optimal channel efficiency in a sensory network spontaneous neural activity has been increasingly recognized as a subject of key relevance in neuroscience it exhibits nontrivial spatiotemporal structure reflecting the organization of the underlying neural network and has proved to be closely intertwined with stimulus induced activity patterns as an additional contribution in this regard we report computational studies that strongly suggest that a stimulus free feature rules the behavior of an important psychophysical measure of the sensibility of a sensory system to a stimulus the so called dynamic range indeed in this paper we show that the entropy of the distribution of avalanche lifetimes information efficiency since it can be interpreted as the efficiency of the network seen as a communication channel always accompanies the dynamic range in the benchmark model for sensory systems specifically by simulating the kinouchi copelli kc model on two broad families of model networks we generically observed that both quantities always increase or decrease together as functions of the average branching ratio the control parameter of the kc model and that the information efficiency typically exhibits critical optimization jointly with the dynamic range i e both quantities are optimized at the same value of that control parameter that turns out to be the critical point of a nonequilibrium phase transition in contrast with the practice of taking power laws to identify critical points in most studies describing measured neuronal avalanches we rely on data collapses as more robust signatures of criticality to claim that critical optimization may happen even when the distribution of avalanche lifetimes is not a power law as suggested by a recent experiment finally we note that the entropy of the size distribution of avalanches information capacity does not always follow the dynamic range and the information efficiency when they are critically optimized despite being more widely used than the latter to describe the computational capabilities of a neural network this strongly suggests that dynamical rules allowing a proper temporal matching of the states of the interacting neurons is the key for achieving good performance in information processing rather than increasing the number of available units

approximate finite dimensional filtering for polynomial states over polynomial observations in this article the mean square filtering problem for polynomial system states over polynomial observations is studied proceeding from the general expression for the stochastic ito differentials o

adaptive estimation of the dynamics of a discrete time stochastic volatility model abstract this paper is concerned with the discrete time stochastic volatility model y i exp x i 2 i x i 1 b x i x i i 1 where only y i is observed the model is rewritten as a particular hidden model z i x i e i x i 1 b x i x i i 1 where i and e i are independent sequences of i i d noise moreover the sequences x i and e i are independent and the distribution of e is known then our aim is to estimate the functions b and 2 when only observations z 1 z n are available we propose to estimate b f and b 2 2 f and study the integrated mean square error of projection estimators of these functions on automatically selected projection spaces by ratio strategy estimators of b and 2 are then deduced the mean square risk of the resulting estimators are studied and their rates are discussed lastly simulation experiments are provided constants in the penalty functions defining the estimators are calibrated and the quality of the estimators is checked on several examples

spatially inhomogeneous linear inverse problems with possible singularities the objective of the present paper is to introduce the concept of a spatially inhomogeneous linear inverse problem which to the best of the author s knowledge has never been considered previously in statistical framework but is emerging due to a variety of practical applications the special feature of the problem is that the degree of ill posedness depends not only on the scale but also on location in this case the rates of convergence are determined by the interaction of four parameters the smoothness and spatial homogeneity of the unknown function f and degrees of ill posedness and spatial inhomogeneity of operator q an interesting property here is that if operator q is weakly inhomogeneous then the rates of convergence are not influenced by spatial inhomogeneity of operator q and coincide with the rates which are usual for homogeneous linear inverse problems on the other hand if operator q is moderately or strongly inhomogeneous convergence rates are significantly affected by the degree of spatial inhomogeneity estimators obtained in the paper are based either on wavelet vaguelette decomposition if the norms of all vaguelettes are finite or on a hybrid of wavelet vaguelette decomposition and galerkin method if vaguelettes in the neighborhood of the singularity point have infinite norms the hybrid estimator is a combination of a linear part in the vicinity of the singularity point and the nonlinear block thresholding wavelet estimator elsewhere to attain adaptivity an optimal resolution level for the linear singularity affected portion of the estimator is obtained using lepskii 1990 1999 method subsequently this resolution level is used as the lowest resolution level for the nonlinear wavelet estimator we show that convergence rates of the hybrid estimator lie within a logarithmic factor of the optimal minimax convergence rates the theory presented in the paper is supplemented by examples of deconvolution based on irregularly spaced observations or in the presence of a heteroscedastic noise the latter problem is also examined via a limited simulation study which demonstrates advantages of the hybrid estimator when the degree of spatial inhomogeneity is high

h_ infty filtering for nonlinear discrete time systems subject to quantization and packet dropouts this paper investigates the problem of h filtering for a class of nonlinear discrete time systems with measurement quantization and packet dropouts each output is transmitted via an independent communication channel and the phenomenon of packet dropouts in transmission is governed by an individual random binary distribution while the quantization errors are treated as sector bound uncertainties based on a piecewise lyapunov function an approach to the design of h piecewise filter is pro posed such that the filtering error system is stochastically stable with a guaranteed h performance some slack matrices are introduced to facilitate the filter design procedure by eliminating the coupling between the lyapunov matrices and the system matrices the filter parameters can be obtained by solving a set of linear matrix inequalities lmis which are numerically tractable with commercially available software finally two illustrative examples are provided to show the effectiveness of the proposed method

a deconvolution approach to estimation of a common shape in a shifted curves model this paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model we show that this problem can be transformed into a linear inverse problem where the density of the random shifts plays the role of a convolution operator an adaptive estimator of the mean pattern based on wavelet thresholding is proposed we study its consistency for the quadratic risk as the number of observed curves tends to infinity and this estimator is shown to achieve a near minimax rate of convergence over a large class of besov balls this rate depends both on the smoothness of the common shape of the curves and on the decay of the fourier coefficients of the density of the random shifts hence this paper makes a connection between mean pattern estimation and the statistical analysis of linear inverse problems which is a new point of view on curve registration and image warping problems we also provide a new method to estimate the unknown random shifts between curves some numerical experiments are given to illustrate the performances of our approach and to compare them with another algorithm existing in the literature

