13,414 research outputs found
Stochastic forward-backward and primal-dual approximation algorithms with application to online image restoration
Stochastic approximation techniques have been used in various contexts in
data science. We propose a stochastic version of the forward-backward algorithm
for minimizing the sum of two convex functions, one of which is not necessarily
smooth. Our framework can handle stochastic approximations of the gradient of
the smooth function and allows for stochastic errors in the evaluation of the
proximity operator of the nonsmooth function. The almost sure convergence of
the iterates generated by the algorithm to a minimizer is established under
relatively mild assumptions. We also propose a stochastic version of a popular
primal-dual proximal splitting algorithm, establish its convergence, and apply
it to an online image restoration problem.Comment: 5 Figure
Stochastic Approximations and Perturbations in Forward-Backward Splitting for Monotone Operators
We investigate the asymptotic behavior of a stochastic version of the
forward-backward splitting algorithm for finding a zero of the sum of a
maximally monotone set-valued operator and a cocoercive operator in Hilbert
spaces. Our general setting features stochastic approximations of the
cocoercive operator and stochastic perturbations in the evaluation of the
resolvents of the set-valued operator. In addition, relaxations and not
necessarily vanishing proximal parameters are allowed. Weak and strong almost
sure convergence properties of the iterates is established under mild
conditions on the underlying stochastic processes. Leveraging these results, we
also establish the almost sure convergence of the iterates of a stochastic
variant of a primal-dual proximal splitting method for composite minimization
problems
Stochastic Quasi-Fej\'er Block-Coordinate Fixed Point Iterations with Random Sweeping
This work proposes block-coordinate fixed point algorithms with applications
to nonlinear analysis and optimization in Hilbert spaces. The asymptotic
analysis relies on a notion of stochastic quasi-Fej\'er monotonicity, which is
thoroughly investigated. The iterative methods under consideration feature
random sweeping rules to select arbitrarily the blocks of variables that are
activated over the course of the iterations and they allow for stochastic
errors in the evaluation of the operators. Algorithms using quasinonexpansive
operators or compositions of averaged nonexpansive operators are constructed,
and weak and strong convergence results are established for the sequences they
generate. As a by-product, novel block-coordinate operator splitting methods
are obtained for solving structured monotone inclusion and convex minimization
problems. In particular, the proposed framework leads to random
block-coordinate versions of the Douglas-Rachford and forward-backward
algorithms and of some of their variants. In the standard case of block,
our results remain new as they incorporate stochastic perturbations
Free-energy model for fluid helium at high density
We present a semi-analytical free-energy model aimed at characterizing the
thermodynamic properties of dense fluid helium, from the low-density atomic
phase to the high-density fully ionized regime. The model is based on a
free-energy minimization method and includes various different contributions
representative of the correlations between atomic and ionic species and
electrons. This model allows the computation of the thermodynamic properties of
dense helium over an extended range of density and temperature and leads to the
computation of the phase diagram of dense fluid helium, with its various
temperature and pressure ionization contours. One of the predictions of the
model is that pressure ionization occurs abruptly at \rho \simgr 10 g
cm, {\it i.e.} P\simgr 20 Mbar, from atomic helium He to fully ionized
helium He, or at least to a strongly ionized state, without He
stage, except at high enough temperature for temperature ionization to become
dominant. These predictions and this phase diagram provide a guide for future
dynamical experiments or numerical first-principle calculations aimed at
studying the properties of helium at very high density, in particular its
metallization. Indeed, the characterization of the helium phase diagram bears
important consequences for the thermodynamic, magnetic and transport properties
of cool and dense astrophysical objects, among which the solar and the numerous
recently discovered extrasolar giant planets.Comment: Accepted for publication in Phys. Rev.
Observability and Synchronization of Neuron Models
Observability is the property that enables to distinguish two different
locations in -dimensional state space from a reduced number of measured
variables, usually just one. In high-dimensional systems it is therefore
important to make sure that the variable recorded to perform the analysis
conveys good observability of the system dynamics. In the case of networks
composed of neuron models, the observability of the network depends
nontrivially on the observability of the node dynamics and on the topology of
the network. The aim of this paper is twofold. First, a study of observability
is conducted using four well-known neuron models by computing three different
observability coefficients. This not only clarifies observability properties of
the models but also shows the limitations of applicability of each type of
coefficients in the context of such models. Second, a multivariate singular
spectrum analysis (M-SSA) is performed to detect phase synchronization in
networks composed by neuron models. This tool, to the best of the authors'
knowledge has not been used in the context of networks of neuron models. It is
shown that it is possible to detect phase synchronization i)~without having to
measure all the state variables, but only one from each node, and ii)~without
having to estimate the phase
Terahertz Magnetoplasmon Energy Concentration and Splitting in Graphene PN Junctions
Terahertz plasmons and magnetoplasmons propagating along electrically and
chemically doped graphene p-n junctions are investigated. It is shown that such
junctions support non-reciprocal magnetoplasmonic modes which get concentrated
at the middle of the junction in one direction and split away from the middle
of the junction in the other direction under the application of an external
static magnetic field. This phenomenon follows from the combined effects of
circular birefringence and carrier density non-uniformity. It can be exploited
for the realization of plasmonic isolators.Comment: 6 Pages, 10 figure
Effect of connecting wires on the decoherence due to electron-electron interaction in a metallic ring
We consider the weak localization in a ring connected to reservoirs through
leads of finite length and submitted to a magnetic field. The effect of
decoherence due to electron-electron interaction on the harmonics of AAS
oscillations is studied, and more specifically the effect of the leads. Two
results are obtained for short and long leads regimes. The scale at which the
crossover occurs is discussed. The long leads regime is shown to be more
realistic experimentally.Comment: LaTeX, 4 pages, 4 eps figure
- âŠ