convergence in mean for els based adaptive control abstract almost sure global convergence results are available for stochastic adaptive control this note looks at the nontrivial technical details required to ensure corresponding convergence in p th mean results both convergence results are strong but are not implied by the other and so together almost sure and p th mean convergence are stronger than either the other aim of this paper is to show that the combination of these two forms of convergence results makes the stability results more robust and potentially of more practical significance

a robust algorithm for random parameter tracking an algorithm for tracking time varying parameters is studied it is shown to be exponentially stable independently of the choice of algorithm parameters we derive some useful nonasymptotic estimates for the tracking error and develop the asymptotically optimal version of the method

stochastic linear quadratic adaptive control for continuous time first order systems in this paper we discuss the linear quadratic lq adaptive control problem for the following continuous time first order scalar stochastic system dxt axt dt but dt c dwt with cost function min lim sup jt u u u t where jt u 1t 0t q1x2s q2u2s ds q1 0 0 based on the self convergence property of continuous time weighted least squares cwls algorithm 9 and the similar parameter modification method 13 the stability of the closed loop system is achieved without invoking any excitations here self convergence means that the convergence is automatic in the sense that no excitation conditions on the signals or measurements is needed it is a terminology from 10 the strong consistency of cwls and the optimality of the adaptive control are established by incorporating with diminishing excitations

technical communique the convergence of an instrumental variable like recursion the convergence of a modified form of the iv instrumental variable recursion actually a case of the integral adaptation algorithm of landau for the parameters of a scalar transfer function time series model is considered it is known that this algorithm requires at least a positive real condition for its convergence here it is shown that the recursion converges without being monitored in any case the result is disappointing because the positive real condition depends on the transfer function characteristic function

persistency of excitation in possible unstable continuous time systems identification and indirect adaptive control the author proves persistency of excitation of the output of an output reachable possibly unstable linear system under certain input conditions and applies this result to adaptive identification and indirect adaptive control in adaptive identification he proves exponential parameter convergence regardless of stability of the identified plant in indirect adaptive control he proves exponential parameter convergence along with asymptotic time invariance and global experimental stability of the controlled closed loop system

low dimensional firing rate dynamics for populations of renewal type spiking neurons the macroscopic dynamics of large populations of neurons can be mathematically analyzed using low dimensional firing rate or neural mass models however these models fail to capture spike synchronization effects and nonstationary responses of the population activity to rapidly changing stimuli here we derive low dimensional firing rate models for homogeneous populations of neurons modeled as time dependent renewal processes the class of renewal neurons includes integrate and fire models driven by white noise and has been frequently used to model neuronal refractoriness and spike synchronization dynamics the derivation is based on an eigenmode expansion of the associated refractory density equation which generalizes previous spectral methods for fokker planck equations to arbitrary renewal models we find a simple relation between the eigenvalues characterizing the timescales of the firing rate dynamics and the laplace transform of the interspike interval density for which explicit expressions are available for many renewal models retaining only the first eigenmode already yields a reliable low dimensional approximation of the firing rate dynamics that captures spike synchronization effects and fast transient dynamics at stimulus onset we explicitly demonstrate the validity of our model for a large homogeneous population of poisson neurons with absolute refractoriness and other renewal models that admit an explicit analytical calculation of the eigenvalues the eigenmode expansion presented here provides a systematic framework for alternative firing rate models in computational neuroscience based on spiking neuron dynamics with refractoriness

consistency property of extended least squares parameter estimation for stochastic diffusion equation the extended least squares parameter estimate for stochastic heat diffusion equations is considered the unknown parameter is a heat diffusion coefficient which is a function of a spatial variable almost sure convergence for the estimated parameter is proved a numerical example is demonstrated for supporting the theoretical results developed here

metastable states and quasicycles in a stochastic wilson cowan model of neuronal population dynamics we analyze a stochastic model of neuronal population dynamics with intrinsic noise in the thermodynamic limit n infinity where n determines the size of each population the dynamics is described by deterministic wilson cowan equations on the other hand for finite n the dynamics is described by a master equation that determines the probability of spiking activity within each population we first consider a single excitatory population that exhibits bistability in the deterministic limit the steady state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network the relative weighting of the two maxima depends on the system size for large but finite n we calculate the exponentially small rate of noise induced transitions between the resulting metastable states using a wentzel kramers brillouin wkb approximation and matched asymptotic expansions we then consider a two population excitatory inhibitory network that supports limit cycle oscillations using a diffusion approximation we reduce the dynamics to a neural langevin equation and show how the intrinsic noise amplifies subthreshold oscillations quasicycles

fast global oscillations in networks of integrate and fire neurons with low firing rates we study analytically the dynamics of a network of sparsely connected inhibitory integrate and fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate in the limit when the number of neurons n 1 the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized the activity becomes oscillatory when the inhibitory feedback is strong enough the period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input in large but finite networks the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold their characteristics are determined as functions of systems parameters in these two different regimes the results are found to be in good agreement with numerical simulations

