Related papers: Hopfield model for patterns with internal structur…
Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and…
There is a growing belief that the mode coupling theory is the proper microscopic theory for the dynamics of the undercooled liquid above a critical temperature T_c. In addition, there is some evidence that the system leaves the…
Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…
We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense,…
Human eye movement mechanisms (saccades) are very useful for scene analysis, including object representation and pattern recognition. In this letter, a Hopfield neural network to emulate saccades is proposed. The network uses an energy…
We develop a model free energy from an expansion that basically includes graphs without loops. From this calculation, we derive the temperature dependence of the density (or specific volume), the typical time scale of the…
Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns.…
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…
The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the $\alpha$ (the…
The lattice spin model, with nearest neighbor ferromagnetic exchange and long range dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon…
The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
The Thouless, Anderson, Palmer (TAP) approach to thermodynamics of mean field spin-glasses is generalised to dynamics. A method to compute the dynamical TAP equations is developed and applied to the p-spin spherical model. In this context…
Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…
The Ghatak-Sherrington (GS) spin glass model is a random probability measure defined on the configuration space $\{0,\pm1,\pm2,\ldots, \pm \mathcal{S} \}^N$ with system size $N$ and $\mathcal{S}\ge1$ finite. This generalizes the classical…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk…
In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the…
A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…
The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature…