multifractality in forgetful memories learning rules of a forgetful memory generate their synaptic efficacies through iterative procedures that operate on the input data random patterns we analyse invariant distributions of the synaptic couplings as they arise asymptotically and show that they exhibit fractal or multifractal properties we also discuss their dependence upon the learning rule and the parameters specifying it and indicate how the nature of the invariant distribution is related to the network performance

parameter induced aperiodic stochastic resonance in the presence of multiplicative noise and additive noise abstract parameter induced aperiodic stochastic resonance sr in the presence of multiplicative and additive noise is investigated in detail using theoretical and numerical analysis we evaluate the dynamical probability density by which the bit error rate is defined as a quantity to optimize in the aperiodic sr problem via tuning the system parameters tuning the system parameters includes two cases one is parameter optimized and the other is parameter induced sr to distinguish them we use the conventional method in which sr is realized by varying the noise intensity essentially parameter induced sr is based on the cooperative effect between the stochastic subjected dynamical system and the input signal by changing the intrinsic characteristic of the nonlinear system via tuning the system parameters rather than by adding noise the theory is tested against numerical simulations

receiver operating characteristic curves for a simple stochastic process that carries a static signal the detection of a weak signal in the presence of noise is an important problem that is often studied in terms of the receiver operating characteristic roc curve in which the probability of correct detection is plotted against the probability for a false positive this kind of analysis is typically applied to the situation in which signal and noise are stochastic variables the detection problem emerges however also often in a context in which both signal and noise are stochastic processes and the correct or false detection is said to take place when the process crosses a threshold in a given time window here we consider the problem for a combination of a static signal which has to be detected against a dynamic noise process the well known ornstein uhlenbeck process we give exact but difficult to evaluate quadrature expressions for the detection rates for false positives and correct detections investigate systematically a simple sampling approximation suggested earlier compare to an approximation by stratonovich for the limit of high threshold and briefly explore the case of multiplicative signal all theoretical results are compared to extensive numerical simulations of the corresponding langevin equation our results demonstrate that the sampling approximation provides a reasonable description of the roc curve for this system and it clarifies limit cases for the roc curve

double stochastic resonance in an insect ecosystem with time delays abstract considering additive and multiplicative periodic signals we have investigated the stochastic resonance sr phenomenon in an insect ecosystem with two different types of time delays at which the insect dynamics is assumed to be disturbed by both additive and multiplicative noises the signal to noise ratio snr is calculated when two different weak periodic signals are added to the insect system it is shown from the snr that the additive and multiplicative periodic signals can cause the sr and double sr in the case of time delays in the stochastic and deterministic force respectively a detailed study of the snr depending on various noise characteristics is performed and the main results about sr are compared for two different cases of time delays

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

fractional gaussian noise enhanced information capacity of a nonlinear neuron model with binary signal input this paper reveals the effect of fractional gaussian noise with hurst exponent h 1 2 1 on the information capacity of a general nonlinear neuron model with binary signal input the fgn and its corresponding fractional brownian motion exhibit long range strong dependent increments it extends standard brownian motion to many types of fractional processes found in nature such as the synaptic noise in the paper for the subthreshold binary signal sufficient conditions are given based on the forbidden interval theorem to guarantee the occurrence of stochastic resonance while for the suprathreshold binary signal the simulated results show that additive fgn with hurst exponent h 1 2 1 could increase the mutual information or bits count the investigation indicated that the synaptic noise with the characters of long range dependence and self similarity might be the driving factor for the efficient encoding and decoding of the nervous system

noise driven switching between limit cycles and adaptability in a small dimensional excitable network with balanced coupling we study a system of globally coupled fitzhugh nagumo equations each unit is either excitatory or inhibitory if the numbers of units of both types are in a specific ratio we observe the presence of multistable oscillatory states with different excitation or firing rates in the presence of noise there is noise driven switching between these states and the resultant firing pattern is long range correlated the choice between higher and lower frequency oscillations depends on the input which results in increasing adaptability of the system s output to the periodic input

an integrated approach to ladder and shift operators for the morse oscillator radial coulomb and radial oscillator potentials the morse oscillator radial coulomb and radial harmonic oscillator problems can be solved exactly using a variety of algebraic methods these problems correspond to different realizations of the so 2 1 algebra and a comparison of the generators of the algebra may be used to identify mappings between each pair of systems the resultant transition operators act as ladder or energy changing operators in the cases of the coulomb and harmonic oscillator potentials whereas they act as shift operators acting at constant energy in the case of the morse potential this is a consequence of the so 2 1 dynamical symmetry whereby the morse hamiltonian is expressible solely in terms of the casimir operator of the algebra an alternative algebraic approach the use of the method of supersymmetric quantum mechanics or factorization produces in each case a set of shift operators relations between the various ladder and shift operators may be identified by means of the appropriate mappings and these results can be generalized so as to relate the one dimensional morse oscillator to the radial coulomb and radial harmonic oscillator potentials involving an arbitrary number of angular dimensions