h sub spl infin nonlinear filtering of discrete time processes this correspondence investigates the problem of h sub spl infin estimation of a discrete time nonlinear process an estimator which may be nonlinear is introduced so that an h sub spl infin norm like of what we call a generalized estimation error is guaranteed to be bounded by a prescribed level conditions for the existence of such an estimator and formulae for its derivation are obtained utilizing a discrete time analog of the hamilton jacobi inequality an approximate filter based on linearization is developed this filter relates to the extended kalman filter in the same way that the linear h sub spl infin filter relates to the kalman filter

robust reduced order h output feedback control of retarded stochastic linear systems a method for designing reduced order output feedback controllers for linear time invariant retarded systems with state multiplicative wiener type noise is introduced which achieves a minimum bound on the h performance level a cost function is defined that is the expected value of the standard h performance cost with respect to the stochastic parameters a solution is thus obtained for the reduced order h output feedback control problem for the stationary case via the input output approach where the system is replaced by a non retarded one that contains deterministic norm bounded uncertainties the results achieved for the nominal case are extended to the uncertain case where the system matrices reside in a given polytope a numerical example taken from the field of aircraft control is given that demonstrates the applicability of the theory developed

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

deterministic excitable media under poisson drive power law responses spiral waves and dynamic range when each site of a spatially extended excitable medium is independently driven by a poisson stimulus with rate h the interplay between creation and annihilation of excitable waves leads to an average activity f it has recently been suggested that in the low stimulus regime h approximately 0 the response function f h of hypercubic deterministic systems behaves as a power law f approximately h m moreover the response exponent m has been predicted to depend only on the dimensionality d of the lattice m 1 1 d t ohta and t yoshimura physica d 205 189 2005 in order to test this prediction we study the response function of excitable lattices modeled by either coupled morris lecar equations or greenberg hastings cellular automata we show that the prediction is verified in our model systems for d 1 2 and 3 provided that a minimum set of conditions is satisfied under these conditions the dynamic range which measures the range of stimulus intensities that can be coded by the network activity increases with the dimensionality d of the network the power law scenario breaks down however if the system can exhibit self sustained activity spiral waves in this case we recover a scenario that is common to probabilistic excitable media as a function of the conductance coupling g among the excitable elements the dynamic range is maximized precisely at the critical value g c above which self sustained activity becomes stable we discuss the implications of these results in the context of neural coding

simple deterministically constructed cycle reservoirs with regular jumps a new class of state space models reservoir models with a fixed state transition structure the reservoir and an adaptable readout from the state space has recently emerged as a way for time series processing and modeling echo state network esn is one of the simplest yet powerful reservoir models esn models are generally constructed in a randomized manner in our previous study rodan ti o 2011 we showed that a very simple cyclic deterministically generated reservoir can yield performance competitive with standard esn in this contribution we extend our previous study in three aspects first we introduce a novel simple deterministic reservoir model cycle reservoir with jumps crj with highly constrained weight values that has superior performance to standard esn on a variety of temporal tasks of different origin and characteristics second we elaborate on the possible link between reservoir characterizations such as eigenvalue distribution of the reservoir matrix or pseudo lyapunov exponent of the input driven reservoir dynamics and the model performance it has been suggested that a uniform coverage of the unit disk by such eigenvalues can lead to superior model performance we show that despite highly constrained eigenvalue distribution crj consistently outperforms esn which has much more uniform eigenvalue coverage of the unit disk also unlike in the case of esn pseudo lyapunov exponents of the selected optimal crj models are consistently negative third we present a new framework for determining the short term memory capacity of linear reservoir models to a high degree of precision using the framework we study the effect of shortcut connections in the crj reservoir topology on its memory capacity

brief paper h filtering for nonlinear discrete time stochastic systems with randomly varying sensor delays this paper is concerned with the h filtering problem for a general class of nonlinear discrete time stochastic systems with randomly varying sensor delays where the delayed sensor measurement is governed by a stochastic variable satisfying the bernoulli random binary distribution law in terms of the hamilton jacobi isaacs inequalities preliminary results are first obtained that ensure the addressed system to possess an l 2 gain less than a given positive scalar c next a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the h performance constraint for all nonzero exogenous disturbances under the zero initial condition such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation furthermore it is shown that our main results can be readily specialized to the case of linear stochastic systems finally a numerical simulation example is used to demonstrate the effectiveness of the results derived

wavelet deconvolution in a periodic setting in this paper we present an inverse estimation procedure which combines fourier analysis with wavelet expansion in the periodic setting our method can recover a blurred function observed in white noise the blurring process is achieved through a convolution operator which can either be smooth polynomial decay of the fourier transform or irregular such as the convolution with a box car the proposal is non linear and does not require any prior knowledge of the smoothness class it enjoys fast computation and is spatially adaptive this contrasts with more traditional ltering methods which demand a certain amount of regularisation and often fail to recover non homogeneous functions a ne tuning of our method is derived via asymptotic minimax theory which reveals some key dierences with the direct case of donoho et al 1995 a band limited wavelet families have nice theoretical and computing features b the high frequency cut o depends on the spectral characteristics of the convolution kernel c thresholds are level dependent in a geometric fashion we tested our method using simulated lidar data for underwater remote sensing both visual and numerical results show an improvement over existing methods finally the theory behind our estimation paradigm gives a complete characterisation of the maxiset of the method i e the set of functions where the method attains a near optimal rate of convergence for a variety of l p loss functions

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

real time computation at the edge of chaos in recurrent neural networks depending on the connectivity recurrent networks of simple computational units can show very different types of dynamics ranging from totally ordered to chaotic we analyze how the type of dynamics ordered or chaotic exhibited by randomly connected networks of threshold gates driven by a time varying input signal depends on the parameters describing the distribution of the connectivity matrix in particular we calculate the critical boundary in parameter space where the transition from ordered to chaotic dynamics takes place employing a recently developed framework for analyzing real time computations we show that only near the critical boundary can such networks perform complex computations on time series hence this result strongly supports conjectures that dynamical systems that are capable of doing complex computational tasks should operate near the edge of chaos that is the transition from ordered to chaotic dynamics