the earth mover s distance as a metric for image retrieval we investigate the properties of a metric between two distributions the earth mover s distance emd for content based image retrieval the emd is based on the minimal cost that must be paid to transform one distribution into the other in a precise sense and was first proposed for certain vision problems by peleg werman and rom for image retrieval we combine this idea with a representation scheme for distributions that is based on vector quantization this combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods the emd is based on a solution to the transportation problem from linear optimization for which efficient algorithms are available and also allows naturally for partial matching it is more robust than histogram matching techniques in that it can operate on variable length representations of the distributions that avoid quantization and other binning problems typical of histograms when used to compare distributions with the same overall mass the emd is a true metric in this paper we focus on applications to color and texture and we compare the retrieval performance of the emd with that of other distances

multiresolution feature extraction and selection for texture segmentation an approach is described for unsupervised segmentation of textured images local texture properties are extracted using local linear transforms that have been optimized for maximal texture discrimination local statistics texture energy measures are estimated at the output of an equivalent filter bank by means of a nonlinear transformation absolute value followed by an iterative gaussian smoothing algorithm this procedure generates a multiresolution sequence of feature planes with a half octave scale progression a feature reduction technique is then applied to the data and is determined by simultaneously diagonalizing scatter matrices evaluated at two different spatial resolutions this approach provides a good approximation of r a fisher s 1950 multiple linear discriminants and has the advantage of requiring no a priori knowledge this feature reduction methods appears to be an improvement on the commonly used karhunen loeve transform and allows efficient texture segmentation based on simple thresholding

adaptive control with recursive identification for stochastic linear systems this paper presents a stochastic adaptive control algorithm which is shown to possess the following properties when applied to a possibly unstable inverse stable linear stochastic system with unknown parameters whenever that system satisfies a certain positive real condition on its moving average noise dynamics 1 the adaptive control part of the algorithm stabilizes and asymptotically optimizes the behavior of the system in the sense that the limit of the sample mean square variation of the output around a given demand level equals that of a minimum variance control strategy implemented with known parameters this optimal behavior is subject to an offset 2where 2is the variance of a dither signal added to the control action in order to produce a continually disturbed control for mu 2 0 it is shown that the input output process satisfies a persistent excitation property and hence subject to a simple identifiability condition the next property holds 2 the observed input and output of the controlled system may be taken as inputs to an approximate maximum likelihood algorithm aml which generates strongly consistent estimates of the system s parameters results are presented for the scalar and multivariable cases

sufficiency of excitation in the context of adaptive identification and adaptive control of linear systems the concept of a sufficiently exciting input play a key role in this note necessary and sufficient conditions are presented for an input function of a single input linear stationary system to be sufficiently exciting these conditions are independent of the stability properties of the linear system

the ornstein uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex cortical neurons of behaving animals generate irregular spike sequences recently there has been a heated discussion about the origin of this irregularity softky and koch 1993 pointed out the inability of standard single neuron models to reproduce the irregularity of the observed spike sequences when the model parameters are chosen within a certain range that they consider to be plausible shadlen and newsome 1994 on the other hand demonstrated that a standard leaky integrate and fire model can reproduce the irregularity if the inhibition is balanced with the excitation motivated by this discussion we attempted to determine whether the ornstein uhlenbeck process which is naturally derived from the leaky integration assumption can in fact reproduce higher order statistics of biological data for this purpose we consider actual neuronal spike sequences recorded from the monkey prefrontal cortex to calculate the higher order statistics of the interspike intervals consistency of the data with the model is examined on the basis of the coefficient of variation and the skewness coefficient which are respectively a measure of the spiking irregularity and a measure of the asymmetry of the interval distribution it is found that the biological data are not consistent with the model if the model time constant assumes a value within a certain range believed to cover all reasonable values this fact suggests that the leaky integrate and fire model with the assumption of uncorrelated inputs is not adequate to account for the spiking in at least some cortical neurons

asymptotically optimum recursive prediction error methods in adaptive estimation and control abstract the challenge taken up in this paper is to devise a parameter identification algorithm for linear discrete time stochastic plants which exploits the strengths of both the extended least squares els and the recursive prediction error rpe parameter estimation methods the focus is on adaptive control of parameterized state space models which exploit a priori plant information in that the unknown parameter vector r is of lower dimension than that for a corresponding input output model parameterized by a triple parameter estimation scheme consisting of els rpe and a hybrid of the two denoted hpe is proposed the purpose of the hpe scheme is to permit information flow from the els to rpe algorithms so as to effectively project rpe into a stability domain and to have it avoid local prediction error index minima that are not the global minimum

