multidimensional density shaping by sigmoids an estimate of the probability density function of a random vector is obtained by maximizing the output entropy of a feedforward network of sigmoidal units with respect to the input weights classification problems can be solved by selecting the class associated with the maximal estimated density newton s optimization method applied to the estimated density yields a recursive estimator for a random variable or a random sequence a constrained connectivity structure yields a linear estimator which is particularly suitable for real time prediction a gaussian nonlinearity yields a closed form solution for the network s parameters which may also be used for initializing the optimization algorithm when other nonlinearities are employed a triangular connectivity between the neurons and the input which is naturally suggested by the statistical setting reduces the number of parameters applications to classification and forecasting problems are demonstrated

what is the goal of sensory coding a number of recent attempts have been made to describe early sensory coding in terms of a general information processing strategy in this paper two strategies are contrasted both strategies take advantage of the redundancy in the environment to produce more effective representations the first is described as a compact coding scheme a compact code performs a transform that allows the input to be represented with a reduced number of vectors cells with minimal rms error this approach has recently become popular in the neural network literature and is related to a process called principal components analysis pca a number of recent papers have suggested that the optimal compact code for representing natural scenes will have units with receptive field profiles much like those found in the retina and primary visual cortex however in this paper it is proposed that compact coding schemes are insufficient to account for the receptive field properties of cells in the mammalian visual pathway in contrast it is proposed that the visual system is near to optimal in representing natural scenes only if optimality is defined in terms of sparse distributed coding in a sparse distributed code all cells in the code have an equal response probability across the class of images but have a low response probability for any single image in such a code the dimensionality is not reduced rather the redundancy of the input is transformed into the redundancy of the firing pattern of cells it is proposed that the signature for a sparse code is found in the fourth moment of the response distribution i e the kurtosis in measurements with 55 calibrated natural scenes the kurtosis was found to peak when the bandwidths of the visual code matched those of cells in the mammalian visual cortex codes resembling wavelet transforms are proposed to be effective because the response histograms of such codes are sparse i e show high kurtosis when presented with natural scenes it is proposed that the structure of the image that allows sparse coding is found in the phase spectrum of the image it is suggested that natural scenes to a first approximation can be considered as a sum of self similar local functions the inverse of a wavelet possible reasons for why sensory systems would evolve toward sparse coding are presented

new eigenvalue estimates for complex matrices abstract in a recent work 1 we have proved that all the eigenvalues j of a complex matrix a of order n lie in a disk with center at tr a n and radius n 1 n k 1 n k 2 tr a 2 n 1 2 in this paper we prove that the eigenvalues of a are contained in a rectangle with vertices on the boundary circle of the mentioned disk improving in this way the result in 1 we recall some inequalities which alloww us to bound the radius of the disk and the rectangle the bounds can be computed without knowing the eigenvalues of a

localization of eigenvalues in elliptic regions abstract we prove that the eigenvalues j of an n by n complex matrix a with its characteristic polynomial having real coefficients lie in the elliptic region defined by 2 tr a n 2 2 y 2 2 2 where n 1 n n 1 n re k 2 re te a 2 n 1 2 and n 1 n k 1 n im k 2 1 2 this region is intersected with the strip y 1 2 k 1 u im k 2 1 2 to obtain an improved eigenvalue localization region we also give bounds for the semiaxes which can be computed without knowing the eigenvalues of a when a has r n nonzero eigenvalues we obtain a smaller elliptic region containing such nonzero eigenvalues

new conditions for the additive inverse eigenvalue problem for matrices abstract this paper deals with the following inverse eigenvalue problem given an n by n real symmetric matrix a and a set of real numbers i 1 n find a diagonal matrix d such that a d has eigenvalues i for the solvability of this problem a number of necessary conditions and sufficient conditions are known in this work new necessary conditions are derived while some sufficient conditions are optimized in particular one sufficient condition due to morel is obtained by optimizing a sufficient condition discovered by laborde