thresholding estimators for linear inverse problems and deconvolutions thresholding algorithms in an orthonormal basis are studied to estimate noisy discrete signals degraded by a linear operator whose inverse is not bounded for signals in a set sufficient conditions are established on the basis to obtain a maximum risk with minimax rates of convergence deconvolutions with kernels having a fourier transform which vanishes at high frequencies are examples of unstable inverse problems where a thresholding in a wavelet basis is a suboptimal estimator a new mirror wavelet basis is constructed to obtain a deconvolution risk which is proved to be asymptotically equivalent to the minimax risk over bounded variation signals this thresholding estimator is used to restore blurred satellite images

distributions of covariances as a window into the operational regime of neuronal networks massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons their low average is well understood but an explanation for the wide distribution in relation to the static quenched disorder of the connectivity in recurrent random networks was so far elusive we here derive a finite size mean field theory that reduces a disordered to a highly symmetric network with fluctuating auxiliary fields the exposed analytical relation between the statistics of connections and the statistics of pairwise covariances shows that both average and dispersion of the latter diverge at a critical coupling at this point a network of nonlinear units transits from regular to chaotic dynamics applying these results to recordings from the mammalian brain suggests its operation close to this edge of criticality

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

some remarks on general nonlinear stochastic h_ infty control with state control and disturbance dependent noise this technical note studies the nonlinear stochastic h control of ito type differential systems with all the state control input and external disturbance dependent noise x u v dependent noise for short a sufficient condition is given for the finite infinite horizon h control of such a system by means of an hamilton jacobi inequality hji instead of three coupled hamilton jacobi equations hjes as in previous literature

a new fault detection scheme for networked control systems subject to uncertain time varying delay fault detection of networked control systems ncs subject to uncertain time varying delay is studied in this paper for the convenience of residual generator design influence caused by network induced delay is first transformed into time varying polytopic uncertainty which greatly facilitates further manipulation then design of the optimal residual generator is formulated as a model matching problem i e to design a residual generator best matching the optimal residual generator of ncs in the delay free case this procedure is assisted by parameter dependent lyapunov function matrix based bounded real lemma which has been proved to be much better than single constant lyapunov function matrix based results this approach not only can be used in conditions that the variation part of the delay is less than one sampling period but also can be applied to scenarios where the variation part of the delay is larger than one sampling period simulation results are also given to illustrate effectiveness of the proposed method

adaptive sup norm estimation of the wigner function in noisy quantum homodyne tomography in quantum optics the quantum state of a light beam is represented through the wigner function a density on r 2 which may take negative values but must respect intrinsic positivity constraints imposed by quantum physics in the framework of noisy quantum homodyne tomography with efficiency parameter 1 2 1 we study the theoretical performance of a kernel estimator of the wigner function we prove that it is minimax efficient up to a logarithmic factor in the sample size for the l risk over a class of infinitely differentiable functions we also compute the lower bound for the l 2 risk we construct an adaptive estimator i e which does not depend on the smoothness parameters and prove that it attains the minimax rates for the corresponding smoothness of the class of functions up to a logarithmic factor in the sample size finite sample behaviour of our adaptive procedure is explored through numerical experiments

lyapunov exponents in random boolean networks a new order parameter approximation to random boolean networks rbn is introduced based on the concept of boolean derivative a statistical argument involving an annealed approximation is used allowing to measure the order parameter in terms of the statistical properties of a random matrix using the same formalism a lyapunov exponent is calculated allowing to provide the onset of damage spreading through the network and how sensitive it is to minimal perturbations finally the lyapunov exponents are obtained by means of dierent approximations through distance method and a discrete variant of the wolf s method for continuous systems c 2000 elsevier science b v all rights reserved

filtering of stochastic nonlinear differential systems via a carleman approximation approach this paper deals with the state estimation problem for stochastic nonlinear differential systems driven by standard wiener processes and presents a filter that is a generalization of the classical extended kalman bucy filter ekbf while the ekbf is designed on the basis of a first order approximation of the system around the current estimate the proposed filter exploits a carleman like approximation of a chosen degree v ges 1 the approximation procedure applied to both the state and the measurement equations allows to define an approximate representation of the system by means of a bilinear system for which a filtering algorithm is available from the literature numerical simulations on an example show the improvement in terms of sample error covariance of the filter based on the first order second order and third order system approximations v 1 2 3

functional deconvolution in a periodic setting uniform case we extend deconvolution in a periodic setting to deal with functional data the resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover initial or boundary conditions on the basis of observations from a noisy solution of a partial differential equation in the case when it is observed at a finite number of distinct points the proposed functional deconvolution model can also be viewed as a multichannel deconvolution model we derive minimax lower bounds for the l 2 risk in the proposed functional deconvolution model when f is assumed to belong to a besov ball and the blurring function is assumed to possess some smoothness properties including both regular smooth and super smooth convolutions furthermore we propose an adaptive wavelet estimator of f that is asymptotically optimal in the minimax sense or near optimal within a logarithmic factor in a wide range of besov balls in addition we consider a discretization of the proposed functional deconvolution model and investigate when the availability of continuous data gives advantages over observations at the asymptotically large number of points as an illustration we discuss particular examples for both continuous and discrete settings

adaptive wavelet estimator for nonparametric density deconvolution 1999 institute of mathematical statistics the electronic version of this article is the complete one and can be found online at http projecteuclid org euclid aos 1017939249

wavelet deconvolution with noisy eigenvalues over the last decade there has been a lot of interest in wavelet vaguelette methods for the recovery of noisy signals or images in motion blur nonlinear wavelet estimators are known to have good adaptive properties and to outperform linear approximations over a wide range of signals and images see e g the recent waved method of johnstone kerkyacharian picard and raimondo 2004 or the forward method of neelamani choi and baraniuk 2004 and also fan and koo 2002 in the density setting in the deblurring setting wavelet vaguelette methods rely on the complete knowledge of a convolution operator s eigenvalues this is an unlikely situation in practice however a more realistic scenario such as would arise when passing the fourier basis as an input signal through a linear time invariant system is to imagine that one also observes a set of noisy eigenvalues in this paper we define a version of the waved estimator which is near optimal when used with noisy eigenvalues a key feature of our method includes a data driven method for choosing the fine resolution level in waved estimation asymptotic theory is illustrated with a wide range of finite sample examples