nonasymptotic results for finite memory wls filters a nonasymptotic analysis of properties of weighted least squares wls adaptive filters used for identification of time varying systems is presented it is shown that the problem of mean square boundedness of wls estimates is closely related to the problem of invertibility in the mean sense of the corresponding regression matrix necessary and sufficient conditions are discussed for such invertibility to hold based on that a number of results are derived paralleling those already obtained for least mean square lms filters and the problem of statistical robustness of the wls estimator is briefly discussed

stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses in this paper the stochastic optimal control of linear networked control system ncs with uncertain system dynamics and in the presence of network imperfections such as random delays and packet losses is derived the proposed stochastic optimal control method uses an adaptive estimator ae and ideas from q learning to solve the infinite horizon optimal regulation of unknown ncs with time varying system matrices next a stochastic suboptimal control scheme which uses ae and q learning is introduced for the regulation of unknown linear time invariant ncs that is derived using certainty equivalence property update laws for online tuning the unknown parameters of the ae to obtain the q function are derived lyapunov theory is used to show that all signals are asymptotically stable as and that the estimated control signals converge to optimal or suboptimal control inputs simulation results are included to show the effectiveness of the proposed schemes the result is an optimal control scheme that operates forward in time manner for unknown linear systems in contrast with standard riccati equation based schemes which function backward in time

stability condition for sampled data based control of linear continuous switched systems abstract most practical systems are continuous in nature but with discrete sampled feedback when digital control is utilized this paper investigates the stabilization problem of switched linear continuous time systems with sampled data based control for both known and unknown arbitrary switching processes on the basis of lyapunov stability theory a sufficient global exponential stability condition related to dwell time and sampling period is established for the latter case on line one step adaptive estimation algorithm is derived and integrated with sampled feedback for control design validation and verification of the established result are conducted through cruise control of train systems

dynamics of encoding in neuron populations some general mathematical features the use of a population dynamics approach promises efficient simulation of large assemblages of neurons depending on the issues addressed and the degree of realism incorporated in the simulated neurons a wide range of different population dynamics formulations can be appropriate here we present a common mathematical structure that these various formulations share and that implies dynamical behaviors that they have in common this underlying structure serves as a guide toward efficient means of simulation as an example we derive the general population firing rate frequency response and show how it may be used effectively to address a broad range of interacting population response and stability problems a few specific cases will be worked out a summary of this work appears at the end before the appendix

recursive identification of overparametrized systems a recursive identification algorithm based on extended least squares is proposed to deal with the contingency of overparametrization the algorithm is relatively simple compared to those involving online order determination being based on adaptively introducing suitable excitation into the algorithm to avoid ill conditioning in the case of extended least squares based adaptive estimation then the regressors are appropriately stochastically perturbed the algorithm is shown to converge to a uniquely defined signal model with any pole zero cancellations at the origin

on parameter convergence in adaptive control it is well known that the parameter error as well as the model plant mismatch error in a model reference adaptive scheme tends exponentially to zero iff a certain sufficient richness condition holds for signals inside the time varying plant control loop in this paper we give conditions on the reference signal the exogenous input to the adaptive loop namely that it have as many spectral lines as there are unknown parameters in order to guarantee parameter convergence

convergence results for continuous time adaptive stochastic filtering algorithms abstract the adaptive stochastic filtering problem for gaussian processes is considered the self tuning synthesis procedure is used to derive two algorithms for this problem almost sure convergence for the parameter estimate and the filtering error will be established the convergence analysis is based on an almost supermartingale convergence lemma that allows a stochastic lyapunov like approach

stochastic dynamics of a finite size spiking neural network we present a simple markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite size spiking neural network we give closed form estimates for the equilibrium distribution mean rate variance and autocorrelation function of the network activity the model is applicable to any network where the probability of firing of a neuron in the network depends on only the number of neurons that fired in a previous temporal epoch networks with statistically homogeneous connectivity and membrane and synaptic time constants that are not excessively long could satisfy these conditions our model completely accounts for the size of the network and correlations in the firing activity it also allows us to examine how the network dynamics can deviate from mean field theory we show that the model and solutions are applicable to spiking neural networks in biophysically plausible parameter regimes

theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback a network of leaky integrate and fire neurons with global inhibitory feedback and under the influence of spatially correlated noise is studied we calculate the spectral statistics of the network power spectrum of the population activity cross spectrum between spike trains of different neurons as well as of a single neuron power spectrum of spike train cross spectrum between external noise and spike train within the network as shown by comparison with numerical simulations our theory works well for arbitrary network size if the feedback is weak and the amount of external noise does not exceed that of the internal noise by means of our analytical results we discuss the quality of the correlation induced oscillation in a large network as a function of the transmission delay and the internal noise intensity it is shown that the strongest oscillation is obtained in a system with zero internal noise and adiabatically long delay i e the delay period is longer than any other time scale in the system for a neuron with a strong intrinsic frequency the oscillation becomes strongly anharmonic in the case of a long delay time we also discuss briefly the kind of synchrony introduced by the feedback induced oscillation

