arXiv subjects

Hideo Hasegawa

Publications and source records attributed to Hideo Hasegawa.

69 records · Page 4Linked to original sources

arXiv2002

Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises

Dynamics of an ensemble of $N$-unit FitzHugh-Nagumo (FN) neurons subject to white noises has been studied by using a semi-analytical dynamical mean-field (DMF) theory in which the original $2 N$-dimensional {\it stochastic} differential equations are replaced by 8-dimensional {\it deterministic} differential equations expressed in terms of moments of local and global variables. Our DMF theory, which assumes weak noises and the Gaussian distribution of state variables, goes beyond weak couplings among constituent neurons. By using the expression for the firing probability due to an applied single spike, we have discussed effects of noises, synaptic couplings and the size of the ensemble on the spike timing precision, which is shown to be improved by increasing the size of the neuron ensemble, even when there are no couplings among neurons. When the coupling is introduced, neurons in ensembles respond to an input spike with a partial synchronization. DMF theory is extended to a large cluster which can be divided into multiple sub-clusters according to their functions. A model calculation has shown that when the noise intensity is moderate, the spike propagation with a fairly precise timing is possible among noisy sub-clusters with feed-forward couplings, as in the synfire chain. Results calculated by our DMF theory are nicely compared to those obtained by direct simulations. A comparison of DMF theory with the conventional moment method is also discussed.

cond-mat.dis-nn↗

arXiv2002

Responses of Ensemble Neurons to Spike-Train Signals with Independent Noises: Stochastic Resonance and Spike Variability

Responses have been numerically studied of an ensemble of $N$ (=1, 10, and 100) Hodgkin-Huxley (HH) neurons to coherent spike-train inputs applied with independent Poisson spike-train (ST) noise and Gaussian white noise. Three interrelated issues have been investigated: (1) the difference and the similarity between the effects of the two noises, (2) the size effect of a neuron ensemble on the signal-to-noise ratio (SNR), and (3) the compatibility of a large firing variability with fairly good information transmission. (1) The property of stochastic resonance (SR) for ST noise is shown to be rather different from that for white noise. When SNR for sub-threshold inputs obtained in our simulation is analyzed by the expression given by $SNR=10 {\rm log_{10}} [(A/X^α) {\rm exp}(-B/X)]$ where $X$ expresses the noise intensity and $A$ and $B$ are constants, the index $α$ is $α=3$ for the ST noise and $α=2$ for the white noise: the former is different from the conventional value of $α=2$ realized in many non-linear systems. ST noise works less effectively for SR than white noise. (2) The transmission fidelity evaluated by SNR is much improved by increasing $N$, the size of ensemble neurons. In a large-scale neuron ensemble, SNR for supra-threshold inputs is shown to be not significantly degraded by weak noises responsible to SR for sub-threshold inputs. (3) Interspike intervals (ISIs) of output spikes for sub-threshold inputs have a large variability ($c_{v} \siml 0.8$), which is comparable to the data observed in cortical neurons. Despite variable firings of individual neurons, output signals summed over an ensemble may carry information with a fairly good SNR by the aid of SR and a pooling effect.

cond-mat.dis-nn↗

arXiv2001

Stochastic Resonance of Ensemble Neurons for Transient Spike Trains: A Wavelet Analysis

By using the wavelet transformation (WT), we have analyzed the response of an ensemble of $N$ (=1, 10, 100 and 500) Hodgkin-Huxley (HH) neurons to {\it transient} $M$-pulse spike trains ($M=1-3$) with independent Gaussian noises. The cross-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 {\it denoising} method within the WT, by which the noise contribution is extracted from output signals. Although the response of a single (N=1) neuron to sub-threshold 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 play 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 supra-threshold transient spikes is not significantly degraded by a weak noise which is responsible to SR for sub-threshold inputs.

cond-mat.dis-nn↗

arXiv2001

A Wavelet Analysis of Transient Spike Trains of Hodgkin-Huxley Neurons

Transient spike trains consisting of $M$ (= 1 - 5) pulses generated by single Hodgkin-Huxley (HH) neurons, have been analyzed by using both the continuous and discrete wavelet transformations (WT). We have studied effects of variations in the interspike intervals (ISI) of the spikes and effects of noises on the energy distribution and the wavelet entropy, which are expressed in terms of the WT expansion coefficients. The results obtained by the WT are discussed in connection with those obtained by the Fourier transformation.