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

multiscale methods for shape constraints in deconvolution confidence statements for qualitative features we derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density an important example covered within this framework is to test for local monotonicity on all scales simultaneously we investigate the moderately ill posed setting where the fourier transform of the error density in the deconvolution model is of polynomial decay for multiscale testing we consider a calibration motivated by the modulus of continuity of brownian motion we investigate the performance of our results from both the theoretical and simulation based point of view a major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task although the minimax rates for pointwise estimation are very slow

correspondence between neural threshold networks and kauffman boolean cellular automata for an asymmetric version of the mcculloch pitts neural network 1943 and for kauffman s infinite range boolean network model 1984 the time evolution of the hamming distances between two different initial configurations are compared in the thermodynamic limit it is shown that in both models phase transitions occur for corresponding values of the transition parameters and that their hamming distances can have the same time evolution leading to quantitatively the same dynamics as known from time dependent landau theory for phase transitions

broad edge of chaos in strongly heterogeneous boolean networks the dynamic stability of the boolean networks representing a model for the gene transcriptional regulation kauffman model is studied by calculating analytically and numerically the hamming distance between two evolving configurations this turns out to behave in a universal way close to the phase boundary only for in degree distributions with a finite second moment in degree distributions of the form pd k k with 2 3 thus having a diverging second moment lead to a slower increase of the hamming distance when moving towards the unstable phase and to a broadening of the phase boundary for finite n with decreasing we conclude that the heterogeneous regulatory network connectivity facilitates the balancing between robustness and evolvability in living organisms

binary threshold networks as a natural null model for biological networks spin models of neural networks and genetic networks are considered elegant as they are accessible to statistical mechanics tools for spin glasses and magnetic systems however the conventional choice of variables in spin systems may cause problems in some models when parameter choices are unrealistic from a biological perspective obviously this may limit the role of a model as a template model for biological systems perhaps less obviously also ensembles of random networks are affected and may exhibit different critical properties we consider here a prototypical network model that is biologically plausible in its local mechanisms we study a discrete dynamical network with two characteristic properties nodes with binary states 0 and 1 and a modified threshold function with ensuremath theta 0 0 0 we explore the critical properties of random networks of such nodes and find a critical connectivity k c 2 0 with activity vanishing at the critical point finally we observe that the present model allows a more natural implementation of recent models of budding yeast and fission yeast cell cycle control networks

recurrent information optimization with local metaplastic synaptic dynamics we consider the problem of optimizing information theoretic quantities in recurrent networks via synaptic learning in contrast to feedforward networks the recurrence presents a key challenge insofar as an optimal learning rule must aggregate the joint distribution of the whole network this challenge in particular makes a local policy i e one that depends on only pairwise interactions difficult here we report a local metaplastic learning rule that performs approximate optimization by estimating whole network statistics through the use of several slow nested dynamical variables these dynamics provide the rule with both anti hebbian and hebbian components thus allowing for decorrelating and correlating learning regimes that can occur when either is favorable for optimality we demonstrate the performance of the synthesized rule in comparison to classical bcm dynamics and use the networks to conduct history dependent tasks that highlight the advantages of recurrence finally we show the consistency of the resultant learned networks with notions of criticality including balanced ratios of excitation and inhibition

nonlinear h control and estimation of optimal h gain abstract the structure of nonlinear h controller and the estimation of optimal h gain are investigated in this paper the essential problem boils down to the existence of semipositive solution to the hamilton jacobi isaacs inequality further the solvability of this first order fully nonlinear differential inequality is discussed we look for one kind of special semipositive radial solution to the hamilton jacobi isaacs inequality an explicit estimation of optimal h gain and explicit formulas of semipositive radial solutions to the hamilton jacobi isaacs inequality are obtained the results are quite simple and intuitive they even shed a new insight on the linear h theory

analysis and design of echo state networks the design of echo state network esn parameters relies on the selection of the maximum eigenvalue of the linearized system around zero spectral radius however this procedure does not quantify in a systematic manner the performance of the esn in terms of approximation error this article presents a functional space approximation framework to better understand the operation of esns and proposes an information theoretic metric the average entropy of echo states to assess the richness of the esn dynamics furthermore it provides an interpretation of the esn dynamics rooted in system theory as families of coupled linearized systems whose poles move according to the input signal dynamics with this interpretation a design methodology for functional approximation is put forward where esns are designed with uniform pole distributions covering the frequency spectrum to abide by the richness metric irrespective of the spectral radius a single bias parameter at the esn input adapted with the modeling error configures the esn spectral radius to the input output joint space function approximation examples compare the proposed design methodology versus the conventional design

criticality in random threshold networks annealed approximation and beyond random threshold networks with sparse asymmetric connections show complex dynamical behavior similar to random boolean networks with a transition from ordered to chaotic dynamics at a critical average connectivity kc in this type of model contrary to boolean networks propagation of local perturbations damage depends on the in degree of the sites kc is d eterminedanalytically using an annealedapproximation andthe results are con2rmedby numerical simulations it is shown that the statistical distributions of damage spreading near the percolation transition obey power laws andd ynamical correlations between active network clusters become maximal we investigate the e4ect of local damage suppression at highly connected nodes for networks with scale free in degree distributions possible relations of our 2ndings to properties of real world networks like robustness and non trivial degree distributions are discussed c

state feedback ℋ control for stochastic time delay nonlinear systems with state and disturbance dependent noise this article focuses on the state feedback control problem for the stochastic nonlinear systems with state and disturbance dependent noise and time varying state delays based on the maxmin optimisation approach both the delay independent and the delay dependent hamilton jacobi inequalities hjis are developed for synthesising the state feedback controller for a general type of stochastic nonlinear systems it is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level for a class of stochastic affine nonlinear systems the delay independent as well as delay dependent matrix valued inequalities are proposed the resulting control system satisfies global asymptotic stability in the mean square sense and the required disturbance attenuation level by modelling the nonlinearities as uncertainties in corresponding stochastic time delay systems the sufficient conditions in terms of a linear matrix inequality lmi and a bili

neutral stability rate propagation and critical branching in feedforward networks recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks critical branching neutral stability and production of a wide range of firing patterns we seek the simplest setting in which these properties emerge clarifying their origin and relationship in random feedforward networks of mccullochs pitts neurons two key parameters are the thresholds at which neurons fire spikes and the overall level of feedforward connectivity when neurons have low thresholds we show that there is always a connectivity for which the properties in question all occur that is these networks preserve overall firing rates from layer to layer and produce broad distributions of activity in each layer this fails to occur however when neurons have high thresholds a key tool in explaining this difference is the eigenstructure of the resulting mean field markov chain as this reveals which activity modes will be preserved from layer to layer we extend our analysis from purely excitatory networks to more complex models that include inhibition and local noise and find that both of these features extend the parameter ranges over which networks produce the properties of interest

