desynchronization in diluted neural networks the dynamical behavior of a weakly diluted fully inhibitory network of pulse coupled spiking neurons is investigated upon increasing the coupling strength a transition from regular to stochasticlike regime is observed in the weak coupling phase a periodic dynamics is rapidly approached with all neurons firing with the same rate and mutually phase locked the strong coupling phase is characterized by an irregular pattern even though the maximum lyapunov exponent is negative the paradox is solved by drawing an analogy with the phenomenon of stable chaos i e by observing that the stochasticlike behavior is limited to an exponentially long with the system size transient remarkably the transient dynamics turns out to be stationary

the reflexive and anti reflexive solutions of the matrix equation ax b abstract an n n complex matrix p is said to be a generalized reflection matrix if p h p and p 2 i an n n complex matrix a is said to be a reflexive or anti reflexive matrix with respect to the generalized reflection matrix p if a pap or a pap this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the reflexive and anti reflexive with respect to a generalized reflection matrix p solutions of the matrix equation ax b in addition in corresponding solution set of the equation the explicit expression of the nearest matrix to a given matrix in the frobenius norm have been provided

network amplification of local fluctuations causes high spike rate variability fractal firing patterns and oscillatory local field potentials we investigate a model for neural activity in a two dimensional sheet of leaky integrate and fire neurons with feedback connectivity consisting of local excitation and surround inhibition each neuron receives stochastic input from an external source independent in space and time as recently suggested by softky and koch 1992 1993 independent stochastic input alone cannot explain the high interspike interval variability exhibited by cortical neurons in behaving monkeys we show that high variability can be obtained due to the amplification of correlated fluctuations in a recurrent network furthermore the cross correlation functions have a dual structure with a sharp peak on top of a much broader hill this is due to the inhibitory and excitatory feedback connections which cause hotspots of neural activity to form within the network these localized patterns of excitation appear as clusters or stripes that coalesce disintegrate or fluctuate in size while simultaneously moving in a random walk constrained by the interaction with other clusters the synaptic current impinging upon a single neuron shows large fluctuations at many time scales leading to a large coefficient of variation cv for the interspike interval statistics the power spectrum associated with single units shows a 1 f decay for small frequencies and is flat at higher frequencies while the power spectrum of the spiking activity averaged over many cells equivalent to the local field potential shows no 1 f decay but a prominent peak around 40 hz in agreement with data recorded from cat and monkey cortex gray et al 1990 eckhorn et al 1993 firing rates exhibit self similarity between 20 and 800 msec resulting in 1 f like noise consistent with the fractal nature of neural spike trains teich 1992

a class of initials dependent dynamical systems the dynamics of initial dependent system is investigated the potential mechanism for initial dependent property is discussed general scheme is proposed to design initial dependent dynamical system this scheme can be used for chaos control by initial setting with memristor nonlinear term is critical for emergence of chaos in autonomous dynamical systems the sampled time series in chaotic system are dependent on the initial selection of variables while the attractors are invariant for fixed parameters in this paper the dynamical behavior of a class of dynamical system is investigated at fixed parameter region it is found that the state selection is dependent on the initials and the potential mechanism is discussed it is confirmed that the system can be switched between stable state periodical state and even chaotic state by selecting appropriate initials even the parameters are fixed we think that nonlinear cross terms with higher order could account for the emergence of this behavior it indicates that initial selection and resetting can be also effective to control some chaotic systems and these chaotic systems could enhance security for possible secure communication because the chaotic attractor depends on the parameter and initials selection as well in the case of secure communication the reconstruction of phase space becomes more difficult because the attractors are changed arbitrarily thus the safety for secure keys is enhanced for chaos control when the initials are reset the controller can be removed and the system can develop to step into the desired target by itself

procrustes problems in finite dimensional indefinite scalar product spaces abstract some applications from multidimensional scaling in an environment of indefinite scalar products are investigated in particular the construction of points from given distances is considered and two variants of procrustes problems are discussed it is found that both procrustes problems can be solved with the help of h polar decompositions or g h polar decompositions of specified matrices furthermore a method for the numerical computation of h or g h polar decompositions of nonsingular matrices is described

