124 research outputs found
Can distributed delays perfectly stabilize dynamical networks?
Signal transmission delays tend to destabilize dynamical networks leading to
oscillation, but their dispersion contributes oppositely toward stabilization.
We analyze an integro-differential equation that describes the collective
dynamics of a neural network with distributed signal delays. With the gamma
distributed delays less dispersed than exponential distribution, the system
exhibits reentrant phenomena, in which the stability is once lost but then
recovered as the mean delay is increased. With delays dispersed more highly
than exponential, the system never destabilizes.Comment: 4pages 5figure
Kernel bandwidth optimization in spike rate estimation
Kernel smoother and a time-histogram are classical tools for estimating an instantaneous rate of spike occurrences. We recently established a method for selecting the bin width of the time-histogram, based on the principle of minimizing the mean integrated square error (MISE) between the estimated rate and unknown underlying rate. Here we apply the same optimization principle to the kernel density estimation in selecting the width or “bandwidth” of the kernel, and further extend the algorithm to allow a variable bandwidth, in conformity with data. The variable kernel has the potential to accurately grasp non-stationary phenomena, such as abrupt changes in the firing rate, which we often encounter in neuroscience. In order to avoid possible overfitting that may take place due to excessive freedom, we introduced a stiffness constant for bandwidth variability. Our method automatically adjusts the stiffness constant, thereby adapting to the entire set of spike data. It is revealed that the classical kernel smoother may exhibit goodness-of-fit comparable to, or even better than, that of modern sophisticated rate estimation methods, provided that the bandwidth is selected properly for a given set of spike data, according to the optimization methods presented here
Equation of State for Parallel Rigid Spherocylinders
The pair distribution function of monodisperse rigid spherocylinders is
calculated by Shinomoto's method, which was originally proposed for hard
spheres. The equation of state is derived by two different routes: Shinomoto's
original route, in which a hard wall is introduced to estimate the pressure
exerted on it, and the virial route. The pressure from Shinomoto's original
route is valid only when the length-to-width ratio is less than or equal to
0.25 (i.e., when the spherocylinders are nearly spherical). The virial equation
of state is shown to agree very well with the results of numerical simulations
of spherocylinders with length-to-width ratio greater than or equal to 2
Residual Energies after Slow Quantum Annealing
Features of the residual energy after the quantum annealing are investigated.
The quantum annealing method exploits quantum fluctuations to search the ground
state of classical disordered Hamiltonian. If the quantum fluctuation is
reduced sufficiently slowly and linearly by the time, the residual energy after
the quantum annealing falls as the inverse square of the annealing time. We
show this feature of the residual energy by numerical calculations for
small-sized systems and derive it on the basis of the quantum adiabatic
theorem.Comment: 4 pages, 2 figure
Stochastic synchronization in globally coupled phase oscillators
Cooperative effects of periodic force and noise in globally Cooperative
effects of periodic force and noise in globally coupled systems are studied
using a nonlinear diffusion equation for the number density. The amplitude of
the order parameter oscillation is enhanced in an intermediate range of noise
strength for a globally coupled bistable system, and the order parameter
oscillation is entrained to the external periodic force in an intermediate
range of noise strength. These enhancement phenomena of the response of the
order parameter in the deterministic equations are interpreted as stochastic
resonance and stochastic synchronization in globally coupled systems.Comment: 5 figure
Hierarchical Self-Programming in Recurrent Neural Networks
We study self-programming in recurrent neural networks where both neurons
(the `processors') and synaptic interactions (`the programme') evolve in time
simultaneously, according to specific coupled stochastic equations. The
interactions are divided into a hierarchy of groups with adiabatically
separated and monotonically increasing time-scales, representing sub-routines
of the system programme of decreasing volatility. We solve this model in
equilibrium, assuming ergodicity at every level, and find as our
replica-symmetric solution a formalism with a structure similar but not
identical to Parisi's -step replica symmetry breaking scheme. Apart from
differences in details of the equations (due to the fact that here
interactions, rather than spins, are grouped into clusters with different
time-scales), in the present model the block sizes of the emerging
ultrametric solution are not restricted to the interval , but are
independent control parameters, defined in terms of the noise strengths of the
various levels in the hierarchy, which can take any value in [0,\infty\ket.
This is shown to lead to extremely rich phase diagrams, with an abundance of
first-order transitions especially when the level of stochasticity in the
interaction dynamics is chosen to be low.Comment: 53 pages, 19 figures. Submitted to J. Phys.
Nonequilibrium coupled Brownian phase oscillators
A model of globally coupled phase oscillators under equilibrium (driven by
Gaussian white noise) and nonequilibrium (driven by symmetric dichotomic
fluctuations) is studied. For the equilibrium system, the mean-field state
equation takes a simple form and the stability of its solution is examined in
the full space of order parameters. For the nonequilbrium system, various
asymptotic regimes are obtained in a closed analytical form. In a general case,
the corresponding master equations are solved numerically. Moreover, the
Monte-Carlo simulations of the coupled set of Langevin equations of motion is
performed. The phase diagram of the nonequilibrium system is presented. For the
long time limit, we have found four regimes. Three of them can be obtained from
the mean-field theory. One of them, the oscillating regime, cannot be predicted
by the mean-field method and has been detected in the Monte-Carlo numerical
experiments.Comment: 9 pages 8 figure
Diluted neural networks with adapting and correlated synapses
We consider the dynamics of diluted neural networks with clipped and adapting
synapses. Unlike previous studies, the learning rate is kept constant as the
connectivity tends to infinity: the synapses evolve on a time scale
intermediate between the quenched and annealing limits and all orders of
synaptic correlations must be taken into account. The dynamics is solved by
mean-field theory, the order parameter for synapses being a function. We
describe the effects, in the double dynamics, due to synaptic correlations.Comment: 6 pages, 3 figures. Accepted for publication in PR
- …