control of cardiac function and noise from a decaying power spectrum evidence is presented that adds to the debate surrounding the question to what extent does neural control of cardiac output exploit noise the transduction capability of cardiac afferent neurons situated in and adjacent to the heart is vital to feedback in control of cardiac function an analysis of in situ cardiac afferent activity shows evidence of independent and exponentially distributed interspike intervals an anatomical basis for such memoryless interspike intervals ultimately derives from the fact that each afferent neuron is associated with a field of sensory neurites or bare nerve endings that transduce local chemical and mechanical stimuli in a many to one fashion as such cardiac afferent neurons and their sensory neurite inputs are respectively modeled here by the hodgkin huxley equations forced by red noise decaying power spectrum perturbing an otherwise constant subthreshold input a variable barrier competition model is derived from these equations in order to address the question how are noisy inputs being processed by sensory neurons to cause each spike it is found that ion channels are responsible for significant input whitening increased spectral power at higher frequency through differentiation of the inputs such whitening is a means to distinguish low frequency control signals from otherwise red noise fluctuations furthermore spiking occurs when backward moving averages of the whitened inputs over a window of the order of the sodium activation time scale exceed an approximately constant barrier

competition model for aperiodic stochastic resonance in a fitzhugh nagumo model of cardiac sensory neurons regional cardiac control depends upon feedback of the status of the heart from afferent neurons responding to chemical and mechanical stimuli as transduced by an array of sensory neurites emerging experimental evidence shows that neural control in the heart may be partially exerted using subthreshold inputs that are amplified by noisy mechanical fluctuations this amplification is known as aperiodic stochastic resonance asr neural control in the noisy subthreshold regime is difficult to see since there is a near absence of any correlation between input and the output the latter being the average firing spiking rate of the neuron this lack of correlation is unresolved by traditional energy models of asr since these models are unsuitable for identifying cause and effect between such inputs and outputs in this paper the competition between averages model is used to determine what portion of a noisy subthreshold input is responsible on average for the output of sensory neurons as represented by the fitzhugh nagumo equations a physiologically relevant conclusion of this analysis is that a nearly constant amount of input is responsible for a spike on average and this amount is approximately independent of the firing rate hence correlation measures are generally reduced as the firing rate is lowered even though neural control under this model is actually unaffected

analytical approach to the stochastic fitzhugh nagumo system and coherence resonance we consider the fitzhugh nagumo system under the influence of white gaussian noise in the excitable regime we present an analytical approximation in the limit of fast activator time scale marginal probability densities of a reduced system and dynamical quantities such as the pulse rate are found and the mean interspike interval and its relative standard deviation are investigated the latter quantities allow a quantitative description of the phenomenon of coherence resonance as comparisons with simulations show

inequalities and local uncertainty principles inequalities for fourier transforms are developed which describe local uncertainty principles in the sense that if the uncertainty of momentum is small then so is the probability of being localized at any point they give estimates for essentially all states and lead to lower bounds for hamiltonians

stochastic resonance in neuron models periodically stimulated sensory neurons typically exhibit a kind of statistical phase locking to the stimulus they tend to fire at a preferred phase of the stimulus cycle but not at every cycle hence the histogram of interspike intervals isih i e of times between successive firings is multimodal for these neurons with peaks centered at integer multiples of the driving period a particular kind of residence time histogram for a large class of noisy bistable systems has recently been shown to exhibit the major features of the neural data in the present paper we show that an excitable cell model the fitzhugh nagumo equations also reproduces these features when driven by additive periodic and stochastic forces this model exhibits its own brand of stochastic resonance as the peaks of the isih successively go through a maximum when the noise intensity is increased further the presence of a noise induced limit cycle introduces a third time scale in the problem this limit cycle is found to modify qualitatively the phase locking picture e g by suppressing certain peaks in the isih finally the role of noise and possibly of stochastic resonance sr in the neural encoding of sensory information is discussed