solving balanced procrustes problem with some constraints by eigenvalue decomposition the balanced procrustes problem with some special constraints such as symmetric orthogonality and symmetric idempotence are considered by one time eigenvalue decomposition of the matrix product generated by the matrices a and b the constrained solutions are constructed simply similar strategy is applied to the problem with the corresponding p commuting constraints with a given symmetric matrix p numerical examples are presented to show the efficiency of the proposed methods

population rate codes carried by mean fluctuation and synchrony of neuronal firings abstract a population of firing neurons is expected to carry information not only by the mean firing rate but also by fluctuation and synchrony among neurons in order to examine this possibility we have studied responses of neuronal ensembles to three kinds of inputs mean fluctuation and synchrony driven inputs the generalized rate code model including additive and multiplicative noise h hasegawa phys rev e 75 2007 051904 has been studied by direct simulations dss and the augmented moment method amm in which equations of motion for mean firing rate fluctuation and synchrony are derived results calculated by the amm are in good agreement with those by dss the independent component analysis ica of our results has shown that mean firing rate fluctuation or variability and synchrony may carry independent information in the population rate code model the input output relation of mean firing rates is shown to have higher sensitivity for larger multiplicative noise as recently observed in prefrontal cortex a comparison is made between results obtained by the integrate and fire if model and our rate code model

spike output jitter mean firing time and coefficient of variation to understand how a single neurone processes information it is critical to examine the relationship between input and output marsalek koch and maunsell s study focused on output jitter standard deviation of output interpike interval found that for the integrate and fire if whereas an input distribution with a more slowly decreasing tail induces divergence of output jitter exact formulae for mean firing time are also obtained which enable us to estimate the coefficient of variation the i f model with leakage is also briefly considered

bistability and resonance in the periodically stimulated hodgkin huxley model with noise we describe general characteristics of the hodgkin huxley neuron s response to a periodic train of short current pulses with gaussian noise the deterministic neuron is bistable for antiresonant frequencies when the stimuli arrive at the resonant frequency the firing rate is a continuous function of the current amplitude i 0 and scales as i 0 i th 1 2 characteristic of a saddle node bifurcation at the threshold i th intervals of continuous irregular response alternate with integer mode locked regions with bistable excitation edge there is an even all multimodal transition between the 2 1 and 3 1 states in the vicinity of the main resonance which is analogous to the odd all transition discovered earlier in the high frequency regime for i 0 i th and small noise the firing rate has a maximum at the resonant frequency for larger noise and subthreshold stimulation the maximum firing rate initially shifts toward lower frequencies then returns to higher frequencies in the limit of large noise the stochastic coherence antiresonance defined as a simultaneous occurrence of i the maximum of the coefficient of variation and ii the minimum of the firing rate vs the noise intensity occurs over a wide range of parameter values including monostable regions results of this work can be verified experimentally

responses of a hodgkin huxley neuron to various types of spike train inputs numerical investigations have been made of responses of a hodgkin huxley hh neuron to spike train inputs whose interspike interval isi is modulated by deterministic semi deterministic chaotic and stochastic signals as deterministic one we adopt inputs with the time independent isi and with time dependent isi modulated by sinusoidal signal the rossler and lorentz models are adopted for chaotic modulations of isi stochastic isi inputs with the gamma distribution are employed it is shown that distribution of output isi data depends not only on the mean of isis of spike train inputs but also on their fluctuations the distinction of responses to the three kinds of inputs can be made by return maps of input and output isis but not by their histograms the relation between the variations of input and output isis is shown to be different from that of the integrate and fire if model because of the refractory period in the hh neuron

dynamical mean field theory of noisy spiking neuron ensembles application to the hodgkin huxley model a dynamical mean field approximation dma previously proposed by the present author h hasegawa phys rev e 67 041903 2003 has been extended to ensembles described by a general noisy spiking neuron model ensembles of n unit neurons each of which is expressed by coupled k dimensional differential equations des are assumed to be subject to spatially correlated white noises the original mathrm kn dimensional stochastic des have been replaced by k k 2 dimensional deterministic des expressed in terms of means and the second order moments of local and global variables the fourth order contributions are taken into account by the gaussian decoupling approximation our dma has been applied to an ensemble of hodgkin huxley hh neurons k 4 for which effects of the noise the coupling strength and the ensemble size on the response to a single spike input have been investigated numerical results calculated by the dma theory are in good agreement with those obtained by direct simulations although the former computation is about a thousand times faster than the latter for a typical hh neuron ensemble with n 100