quasi least squares identification and its strong consistency simple identification algorithms are proposed for both continuous and discrete time systems with correlated noise by a combined method connecting the martingale method with the ordinary differential equation method quite simple conditions are obtained to guarantee strong consistency of the proposed algorithms which give estimates for the unknown coefficients in both the dynamic system and the noise model

efficient evaluation of neuron populations receiving colored noise current based on a refractory density method the expected firing probability of a stochastic neuron is approximated by a function of the expected subthreshold membrane potential for the case of colored noise we propose this approximation in order to extend the recently proposed white noise model a v chizhov and l j graham phys rev e 75 011924 2007 to the case of colored noise applying a refractory density approach to conductance based neurons the uncoupled neurons of a single population receive a common input and are dispersed by the noise within the framework of the model the effect of noise is expressed by the so called hazard function which is the probability density for a single neuron to fire given the average membrane potential in the presence of a noise term to derive the hazard function we solve the kolmogorov fokker planck equation for a mean voltage driven neuron fluctuating due to colored noisy current we show that a sum of both a self similar solution for the case of slow changing mean voltage and a frozen stationary solution for fast changing mean voltage gives a satisfactory approximation for the hazard function in the arbitrary case we demonstrate the quantitative effect of a temporal correlation of noisy input on the neuron dynamics in the case of leaky integrate and fire and detailed conductance based neurons in response to an injected current step

convergence rates of continuous time stochastic els parameter estimation discrete time convergence rates for extended least squares els algorithms are generalized to the continuous time case an essential difference in the estimation is the appropriate prefiltering while in the theory the existence of solutions of the stochastic equations is a concern

observer design for a class of nonlinear systems a viable design methodology to construct observers for a class of nonlinear systems is developed the proposed technique is based on the off line solution of a riccati equation and can be solved using commercially available software packages for globally valid results the class of systems considered is characterized by globally lipschitz nonlinearities local results relax this assumption to only a local requirement for a more general description of nonlinear systems the methodology yields approximate observers locally the proposed theory is used to design an observer for a single link flexible joint robot this observer estimates the robot link variables based on the joint measurements

persistence of excitation in linear systems abstract this paper develops output reachability characterizations of linear finite dimensional multivariate systems so as to translate excitation properties of system inputs to excitation properties of system outputs states or associated regression vectors such properties are of fundamental concern for convergence of algorithms involving on line identification adaptive state estimation prediction and control persistence of excitation guarantees convergence without a priori stability assumptions and ensures robustness properties

neural network based finite horizon optimal control of uncertain affine nonlinear discrete time systems in this paper the finite horizon optimal control design for nonlinear discrete time systems in affine form is presented in contrast with the traditional approximate dynamic programming methodology which requires at least partial knowledge of the system dynamics in this paper the complete system dynamics are relaxed utilizing a neural network nn based identifier to learn the control coefficient matrix the identifier is then used together with the actor critic based scheme to learn the time varying solution referred to as the value function of the hamilton jacobi bellman hjb equation in an online and forward in time manner since the solution of hjb is time varying nns with constant weights and time varying activation functions are considered to properly satisfy the terminal constraint an additional error term is incorporated in the novel update law such that the terminal constraint error is also minimized over time policy and or value iterations are not needed and the nn weights are updated once a sampling instant the uniform ultimate boundedness of the closed loop system is verified by standard lyapunov stability theory under nonautonomous analysis numerical examples are provided to illustrate the effectiveness of the proposed method

field theoretic approach to fluctuation effects in neural networks a well defined stochastic theory for neural activity which permits the calculation of arbitrary statistical moments and equations governing them is a potentially valuable tool for theoretical neuroscience we produce such a theory by analyzing the dynamics of neural activity using field theoretic methods for nonequilibrium statistical processes assuming that neural network activity is markovian we construct the effective spike model which describes both neural fluctuations and response this analysis leads to a systematic expansion of corrections to mean field theory which for the effective spike model is a simple version of the wilson cowan equation we argue that neural activity governed by this model exhibits a dynamical phase transition which is in the universality class of directed percolation more general models which may incorporate refractoriness can exhibit other universality classes such as dynamic isotropic percolation because of the extremely high connectivity in typical networks it is expected that higher order terms in the systematic expansion are small for experimentally accessible measurements and thus consistent with measurements in neocortical slice preparations we expect mean field exponents for the transition we provide a quantitative criterion for the relative magnitude of each term in the systematic expansion analogous to the ginsburg criterion experimental identification of dynamic universality classes in vivo is an outstanding and important question for neuroscience