recursive state estimation for two dimensional shift varying systems with random parameter perturbation and dynamical bias abstract in this paper the state estimation problem is investigated for a class of two dimensional 2 d stochastic systems with shift varying parameters the stochasticity with the underlying system comes from three sources namely random parameter perturbations dynamical biases and additive white noises the measurement output is subject to the uniform quantization as a result of communication constraints on the sensors the purpose of the addressed problem is to recursively estimate the system states with prescribed estimation performance in spite of the stochastic disturbances and the uniform quantizations an augmented model is first constructed to combine the information about the state and the bias and the dynamical evolution is subsequently discussed furthermore through stochastic analysis and mathematical induction the estimator design algorithm is developed to acquire certain upper bound on the estimation error variance and such an upper bound is then minimized in the matrix trace sense moreover the boundedness issue of the estimation errors is investigated via matrix inversion lemma and inductive analysis technique finally the effectiveness of the proposed state estimation algorithm is validated on a typical 2 d system modeled by the well known darboux equation with extensive application potentials in industrial processes

general two stage extended kalman filters a general two stage extended kalman filter gtsekf which extends the linear general two stage kalman filter to nonlinear systems is further proposed a new nonlinear two stage transformation is introduced to facilitate achieving this extension as in the linear one the gtsekf is derived mainly by applying the nonlinear two stage transformation to the well known extended kalman filter ekf and is shown to be equivalent to the ekf with a decoupled computing structure a nonlinear filter for estimating constant parameters in dynamic systems is presented to illustrate one application of the proposed gtsekf a literature example is also given to demonstrate the correctness and usefulness of the proposed results

information capacity of stochastic pooling networks is achieved by discrete inputs stochastic pooling networks spn are sensor networks where multiple sensors make independently noisy and compressed measurements of the same information source which are combined via pooling examples of spns range from nanoelectronics to biological sensory neurons here it is shown that optimal information transmission in spns with nodes that quantize to a finite number of states requires the input signal distribution to be discrete this is illustrated numerically for a simple spn consisting of n binary quantizing sensors the resultant information capacity is shown to be independent of the noise distribution when the signal distribution can be freely chosen but to imply an optimal noise distribution if the signal distribution is fixed while larger than the best performance of previously studied continuously valued input signals the capacity does not scale faster than the previous best result of text log 2 sqrt n bits per channel use it is also shown that a plot of the optimal input distribution contains bifurcations as n increases and that suprathreshold stochastic resonance occurs when the mutual information is determined for a suboptimal noise distribution

information measures quantifying aperiodic stochastic resonance aperiodic stochastic resonance asr is a phenomenon in which the response of a nonlinear system to a subthreshold information bearing signal is optimized by the presence of noise we have previously characterized this effect by the use of cross correlation based measures here we apply a measure transinformation that directly quantifies the rate of information transfer from stimulus to response and show that the presence of noise optimizes the information transfer rate by considering a nonlinear system the fitzhugh nagumo model that captures the functional dynamics of neuronal firing we demonstrate that sensory neurons could in principle harness asr to optimize the detection and transmission of weak stimuli s1063 651x 96 51309 7

optimal solution of the two stage kalman estimator the two stage kalman estimator was originally proposed to reduce the computational complexity of the augmented state kalman filter it was also applied to the tracking of maneuvering targets by treating the target acceleration as a bias term except in certain restrictive conditions the conventional two stage estimators are suboptimal in the sense that they are not equivalent to the augmented state filter in this paper the authors propose a new two stage kalman estimator i e new structure which is an extension of friedland s estimator and is optimal in general conditions in addition we provide some analytic results to demonstrate the computational advantages of two stage estimators over augmented ones

