3,214 research outputs found
Pattern reconstruction and sequence processing in feed-forward layered neural networks near saturation
The dynamics and the stationary states for the competition between pattern
reconstruction and asymmetric sequence processing are studied here in an
exactly solvable feed-forward layered neural network model of binary units and
patterns near saturation. Earlier work by Coolen and Sherrington on a parallel
dynamics far from saturation is extended here to account for finite stochastic
noise due to a Hebbian and a sequential learning rule. Phase diagrams are
obtained with stationary states and quasi-periodic non-stationary solutions.
The relevant dependence of these diagrams and of the quasi-periodic solutions
on the stochastic noise and on initial inputs for the overlaps is explicitly
discussed.Comment: 9 pages, 7 figure
Instability of frozen-in states in synchronous Hebbian neural networks
The full dynamics of a synchronous recurrent neural network model with Ising
binary units and a Hebbian learning rule with a finite self-interaction is
studied in order to determine the stability to synaptic and stochastic noise of
frozen-in states that appear in the absence of both kinds of noise. Both, the
numerical simulation procedure of Eissfeller and Opper and a new alternative
procedure that allows to follow the dynamics over larger time scales have been
used in this work. It is shown that synaptic noise destabilizes the frozen-in
states and yields either retrieval or paramagnetic states for not too large
stochastic noise. The indications are that the same results may follow in the
absence of synaptic noise, for low stochastic noise.Comment: 14 pages and 4 figures; accepted for publication in J. Phys. A: Math.
Ge
Period-two cycles in a feed-forward layered neural network model with symmetric sequence processing
The effects of dominant sequential interactions are investigated in an
exactly solvable feed-forward layered neural network model of binary units and
patterns near saturation in which the interaction consists of a Hebbian part
and a symmetric sequential term. Phase diagrams of stationary states are
obtained and a new phase of cyclic correlated states of period two is found for
a weak Hebbian term, independently of the number of condensed patterns .Comment: 8 pages and 5 figure
Symmetric sequence processing in a recurrent neural network model with a synchronous dynamics
The synchronous dynamics and the stationary states of a recurrent attractor
neural network model with competing synapses between symmetric sequence
processing and Hebbian pattern reconstruction is studied in this work allowing
for the presence of a self-interaction for each unit. Phase diagrams of
stationary states are obtained exhibiting phases of retrieval, symmetric and
period-two cyclic states as well as correlated and frozen-in states, in the
absence of noise. The frozen-in states are destabilised by synaptic noise and
well separated regions of correlated and cyclic states are obtained. Excitatory
or inhibitory self-interactions yield enlarged phases of fixed-point or cyclic
behaviour.Comment: Accepted for publication in Journal of Physics A: Mathematical and
Theoretica
Transition between localized and extended states in the hierarchical Anderson model
We present strong numerical evidence for the existence of a
localization-delocalization transition in the eigenstates of the 1-D Anderson
model with long-range hierarchical hopping. Hierarchical models are important
because of the well-known mapping between their phases and those of models with
short range hopping in higher dimensions, and also because the renormalization
group can be applied exactly without the approximations that generally are
required in other models. In the hierarchical Anderson model we find a finite
critical disorder strength Wc where the average inverse participation ratio
goes to zero; at small disorder W < Wc the model lies in a delocalized phase.
This result is based on numerical calculation of the inverse participation
ratio in the infinite volume limit using an exact renormalization group
approach facilitated by the model's hierarchical structure. Our results are
consistent with the presence of an Anderson transition in short-range models
with D > 2 dimensions, which was predicted using renormalization group
arguments. Our finding should stimulate interest in the hierarchical Anderson
model as a simplified and tractable model of the Anderson localization
transition which occurs in finite-dimensional systems with short-range hopping.Comment: 7 pages, 7 figure
Spectra of sparse non-Hermitian random matrices: an analytical solution
We present the exact analytical expression for the spectrum of a sparse
non-Hermitian random matrix ensemble, generalizing two classical results in
random-matrix theory: this analytical expression forms a non-Hermitian version
of the Kesten-Mckay law as well as a sparse realization of Girko's elliptic
law. Our exact result opens new perspectives in the study of several physical
problems modelled on sparse random graphs. In this context, we show
analytically that the convergence rate of a transport process on a very sparse
graph depends upon the degree of symmetry of the edges in a non-monotonous way.Comment: 5 pages, 5 figures, 12 pages supplemental materia
A dynamical trichotomy for structured populations experiencing positive density-dependence in stochastic environments
Positive density-dependence occurs when individuals experience increased
survivorship, growth, or reproduction with increased population densities.
Mechanisms leading to these positive relationships include mate limitation,
saturating predation risk, and cooperative breeding and foraging. Individuals
within these populations may differ in age, size, or geographic location and
thereby structure these populations. Here, I study structured population models
accounting for positive density-dependence and environmental stochasticity i.e.
random fluctuations in the demographic rates of the population. Under an
accessibility assumption (roughly, stochastic fluctuations can lead to
populations getting small and large), these models are shown to exhibit a
dynamical trichotomy: (i) for all initial conditions, the population goes
asymptotically extinct with probability one, (ii) for all positive initial
conditions, the population persists and asymptotically exhibits unbounded
growth, and (iii) for all positive initial conditions, there is a positive
probability of asymptotic extinction and a complementary positive probability
of unbounded growth. The main results are illustrated with applications to
spatially structured populations with an Allee effect and age-structured
populations experiencing mate limitation
Effet d’un programme d’activité physique intermittent de haute intensité sur la perte de masse grasse abdominale chez la femme DT2 ménopausée
Contexte : A la ménopause, la diminution des taux d’estrogènes favorise un dépôt de masse grasse (MG) abdominal (sous-cutané et viscéral). La MG viscérale est corrélée aux maladies cardio-vasculaires (MCV). Ce risque est accentué chez les sujets présentant un diabète de type 2 (DT2).Objectif : Comparer deux modalités d’entraînement, continu de moyenne intensité (SSE) vs. intermittent de haute intensité (HIIE), sur la perte de MG abdominale (dont viscérale) chez des femmes DT2 ménopausées.Matériels et méthode : Seize femmes DT2 ménopausées (69±1ans; IMC : 31±1 kg/m²) ont été réparties aléatoirement en deux groupes. Pendant quatre mois, deux fois par semaine, 8 d’entre elles ont réalisé un entraînement SSE (40 min de pédalage à 50% de la FCmax de réserve), et 8 ont réalisé un entraînement HIIE (8s de sprint suivies de 12s de récupération active, pendant 20 min). Pré (T0) et post entraînement (T4), la composition corporelle et la MG abdominale totale ont été mesurées par DXA (Dual Energy X-ray Absorptiometry). La MG viscérale a été estimée à partir de la méthode de Martin et Jensen1. A T0 et T4, les apports énergétiques et le niveau d’activité physique ont été déterminés (questionnaires et accéléromètrie validée2 intégrée sur smartphone).Résultats : Après 16 semaines d’intervention, sans modification des apports énergétiques et du niveau d’activité physique total, une perte de MG totale et un gain de masse maigre est observé (effet temps, p<0.05). La diminution de MG abdominale est supérieure dans le groupe HIIE (0.32% ± 2.07 vs 8.32 % ± 2.19, p<0.05) et la perte de MG viscérale n’est observée que dans le groupe HIIE (p<0.05).Conclusion : L’entraînement de type HIIE apparait comme un programme alternatif intéressant chez la femme DT2 ménopausée en diminuant significativement la MG abdominale totale et viscérale
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