Related papers: The synchronous BEG neural network with variable d…
The three-state Ising neural network with synchronous updating and variable dilution is discussed starting from the appropriate Hamiltonians. The thermodynamic and retrieval properties are examined using replica mean-field theory.…
The thermodynamic and retrieval properties of fully connected Blume-Emery-Griffiths networks, storing ternary patterns, are studied using replica mean-field theory. Capacity-temperature phase diagrams are derived for several values of the…
The optimal capacity of a diluted Blume-Emery-Griffiths neural network is studied as a function of the pattern activity and the embedding stability using the Gardner entropy approach. Annealed dilution is considered, cutting some of the…
The retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks are derived and studied in replica-symmetric mean-field theory generalizing earlier works on either the fully connected or the symmetrical…
The subject of study is a neural network with binary neurons, randomly diluted synapses and variable pattern activity. We look at the system with parallel updating using a probabilistic approach to solve the one step dynamics with one…
Fully connected Blume-Emery-Griffiths neural networks performing pattern recognition and associative memory have been heuristically studied in the past (mainly via the replica trick and under the replica symmetric assumption) as…
We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…
The time evolution of the extremely diluted Blume-Emery-Griffiths neural network model is studied, and a detailed equilibrium phase diagram is obtained exhibiting pattern retrieval, fluctuation retrieval and self-sustained activity phases.…
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied at zero temperature for arbitrary using a probabilistic approach. A recursive scheme is found determining the complete time evolution of the…
Using the replica-symmetric mean-field theory approach the thermodynamic and retrieval properties of extremely diluted {\it symmetric} $Q$-Ising neural networks are studied. In particular, capacity-gain parameter and capacity-temperature…
The thermodynamic and retrieval properties of the Ashkin-Teller neural network model storing an infinite number of patterns are examined in the replica-symmetric mean-field approximation. In particular, for linked patterns…
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied for arbitrary temperature. By employing a probabilistic signal-to-noise approach, a recursive scheme is found determining the time evolution…
The parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network is studied using signal-to-noise analysis techniques. Evolution equations for the order parameters are derived, both at zero and finite temperature. The…
A new mathematical model of neural networks described by diffusive FitzHugh-Nagumo equations with memristors and linear synaptic coupling is proposed and investigated. The existence of absorbing set for the solution semiflow in the energy…
We analyze the Blume-Emery-Griffiths (BEG) associative memory with sparse patterns and at zero temperature. We give bounds on its storage capacity provided that we want the stored patterns to be fixed points of the retrieval dynamics. We…
This contribution reviews the parallel dynamics of Q-Ising neural networks for various architectures: extremely diluted asymmetric, layered feedforward, extremely diluted symmetric, and fully connected. Using a probabilistic signal-to-noise…
We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network…
The parallel dynamics of extremely diluted symmetric Q-Ising neural networks is studied for arbitrary Q using a probabilistic approach. In spite of the extremely diluted architecture the feedback correlations arising from the symmetry…
Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists…
We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…