cond-mat.dis-nn↗

arXiv2000

Spike-Train Responses of a Pair of Hodgkin-Huxley Neurons with Time-Delayed Couplings

Model calculations have been performed on the spike-train response of a pair of Hodgkin-Huxley (HH) neurons coupled by recurrent excitatory-excitatory couplings with time delay. The coupled, excitable HH neurons are assumed to receive the two kinds of spike-train inputs: the transient input consisting of $M$ impulses for the finite duration ($M$: integer) and the sequential input with the constant interspike interval (ISI). The distribution of the output ISI $T_{\rm o}$ shows a rich of variety depending on the coupling strength and the time delay. The comparison is made between the dependence of the output ISI for the transient inputs and that for the sequential inputs.

cond-mat.dis-nn↗

arXiv2000

An associative memory of Hodgkin-Huxley neuron networks with Willshaw-type synaptic couplings

An associative memory has been discussed of neural networks consisting of spiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which memorize P patterns in their synaptic weights. In addition to excitatory synapses whose strengths are modified after the Willshaw-type learning rule with the 0/1 code for quiescent/active states, the network includes uniform inhibitory synapses which are introduced to reduce cross-talk noises. Our simulations of the HH neuron network for the noise-free state have shown to yield a fairly good performance with the storage capacity of $α_c = P_{\rm max}/N \sim 0.4 - 2.4$ for the low neuron activity of $f \sim 0.04-0.10$. This storage capacity of our temporal-code network is comparable to that of the rate-code model with the Willshaw-type synapses. Our HH neuron network is realized not to be vulnerable to the distribution of time delays in couplings. The variability of interspace interval (ISI) of output spike trains in the process of retrieving stored patterns is also discussed.

cond-mat.dis-nn↗

arXiv2000

Slave-boson mean-field theory of spin- and orbital-ordered states in the degenerate Hubbard model

The mean-field theory with the use of the slave-boson functional method is generalized to take account of the spin- and orbital-ordered state in the doubly degenerate Hubbard model. Some numerical calculations are presented of the antiferromagnetic orbital-ordered state in the half-filled simple-cubic model. The orbital order in the present theory is much reduced compared with that in the Hartree-Fock approximation because of the large orbital fluctuations. From a comparison of the ground-state energy, the antiferromagnetic orbital state is shown to be unstable against the antiferromagnetic spin state, although the situation becomes reversed when the exchange interaction is {\it negative}.

cond-mat.str-el↗

arXiv1999

Spike-train responses of a pair of Hodgkin-Huxley neurons coupled by excitatory and inhibitory synapses and axons with time delay

Numerical calculations have been made on the spike-train response of a pair of Hodgkin-Huxley (HH) neurons coupled by synapses and axons with time delay. The recurrent excitatory-excitatory, inhibitory-inhibitory, excitatory-inhibitory, and inhibitory-excitatory couplings are adopted. The coupled, excitable HH neurons are assumed to receive the two kinds of spike-train inputs: the transient input consisting of M impulses for the finite duration (M: integer) and the sequential input with the constant interspike interval (ISI). The HH neurons in all the kinds of couplings are found to play a role of memory storage with on-off switching. When the coupling strength and the time delay are changed, the distribution of the output ISI $T_{\rm o}$ shows bifurcation (multifurcation), metastability and chaotic behavior. The calculation of the time correlation shows that the synchronization between the two HH neurons is well preserved even when the distribution of their $T_{\rm o}$ is chaotic. The correlation dimension of the cycles of $T_{\rm o}$ is shown to depend not only on the model parameters but also on the type of input ISIs.

cond-mat.dis-nn↗

arXiv1999

A quantitative comparison between spike-train responses of the Hodgkin-Huxley and integrate-and-fire neurons

Spike-train responses of single Hodgkin-Huxley (HH) and integrate-and-fire (IF) neurons with and without the refractory period, are calculated and compared. The HH and IF neurons are assumed to receive spike-train inputs with the constant interspike intervals (ISIs) and stochastic ISIs given by the Gamma distribution, through excitatory and inhibitory synaptic couplings: for both the couplings the HH neuron can fire while the IF neuron can only for the excitatory one. It is shown that the response to the constant-ISI inputs of the IF neuron strongly depends on the refractory period and the synaptic strength and that its response is rather different from that of the HH neuron. The variability of HH and IF neurons depends not only on the jitter of the stochastic inputs but also on their mean and the synaptic strength. Even for the excitatory inputs, the type-I IF neuron may be a good substitute of the type-II HH neuron only in the limited parameter range

cond-mat.dis-nn↗

arXiv1999

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 Rössler 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.