a master equation formalism for macroscopic modeling of asynchronous irregular activity states many efforts have been devoted to modeling asynchronous irregular ai activity states which resemble the complex activity states seen in the cerebral cortex of awake animals most of models have considered balanced networks of excitatory and inhibitory spiking neurons in which ai states are sustained through recurrent sparse connectivity with or without external input in this letter we propose a mesoscopic description of such ai states using master equation formalism we derive a second order mean field set of ordinary differential equations describing the temporal evolution of randomly connected balanced networks this formalism takes into account finite size effects and is applicable to any neuron model as long as its transfer function can be characterized we compare the predictions of this approach with numerical simulations for different network configurations and parameter spaces considering the randomly connected network as a unit this approach could be used to build large scale networks of such connected units with an aim to model activity states constrained by macroscopic measurements such as voltage sensitive dye imaging

transfer function identification with filtering techniques this paper addresses the problem of identifying the transfer function of a plant with the aid of filtering techniques conditions for obtaining fair estimates of a transfer function are derived it is shown that to be able to reduce the effect of noise and other stochastic effects highly tuned filters are required it is also found that proper excitation signals are necessary for effective implementation of the proposed scheme some methods for designing the required highly tuned filters are proposed the relationship between the proposed scheme and existing methods is discussed it is shown that for some specific cases the proposed scheme is in effect a computationally efficient implementation of existing methods however for some other cases the proposed scheme gives more accurate results the theoretical predictions are substantiated with computer simulations

an ordinary differential equation technique for continuous time parameter estimation an ordinary differential equation technique is developed via averaging theory and weak convergence theory to analyze the asymptotic behavior of continuous time recursive stochastic parameter estimators this technique is an extension of l ljung s 1977 work in discrete time using this technique the following results are obtained for various continuous time parameter estimators the recursive prediction error method with probability one converges to a minimum of the likelihood function the same is true of the gradient method the extended kalman filter fails with probability one to converge to the true values of the parameters in a system whose state noise covariance is unknown an example of the extended least squares algorithm is analyzed in detail analytic bounds are obtained for the asymptotic rate of convergence of all three estimators applied to this example

stability of a class of hybrid linear stochastic systems the objective of the paper is to establish l q stability results for the state processes of a new class of slowly time varying hybrid continuous time linear stochastic systems the systems are hybrid in the sense that jumps both in the dynamics and the state may occur in both cases a jump amounts to resetting to an initial value jump times are defined by a more or less arbitrary point process most of the analysis is based on a carefully organized stochastic lyapunov function argument we motivate our study by a brief summary of some basic problems in continuous time recursive estimation of linear stochastic systems within a framework analogous to the one developed by benveniste et al

stochastic neural field theory and the system size expansion we analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of n identical neurons the state of the network is specified by the fraction of active or spiking neurons in each population and transition rates are chosen so that in the thermodynamic or deterministic limit n rightarrow infty we recover standard activity based or voltage based rate models we derive the lowest order corrections to these rate equations for large but finite n using two different approximation schemes one based on the van kampen system size expansion and the other based on path integral methods both methods yield the same series expansion of the moment equations which at mathcal o 1 n can be truncated to form a closed system of equations for the first and second order moments taking a continuum limit of the moment equations while keeping the system size n fixed generates a system of integrodifferential equations for the

continuous time stochastic adaptive control non explosion e consistency and stability abstract for completely observed continuous time constant parameter stochastic linear systems an indirect adaptive control law is presented which subject principally to a weak location hypothesis concerning the true parameter and a persistent excitation hypothesis generates consistent recursive least squares parameter estimates and ensures the system is mean square sample path stable the adaptive control algorith mentails i recursively calculating the least squares estimate of the system parameter and ii recursively generating the lqr feedback gain matrix lying in a set of matrix gains known to contain a stabilizing gain the a s non explosion of the system is a direct consequence of this construction

control theory methods for consistency in some least squares identification problems the consistency of a family of least squares estimates of some unknown parameters of a continuous time linear stochastic system is verified the unknown parameters appear affinely in the linear transformations of the state and the control the method of verification of consistency associates a family of control problems to the identification problem and the asymptotic behavior of the solutions of a family of algebraic riccati equations from the control problems implies a persistent excitation property for the identification problem

