1,324 research outputs found
Retrieval Properties of Hopfield and Correlated Attractors in an Associative Memory Model
We examine a previouly introduced attractor neural network model that
explains the persistent activities of neurons in the anterior ventral temporal
cortex of the brain. In this model, the coexistence of several attractors
including correlated attractors was reported in the cases of finite and
infinite loading. In this paper, by means of a statistical mechanical method,
we study the statics and dynamics of the model in both finite and extensive
loading, mainly focusing on the retrieval properties of the Hopfield and
correlated attractors. In the extensive loading case, we derive the evolution
equations by the dynamical replica theory. We found several characteristic
temporal behaviours, both in the finite and extensive loading cases. The
theoretical results were confirmed by numerical simulations.Comment: 12 pages, 7 figure
Phase Transitions of an Oscillator Neural Network with a Standard Hebb Learning Rule
Studies have been made on the phase transition phenomena of an oscillator
network model based on a standard Hebb learning rule like the Hopfield model.
The relative phase informations---the in-phase and anti-phase, can be embedded
in the network. By self-consistent signal-to-noise analysis (SCSNA), it was
found that the storage capacity is given by , which is better
than that of Cook's model. However, the retrieval quality is worse. In
addition, an investigation was made into an acceleration effect caused by
asymmetry of the phase dynamics. Finally, it was numerically shown that the
storage capacity can be improved by modifying the shape of the coupling
function.Comment: 10 pages, 6 figure
Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase Responses
In many real-world oscillator systems, the phase response curves are highly
heterogeneous. However, dynamics of heterogeneous oscillator networks has not
been seriously addressed. We propose a theoretical framework to analyze such a
system by dealing explicitly with the heterogeneous phase response curves. We
develop a novel method to solve the self-consistent equations for order
parameters by using formal complex-valued phase variables, and apply our theory
to networks of in vitro cortical neurons. We find a novel state transition that
is not observed in previous oscillator network models.Comment: 4 pages, 3 figure
Thermodynamics of impurity-enhanced vacancy formation in metals
Hydrogen induced vacancy formation in metals and metal alloys has been of great interest during the past couple of decades. The main reason for this phenomenon, often referred to as the superabundant vacancy formation, is the lowering of vacancy formation energy due to the trapping of hydrogen. By means of thermodynamics, we study the equilibrium vacancy formation in fcc metals (Pd, Ni, Co, and Fe) in correlation with the H amounts. The results of this study are compared and found to be in good agreement with experiments. For the accurate description of the total energy of the metal-hydrogen system, we take into account the binding energies of each trapped impurity, the vibrational entropy of defects, and the thermodynamics of divacancy formation. We demonstrate the effect of vacancy formation energy, the hydrogen binding, and the divacancy binding energy on the total equilibrium vacancy concentration. We show that the divacancy fraction gives the major contribution to the total vacancy fraction at high H fractions and cannot be neglected when studying superabundant vacancies. Our results lead to a novel conclusion that at high hydrogen fractions, superabundant vacancy formation takes place regardless of the binding energy between vacancies and hydrogen. We also propose the reason of superabundant vacancy formation mainly in the fcc phase. The equations obtained within this work can be used for any metal-impurity system, if the impurity occupies an interstitial site in the lattice. Published by AIP Publishing.Peer reviewe
Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile
The rotor-router model is a deterministic analogue of random walk. It can be
used to define a deterministic growth model analogous to internal DLA. We prove
that the asymptotic shape of this model is a Euclidean ball, in a sense which
is stronger than our earlier work. For the shape consisting of
sites, where is the volume of the unit ball in , we show that
the inradius of the set of occupied sites is at least , while the
outradius is at most for any . For a related
model, the divisible sandpile, we show that the domain of occupied sites is a
Euclidean ball with error in the radius a constant independent of the total
mass. For the classical abelian sandpile model in two dimensions, with particles, we show that the inradius is at least , and the
outradius is at most . This improves on bounds of Le Borgne
and Rossin. Similar bounds apply in higher dimensions.Comment: [v3] Added Theorem 4.1, which generalizes Theorem 1.4 for the abelian
sandpile. [v4] Added references and improved exposition in sections 2 and 4.
[v5] Final version, to appear in Potential Analysi
Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators
We show that a wide class of uncoupled limit cycle oscillators can be
in-phase synchronized by common weak additive noise. An expression of the
Lyapunov exponent is analytically derived to study the stability of the
noise-driven synchronizing state. The result shows that such a synchronization
can be achieved in a broad class of oscillators with little constraint on their
intrinsic property. On the other hand, the leaky integrate-and-fire neuron
oscillators do not belong to this class, generating intermittent phase slips
according to a power low distribution of their intervals.Comment: 10 pages, 3 figure
Oscillator neural network model with distributed native frequencies
We study associative memory of an oscillator neural network with distributed
native frequencies. The model is based on the use of the Hebb learning rule
with random patterns (), and the distribution function of
native frequencies is assumed to be symmetric with respect to its average.
Although the system with an extensive number of stored patterns is not allowed
to get entirely synchronized, long time behaviors of the macroscopic order
parameters describing partial synchronization phenomena can be obtained by
discarding the contribution from the desynchronized part of the system. The
oscillator network is shown to work as associative memory accompanied by
synchronized oscillations. A phase diagram representing properties of memory
retrieval is presented in terms of the parameters characterizing the native
frequency distribution. Our analytical calculations based on the
self-consistent signal-to-noise analysis are shown to be in excellent agreement
with numerical simulations, confirming the validity of our theoretical
treatment.Comment: 9 pages, revtex, 6 postscript figures, to be published in J. Phys.
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