diffusion entropy approach to complexity for a hodgkin huxley neuron abstract by means of the diffusion entropy method de we analyze the responses of a hodgkin huxley hh neuron to two types of spike train inputs the stimuli can create a living state matter lsm an intermediate condition between dynamics and thermodynamics an anomalous scaling can also be found which is corresponding to the thermodynamic condition the living state matter lsm regresses slowly to the anomalous scaling with almost an exact period the anomalous scaling exponent and the period may be two measures of the dynamical process of a hh neuron under the considered stimuli

completely continuous functions and r map in fuzzifying topological space this paper considers fuzzifying topologies a special case of i fuzzy topologies introduced by ying the concepts of fuzzifying regular derived set fuzzifying regular interior and fuzzifying regular convergence are studied and some results on above concepts are obtained also the concepts of fuzzifying completely continuous functions and fuzzifying r map are introduced and some important characterizations are obtained furthermore some compositions of fuzzifying continuity with fuzzifying completely continuous functions and fuzzifying r map are presented

response of autaptic hodgkin huxley neuron with noise to subthreshold sinusoidal signals abstract in this work we investigated the response of a stochastic hodgkin huxley hh neuron with an autapse to subthreshold sinusoidal signals it is found that the autapse not only adjusts the stochastic responses but also improves the detection of subthreshold signals in the case of weak noise the autapse facilitates the response of neuron to the subthreshold sinusoidal signals with a small parameter region in t d e l a y space the increased noise intensity enlarges this parameter region and increases the corresponding response frequency in such range as the autaptic intensity increases however this parameter region shrunks we also observed that there is an optimal range of the delay time of autapse within which the stochastic hh neuron fires action potentials with high frequency the corresponding response spike train for the optimal delay time is nearly a regular sequence with the interspike intervals approximated to the delay time the current results reveal a novel resonance phenomenon facilitated by autapse named autaptic delay induced coherence resonance

a new approach for fuzzy topology ii abstract we point out a new approach for fuzzy topology with fuzzy logic and discuss the neighborhood structure of a point and the convergence of nets and filters in this new framework

dynamical response of the hodgkin huxley model in the high input regime the response of the hodgkin huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post synaptic potentials is analyzed in detail the model is examined in its three fundamental dynamical regimes silence bistability and repetitive firing its response is characterized in terms of statistical indicators interspike interval distributions and their first moments as well as of dynamical indicators autocorrelation functions and conditional entropies in the silent regime the coexistence of two different coherence resonances is revealed one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state the second one at intermediate noise variance is associated with the regularization of the sequence of spikes emitted by the neuron bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations in the repetitive firing regime a maximization of incoherence is observed at finite noise variance finally the mechanisms responsible for the different features appearing in the interspike interval distributions like multimodality and exponential tails are clearly identified in the various regimes

the procrustes problem for orthogonal stiefel matrices in this paper we consider the procrustes problem on the manifold of orthogonal stiefel matrices given matrices cal a in bbb r m times k cal b in bbb r m times p m ge p ge k we seek the minimum of cal a cal b q 2 for all matrices q in bbb r p times k q tq i k times k we introduce a class of relaxation methods for generating sequences of approximations to a minimizer and offer a geometric interpretation of these methods results of numerical experiments illustrating the convergence of the methods are given

discrimination with spike times and isi distributions we study the discrimination capability of spike time sequences using the chernoff distance as a metric we assume that spike sequences are generated by renewal processes and study how the chernoff distance depends on the shape of interspike interval isi distribution first we consider a lower bound to the chernoff distance because it has a simple closed form then we consider specific models of isi distributions such as the gamma inverse gaussian ig exponential with refractory period er and that of the leaky integrate and fire lif neuron we found that the discrimination capability of spike times strongly depends on high order moments of isi and that it is higher when the spike time sequence has a larger skewness and a smaller kurtosis high variability in terms of coefficient of variation cv does not necessarily mean that the spike times have less discrimination capability spike sequences generated by the gamma distribution have the minimum discrimination capability for a given mean and variance of isi we used series expansions to calculate the mean and variance of isis for lif neurons as a function of the mean input level and the input noise variance spike sequences from an lif neuron are more capable of discrimination than those of ig and gamma distributions when the stationary voltage level is close to the neuron s threshold value of the neuron