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

rapid and brief communication multivalued type dissimilarity measure and concept of mutual dissimilarity value for clustering symbolic patterns a successful attempt in exploring a dissimilarity measure which captures the reality is made in this paper the proposed measure unlike other measures pattern recognition 24 6 1991 567 pattern recognition lett 16 1995 647 pattern recognition 28 8 1995 1277 ieee trans syst man cybern 24 4 1994 is multivalued and non symmetric the concept of mutual dissimilarity value is introduced to make the existing conventional clustering algorithms work on the proposed unconventional dissimilarity measure

globally convergent adaptive iir filters based on fixed pole locations a new class of adaptive filters dubbed fixed pole adaptive filters fpaf s is introduced these adaptive filters have infinite impulse responses yet their adaptation exhibits provable global convergence good filter performance with a relatively small number of adapted parameters is permitted by the new filter structure thus reducing the computational burden needed to implement adaptive filters the implementation and computational complexity of the fpaf is described and its modeling capabilities are determined excitation conditions on the filter input are established that guarantee global convergence of a standard set of adaptive algorithms some methods are described for selecting the fixed pole locations based on a priori information regarding the operating environment of the adaptive filter the fpaf is tailored to applications by such a procedure enabling improved performance in examples the fpaf is shown to achieve a smaller minimum mean square error given an equal number of adapted parameters in comparison with adaptive fir filters and adaptive filters based on laguerre and kautz models

central tendency adaptive pole assignment the concept of central tendency adaptive control for achieving minimum variance objectives proposed by the authors in a companion paper 1989 is applied to adaptive pole assignment at any iteration given plant parameter estimate and their uncertainty a controller is designed which is most likely to achieve the pole assignment objectives simulations show a factor of 100 improvement in transient response over certainty equivalent adaptive pole assignment schemes for one example

central tendency minimum variance adaptive control the authors propose designing indirect adaptive controllers using measures of central tendency of the a posteriori probability function of the control for parameters that is given a knowledge of plant uncertainty at each time instant from estimation algorithms and a controller design rule controller parameters are sought which maximize the likelihood of achieving the control objectives the particular case of adaptive minimum variance control is studied in detail

asymptotically optimal parameter estimation with scheduled measurements to reduce the communication cost of a sensor node this paper is concerned with an estimation framework with scheduled measurements for a linear system a scheduler is designed to control the transmission of measurements from sensor to estimator which results in that only a subset of measurements is transmitted to the estimator we propose an innovation based scheduler and derive an analytical expression for the cramer rao lower bound crlb for the given scheduling strategy under a communication constraint an adaptive scheduler and a corresponding recursive estimator are jointly designed to asymptotically attain the crlb the structure of the estimator bears close resemblance to the standard least square estimator lse with the full set of sensor measurements moreover we prove that the estimation performance in terms of mean square estimation error is comparable to the standard lse even under a moderate communication cost the theoretical results are verified by simulations

convergence of adaptive minimum variance algorithms via weighting coefficient selection weighted least squares and related stochastic approximation algorithms are studied for parameter estimation adaptive state estimation adaptive n step ahead prediction and adaptive control in both white and colored noise environments for the fundamental algorithm which is the basis for the various applications the step size in the stochastic approximation versions and the weighting coefficient in the weighted least squares schemes are selected according to a readily calculated stability measure associated with the estimator the selection is guided by the convergence theory in this way strong global convergence of the parameter estimates state estimates and prediction or tracking errors is not only guaranteed under the appropriate noise passivity and stability or minimum phase conditions but the convergence is also as fast as it appears reasonable to achieve given the simplicity of the adaptive scheme

on the local stability properties of adaptive parameter estimators with composite errors and split algorithms the stability characteristics of a generalized error system structure are examined for adaptive parameter estimation systems this error system form encompasses the structure of a number of particular applications of adaptive parameter estimation theory which fall outside the framework of more familiar error system models the consequences for error system stability which derive from the added generality are analyzed it is demonstrated that when using averaging theory techniques to analyze the error system stability conditions must be augmented for the basic error system in order to ensure stability for the generalized error system the inadequacy of regressor spectral restrictions and persistent spanning conditions to guarantee local error system stability of the generalized structure is rigorously established alternative conditions which will yield such local stability are demonstrated to illustrate the concepts involved the recursive identification of parameters is examined in a parallel form realization of a linear system

dissimilarity based classification in the absence of local ground truth application to the diagnostic interpretation of chest radiographs in this paper classification on dissimilarity representations is applied to medical imaging data with the task of discrimination between normal images and images with signs of disease we show that dissimilarity based classification is a beneficial approach in dealing with weakly labeled data i e when the location of disease in an image is unknown and therefore local feature based classifiers cannot be trained a modification to the standard dissimilarity based approach is proposed that makes a dissimilarity measure multi valued hence able to retain more information a multi valued dissimilarity between an image and a prototype becomes an image representation vector in classification several classification outputs with respect to different prototypes are further integrated into a final image decision both standard and proposed methods are evaluated on data sets of chest radiographs with textural abnormalities and compared to several feature based region classification approaches applied to the same data on a tuberculosis data set the multi valued dissimilarity based classification performs as well as the best region classification method applied to the fully labeled data with an area under the receiver operating characteristic roc curve a z of 0 82 the standard dissimilarity based classification yields a z 0 80 on a data set with interstitial abnormalities both dissimilarity based approaches achieve a z 0 98 which is closely behind the best region classification method

