessary and sufficient conditions on periodic signals are derived for sufficient richness these conditions are further studied under different system configurations including open loop and feedback systems and different scenarios of noises including actuator noise input measurement noise and output measurement noise in addition to system parameter estimation essential properties of identifiability and input conditions are also derived when sensor thresholds or noise distribution functions are unknown the findings of this paper provide a foundation to study identification of systems that either use binary valued or quantized sensors or involve communication channels which mandate quantization of signals

identification of wiener systems with binary valued output observations this work is concerned with identification of wiener systems whose outputs are measured by binary valued sensors the system consists of a linear fir finite impulse response subsystem of known order followed by a nonlinear function with a known parametrization structure the parameters of both linear and nonlinear parts are unknown input design identification algorithms and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible it is shown that under scaled periodic inputs identification of wiener systems can be decomposed into a finite number of core identification problems the concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the wiener system can be identified with binary valued observations under scaled full rank conditions and joint identifiability a strongly convergent algorithm is constructed the algorithm is shown to be asymptotically efficient for the core identification problem hence achieving asymptotic optimality in its convergence rate for computational simplicity recursive algorithms are also developed

survival information potential a new criterion for adaptive system training recently the information potential ip of order defined as the argument of the log in the order renyi entropy has been successfully used as an information theoretic criterion for supervised adaptive system training in this paper we use the survival function or equivalently the distribution function of an absolute value transformed random variable to define a new information potential named the survival information potential sip compared with the ip the sip has some advantages such as validity in a wide range of distributions robustness and the simplicity in computation the properties of sip and a simple formula for computing the empirical sip are given in the paper finally the sip criterion is applied in adaptive system training and simulation examples on fir adaptive filtering kernel adaptive filtering and time delay neural networks tdnns training are presented to demonstrate the performance