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

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 $c$.Comment: 8 pages and 5 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

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

Structure analysis of the virtual Compton scattering amplitude at low energies

We analyze virtual Compton scattering off the nucleon at low energies in a covariant, model-independent formalism. We define a set of invariant functions which, once the irregular nucleon pole terms have been subtracted in a gauge-invariant fashion, is free of poles and kinematical zeros. The covariant treatment naturally allows one to implement the constraints due to Lorentz and gauge invariance, crossing symmetry, and the discrete symmetries. In particular, when applied to the $ep\to e'p'\gamma$ reaction, charge-conjugation symmetry in combination with nucleon crossing generates four relations among the ten originally proposed generalized polarizabilities of the nucleon.Comment: 19 pages, LaTeX2e/RevTeX, no figures, original sections IV.-VI. removed, to be discussed in a separate publication, none of the conclusions change