cond-mat.dis-nn↗

arXiv1997

The Metal-Insulator Transition in the Doubly Degenerate Hubbard Model

A systematic study has been made on the metal-insulator (MI) transition of the doubly degenerate Hubbard model (DHM) in the paramagnetic ground state, by using the slave-boson mean-field theory which is equivalent to the Gutzwiller approximation (GA). For the case of infinite electron-electron interactions, we obtain the analytic solution, which becomes exact in the limit of infinite spatial dimension. On the contrary, the finite-interaction case is investigated by numerical methods with the use of the simple-cubic model with the nearest-neighbor hopping. The mass-enhancement factor, $Z$, is shown to increase divergently as one approaches the integer fillings ($N = 1, 2, 3$), at which the MI transition takes place, $N$ being the total number of electrons. The calculated $N$ dependence of $Z$ is compared with the observed specific-heat coefficient, $γ$, of $Sr_{1-x}La_xTiO_3$ which is reported to significantly increase as $x$ approaches unity.

cond-mat.str-el↗

arXiv1997

Slave-Boson Mean-Field Theory of the Antiferromagnetic State in the Doubly Degenerate Hubbard Model - the Half-Filled Case -

The antiferromagnetic ground state of the half-filled Hubbard model with the doubly degenerate orbital has been studied by using the slave-boson mean-field theory which was previously proposed by the present author. Numerical calculations for the simple cubic model have shown that the metal-insulator transition does not take place except at the vanishing interaction point, in strong contrast with its paramagnetic solution. The energy gap in the density of states of the antiferromagnetic insulator is much reduced by the effect of electron correlation. The exchange interaction $J$ plays an important role in the antiferromagnetism: although for $J = 0$ the sublattice magnetic moment $m$ in our theory is fairly smaller than $m_{HFA}$ obtained in the Hartree-Fock approximation, $m$ for $J/U > 0.2$ ($U$: the Coulomb interaction) is increased to become comparable to $m_{HFA}$. Surprisingly, the antiferromagnetic state is easily destroyed if a small, negative exchange interaction ($J/U < -0.05$) is introduced.

cond-mat.str-el↗

arXiv1997

Slave-Boson Functional-Integral Approach to the Hubbard Model with Orbital Degeneracy

A slave-boson functional-integral method has been developed for the Hubbard model with arbitrary, orbital degeneracy $D$. Its saddle-point mean-field theory is equivalent to the Gutzwiller approximation, as in the case of single-band Hubbard model. Our theory is applied to the doubly degenerate ($D = 2$) model, and numerical calculations have been performed for this model in the paramagnetic states. The effect of the exchange interaction on the metal-insulator (MI) transition is discussed. The critical interaction for the MI transition is analytically calculated as functions of orbital degeneracy and electron occupancy.

cond-mat.str-el↗

arXiv1997

First-principles calculation of exchange interaction and exchange force between magnetic Fe films

First-principles calculations have been performed for the exchange interaction and exchange force between two magnetic Fe(100) thin films. It is shown that the magnitude of the calculated exchange force is of the order of $10^{-9} $N at $d/a < 1$ and of the order of $10^{-10} $N at $1 < d/a < 1.5$, where $d$ denotes the distance between surfaces of the two thin films and $a$ the lattice constant of bulk Fe. The obtained forces are sufficiently larger than the sensitivity of the current atomic force microscopy of $10^{-12} - 10^{-13}$N, which suggests the feasibility of the exchange force microscopy.

cond-mat.mes-hall↗

arXiv1995

Theory on the Temperature Dependence of Giant Magnetoresistance

The temperature dependence of the giant magnetoresistance (GMR) for currents parallel and perpendicular to the multilayer plane, is discussed by taking account of the random exchange potentials, phonon scatterings and spin fluctuations. The effect of spin fluctuations, which plays an important role at finite temperatures, is included by means of the static functional-integral method developed previously by the present author. Our model calculations well explain the observed features of the parallel and perpendicular GMR of Fe/Cr and Co/Cu multilayers recently reported by Gijs {\it et al}.

cond-mat↗