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1.
This paper is a review dealing with the study of large
size random recurrent neural networks. The connection weights are
varying according to a probability law and it is possible to predict
the network dynamics at a macroscopic scale using an averaging
principle. After a first introductory section, the
section 2 reviews the various models from the points of
view of the single neuron dynamics and of the global network
dynamics. A summary of notations is presented, which is quite
helpful for the sequel. In section 3, mean-field dynamics
is developed. The probability distribution characterizing global
dynamics is computed. In section 4, some applications
of mean-field theory to the prediction of chaotic regime for Analog
Formal Random Recurrent Neural Networks (AFRRNN) are displayed. The
case of AFRRNN with an homogeneous population of neurons is studied
in section 4.1. Then, a two-population model is studied in
section 4.2. The occurrence of a cyclo-stationary chaos is
displayed using the results of [16]. In
section 5, an insight of the application of mean-field
theory to IF networks is given using the results
of [9]. 相似文献
2.
V. I. Nekorkin D. V. Kasatkin A. S. Dmitrichev 《Radiophysics and Quantum Electronics》2010,53(1):45-52
We propose a new model of synaptic transmission on the basis of a FitzHugh–Nagumo system with nonlinear recovery. It is shown
that the Morrice–Lecar neuron ensemble formed by such couplings shows various structurally stable regimes of transient dynamics
in the form of sequential transitions between various metastable oscillatory states of the system. 相似文献
3.
We demonstrate that two key theoretical objects used widely in computational neuroscience, the phase-resetting curve (PRC) from dynamics and the spike triggered average (STA) from statistical analysis, are closely related when neurons fire in a nearly regular manner and the stimulus is sufficiently small. We prove that the STA due to injected noisy current is proportional to the derivative of the PRC. We compare these analytic results with numerical calculations for the Hodgkin-Huxley neuron and we apply the method to neurons in the olfactory bulb of mice. This observation allows us to relate the stimulus-response properties of a neuron to its dynamics, bridging the gap between dynamical and information theoretic approaches to understanding brain computations and facilitating the interpretation of changes in channels and other cellular properties as influencing the representation of stimuli. 相似文献
4.
Takeyuki Hida 《Foundations of Physics》1997,27(11):1511-1518
We shall discuss quantum mechanical operators depending on the time or on the manifold in space. There is a similarity to
the case of stochastic processes or random fields, where the innovation approach is one of the powerful tools to investigate
their probabilistic structure. Having had some review of the innovation, similar attempt is made for some cases in quantum
dynamics. 相似文献
5.
The transitions between waking and sleep states are characterized by considerable changes in neuronal firing. During waking, neurons fire tonically at irregular intervals and a desynchronized activity is observed at the electroencephalogram. This activity becomes synchronized with slow wave sleep onset when neurons start to oscillate between periods of firing (up-states) and periods of silence (down-states). Recently, it has been proposed that the connections between neurons undergo potentiation during waking, whereas they weaken during slow wave sleep. Here, we propose a dynamical model to describe basic features of the autonomous transitions between such states. We consider a network of coupled neurons in which the strength of the interactions is modulated by synaptic long term potentiation and depression, according to the spike time-dependent plasticity rule (STDP). The model shows that the enhancement of synaptic strength between neurons occurring in waking increases the propensity of the network to synchronize and, conversely, desynchronization appears when the strength of the connections become weaker. Both transitions appear spontaneously, but the transition from sleep to waking required a slight modification of the STDP rule with the introduction of a mechanism which becomes active during sleep and changes the proportion between potentiation and depression in accordance with biological data. At the neuron level, transitions from desynchronization to synchronization and vice versa can be described as a bifurcation between two different states, whose dynamical regime is modulated by synaptic strengths, thus suggesting that transition from a state to an another can be determined by quantitative differences between potentiation and depression. 相似文献
6.
Precise timing of spikes and temporal locking are key elements of neural computation. Here we demonstrate how even strongly heterogeneous, deterministic neural networks with delayed interactions and complex topology can exhibit periodic patterns of spikes that are precisely timed. We develop an analytical method to find the set of all networks exhibiting a predefined pattern dynamics. Such patterns may be arbitrarily long and of complicated temporal structure. We point out that the same pattern can exist in very different networks and have different stability properties. 相似文献
7.
M. I. Rabinovich 《Radiophysics and Quantum Electronics》1996,39(6):502-510
Small neural networks (central pattern generators), which control rythmic behavior of animals, are considered. The mechanisms responsible for regularity, reliability, and plasticity of such behavior (swimming, running, walking, etc.) are analyzed. New data on the origin of regular cooperative behavior of neurons are obtained by using methods of nonlinear dynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 6, pp. 757–770, June, 1996. 相似文献
8.