speed and rotor flux estimation of induction machines using a two stage extended kalman filter this paper presents an effective implementation of an extended kalman filter used for the estimation of both rotor flux and rotor velocity of an induction motor an algorithm proposed by hsieh and chen in hsieh c s chen f c 1999 optimal solution of the two stage kalman estimator ieee transactions on automatic control 44 1 194 199 for linear parameter estimation is extended to non linear estimation where parameters such as the velocity of an induction machine are present in the transition matrix and in the augmented state space compared to a straightforward implementation of an extended kalman filter our modified optimal two stage kalman estimator reduces the number of arithmetic operations by 25 allowing higher sampling rate or the use of a cheaper microcontroller

multifractal characterization of stochastic resonance we use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals to characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence we use wavelet transform modulus maxima method for the singularity spectrum computations it is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic stochastic or chaotic input signals we show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization this fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also moreover our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence we use also the proposed approach to characterize the noise enhanced dynamics of a coupled stochastic neurons model

emergence of spike correlations in periodically forced excitable systems in sensory neurons the presence of noise can facilitate the detection of weak information carrying signals which are encoded and transmitted via correlated sequences of spikes here we investigate the relative temporal order in spike sequences induced by a subthreshold periodic input in the presence of white gaussian noise to simulate the spikes we use the fitzhugh nagumo model and to investigate the output sequence of interspike intervals isis we use the symbolic method of ordinal analysis we find different types of relative temporal order in the form of preferred ordinal patterns that depend on both the strength of the noise and the period of the input signal we also demonstrate a resonancelike behavior as certain periods and noise levels enhance temporal ordering in the isi sequence maximizing the probability of the preferred patterns our findings could be relevant for understanding the mechanisms underlying temporal coding by which single sensory neurons represent in spike sequences the information about weak periodic stimuli

an alternate derivation and extension of friendland s two stage kalman estimator an alternate simplified derivation of friedland s two stage kalman estimator is given for a somewhat more general class of problems than considered by friedland friedland s result is also extended to encompass two variations on the basic idea which are of practical interest

uncertainty principle for the quaternion fourier transform abstract the two sided quaternion fourier transform was introduced for the analysis of 2d linear time invariant partial differential systems it has been shown to be a powerful tool in image processing in this paper several uncertainty inequalities for the two sided quaternion fourier transform are given with optimal constants including the pitt s inequality logarithmic uncertainty inequality hausdorff young inequality hirschman s entropy inequality generalized heisenberg inequality local uncertainty principle and qualitative uncertainty principle

on the optimality of two stage state estimation in the presence of random bias sufficient conditions for the optimality of a two stage state estimator in the presence of random bias are derived under an algebraic constraint on the correlation between the state and bias process noises the optimal estimate of the system state can be obtained as a linear combination of the output of the first stage a bias free filter and the second stage a bias filter because the algebraic constraint is restrictive in practice the results indirectly indicate that for most practical systems the proposed solution to the two stage estimation problem will be suboptimal

state estimate recovery via nonlinear transforms during periods of destabilisation initiated by measurement uncertainty a parallel approach is being proposed for the construction of a nonlinear based state estimator for closed loop systems failing the hurwitz criteria during finite time intervals the instability originates from sensor errors and it is assumed that a kalman bucy luenberger estimator is being processed in closed loop it is shown that a bounded nonlinear state estimator can be constructed via nonlinear state transforms over a finite time interval and makes use of the control input and the measured output of the destabilised closed loop system the filter presented provides an interesting new approach for the correction of state estimation due to sensor bias in cases where the closed loop plant remains stable this approach is useful for dealing with pure sensor bias without the need for high gain filtering the original uncontrolled open loop system is assumed stable as a preemptive criterion throughout this study

pitt s inequality and the uncertainty principle associated with the quaternion fourier transform abstract the quaternion fourier transform a generalized form of the classical fourier transform has been shown to be a powerful analyzing tool in image and signal processing this paper investigates pitt s inequality and uncertainty principle associated with the two sided quaternion fourier transform it is shown that by applying the symmetric form f f 1 i f 2 f 3 j i f 4 j of quaternion from hitzer and the novel module or l p norm of the quaternion fourier transform f then any nonzero quaternion signal and its quaternion fourier transform cannot both be highly concentrated two part results are provided one part is heisenberg weyl s uncertainty principle associated with the quaternion fourier transform it is formulated by using logarithmic estimates which may be obtained from a sharp of pitt s inequality the other part is the uncertainty principle of donoho and stark associated with the quaternion fourier transform