physiological gain leads to high isi variability in a simple model of a cortical regular spiking cell to understand the interspike interval isi variability displayed by visual cortical neurons softky koch 1993 it is critical to examine the dynamics of their neuronal integration as well as

propagation of firing rate by synchronization and coherence of firing pattern in a feed forward multilayer neural network when neurons in layer 1 fire irregularly under stochastic noise it is found synchronous firings can develop gradually in latter layers within a feed forward multilayer neural network which is consistent with experimental findings the underlying mechanism of propagation of firing rate is explored then rate encoding realized by synchronization is clarified furthermore the effects of connection probability between nearest layers stochastic noise and ratio of inhibitory connections to total connection on i propagation of firing rate by synchronization and ii coherence of firing pattern are investigated respectively it is observed that i there is a threshold for connection probability beyond which firing rate of each layer can propagate successfully through the whole network by synchronization the dependence of firing rate on layer index is very different for different connection probability in addition larger the connection probability is more rapidly the synchrony is built up ii increasing intensity of stochastic noise enhances firing rate in output layer stochastic noise plays a constructive role in improving synchrony by causing the synchronization more quickly iii the inhibitory connection offsets excitatory input therefore reduces firing rate and synchrony as layer index increases coherence measure goes through a peak i e the coherence of firing pattern is the worst at certain a layer with increasing the ratio of inhibitory connections the variability of firing train is enhanced exhibiting destructive role of inhibitory connections on coherence of firing pattern

response of a hodgkin huxley neuron to a high frequency input we study the response of a hodgkin huxley neuron stimulated by a periodic sequence of conductance pulses arriving through the synapse in the high frequency regime in addition to the usual excitation threshold there is a smooth crossover from the firing to the silent regime for increasing pulse amplitude g syn the amplitude of the voltage spikes decreases approximately linearly with g syn in some regions of parameter space the response is irregular probably chaotic in the chaotic regime between the mode locked regions 3 1 and 2 1 near the lower excitation threshold the output interspike interval histogram isih undergoes a sharp transition if the driving period is below the critical value t i l t ensuremath ast the output histogram contains only odd multiples of t i for t i g t ensuremath ast even multiples of t i also appear in the histogram starting from the largest values near t ensuremath ast the isih scales logarithmically on both sides of the transition the coefficient of variation of isih has a cusp singularity at t ensuremath ast the average response period has a maximum slightly above t ensuremath ast near the excitation threshold in the chaotic regime the average firing rate rises sublinearly from frequencies of order 1 hz

pre continuity and d c p continuity in fuzzifying topology the concepts of fuzzy pre continuity and fuzzy cpre continuity are introduced and studied in fuzzifying topology essentially in order to give decompositions of fuzzy continuity

interspike interval attractors from chaotically driven neuron models abstract sequences of intervals between firing times interspike intervals isis from single neuron models with chaotic forcing are investigated we analyze how the dynamical properties of the chaotic input determine those of the output isi sequence and assess how various biophysical parameters affect this input output relationship the attractors constructed from delay embeddings of isis and of the chaotic input are compared from the points of view of geometry and nonlinear forecastability for the three integrate and fire if models investigated the similarity between these attractors is high only when the mean firing rate is high and when firings occur over a large range of the input signal when these conditions are satisfied isis are related to input values at which firings occur by a simple map and their distribution can be derived from that of input signal values attractor reconstruction is found to be more sensitive to mean firing rate than to isi distribution at low firing rates for which the input is under sampled and isis become larger than the short term prediction horizon or when the dynamics do not allow a smooth invertible mapping between signal and isis information is lost our results relevant to all dynamical systems generating events show that information about continuous time dynamics is difficult to retrieve at low event rates and that information about inputs can be isolated only under restricted conditions