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

determination of the edge of criticality in echo state networks through fisher information maximization it is a widely accepted fact that the computational capability of recurrent neural networks rnns is maximized on the so called edge of criticality once the network operates in this configuration it performs efficiently on a specific application both in terms of 1 low prediction error and 2 high short term memory capacity since the behavior of recurrent networks is strongly influenced by the particular input signal driving the dynamics a universal application independent method for determining the edge of criticality is still missing in this paper we aim at addressing this issue by proposing a theoretically motivated unsupervised method based on fisher information for determining the edge of criticality in rnns it is proved that fisher information is maximized for finite size systems operating in such critical regions however fisher information is notoriously difficult to compute and requires the analytic form of the probability density function ruling the system behavior this paper takes advantage of a recently developed nonparametric estimator of the fisher information matrix and provides a method to determine the critical region of echo state networks esns a particular class of recurrent networks the considered control parameters which indirectly affect the esn performance are explored to identify those configurations lying on the edge of criticality and as such maximizing fisher information and computational performance experimental results on benchmarks and real world data demonstrate the effectiveness of the proposed method

non parametric confidence bands in deconvolution density estimation summary uniform confidence bands for densities f via non parametric kernel estimates were first constructed by bickel and rosenblatt in this paper this is extended to confidence bands in the deconvolution problem g f for an ordinary smooth error density under certain regularity conditions we obtain asymptotic uniform confidence bands based on the asymptotic distribution of the maximal deviation l distance between a deconvolution kernel estimator and f further consistency of the simple non parametric bootstrap is proved for our theoretical developments the bias is simply corrected by choosing an undersmoothing bandwidth for practical purposes we propose a new data driven bandwidth selector that is based on heuristic arguments which aims at minimizing the l distance between and f although not constructed explicitly to undersmooth the estimator a simulation study reveals that the bandwidth selector suggested performs well in finite samples in terms of both area and coverage probability of the resulting confidence bands finally the methodology is applied to measurements of the metallicity of local f and g dwarf stars our results confirm the g dwarf problem i e the lack of metal poor g dwarfs relative to predictions from closed box models of stellar formation

on the synthesis of linear h filters for polynomial systems abstract this paper is concerned with the h filtering problem for polynomial systems by means of lyapunov theory and matrix inequality techniques sufficient conditions are first obtained to ensure that the filtering error system is asymptotically stable and satisfies h performance constraint then a sufficient condition for the existence of desired filters is established with a free matrix introduced which will greatly facilitate the design of filter matrices by virtue of sum of squares sos approaches a convergent iterative algorithm is developed to tackle the polynomial h filtering problem note that the approach can be efficiently implemented by means of recently developed sos decomposition techniques and the filter matrices can be designed explicitly finally a numerical example is given to illustrate the main results of this paper

new approach to general nonlinear discrete time stochastic h_ infty control in this paper a new approach based on convex analysis is introduced to solve the h infty problem for discrete time nonlinear stochastic systems first by using the disintegration property of the conditional expectation sufficient necessary conditions are given for the internal stability of the concerned systems second in order to separate the unknown exogenous disturbance from the state variables the properties of convex functions are applied to prove the stochastic version of bounded real lemma brl third the state feedback h infty control problem is studied and an h infty control is designed based on the brl finally two numerical examples and one real world regulation control example of synthetic genetic circuit are presented to show the effectiveness of our developed theory

nonfragile h_ infty fuzzy filtering with randomly occurring gain variations and channel fadings this paper is concerned with the nonfragile h infty filtering problem for a class of discrete time takagi sugeno t s fuzzy systems with both randomly occurring gain variations rogvs and channel fadings the phenomenon of the rogvs is introduced into the system model so as to account for the parameter fluctuations occurring during the filter implementation two sequences of random variables obeying the bernoulli distribution are employed to describe the phenomenon of the rogvs bounded by prescribed norms in addition the rice fading model is utilized to describe the phenomena of channel fadings where the occurrence probabilities of the random channel coefficients are allowed to time varying through stochastic analysis and lyapunov functional approach sufficient conditions are established under which the filtering error dynamics is exponentially mean square stable with a prespecified h infty performance the set of the desired nonfragile h infty filters is characterized by solving a convex optimization problem via the semidefinite programming method an illustrative example is given to show the usefulness and effectiveness of the proposed design method in this paper

gaussian smoothers for nonlinear systems with one step randomly delayed measurements this technical note is concerned with the nonlinear state smoothing problem in the case that the measurements are randomly delayed by one sampling time under gaussian domain two general gaussian approximation ga and gaussian mixture approximation gma smoothers are proposed in minimum mean square error mmse sense the smoothing implementation is transformed into computing some special posterior covariances which triggers the development of the new unscented kalman smoother uks by applying unscented transformation ut simulation results demonstrate the superior performance of the proposed ga uks and gma uks algorithms

slow synaptic dynamics in a network from exponential to power law forgetting we investigate a mean field model of interacting synapses on a directed neural network our interest lies in the slow adaptive dynamics of synapses which are driven by the fast dynamics of the neurons they connect cooperation is modeled from the usual hebbian perspective while competition is modeled by an original polarity driven rule the emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition this leads to a universal 1 t power law relaxation of the mean synaptic strength along the critical manifold and an equally universal 1 t relaxation at the tricritical point to be contrasted with the exponential relaxation that is otherwise generic in turn this leads to the natural emergence of long and short term memory from different parts of parameter space in a synaptic network which is the most original and important result of our present investigations