comparison of aperiodic stochastic resonance in a bistable system realized by adding noise and by tuning system parameters two methods of realizing aperiodic stochastic resonance asr by adding noise and tuning system parameters in a bistable system after a scale transformation can be compared in a real parameter space in this space the resonance point of asr via adding noise denotes the extremum of a line segment whereas the method of tuning system parameters presents the extrema of a parameter plane we demonstrate that in terms of the system performance the method of tuning system parameters takes the precedence of the approach of adding noise for an adjustable bistable system besides adding noise can be viewed as a specific case of tuning system parameters further research shows that the optimal system found by tuning system parameters may be subthreshold or suprathreshold and the conventional asr effects might not occur in some suprathreshold optimal systems

logical response induced by temperature asymmetry it is known that the reliable logical response can be extracted from a noisy bistable system at an intermediate value of noise strength when two random or periodic two level square waveform serve as the inputs the asymmetry of the potential has a very important role and dictates the type of logical operation such as or or and exhibited by the system here we show that one can construct logic gates with symmetric bistable potential if the two states of the double well are thermalized with two different heat baths it has been found that if a given state is kept at a sufficiently low temperature compared to the other the system shows one kind of logic behavior say or interestingly the system s response turns into the other kind say and if the temperature of the initial low temperature well is increased gradually and the quality of the logical response first improves and then weakens after passing through a maximum at a particular value however the reliability of the second kind of logical response and is not as good as the first kind or and depends on the amplitude of the inputs still one can construct both kinds of logic gates with maximum reliability by properly choosing the initial low temperature well

adaptive stochastic resonance in noisy neurons based on mutual information noise can improve how memoryless neurons process signals and maximize their throughput information such favorable use of noise is the so called stochastic resonance or sr effect at the level of threshold neurons and continuous neurons this work presents theoretical and simulation evidence that 1 lone noisy threshold and continuous neurons exhibit the sr effect in terms of the mutual information between random input and output sequences 2 a new statistically robust learning law can find this entropy optimal noise level and 3 the adaptive sr effect is robust against highly impulsive noise with infinite variance histograms estimate the relevant probability density functions at each learning iteration a theorem shows that almost all noise probability density functions produce some sr effect in threshold neurons even if the noise is impulsive and has infinite variance the optimal noise level in threshold neurons also behaves nonlinearly as the input signal amplitude increases simulations further show that the sr effect persists for several sigmoidal neurons and for gaussian radial basis function neurons

an su 1 1 dynamical algebra for the poschl teller potential an su 1 1 dynamical algebra to describe the continuum part of the spectrum for the modified poschl teller potential is proposed the space associated with this algebra is given in terms of a family of orthonormal functions n characterized by the parameter this set is constructed from polynomials which are orthogonal with respect to a weighting function corresponding to a poschl teller ground state an analysis of the associated algebra is investigated in detail the functions are identified with poschl teller like functions associated with different potential depths we prove that by choosing appropriately the parameter it is possible to decouple the discrete states of a given parity from the continuum part of the spectrum a discussion of the matrix elements of the dipole function operator is also included

robust stochastic resonance for simple threshold neurons simulation and theoretical results show that memoryless threshold neurons benefit from small amounts of almost all types of additive noise and so produce the stochastic resonance or sr effect input output mutual information measures the performance of such threshold systems that use subthreshold signals the sr result holds for all possible noise probability density functions with finite variance the only constraint is that the noise mean must fall outside a forbidden threshold related interval that the user can control a new theorem shows that this condition is also necessary a corollary and simulations show that the sr effect occurs for right sided beta and weibull noise as well these sr results further hold for the entire uncountably infinite class of alpha stable probability density functions alpha stable noise densities have infinite variance and infinite higher order moments and often model impulsive noise environments the stable noise densities include the special case of symmetric bell curve densities with thick tails such as the cauchy probability density the sr result for alpha stable noise densities shows that the sr effect in threshold and thresholdlike systems is robust against occasional or even frequent violent fluctuations in noise regression analysis reveals both an exponential relationship for the optimal noise dispersion as a function of the alpha bell curve tail thickness and an approximate linear relationship for the sr maximal mutual information as a function of the alpha bell curve tail thickness

an su 1 1 dynamical algebra for the morse potential an su 1 1 dynamical algebra to describe both the discrete and the continuum parts of the spectrum for the morse potential is proposed the space associated with this algebra is given in terms of a family of orthonormal functions n characterized by the parameter this set is constructed from polynomials which are orthogonal with respect to a weighting function related to a morse ground state an analysis of the associated algebra is investigated in detail the functions are identified with morse like functions associated with different potential depths we prove that for a particular choice of the discrete and the continuum parts of the spectrum decouple the connection of this treatment with the supersymmetric quantum mechanics approach is established a closed expression for the mecke dipole moment function is obtained