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

effects of degree distributions on signal propagation in noisy feedforward neural networks abstract we focus on the effects of degree distributions on signal propagation in noisy feedforward networks ffns based on the fitzhugh nagumo neuron model three ffn topologies are constructed with the same number of synaptic connections in each layer but different distributions for both the in degree and out degree of neurons as identical uniform and exponential it is found that the propagation of firing patterns and firing rates are affected by the degree distributions of neurons in the ffns the output firing rates in three ffn topologies without noise is nonlinearly dependent on their input firing rates and it can be increased steadily by increasing noise intensity the firing patterns of three ffn topologies can also be influenced by the noise and connection probability interestingly an optimal parameter area corresponding to both the noise intensity and connection probability is found for the propagation of spiking regularity in three ffn topologies respectively in addition the firing synchronization of different layers in three topologies differs obviously from one another moreover synfire enhanced coherence resonance emerges in the later layers of the three ffn topologies these results suggest that the degree distributions of neurons are a key factor that can modulate both the propagation of the firing rates and firing patterns in ffns

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

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

the skew symmetric orthogonal solutions of the matrix equation ax b abstract an n n real matrix x is said to be a skew symmetric orthogonal matrix if xt x and xtx i using the special form of the c s decomposition of an orthogonal matrix with skew symmetric k k leading principal submatrix this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the skew symmetric orthogonal solutions of the matrix equation ax b in addition in corresponding solution set of the equation the explicit expression of the nearest matrix to a given matrix in the frobenius norm have been provided furthermore the procrustes problem of skew symmetric orthogonal matrices is considered and the formula solutions are provided finally an algorithm is proposed for solving the first and third problems numerical experiments show that it is feasible

corrigendum to almost continuity and δ continuity in fuzzifying topology fuzzy sets and systems 116 2000 339 352 abstract in 2000 zahran has introduced the concepts of open sets almost continuity and continuity in fuzzifying topology in this note we show that lemma 2 2 and theorem 2 4 are incorrect

a procrustes problem on the stiefel manifold an orthogonal procrustes problem on the stiefel manifold is studied where a matrix q with orthonormal columns is to be found that minimizes aq b rm f for an l times m matrix a and an l times n matrix b with l geq m and m n based on the normal and secular equations and the properties of the stiefel manifold necessary conditions for a global minimum as well as necessary and sufficient conditions for a local minimum are derived

dynamics of membrane excitability determine interspike interval variability a link between spike generation mechanisms and cortical spike train statistics we propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains the key lies in the nonlinear dynamics of cortical spike generation which are consistent with type i membranes where saddle node dynamics underlie excitability rinzel ermentrout 1989 we present a canonical model for type i membranes the neuron the neuron is a phase model whose dynamics reflect salient features of type i membranes this model generates spike trains with coefficient of variation cv above 0 6 when brought to firing by noisy inputs this happens because the timing of spikes for a type i excitable cell is exquisitely sensitive to the amplitude of the suprathreshold stimulus pulses a noisy input current giving random amplitude kicks to the cell evokes highly irregular firing across a wide range of firing rates an intrinsically oscillating cell gives regular spike trains we corroborate the results with simulations of the morris lecar m l neural model with random synaptic inputs type i m l yields high cvs when this model is modified to have type ii dynamics periodicity arises via a hopf bifurcation however it gives regular spike trains cv below 0 3 our results suggest that the high cv values such as those observed in cortical spike trains are an intrinsic characteristic of type i membranes driven to firing by random inputs in contrast neural oscillators or neurons exhibiting type ii excitability should produce regular spike trains

generalized rate code model for neuron ensembles with finite populations we have proposed a generalized langevin type rate code model subjected to multiplicative noise in order to study stationary and dynamical properties of an ensemble containing a finite number n of neurons calculations using the fokker planck equation have shown that owing to the multiplicative noise our rate model yields various kinds of stationary non gaussian distributions such as ensuremath gamma inverse gaussian like and log normal like distributions which have been experimentally observed the dynamical properties of the rate model have been studied with the use of the augmented moment method amm which was previously proposed by the author from a macroscopic point of view for finite unit stochastic systems in the amm the original n dimensional stochastic differential equations des are transformed into three dimensional deterministic des for the means and fluctuations of local and global variables the dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the amm are in good agreement with those obtained by direct simulation the synchronization in the neuronal ensemble is discussed the variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise which may be a conceivable origin of the observed large variability in cortical neurons

almost continuity and d continuity in fuzzifying topology in this paper we introduce the concepts of open sets closure r nbd system almost continuity and continuity in fuzzifying topology and we give some characterizations of almost continuity and continuity