filtering for a class of nonlinear mimo uncertain time delay stochastic systems in this article a high gain nonlinear observer based approach is proposed for filtering of nonlinear stochastic systems with time delays the system under consideration contains parameter uncertainties stochastic disturbances time delays as well as lipschitz like nonlinearities the objective is to design a robust filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in a sense of mean square a new high gain filter idea is introduced to solve the stochastic filtering problem by using the lyapunov method and stochastic analysis techniques the design of the proposed filter does not necessitate the resolution of any dynamics systems and its expression is explicitly given i e its calibration is achieved through the choice of a single parameter and does not rely on solving any matrix inequalities by numerical computation a simulation example is given to illustrate the performance of the proposed filter

low order approximations in deconvolution and regression with errors in variables summary we suggest two new methods which are applicable to both deconvolution and regression with errors in explanatory variables for nonparametric inference the two approaches involve kernel or orthogonal series methods they are based on defining a low order approximation to the problem at hand and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently of course both techniques could be employed to construct consistent estimators but in many contexts of importance e g those where the errors are gaussian consistency is from a practical viewpoint an unattainable goal we rephrase the problem in a form where an explicit interpretable low order approximation is available the information that we require about the error distribution the error in variables distribution in the case of regression is only in the form of low order moments and so is readily obtainable by a rudimentary analysis of indirect measurements of errors e g through repeated measurements in particular we do not need to estimate a function such as a characteristic function which expresses detailed properties of the error distribution this feature of our methods coupled with the fact that all our estimators are explicitly defined in terms of readily computable averages means that the methods are particularly economical in computing time

inflation of the edge of chaos in a simple model of gene interaction networks we study a set of linearized catalytic reactions to model gene and protein interactions the model is based on experimentally motivated interaction network topologies and is designed to capture some key properties of gene expression statistics we impose a nonlinearity to the system by enforcing a boundary condition which guarantees non negative concentrations of chemical substances system stability is quantified by maximum lyapunov exponents we find that the non negativity constraint leads to a drastic inflation of those regions in parameter space where the lyapunov exponent exactly vanishes within the model this finding can be fully explained as a result of a symmetry breaking mechanism induced by the positivity constraint the robustness of this finding with respect to network topologies and the role of intrinsic molecular and external noise is discussed we argue that systems with inflated edges of chaos could be much more easily favored by natural selection than systems where the lyapunov exponent vanishes only on a parameter set of measure zero

linear estimation for random delay systems this paper is concerned with the linear estimation problems for discrete time systems with random delayed observations when the random delay is known online i e time stamped the random delayed system is reconstructed as an equivalent delay free one by using measurement reorganization technique and then an optimal linear filter is presented based on the kalman filtering technique however the optimal filter is time varying stochastic and does not converge to a steady state in general then an alternative suboptimal filter with deterministic gains is developed under a new criteria the estimator performance in terms of their error covariances is provided and its mean square stability is established finally a numerical example is presented to illustrate the efficiency of proposed estimators

short term synaptic plasticity in the deterministic tsodyks markram model leads to unpredictable network dynamics short term synaptic plasticity strongly affects the neural dynamics of cortical networks the tsodyks and markram tm model for short term synaptic plasticity accurately accounts for a wide range of physiological responses at different types of cortical synapses here we report a route to chaotic behavior via a shilnikov homoclinic bifurcation that dynamically organizes some of the responses in the tm model in particular the presence of such a homoclinic bifurcation strongly affects the shape of the trajectories in the phase space and induces highly irregular transient dynamics indeed in the vicinity of the shilnikov homoclinic bifurcation the number of population spikes and their precise timing are unpredictable and highly sensitive to the initial conditions such an irregular deterministic dynamics has its counterpart in stochastic network versions of the tm model the existence of the shilnikov homoclinic bifurcation generates complex and irregular spiking patterns and acting as a sort of springboard facilitates transitions between the down state and unstable periodic orbits the interplay between the deterministic homoclinic bifurcation and stochastic effects may give rise to some of the complex dynamics observed in neural systems

deconvolution with unknown error distribution we consider the problem of estimating a density fx using a sample y1 yn from fy fx fe where fe is an unknown density we assume that an additional sample e1 em from fe is observed estimators of fx and its derivatives are constructed by using nonparametric estimators of fy and fe and by applying a spectral cut off in the fourier domain we derive the rate of convergence of the estimators in case of a known and unknown error density fe where it is assumed that fx satisfies a polynomial logarithmic or general source condition it is shown that the proposed estimators are asymptotically optimal in a minimax sense in the models with known or unknown error density if the density fx belongs to a sobolev space h mathcal p and fe is ordinary smooth or supersmooth

laplace deconvolution on the basis of time domain data and its application to dynamic contrast enhanced imaging in the present paper we consider the problem of laplace deconvolution with noisy discrete non equally spaced observations on a finite time interval which appears in many different contexts we propose a new method for laplace deconvolution which is based on expansions of the convolution kernel the unknown function and the observed signal over laguerre functions basis which acts as a surrogate eigenfunction basis using regression setting the expansion results in a small system of linear equations with the matrix of the system being triangular and toeplitz the number m of the terms in the expansion of the estimator is controlled via complexity penalty the advantage of this methodology is that it leads to very fast computations produces no boundary effects due to extension at zero and cut off at t and provides an estimator with the risk within a logarithmic factor of m of the oracle risk under no assumptions on the model and within a constant factor of the oracle risk under mild assumptions we emphasize that in the present paper we consider the true observational model with possibly non equispaced observations which are available on a finite interval of length t and account for the bias associated with this model the study is motivated by perfusion imaging using a short injection of contrast agent a procedure which is widely applied for medical assessment of blood flows within tissues such as cancerous tumors presence of a tuning parameter a allows to choose the most advantageous time units so that both the kernel and the unknown right hand side of the equation are well represented for the further deconvolution in addition absence of boundary effects allows for an accurate estimator of the tissue blood flow parameter which is of great interest to medical doctors the methodology is illustrated by an extensive simulation study and a real data example which confirms that the proposed technique is fast efficient accurate usable from a practical point of view and competitive