suprathreshold stochastic resonance in neural processing tuned by correlation suprathreshold stochastic resonance ssr is examined in the context of integrate and fire neurons with an emphasis on the role of correlation in the neuronal firing we employed a model based on a network of spiking neurons which received synaptic inputs modeled by poisson processes stimulated by a stepped input signal the smoothed ensemble firing rate provided an output signal and the mutual information between this signal and the input was calculated for networks with different noise levels and different numbers of neurons it was found that an ssr effect was present in this context we then examined a more biophysically plausible scenario where the noise was not controlled directly but instead was tuned by the correlation between the inputs the ssr effect remained present in this scenario with nonzero noise providing improved information transmission and it was found that negative correlation between the inputs was optimal finally an examination of ssr in the context of this model revealed its connection with more traditional stochastic resonance and showed a trade off between supratheshold and subthreshold components we discuss these results in the context of existing empirical evidence concerning correlations in neuronal firing

noise benefits in quantizer array correlation detection and watermark decoding quantizer noise can improve statistical signal detection in array based nonlinear correlators in neyman pearson and maximum likelihood ml detection this holds even for infinite variance symmetric alpha stable channel noise and for generalized gaussian channel noise noise enhanced correlation detection leads to noise enhanced watermark extraction based on such nonlinear detection at the pixel or bit level this yields a noise based algorithm for digital watermark decoding using two new noise benefit theorems the first theorem gives a necessary and sufficient condition for quantizer noise to increase the detection probability of a constant signal for a fixed false alarm probability if the channel noise is symmetric and if the sample size is large the second theorem shows that the array must contain more than one quantizer for such a stochastic resonance noise benefit if the symmetric channel noise is unimodal it also shows that the noise benefit rate improves in the small quantizer noise limit as the number of array quantizers increases the second theorem further shows that symmetric uniform quantizer noise gives the optimal rate for an initial noise benefit among all finite variance symmetric scale family noise two corollaries give similar results for stochastic resonance noise benefits in ml detection of a signal sequence with known shape but unknown amplitude

information transmission in parallel threshold arrays suprathreshold stochastic resonance the information transmitted through a parallel summing array of noisy threshold elements with a common threshold is considered in particular using theoretical and numerical analysis a recently reported n g stocks phys rev lett 84 2310 2000 form of stochastic resonance termed suprathreshold stochastic resonance ssr is studied in detail ssr is observed to occur in arrays with two or more elements and unlike stochastic resonance sr in a single element gives rise to noise induced information gains that occur independent of the setting of the threshold or the size of the signal the transmitted information is maximized when all thresholds are set to coincide with the signal mean in this situation and for large arrays the noise can enhance performance up to approximately half the theoretical noiseless channel capacity the theory is tested against digital simulation

inconsistencies in the description of a quantum system with a finite number of bound states by a compact dynamical group in a recent paper aldaya v and guerrero j 2005 j phys a math gen 38 6939 it is shown that the bound states of the modified poschl teller potential should be described by the non compact dynamical group su 1 1 instead of the usual compact group su 2 here we prove that su 2 cannot be the dynamical group for a potential with a finite number of bound states on the basis of the modified poschl teller potential and the morse potential this suggests that a quantum system with a continuum spectrum and a finite number of bound states should be described both in the continuum and the discrete spectrum by a non compact dynamical group instead of a compact one

optimal stimulus and noise distributions for information transmission via suprathreshold stochastic resonance suprathreshold stochastic resonance ssr is a form of noise enhanced signal transmission that occurs in a parallel array of independently noisy identical threshold nonlinearities including model neurons unlike most forms of stochastic resonance the output response to suprathreshold random input signals of arbitrary magnitude is improved by the presence of even small amounts of noise in this paper the information transmission performance of ssr in the limit of a large array size is considered using a relationship between shannon s mutual information and fisher information a sufficient condition for optimality i e channel capacity is derived it is shown that capacity is achieved when the signal distribution is jeffrey s prior as formed from the noise distribution or when the noise distribution depends on the signal distribution via a cosine relationship these results provide theoretical verification and justification for previous work in both computational neuroscience and electronics

matrix elements of u and p for the modified poschl teller potential closed analytical expressions in terms of a single sum are obtained for the matrix elements of the momentum and the natural variable u tanh x in the basis of the modified poschl teller mpt bound eigenstates these matrix elements are first expressed in terms of franck condon factors which thereafter are substituted for analytic expressions expansions of the variables p and u in terms of creation and annihilation operators associated with the mpt bound eigenfunctions are also presented