clustering in globally coupled inhibitory neurons abstract a model of a large population of identical excitable neurons with a global slowly decaying inhibitory coupling is studied and its patterns of synchrony are examined in addition to converging to a homogeneous fixed point and a homogeneous limit cycle the system exhibits cluster states in which it breaks spontaneously into a few macroscopically big clusters each of which is fully synchronized a method for calculating the stability of cluster states is described and used for investigating the dynamical behavior of the network versus the parameters that describe the neurons and synapses effects of stochastic noise on the network dynamics are discussed at large enough noise the system goes to a globally stationary state low levels of noise preserve the cluster like neuron trajectories in the regime where a noiseless system converges to a fully synchronized periodic state relatively low noise levels cause neurons to burst only every two or more consecutive time periods

persistence of excitation in extended least squares in least squares parameter estimation schemes persistency of excitation conditions on the plant states are required for consistent estimation in the case of extended least squares the persistency conditions are on the state estimates here these persistency of excitation conditions are translated into sufficiently rich conditions on the plant noise and inputs in the case of adaptive minimum variance control schemes the sufficiently rich conditions are on the noise and specified output trajectory with sufficiently rich input signals guaranteed convergence rates of prediction errors improve and it is conjectured that the algorithms are consequently more robust

a universality advantage of stochastic excitation signals for adaptive control abstract adaptive control schemes usually depend on estimation of system parameters which in turn depends excitation of modes associated with these parameters such excitation is supplied by plant noise the adaptive control signal itself and any external excitation such as a reference signal in this note it is shown that there is a universality advantage for any externally applied signal to be stochastic rather than deterministic the crucial property of a stochastic signal exploited in this note is its unpredictability by any causal system such as an adaptive control scheme when such unpredictable signals excite an adaptive control scheme there is no need to deliberately constrain the adaptation to be slow or excitation maintaining to ensure adequate identification

prototype selection for dissimilarity based classifiers a conventional way to discriminate between objects represented by dissimilarities is the nearest neighbor method a more efficient and sometimes a more accurate solution is offered by other dissimilarity based classifiers they construct a decision rule based on the entire training set but they need just a small set of prototypes the so called representation set as a reference for classifying new objects such alternative approaches may be especially advantageous for non euclidean or even non metric dissimilarities the choice of a proper representation set for dissimilarity based classifiers is not yet fully investigated it appears that a random selection may work well in this paper a number of experiments has been conducted on various metric and non metric dissimilarity representations and prototype selection methods several procedures like traditional feature selection methods here effectively searching for prototypes mode seeking and linear programming are compared to the random selection in general we find out that systematic approaches lead to better results than the random selection especially for a small number of prototypes although there is no single winner as it depends on data characteristics the k centres works well in general for two class problems an important observation is that our dissimilarity based discrimination functions relying on significantly reduced prototype sets 3 10 of the training objects offer a similar or much better classification accuracy than the best k nn rule on the entire training set this may be reached for multi class data as well however such problems are more difficult

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

systematic fluctuation expansion for neural network activity equations population rate or activity equations are the foundation of a common approach to modeling for neural networks these equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity the shortcoming of these equations is that they take into account only the average firing rate while leaving out higher order statistics like correlations between firing a stochastic theory of neural networks that includes statistics at all orders was recently formulated we describe how this theory yields a systematic extension to population rate equations by introducing equations for correlations and appropriate coupling terms each level of the approximation yields closed equations they depend only on the mean and specific correlations of interest without an ad hoc criterion for doing so we show in an example of an all to all connected network how our system of generalized activity equations captures phenomena missed by the mean field rate equations alone

slow fluctuations in recurrent networks of spiking neurons networks of fast nonlinear elements may display slow fluctuations if interactions are strong we find a transition in the long term variability of a sparse recurrent network of perfect integrate and fire neurons at which the fano factor switches from zero to infinity and the correlation time is minimized this corresponds to a bifurcation in a linear map arising from the self consistency of temporal input and output statistics more realistic neural dynamics with a leak current and refractory period lead to smoothed transitions and modified critical couplings that can be theoretically predicted

multi scale texture classification from generalized locally orderless images locally orderless images are families of three intertwined scale spaces that describe local histograms we generalize locally orderless images by considering local histograms of a collection of filtered versions of the image and by extending them to joint probability distributions these constructions can be used to derive texture features and are shown to be a more general description of two established texture classification methods viz filter bank methods and cooccurrence matrices because all scale parameters are stated explicitly in this formulation multi resolution feature sets can be extracted in a systematic way this includes new types of multi resolution analysis not only based on the spatial scale but on the window size and intensity scale as well each multi resolution approach improves texture classification performance the best result being obtained if a multi resolution approach for all scale parameters is used this is demonstrated in experiments on a large data set of 1152 images for 72 texture classes

