131 research outputs found
Thouless-Anderson-Palmer equation for analog neural network with temporally fluctuating white synaptic noise
Effects of synaptic noise on the retrieval process of associative memory
neural networks are studied from the viewpoint of neurobiological and
biophysical understanding of information processing in the brain. We
investigate the statistical mechanical properties of stochastic analog neural
networks with temporally fluctuating synaptic noise, which is assumed to be
white noise. Such networks, in general, defy the use of the replica method,
since they have no energy concept. The self-consistent signal-to-noise analysis
(SCSNA), which is an alternative to the replica method for deriving a set of
order parameter equations, requires no energy concept and thus becomes
available in studying networks without energy functions. Applying the SCSNA to
stochastic network requires the knowledge of the Thouless-Anderson-Palmer (TAP)
equation which defines the deterministic networks equivalent to the original
stochastic ones. The study of the TAP equation which is of particular interest
for the case without energy concept is very few, while it is closely related to
the SCSNA in the case with energy concept. This paper aims to derive the TAP
equation for networks with synaptic noise together with a set of order
parameter equations by a hybrid use of the cavity method and the SCSNA.Comment: 13 pages, 3 figure
Acceleration effect of coupled oscillator systems
We have developed a curved isochron clock (CIC) by modifying the radial
isochron clock to provide a clean example of the acceleration (deceleration)
effect. By analyzing a two-body system of coupled CICs, we determined that an
unbalanced mutual interaction caused by curved isochron sets is the minimum
mechanism needed for generating the acceleration (deceleration) effect in
coupled oscillator systems. From this we can see that the Sakaguchi and
Kuramoto (SK) model which is a class of non-frustrated mean feild model has an
acceleration (deceleration) effect mechanism. To study frustrated coupled
oscillator systems, we extended the SK model to two oscillator associative
memory models, one with symmetric and one with asymmetric dilution of coupling,
which also have the minimum mechanism of the acceleration (deceleration)
effect. We theoretically found that the {\it Onsager reaction term} (ORT),
which is unique to frustrated systems, plays an important role in the
acceleration (de! celeration) effect. These two models are ideal for evaluating
the effect of the ORT because, with the exception of the ORT, they have the
same order parameter equations. We found that the two models have identical
macroscopic properties, except for the acceleration effect caused by the ORT.
By comparing the results of the two models, we can extract the effect of the
ORT from only the rotation speeds of the oscillators.Comment: 35 pages, 10 figure
Associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise
We study associative memory based on temporal coding in which successful
retrieval is realized as an entrainment in a network of simple phase
oscillators with distributed natural frequencies under the influence of white
noise. The memory patterns are assumed to be given by uniformly distributed
random numbers on so that the patterns encode the phase differences
of the oscillators. To derive the macroscopic order parameter equations for the
network with an extensive number of stored patterns, we introduce the effective
transfer function by assuming the fixed-point equation of the form of the TAP
equation, which describes the time-averaged output as a function of the
effective time-averaged local field. Properties of the networks associated with
synchronization phenomena for a discrete symmetric natural frequency
distribution with three frequency components are studied based on the order
parameter equations, and are shown to be in good agreement with the results of
numerical simulations. Two types of retrieval states are found to occur with
respect to the degree of synchronization, when the size of the width of the
natural frequency distribution is changed.Comment: published in Phys. Rev.
Fluctuation Dissipation Relation for a Langevin Model with Multiplicative Noise
A random multiplicative process with additive noise is described by a
Langevin equation. We show that the fluctuation-dissipation relation is
satisfied in the Langevin model, if the noise strength is not so strong.Comment: 11 pages, 6 figures, other comment
First order phase transition in a nonequilibrium growth process
We introduce a simple continuous model for nonequilibrium surface growth. The
dynamics of the system is defined by the KPZ equation with a Morse-like
potential representing a short range interaction between the surface and the
substrate. The mean field solution displays a non trivial phase diagram with a
first order transition between a growing and a bound surface, associated with a
region of coexisting phases, and a tricritical point where the transition
becomes second order. Numerical simulations in 3 dimensions show quantitative
agreement with mean field results, and the features of the phase space are
preserved even in 2 dimensions.Comment: 7 figures, revtex, submitted to Phys. Rev.
Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons
We study associative memory neural networks of the Hodgkin-Huxley type of
spiking neurons in which multiple periodic spatio-temporal patterns of spike
timing are memorized as limit-cycle-type attractors. In encoding the
spatio-temporal patterns, we assume the spike-timing-dependent synaptic
plasticity with the asymmetric time window. Analysis for periodic solution of
retrieval state reveals that if the area of the negative part of the time
window is equivalent to the positive part, then crosstalk among encoded
patterns vanishes. Phase transition due to the loss of the stability of
periodic solution is observed when we assume fast alpha-function for direct
interaction among neurons. In order to evaluate the critical point of this
phase transition, we employ Floquet theory in which the stability problem of
the infinite number of spiking neurons interacting with alpha-function is
reduced into the eigenvalue problem with the finite size of matrix. Numerical
integration of the single-body dynamics yields the explicit value of the
matrix, which enables us to determine the critical point of the phase
transition with a high degree of precision.Comment: Accepted for publication in Phys. Rev.
A statistical mechanics of an oscillator associative memory with scattered natural frequencies
Analytic treatment of a non-equilibrium random system with large degrees of
freedoms is one of most important problems of physics. However, little research
has been done on this problem as far as we know. In this paper, we propose a
new mean field theory that can treat a general class of a non-equilibrium
random system. We apply the present theory to an analysis for an associative
memory with oscillatory elements, which is a well-known typical random system
with large degrees of freedoms.Comment: 8 pages, 4 figure
Spectroscopic signatures of a bandwidth-controlled Mott transition at the surface of 1T-TaSe
High-resolution angle-resolved photoemission (ARPES) data show that a
metal-insulator Mott transition occurs at the surface of the quasi-two
dimensional compound TaSe. The transition is driven by the narrowing of the
Ta band induced by a temperature-dependent modulation of the atomic
positions. A dynamical mean-field theory calculation of the spectral function
of the half-filled Hubbard model captures the main qualitative feature of the
data, namely the rapid transfer of spectral weight from the observed
quasiparticle peak at the Fermi surface to the Hubbard bands, as the
correlation gap opens up.Comment: 4 pages, 4 figures; one modified figure, added referenc
Critical Behaviour of Non-Equilibrium Phase Transitions to Magnetically Ordered States
We describe non-equilibrium phase transitions in arrays of dynamical systems
with cubic nonlinearity driven by multiplicative Gaussian white noise.
Depending on the sign of the spatial coupling we observe transitions to
ferromagnetic or antiferromagnetic ordered states. We discuss the phase
diagram, the order of the transitions, and the critical behaviour. For global
coupling we show analytically that the critical exponent of the magnetization
exhibits a transition from the value 1/2 to a non-universal behaviour depending
on the ratio of noise strength to the magnitude of the spatial coupling.Comment: 4 pages, 5 figure
A canonical ensemble approach to graded-response perceptrons
Perceptrons with graded input-output relations and a limited output precision
are studied within the Gardner-Derrida canonical ensemble approach. Soft non-
negative error measures are introduced allowing for extended retrieval
properties. In particular, the performance of these systems for a linear and
quadratic error measure, corresponding to the perceptron respectively the
adaline learning algorithm, is compared with the performance for a rigid error
measure, simply counting the number of errors. Replica-symmetry-breaking
effects are evaluated.Comment: 26 pages, 10 ps figure
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