stochastic resonance of ensemble neurons for transient spike trains wavelet analysis by using the wavelet transformation wt i have analyzed the response of an ensemble of n 1 10 100 and 500 hodgkin huxley neurons to transient m pulse spike trains m i to 3 with independent gaussian noises thecross correlation between the input and output signals is expressed in terms of the wt expansion coefficients the signal to noise ratio snr is evaluated by using the denoising method within the wt by which the noise contribution is extracted from the output signals although the response of a single n 1 neuron to subthreshold transient signals with noises is quite unreliable the transmission fidelity assessed by the cross correlation and snr is shown to be much improved by increasing the value of n a population of neurons plays an indispensable role in the stochastic resonance sr for transient spike inputs it is also shown that in a large scale ensemble the transmission fidelity for suprathreshold transient spikes is not significantly degraded by a weak noise which is responsible to sr for subthreshold inputs

renyi entropy measure of noise aided information transmission in a binary channel this paper analyzes a binary channel by means of information measures based on the renyi entropy the analysis extends and contains as a special case the classic reference model of binary information transmission based on the shannon entropy measure the extended model is used to investigate further possibilities and properties of stochastic resonance or noise aided information transmission the results demonstrate that stochastic resonance occurs in the information channel and is registered by the renyi entropy measures at any finite order including the shannon order furthermore in definite conditions when seeking the renyi information measures that best exploit stochastic resonance then nontrivial orders differing from the shannon case usually emerge in this way through binary information transmission stochastic resonance identifies optimal renyi measures of information differing from the classic shannon measure a confrontation of the quantitative information measures with visual perception is also proposed in an experiment of noise aided binary image transmission

stochastic resonance driven by two different kinds of colored noise in a bistable system the phenomenon of stochastic resonance in a bistable nonlinear system is investigated when both the multiplicative noise and the coupling between additive and multiplicative noise are colored with different values of noise correlation time ensuremath tau 1 and ensuremath tau 2 combining the functional analysis and unified colored noise approximation the two different kinds of colored noise in the nonlinear system can be simplified the signal to noise ratio is calculated when a weakly periodic signal is added to the system it is found that there appears a transition between one peak and two peaks in the curve of the signal to noise ratio when either the noise correlation time ensuremath tau 1 and ensuremath tau 2 or the coupling strength ensuremath lambda between additive and multiplicative noise is increased the transition between one and two peaks depending on ensuremath tau 1 and ensuremath lambda is more complex than that depending on ensuremath tau 2

noise enhanced fisher information in parallel arrays of sensors with saturation this paper investigates stochastic resonance in parallel arrays of uncoupled saturating devices the fisher information is used to demonstrate the possibility of noise improved parameter estimation for arbitrary parametric signals especially it is shown that improvement by noise always occurs in these arrays for any configuration of the input signal even in optimal configuration the results contribute to establish stochastic resonance in parallel uncoupled arrays as a general mechanism of enhancement by noise which can occur in wide classes of nonlinearities and for various information processing tasks it can supplement other mechanisms of stochastic resonance that take place in isolated nonlinearities but generally in restricted configurations of the input signal

optimal weighted suprathreshold stochastic resonance with multigroup saturating sensors abstract suprathreshold stochastic resonance ssr describes a noise enhanced effect that occurs not in a single element but rather in an array of nonlinear elements when the signal is no longer subthreshold within the context of ssr we investigate the optimization problem of signal recovery through an array of saturating sensors where the response of each element can be optimally weighted prior to summation with a performance measure of mean square error mse we consider groups of sensors individual sensors within each group have identical parameters but each group has distinct parameters we find that optimally weighting the sensor responses provides a lower mse in comparison with the unweighted case for weak and moderate noise intensities moreover as the slope parameter of the nonlinear sensors increases the mse superiority of the optimally weighted array shows a peak and then tends to a fixed value these results indicate that ssr with optimal weights as a general mechanism of enhancement by noise is of potential interest to signal recovery

optimising threshold levels for information transmission in binary threshold networks independent multiplicative noise on each threshold abstract the problem of optimising the threshold levels in multilevel threshold system subject to multiplicative gaussian and uniform noise is considered similar to previous results for additive noise we find a bifurcation phenomenon in the optimal threshold values as the noise intensity changes this occurs when the number of threshold units is greater than one we also study the optimal thresholds for combined additive and multiplicative gaussian noise and find that all threshold levels need to be identical to optimise the system when the additive noise intensity is a constant however this identical value is not equal to the signal mean unlike the case of additive noise when the multiplicative noise intensity is instead held constant the optimal threshold levels are not all identical for small additive noise intensity but are all equal to zero for large additive noise intensity the model and our results are potentially relevant for sensor network design and understanding neurobiological sensory neurons such as in the peripheral auditory system