30,336 research outputs found
Critical and resonance phenomena in neural networks
Brain rhythms contribute to every aspect of brain function. Here, we study
critical and resonance phenomena that precede the emergence of brain rhythms.
Using an analytical approach and simulations of a cortical circuit model of
neural networks with stochastic neurons in the presence of noise, we show that
spontaneous appearance of network oscillations occurs as a dynamical
(non-equilibrium) phase transition at a critical point determined by the noise
level, network structure, the balance between excitatory and inhibitory
neurons, and other parameters. We find that the relaxation time of neural
activity to a steady state, response to periodic stimuli at the frequency of
the oscillations, amplitude of damped oscillations, and stochastic fluctuations
of neural activity are dramatically increased when approaching the critical
point of the transition.Comment: 8 pages, Proceedings of 12th Granada Seminar, September 17-21, 201
Sparse Quadrature for High-Dimensional Integration with Gaussian Measure
In this work we analyze the dimension-independent convergence property of an
abstract sparse quadrature scheme for numerical integration of functions of
high-dimensional parameters with Gaussian measure. Under certain assumptions of
the exactness and the boundedness of univariate quadrature rules as well as the
regularity of the parametric functions with respect to the parameters, we
obtain the convergence rate , where is the number of indices,
and is independent of the number of the parameter dimensions. Moreover, we
propose both an a-priori and an a-posteriori schemes for the construction of a
practical sparse quadrature rule and perform numerical experiments to
demonstrate their dimension-independent convergence rates
Damage spreading transition in glasses: a probe for the ruggedness of the configurational landscape
We consider damage spreading transitions in the framework of mode-coupling
theory. This theory describes relaxation processes in glasses in the mean-field
approximation which are known to be characterized by the presence of an
exponentially large number of meta-stable states. For systems evolving under
identical but arbitrarily correlated noises we demonstrate that there exists a
critical temperature which separates two different dynamical regimes
depending on whether damage spreads or not in the asymptotic long-time limit.
This transition exists for generic noise correlations such that the zero damage
solution is stable at high-temperatures being minimal for maximal noise
correlations. Although this dynamical transition depends on the type of noise
correlations we show that the asymptotic damage has the good properties of an
dynamical order parameter such as: 1) Independence on the initial damage; 2)
Independence on the class of initial condition and 3) Stability of the
transition in the presence of asymmetric interactions which violate detailed
balance. For maximally correlated noises we suggest that damage spreading
occurs due to the presence of a divergent number of saddle points (as well as
meta-stable states) in the thermodynamic limit consequence of the ruggedness of
the free energy landscape which characterizes the glassy state. These results
are then compared to extensive numerical simulations of a mean-field glass
model (the Bernasconi model) with Monte Carlo heat-bath dynamics. The freedom
of choosing arbitrary noise correlations for Langevin dynamics makes damage
spreading a interesting tool to probe the ruggedness of the configurational
landscape.Comment: 25 pages, 13 postscript figures. Paper extended to include
cross-correlation
A Pathwise Ergodic Theorem for Quantum Trajectories
If the time evolution of an open quantum system approaches equilibrium in the
time mean, then on any single trajectory of any of its unravelings the time
averaged state approaches the same equilibrium state with probability 1. In the
case of multiple equilibrium states the quantum trajectory converges in the
mean to a random choice from these states.Comment: 8 page
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