collective dynamics in heterogeneous networks of neuronal cellular automata abstract we examine the collective dynamics of heterogeneous random networks of model neuronal cellular automata each automaton has b active states a single silent state and r b 1 refractory states and can show spiking or bursting behavior depending on the values of b we show that phase transitions that occur in the dynamical activity can be related to phase transitions in the structure of erdos renyi graphs as a function of edge probability different forms of heterogeneity allow distinct structural phase transitions to become relevant we also show that the dynamics on the network can be described by a semi annealed process and as a result can be related to the boolean lyapunov exponent

time scale and noise optimality in self organized critical adaptive networks recent studies have shown that adaptive networks driven by simple local rules can organize into critical global steady states providing another framework for self organized criticality soc we focus on the important convergence to criticality and show that noise and time scale optimality are reached at finite values this is in sharp contrast to the previously believed optimal zero noise and infinite time scale separation case furthermore we discover a noise induced phase transition for the breakdown of soc we also investigate each of these three effects separately by developing models that reveal three generically low dimensional dynamical behaviors time scale resonance a simplified version of stochastic resonance which we call steady state stochastic resonance and noise induced phase transitions

brief paper robust h filtering for nonlinear stochastic systems with uncertainties and markov delays this paper investigates the h filtering problem for a class of general nonlinear stochastic systems considering model uncertainties and random time delays governed by markov chains simultaneously the general algebraic hamilton jacobi inequality hji is established first for general nonlinear stochastic systems with uncertainties and random markovian delays then a set of sufficient conditions are derived for the filtering system to achieve stochastic stability in the sense of mean square and the prescribed disturbance attenuation level moreover the developed results are specialized for a special class of nonlinear stochastic systems by presenting the sufficient conditions in terms of matrix inequalities simulation results demonstrate the effectiveness of the proposed approach

conditional likelihood maximisation a unifying framework for information theoretic feature selection we present a unifying framework for information theoretic feature selection bringing almost two decades of research on heuristic filter criteria under a single theoretical interpretation this is in response to the question what are the implicit statistical assumptions of feature selection criteria based on mutual information to answer this we adopt a different strategy than is usual in the feature selection literature instead of trying to define a criterion we derive one directly from a clearly specified objective function the conditional likelihood of the training labels while many hand designed heuristic criteria try to optimize a definition of feature relevancy and redundancy our approach leads to a probabilistic framework which naturally incorporates these concepts as a result we can unify the numerous criteria published over the last two decades and show them to be low order approximations to the exact but intractable optimisation problem the primary contribution is to show that common heuristics for information based feature selection including markov blanket algorithms as a special case are approximate iterative maximisers of the conditional likelihood a large empirical study provides strong evidence to favour certain classes of criteria in particular those that balance the relative size of the relevancy redundancy terms overall we conclude that the jmi criterion yang and moody 1999 meyer et al 2008 provides the best tradeoff in terms of accuracy stability and flexibility with small data samples

mean field theory of echo state networks dynamical systems driven by strong external signals are ubiquitous in nature and engineering here we study echo state networks networks of a large number of randomly connected nodes which represent a simple model of a neural network and have important applications in machine learning we develop a mean field theory of echo state networks the dynamics of the network is captured by the evolution law similar to a logistic map for a single collective variable when the network is driven by many independent external signals this collective variable reaches a steady state but when the network is driven by a single external signal the collective variable is non stationary but can be characterized by its time averaged distribution the predictions of the mean field theory including the value of the largest lyapunov exponent are compared with the numerical integration of the equations of motion

data driven density estimation in the presence of additive noise with unknown distribution we study the following model of deconvolution y x varepsilon with i i d observations y 1 dots y n and varepsilon 1 dots varepsilon m the x j 1 leq j leq n are i i d with density f independent of the varepsilon j the aim of the paper is to estimate f without knowing the density f varepsilon of the varepsilon j we first define a projection estimator for which we provide bounds for the pointwise and the integrated l 2 risk we consider ordinary smooth and supersmooth noise varepsilon with regard to ordinary smooth and supersmooth densities f then we present an adaptive estimator of the density of f this estimator is obtained by penalization of the projection contrast which provides model selection lastly we present simulation experiments to illustrate the good performances of our estimator and study from the empirical point of view the importance of theoretical constraints

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

discrete transform approach to deconvolution problems summary if fourier series are used as the basis for inference in deconvolution problems the effects of the errors factorise out in a way that is easily exploited empirically this property is the consequence of elementary addition formulae for sine and cosine functions and is not readily available when one is using methods based on other orthogonal series or on continuous fourier transforms it allows relatively simple estimators to be constructed founded on the addition of finite series rather than on integration the performance of these methods can be particularly effective when edge effects are involved since cosine series estimators are quite resistant to boundary problems in this context we point to the advantages of trigonometric series methods for density deconvolution they have better mean squared error performance when edge effects are involved they are particularly easy to code and they admit a simple approach to empirical choice of smoothing parameter in which a version of thresholding familiar in wavelet based inference is used in place of conventional smoothing applications to other deconvolution problems are briefly discussed

robust h sub spl infin filtering for nonlinear stochastic systems this paper describes the robust h sub spl infin filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance dependent noise we assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by ito spl circ type stochastic differential equations for general nonlinear stochastic systems the h sub spl infin filter can be obtained by solving second order nonlinear hamilton jacobi inequalities when the worst case disturbance is considered in the design procedure a mixed h sub 2 h sub spl infin filtering problem is also solved by minimizing the total estimation error energy it is found that for a class of special nonlinear stochastic systems the h sub spl infin filtering design can be given via solving several linear matrix inequalities instead of hamilton jacobi inequalities a few examples show that the proposed methods are effective