We develop random walk representations for the spin-S Heisenberg ferromagnet with nearest neighbor interactions. We show that the spin-S Heisenberg model is a diffusion with local times controlled by the spin-S Ising model. As a consequence, expectations for the Heisenberg model conditioned on zero diffusion are shown to be Ising expectations. 相似文献
9.
10.
Ney Lemke Jeferson J. Arenzon Francisco A. Tamarit 《Journal of statistical physics》1995,79(1-2):415-427
The dynamics of an extremely diluted neural network with high-order synapses acting as corrections to the Hopfield model is investigated. The learning rules for the high-order connections contain mixing of memories, different from all the previous generalizations of the Hopfield model. The dynamics may display fixed points or periodic and chaotic orbits, depending on the weight of the high-order connections , the noise levelT, and the network load, defined as the ratio between the number of stored patterns and the mean connectivity per neuron, =P/C. As in the related fully connected case, there is an optimal value of the weight that improves the storage capacity of the system (the capacity diverges). 相似文献
11.
S. Ejima F. Gebhard R. M. Noack 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,66(2):191-200
We use the Random Dispersion Approximation (RDA) to study the
Mott-Hubbard transition in the Hubbard model at half band filling.
The RDA becomes exact for the Hubbard model in infinite dimensions.
We implement the RDA on finite chains and employ the Lanczos exact
diagonalization method in real space to calculate the ground-state energy,
the average double occupancy, the charge gap, the momentum distribution,
and the quasi-particle weight. We find a satisfactory agreement with
perturbative results in the weak- and strong-coupling limits.
A straightforward extrapolation of the RDA data
for L ≤ 14 lattice results in a continuous Mott-Hubbard transition at
Uc≈W.
We discuss the significance of a possible signature
of a coexistence region between insulating and metallic
ground states in the RDA that would correspond to
the scenario of a discontinuous Mott-Hubbard transition
as found in numerical investigations
of the Dynamical Mean-Field Theory for the Hubbard model. 相似文献
12.
A model of the permanent distortion of an elastic material due to high velocity projectile impact is described using a random walk model, with unusual temporal statistics, of the transport of dislocations. The biased motion of dislocations in a stress field and also in a random environment is considered. A temperature dependence for certain scaling exponents is derived. The experimentally observed scaling of the total integrated momentum as well as the scaling of the penetration and strength of the shock wave with time are obtained with this model. 相似文献
13.
14.
A. Yu. Plakhov 《Radiophysics and Quantum Electronics》1994,37(9):711-718
The dynamics of a convergent iterative unlearning algorithm proposed earlier [7, 8] is examined. A self-consistent system of equations of the spectral dynamics of a synaptic matrix is obtained at the thermodynamic limit. The unlearning intensity (which varies during the iteration process) that optimizes the algorithm's rate of convergence on the projector matrix is found. The synaptic-matrix spectrum dynamics for optimal unlearning is determined.Institute of Physicotechnical Problems, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 9, pp. 1104–1115, September, 1994. 相似文献
15.
16.
Kavita Jain 《Pramana》2008,71(2):275-282
We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and
selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and
have many local peaks separated by low fitness valleys. We mainly focus on the Eigen’s model that describes the deterministic
dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population
forms a quasispecies which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on
rugged fitness landscape follow a punctuated (or steplike) pattern in which a population jumps from a low fitness peak to
a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum
of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of
the quasispecies model.
相似文献
17.
H. Rieger M. Schreckenberg J. Zittartz 《Zeitschrift für Physik B Condensed Matter》1988,72(4):523-533
The Glauber dynamics of the Little-Hopfield model is studied analytically with the help of path-integrals recently introduced by Sommers. The results of Amit, Gutfreund and Sompolinsky concerning the statics of the Little-Hopfield model near saturation are dynamically verified. Their replica-symmetric solution corresponds exactly to the self-consistency equations of the long-time limits of some time-dependent functions emerging in our dynamical treatment. We also found their generalized Almeida-Thouless line where the solution becomes unstable. The time-dependent evolution of the macroscopic overlaps for a finite number of stored patterns is investigated and the problems arising for an infinite number of them are indicated.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln 相似文献
18.
19.
20.
M. Lücke 《Journal of statistical physics》1976,15(6):455-475
The dynamics of the Lorenz model in the turbulent regime (r>r
T is investigated by applying methods for treating many-body systems. Symmetry properties are used to derive relations between correlation functions. The basic ones are evaluated numerically and discussed for several values of the parameterr. A theory for the spectra of the two independent relaxation functions is presented using a dispersion relation representation in terms of relaxation kernels and characteristic frequencies. Their role in the dynamics of the system is discussed and it is shown that their numerical values increase in proportion to r. The approximation of the relaxation kernels that represent nonlinear coupling between the variables by a relaxation time expression and a simple mode coupling approximation, respectively, is shown to explain the two different fluctuation spectra. The coupling strength for the modes is determined by a Kubo relation imposing selfconsistency. Comparison with the experimental spectra is made for three values ofr. 相似文献