information maximization and independent component analysis is there a difference this article provides a detailed and rigorous analysis of the two commonly used methods for redundancy reduction linear independent component analysis ica posed as a direct minimization of a suitably chosen redundancy measure and information maximization infomax of a continuous stochastic signal transmitted through an appropriate nonlinear network the article shows analytically that ica based on the kullbackleibler information as a redundancy measure and infomax lead to the same solution if the parameterization of the output nonlinear functions in the latter method is sufficiently rich furthermore this work discusses the alternative redundancy measures not based on the kullback leibler information distance the practical issues of applying ica and infomax are also discussed and illustrated on the problem of extracting statistically independent factors from a linear pixel by pixel mixture of images

design of robust d stable iir filters using genetic algorithms with embedded stability criterion this paper proposes a novel evolution strategy for a genetic algorithm ga this new algorithm is then applied to design robust d alpha r stable infinite impulse response iir filters unlike existing research on designing iir filters by using ga in which the stability of iir filters is tested by trial and error after the evolution of each generation of a ga the stability criterion in this paper is embedded within the evolution of each generation consequently the stability of this system can be guaranteed without the need for any other checks of the stability criterion in the evolution of each generation numerical experimental results are discussed to illustrate the soundness of the proposed evolution strategy the robustness of the iir filters is achieved by ensuring that all poles of the filters are located inside a disk d alpha r contained in the unit circle in which alpha is the center r is the radius of the disk and ialphai r 1 so in this paper a d alpha r stability criterion will be first derived and then embedded in the ga for the design of robust iir filters finally two examples will be presented to show that the designed filters remain d alpha r stable during the evolution of the ga and will provide satisfactory results

relative optimization for blind deconvolution we propose a relative optimization framework for quasi maximum likelihood qml blind deconvolution and the relative newton method as its particular instance special hessian structure allows fast newton system construction and solution resulting in a fast convergent algorithm with iteration complexity comparable to that of gradient methods we also propose the use of rational infinite impulse response iir restoration kernels which constitute a richer family of filters than the traditionally used finite impulse response fir kernels we discuss different choices of nonlinear functions that are suitable for deconvolution of super and sub gaussian sources and formulate the conditions under which the qml estimation is stable simulation results demonstrate the efficiency of the proposed methods

sufficient stability bounds for slowly varying direct form recursive linear filters and their applications in adaptive iir filters this article derives a sufficient time varying bound on the maximum variation of the coefficients of an exponentially stable time varying direct form homogeneous linear recursive filter the stability bound is less conservative than all previously derived bounds for time varying iir systems the bound is then applied to control the step size of output error adaptive iir filters to achieve bounded input bounded output bibo stability of the adaptive filter experimental results that demonstrate the good stability characteristics of the resulting algorithms are included this article also contains comparisons with other competing output error adaptive iir filters the results indicate that the stabilized method possesses better convergence behavior than other competing techniques

cyclic coverings deformation and torelli theorem 0 1 in 1968 wavrik 20 studied cyclic branched coverings of compact complex manifolds he obtained a criterion that every small deformation of the total space is again a covering of the base then he applied his result to the case of cyclic coverings of the projective space in 1976 peters 14 and in 1985 konno 11 continued the work of wavrik in two directions they studied explicitly coverings over the hirzebruch surfaces s which have deformations themselves and they proved the infinitesimal torelli theorem for coverings of p and s under suitable assumptions on the branch divisor wavrik wrote his paper at a time where the deformation theory of k kodaira and d spencer for compact complex manifolds had reached a culmination in the meantime there has been developed a deformation theory for other objects in complex analysis too and today we can solve problems like the following

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

blind adaptation of stable discrete time iir filters in state space form blind deconvolution consists of extracting a source sequence and impulse response of a linear system from their convolution in the presence of system zeros close to the unit circle which give rise to very long impulse responses infinite impulse response iir adaptive structures are of use whose adaptation should be carefully designed in order to guarantee stability in this paper we propose a blind type discrete time iir adaptive filter structure realized in state space form that with a suitable parameterization of its coefficients remains stable the theory is first developed for a two pole filter whose numerical behavior is investigated via numerical experiments the proposed structure adaptation theory is then extended to a multipole structure realized as a cascade of two pole filters computer based experiments are proposed and discussed which aim at illustrating the behavior of the filter cascade on several cases of study the numerical results obtained show the proposed filters remain stable during adaptation and provide satisfactory deconvolution results

