4,810 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
The Influence of Financial Aid and Student Characteristics on Degree Completion Rates for a Cohort of Two-Year College Students
This study investigated the impact of student background characteristics, college experience variables, federal financial aid awards, and college outcome variables on degree completion rates for a cohort of two-year college students. A model for institutional research suggested by St. John (1992) was adapted and this study sought to determine whether financial aid awards and student characteristic variables influenced degree completion rates for the cohort of students identified in this study
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
Tuning the structural and dynamical properties of a dipolar Bose-Einstein condensate: Ripples and instability islands
It is now well established that the stability of aligned dipolar Bose gases
can be tuned by varying the aspect ratio of the external harmonic confinement.
This paper extends this idea and demonstrates that a Gaussian barrier along the
strong confinement direction can be employed to tune both the structural
properties and the dynamical stability of an oblate dipolar Bose gas aligned
along the strong confinement direction. In particular, our theoretical
mean-field analysis predicts the existence of instability islands immersed in
otherwise stable regions of the phase diagram. Dynamical studies indicate that
these instability islands, which can be probed experimentally with present-day
technology, are associated with the going soft of a Bogoliubov--de Gennes
excitation frequency with radial breathing mode character. Furthermore, we find
dynamically stable ground state densities with ripple-like oscillations along
the radial direction. These structured ground states exist in the vicinity of a
dynamical radial roton-like instability.Comment: 9 pages, 11 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
Macroscopic quantum jumps and entangled state preparation
Recently we predicted a random blinking, i.e. macroscopic quantum jumps, in
the fluorescence of a laser-driven atom-cavity system [Metz et al., Phys. Rev.
Lett. 97, 040503 (2006)]. Here we analyse the dynamics underlying this effect
in detail and show its robustness against parameter fluctuations. Whenever the
fluorescence of the system stops, a macroscopic dark period occurs and the
atoms are shelved in a maximally entangled ground state. The described setup
can therefore be used for the controlled generation of entanglement. Finite
photon detector efficiencies do not affect the success rate of the state
preparation, which is triggered upon the observation of a macroscopic
fluorescence signal. High fidelities can be achieved even in the vicinity of
the bad cavity limit due to the inherent role of dissipation in the jump
process.Comment: 14 pages, 12 figures, proof of the robustness of the state
preparation against parameter fluctuations added, figure replace
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
Note and Comment
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