2,969 research outputs found
Synchronization and Noise: A Mechanism for Regularization in Neural Systems
To learn and reason in the presence of uncertainty, the brain must be capable
of imposing some form of regularization. Here we suggest, through theoretical
and computational arguments, that the combination of noise with synchronization
provides a plausible mechanism for regularization in the nervous system. The
functional role of regularization is considered in a general context in which
coupled computational systems receive inputs corrupted by correlated noise.
Noise on the inputs is shown to impose regularization, and when synchronization
upstream induces time-varying correlations across noise variables, the degree
of regularization can be calibrated over time. The proposed mechanism is
explored first in the context of a simple associative learning problem, and
then in the context of a hierarchical sensory coding task. The resulting
qualitative behavior coincides with experimental data from visual cortex.Comment: 32 pages, 7 figures. under revie
A Multitask Diffusion Strategy with Optimized Inter-Cluster Cooperation
We consider a multitask estimation problem where nodes in a network are
divided into several connected clusters, with each cluster performing a
least-mean-squares estimation of a different random parameter vector. Inspired
by the adapt-then-combine diffusion strategy, we propose a multitask diffusion
strategy whose mean stability can be ensured whenever individual nodes are
stable in the mean, regardless of the inter-cluster cooperation weights. In
addition, the proposed strategy is able to achieve an asymptotically unbiased
estimation, when the parameters have same mean. We also develop an
inter-cluster cooperation weights selection scheme that allows each node in the
network to locally optimize its inter-cluster cooperation weights. Numerical
results demonstrate that our approach leads to a lower average steady-state
network mean-square deviation, compared with using weights selected by various
other commonly adopted methods in the literature.Comment: 30 pages, 8 figures, submitted to IEEE Journal of Selected Topics in
Signal Processin
A quasilinear differential inclusion for viscous and rate-independent damage systems in non-smooth domains
This paper focuses on rate-independent damage in elastic bodies. Since the
driving energy is nonconvex, solutions may have jumps as a function of time,
and in this situation it is known that the classical concept of energetic
solutions for rate-independent systems may fail to accurately describe the
behavior of the system at jumps. Therefore we resort to the (by now
well-established) vanishing viscosity approach to rate-independent modeling,
and approximate the model by its viscous regularization. In fact, the analysis
of the latter PDE system presents remarkable difficulties, due to its highly
nonlinear character. We tackle it by combining a variational approach to a
class of abstract doubly nonlinear evolution equations, with careful regularity
estimates tailored to this specific system, relying on a q-Laplacian type
gradient regularization of the damage variable. Hence for the viscous problem
we conclude the existence of weak solutions, satisfying a suitable
energy-dissipation inequality that is the starting point for the vanishing
viscosity analysis. The latter leads to the notion of (weak) parameterized
solution to our rate-independent system, which encompasses the influence of
viscosity in the description of the jump regime
A rate-independent model for the isothermal quasi-static evolution of shape-memory materials
This note addresses a three-dimensional model for isothermal stress-induced
transformation in shape-memory polycrystalline materials. We treat the problem
within the framework of the energetic formulation of rate-independent processes
and investigate existence and continuous dependence issues at both the
constitutive relation and quasi-static evolution level. Moreover, we focus on
time and space approximation as well as on regularization and parameter
asymptotics.Comment: 33 pages, 3 figure
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