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

the generalized hodge conjecture for the quadratic complex of lines in projective four space we verify the generalized hodge conjecture ghc x 5 2 for the quadratic complex of lines in projective four space

sufficient conditions for the solubility of inverse eigenvalue problems abstract we define an inverse eigenvalue problem which contains as special cases the classical additive and multiplicative inverse eigenvalue problems using some results on the distance of eigenvalues from matrix diagonal elements and brouwer s fixed point theorem we give sufficient conditions for the solubility of the problem

a decreasing sequence of eigenvalue localization regions abstract we construct a decreasing sequence of rectangles rp in such a way that all the eigenvalues of a complex matrix a are contained in each rectangle when a is a matrix with real spectrum or a normal matrix each rp can be obtained without knowing the eigenvalues of a

fast fixed point neural blind deconvolution algorithm the aim of this letter is to introduce a new blind deconvolution algorithm based on fixed point optimization of a bussgang type cost function the cost function relies on approximate bayesian estimation achieved by an adaptive neuron the main feature of the presented algorithm is fast convergence that guarantees good deconvolution performances with limited computational demand as compared with algorithms of the same class

hypersurfaces of the flag variety deformation theory and the theorems of kodaira spencer torelli lefschetz m noether and serre

criteria for multichannel signal separation we consider the problem in which we want to separate two or more signals that are coupled to each other through an unknown multiple input multiple output linear system channel we prove that the signals can be decoupled or separated using only the condition that they are statistically independent and find even weaker sufficient conditions involving their cross polyspectra by imposing these conditions on the reconstructed signals we obtain a class of criteria for signal separation these criteria are universal in the sense that they do not require any prior knowledge or information concerning the nature of the source signals they may be communication signals or speech signals or any other 1 d or multidimensional signals e g images computationally efficient algorithms for implementing the proposed criteria that only involve the iterative solution to a linear least squares problem are presented

statistical independence and novelty detection with information preserving nonlinear maps according to barlow 1989 feature extraction can be understood as finding a statistically independent representation of the probability distribution underlying the measured signals the search for a statistically independent representation can be formulated by the criterion of minimal mutual information which reduces to decorrelation in the case of gaussian distributions if nongaussian distributions are to be considered minimal mutual information is the appropriate generalization of decorrelation as used in linear principal component analyses pca we also generalize to nonlinear transformations by only demanding perfect transmission of information this leads to a general class of nonlinear transformations namely symplectic maps conservation of information allows us to consider only the statistics of single coordinates the resulting factorial representation of the joint probability distribution gives a density estimation we apply this concept to the real world problem of electrical motor fault detection treated as a novelty detection task

deformation of varieties defined by sections in homogeneous vector bundles in the present paper we prove some generalizations of a theorem of k kodaira and d spencer they showed in 1958 that any smooth projective algebraic hypersurface which is not a k3 surface remains projective algebraic under small deformation in a previous paper 13 we have shown that the analogous statement remains valid for projective algebraic complete intersections with singularities too recently there has been studied an interesting and rather different generalization by borcea 2 from his point of view the complex projective space is the most simple example in the class of homogeneous rational k ihler manifolds of rank 1 borcea generalizes the result of kodaira and spencer to smooth complete intersections in homogeneous manifolds of this class which covers for instance all grassmannians all these results correspond to special cases of the following question consider a compact complex manifold z together with a vector bundle e and a section of it vanishing along a subvariety x of z of codimension equal to rank e in which case can every small deformation of x be obtained by varying the section in h e a sufficient criterion is the vanishing of the cohomology groups

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

convergent algorithm for sensory receptive field development an unsupervised developmental algorithm for linear maps is derived which reduces the pixel entropy using the measure introduced in previous work at every update and thus removes pairwise correlations between pixels since the measure of pixel entropy has only a global minimum the algorithm is guaranteed to converge to the minimum entropy map such optimal maps have recently been shown to possess cognitively desirable properties and are likely to be used by the nervous system to organize sensory information the algorithm derived here turns out to be one proposed by goodall for pairwise decorrelation it is biologically plausible since in a neural network implementation it requires only data available locally to a neuron in training over ensembles of two dimensional input signals with the same spatial power spectrum as natural scenes networks develop output neurons with center surround receptive fields similar to those of ganglion cells in the retina some technical issues pertinent to developmental algorithms of this sort such as symmetry fixing are also discussed

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing