Related papers: The Blume-Emery-Griffiths neural network: dynamics…
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…
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 Blume-Emery-Griffiths model with a random crystal field is studied in a random graph architecture, in which the average connectivity is a controllable parameter. The disordered average over the graph realizations is treated by replica…
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 thermodynamic and retrieval properties of the Blume-Emery-Griffiths neural network with synchronous updating and variable dilution are studied using replica mean-field theory. Several forms of dilution are allowed by pruning the…
We study the applicability of the {\it parallel tempering method} (PT) in the investigation of first- order phase transitions. In this method, replicas of the same system are simulated simultaneously at different temperatures and the…
We introduce a spherical version of the frustrated Blume-Emery-Griffiths model and solve exactly the statics and the Langevin dynamics for zero particle-particle coupling (K=0). In this case the model exhibits an equilibrium transition from…
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…
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…
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…
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…
We derive rates of convergence for limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffith model. The theorems consist of scaling limits for the total spin. The model…
We analyze the so called Swapping Algorithm, a parallel version of the well-known Metropolis-Hastings algorithm, on the mean-field version of the Blume-Emery-Griffiths model in statistical mechanics. This model has two parameters and…
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…
Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters…
We develop a spatio-temporal model to forecast sensor output at five locations in North East England. The signal is described using coupled dynamic linear models, with spatial effects specified by a Gaussian process. Data streams are…
We present three different neural network algorithms to calculate thermodynamic properties as well as dynamic correlation functions at finite temperatures for quantum lattice models. The first method is based on purification, which allows…
We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to…
Gradient algorithms are classical in adaptive control and parameter estimation. For instantaneous quadratic cost functions they lead to a linear time-varying dynamic system that converges exponentially under persistence of excitation…
Ensemble forecast post-processing is a necessary step in producing accurate probabilistic forecasts. Conventional post-processing methods operate by estimating the parameters of a parametric distribution, frequently on a per-location or…