sharp inequalities for geometric fourier transform and associated ambiguity function abstract the geometric fourier transform defined using clifford algebra plays an increasingly active role in modern data analysis in particular for color image processing however due to the non commutativity it is hard to obtain many important analytic properties in this paper we prove several important sharp inequalities including the hausdorff young inequality and its converse pitt s inequality and lieb s inequality for clifford ambiguity functions with these inequalities several uncertainty principles with optimal constants are derived for the geometric fourier transform most results in this paper are new even in the easier case i e the quaternion setting the method developed here also works for more general geometric fourier transforms

kalman filter for discrete time stochastic linear systems subject to intermittent unknown inputs state estimation of stochastic discrete time linear systems subject to persistent unknown inputs has been widely studied but only few works have been dedicated to the case where unknown inputs may be simultaneously or sequentially active or inactive in this technical note a kalman filter approach is proposed for state estimation of systems with unknown intermittent inputs the design is based on the minimisation of the trace of the state estimation error covariance matrix under the constraint that the state estimation error is decoupled from the unknown inputs corrupting the system at the current time the necessary and sufficient stability conditions are established considering the upper bound of the prediction error covariance matrix

aperiodic stochastic resonance stochastic resonance sr is a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise recently we presented a method and theory for characterizing sr type behavior in excitable systems with aperiodic i e broadband input signals phys rev e 52 r3321 1995 we coined the term aperiodic stochastic resonance asr to describe this general type of behavior in that earlier study we demonstrated asr in the fitzhugh nagumo neuronal model here we demonstrate asr in three additional systems a bistable well system an integrate and fire neuronal model and the hodgkin huxley hh neuronal model we present computational and theoretical results for each system in the context of the hh model we develop a general theory for asr in excitable membranes this work clearly shows that sr type behavior is not limited to systems with periodic inputs thus in general noise can serve to enhance the response of a nonlinear system to a weak input signal regardless of whether the signal is periodic or aperiodic textcopyright 1996 the american physical society

optimal and suboptimal separate bias kalman estimators for a stochastic bias addresses two issues concerning the separate bias kalman estimator the first of these issues deals with the derivation of the optimal estimator for the general case in which the bias vector is stochastic in nature and the second issue deals with defining a suitable suboptimal realization of the generalized estimator

nonstationary stochastic resonance it is by now established that remarkably the addition of noise to a nonlinear system may sometimes facilitate rather than hamper the detection of weak signals this phenomenon usually referred to as stochastic resonance was originally associated with strictly periodic signals but it was eventually shown to occur for stationary aperiodic signals as well however in several situations of practical interest the signal can be markedly nonstationary we demonstrate that the phenomenon of stochastic resonance extends to nonstationary signals as well and thus could be relevant to a wider class of biological and electronic applications building on both nondynamic and aperiodic stochastic resonance our scheme is based on a multilevel trigger mechanism which could be realized as a parallel network of differentiated threshold sensors we find that optimal detection is reached for a number of thresholds of order 10 and that little is gained by going much beyond that number we raise the question of whether this is related to the fact that evolution has favored some fixed numbers of precisely this order of magnitude in certain aspects of sensory perception

a separate bias u d factorization filter two forms of friedland s separate bias estimation algorithm with u d factorization of the covariance matrices are provided each is suited to implementation in a particular computing environment we consider matlab and compiled computer languages we reduce the computation time substantially primarily at the time propagation stage by using a separated bias formulation while retaining the desirable numerical properties of the u d factorization the perecentage reduction typically increases with ratio of bias state dimension to dynamic state dimension a numerical evaluation is given for the matlab algorithm