time structure of the activity in neural network models several neural network models in continuous time are reconsidered in the framework of a general mean field theory which is exact in the limit of a large and fully connected network the theory assumes pointlike spikes which are generated by a renewal process the effect of spikes on a receiving neuron is described by a linear response kernel which is the dominant term in a weak coupling expansion it is shown that the resulting spike response model is the most general renewal model with linear inputs the standard integrate and fire model forms a special case in a network structure with several pools of identical spiking neurons the global states and the dynamic evolution are determined by a nonlinear integral equation which describes the effective interaction within and between different pools we derive explicit stability criteria for stationary incoherent and oscillatory coherent solutions it is shown that the stationary state of noiseless systems is almost always unstable noise suppresses fast oscillations and stabilizes the system furthermore collective oscillations are stable only if the firing occurs while the synaptic potential is increasing in particular collective oscillations in a network with delayless excitatory interaction are at most semistable inhibitory interactions with short delays or excitatory interactions with long delays lead to stable oscillations our general results allow a straightforward application to different network models with spiking neurons furthermore the theory allows an estimation of the errors introduced in firing rate or graded response models

a note on continuous time els abstract the parameter estimation of continuous time finite dimensional linear stochastic systems is a problem of long standing interest the method usually used is the extended least squares els algorithm described by a nonlinear stochastic differential equation sld with the existence of the global strong solution assumed this paper shows that the els estimate does exist in 0 and at the same time presents a number of convergence results paralleling those for the discrete time case

on robustness to noise of least squares based adaptive control abstract current engineering practice for adaptive control schemes is to base the design on globally convergent schemes for simple plant models an important class of such schemes uses least squares estimation of assumed simple input output models and constructs the controller using the parameter estimates this paper studies the robustness of such schemes to the presence of unmodelled plant coloured noise such noise is sometimes an adequate model for unmodelled plant dynamics the theory of the paper makes a connection between the least squares parameter error equations and those associated with extended least squares using a posteriori noise estimates for which there are known global convergence results for the case of adaptive minimum variance control of minimum phase plants this connection permits stronger convergence results than those hitherto derived from the theory of extended least squares based on a priori noise estimates

on persistent excitation for linear systems with stochastic coefficients a wiener input process is shown to be persistently exciting pe for linear stochastic systems with time varying convergent random coefficients provided asymptotic noise controllability holds a s the pe result is in the sense that the minimum eigenvalue of the integrated outer product of the state process is of o t t being the upper time limit of the integral

adaptive neural network based event triggered control of single input single output nonlinear discrete time systems this paper presents a novel adaptive neural network nn control of single input and single output uncertain nonlinear discrete time systems under event sampled nn inputs in this control scheme the feedback signals are transmitted and the nn weights are tuned in an aperiodic manner at the event sampled instants after reviewing the nn approximation property with event sampled inputs an adaptive state estimator se consisting of linearly parameterized nns is utilized to approximate the unknown system dynamics in an event sampled context the se is viewed as a model and its approximated dynamics and the state vector during any two events are utilized for the event triggered controller design an adaptive event trigger condition is derived by using both the estimated nn weights and a dead zone operator to determine the event sampling instants this condition both facilitates the nn approximation and reduces the transmission of feedback signals the ultimate boundedness of both the nn weight estimation error and the system state vector is demonstrated through the lyapunov approach as expected during an initial online learning phase events are observed more frequently over time with the convergence of the nn weights the inter event times increase thereby lowering the number of triggered events these claims are illustrated through the simulation results

asynchronous states in networks of pulse coupled oscillators we use a mean field approach to analyze the stability of the asynchronous state in a population of all to all pulse coupled nonlinear oscillators we determine the conditions that must be satisfied by the time constants and phase dependence characterizing the coupling between the oscillators in order for the asynchronous state to be stable we also consider the effects of noise this work complements results on synchronous states in similar models and allows us to study the validity of firing rate models commonly used for neural networks

a globally convergent adaptive predictor this paper establishes global convergence for an adaptive prediction algorithm key features of the algorithm are i a priori residuals are used in the regression vector ii the input signal need not be persistently exciting iii only an upper bound is required on the system order iv no monitoring or projection procedure is required to guarantee stability and v arbitrary feedback is allowed between output and input

population dynamics of spiking neurons fast transients asynchronous states and locking an integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate and fire type is discussed it is analytically shown that transients from a state of incoherent firing can be immediate the stability of incoherent firing is analyzed in terms of the noise level and transmission delay and a bifurcation diagram is derived the response of a population of noisy integrate and fire neurons to an input current of small amplitude is calculated and characterized by a linear filter l the stability of perfectly synchronized locked solutions is analyzed