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

self organized critical neural networks a mechanism for self organization of the degree of connectivity in model neural networks is studied network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable at the single synapse level this principle is studied in a two dimensional neural network with randomly wired asymmetric weights in this class of networks network connectivity is closely related to a phase transition between ordered and disordered dynamics a slow topology change is imposed on the network through a local rewiring rule motivated by activity dependent synaptic development neighbor neurons whose activity is correlated on average develop a new connection while uncorrelated neighbors tend to disconnect as a result robust self organization of the network towards the order disorder transition occurs convergence is independent of initial conditions robust against thermal noise and does not require fine tuning of parameters

passivity criteria for continuous time neural networks with mixed time varying delays abstract this paper is concerned with the problem of passivity analysis for uncertain continuous time neural networks with mixed time varying delays the mixed time varying delays consist of both discrete and distributed delays in which the discrete delays are assumed to be varying within a given interval in addition the uncertainties are assumed to be norm bounded by employing a novel lyapunov krasovskii functional new passivity delay interval dependent criteria are established to guarantee the passivity performance when estimating an upper bound of the derivative of the lyapunov krasovskii functional we handle the terms related to the discrete and distributed delays appropriately so as to develop less conservative results these passivity conditions are presented in terms of linear matrix inequalities which can be easily solved via standard numerical software some numerical examples are given to illustrate the effectiveness of the proposed method

stimulus dependent suppression of chaos in recurrent neural networks neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli using mean field analysis we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input we find that inputs not only drive network responses but they also actively suppress ongoing activity ultimately leading to a phase transition in which chaos is completely eliminated the critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency revealing a resonant frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially a prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate

connectivity dynamics and memory in reservoir computing with binary and analog neurons reservoir computing rc systems are powerful models for online computations on input sequences they consist of a memoryless readout neuron that is trained on top of a randomly connected recurrent neural network rc systems are commonly used in two flavors with analog or binary spiking neurons in the recurrent circuits previous work indicated a fundamental difference in the behavior of these two implementations of the rc idea the performance of an rc system built from binary neurons seems to depend strongly on the network connectivity structure in networks of analog neurons such clear dependency has not been observed in this letter we address this apparent dichotomy by investigating the influence of the network connectivity parameterized by the neuron in degree on a family of network models that interpolates between analog and binary networks our analyses are based on a novel estimation of the lyapunov exponent of the network dynamics with the help of branching process theory rank measures that estimate the kernel quality and generalization capabilities of recurrent networks and a novel mean field predictor for computational performance these analyses reveal that the phase transition between ordered and chaotic network behavior of binary circuits qualitatively differs from the one in analog circuits leading to differences in the integration of information over short and long timescales this explains the decreased computational performance observed in binary circuits that are densely connected the mean field predictor is also used to bound the memory function of recurrent circuits of binary neurons

shearlet based deconvolution in this paper a new type of deconvolution algorithm is proposed that is based on estimating the image from a shearlet decomposition shearlets provide a multidirectional and multiscale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets constructions such as curvelets and contourlets share similar properties yet their implementations are significantly different from that of shearlets taking advantage of unique properties of a new m channel implementation of the shearlet transform we develop an algorithm that allows for the approximation inversion operator to be controlled on a multiscale and multidirectional basis a key improvement over closely related approaches such as forward is the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation gcv various tests show that this method can perform significantly better than many competitive deconvolution algorithms

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

moment stability of nonlinear discrete stochastic systems with time delays based on h representation technique in this paper mean square stability of nonlinear discrete stochastic systems with time delays is investigated we obtain the second order moment equations of discrete stochastic systems by virtue of the h representation technique by the comparison principle and the established moment equations some moment stability theorems for nonlinear discrete stochastic systems with time delays are established a numerical example is presented to illustrate the efficiency of our results at the end of the paper

adaptive kalman filtering in networked systems with random sensor delays multiple packet dropouts and missing measurements in this paper adaptive filtering schemes are proposed for state estimation in sensor networks and or networked control systems with mixed uncertainties of random measurement delays packet dropouts and missing measurements that is all three uncertainties in the measurement have certain probability of occurrence in the network the filter gains can be derived by solving a set of recursive discrete time riccati equations examples are presented to demonstrate the applicability and performances of the proposed schemes

wavelet deconvolution this paper studies the issue of optimal deconvolution density estimation using wavelets the approach taken here can be considered as orthogonal series estimation in the more general context of the density estimation we explore the asymptotic properties of estimators based on thresholding of estimated wavelet coefficients minimax rates of convergence under the integrated square loss are studied over besov classes b sub spl sigma pq of functions for both ordinary smooth and supersmooth convolution kernels the minimax rates of convergence depend on the smoothness of functions to be deconvolved and the decay rate of the characteristic function of convolution kernels it is shown that no linear deconvolution estimators can achieve the optimal rates of convergence in the besov spaces with p 2 when the convolution kernel is ordinary smooth and super smooth if the convolution kernel is ordinary smooth then linear estimators can be improved by using thresholding wavelet deconvolution estimators which are asymptotically minimax within logarithmic terms adaptive minimax properties of thresholding wavelet deconvolution estimators are also discussed

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

nonparametric density estimation from covariate information an increasing number of statistical problems arise in connection with functional calibration in each case inexpensive indirect data in a particular context are combined with direct expensive to acquire data from different but related settings to estimate quantities in the former case sometimes e g in chemometrics problems where spectroscopic calibration is used the indirect data are functional but more commonly they are scalar or vector valued and the functional component is the quantity that we wish to estimate the problem treated here is of the latter type we observe data that give us access to the distribution of u given v and from these and data on u we wish to estimate the density of v the motivating real datasets are of age and covariate information in fish populations we suggest two methodologies each of which is based on transforming the problem to one involving inversion of a symmetric linear operator our techniques have connections to methods for functional data analysis and fo

quasicritical brain dynamics on a nonequilibrium widom line is the brain really operating at a critical point we study the nonequilibrium properties of a neural network which models the dynamics of the neocortex and argue for optimal quasicritical dynamics on the widom line where the correlation length and information transmission are optimized we simulate the network and introduce an analytical mean field approximation characterize the nonequilibrium phase transitions and present a nonequilibrium phase diagram which shows that in addition to an ordered and disordered phase the system exhibits a quasiperiodic phase corresponding to synchronous activity in simulations which may be related to the pathological synchronization associated with epilepsy

brief nonlinear h filtering of sampled data systems this paper considers the problem of h filtering for nonlinear sampled data systems sufficient conditions are obtained for the existence of filters that guarantee the l 2 gain from an exogenous input to an estimation error is less than or equal to a prescribed value these conditions are expressed in terms of both continuous and discrete hamilton jacobi equations