In this paper, we propose a mean-field model which attempts to bridge the gap between random Boolean networks and more realistic stochastic modeling of genetic regulatory networks. The main idea of the model is to replace all regulatory interactions to any one gene with an average or effective interaction, which takes into account the repression and activation mechanisms. We find that depending...

The triangular lattice of S=1/2 spins with XXZ anisotropy is a ubiquitous model for various frustrated systems in different contexts. We determine the quantum phase diagram of the model in the plane of the anisotropy parameter and the magnetic field by means of a large-size cluster mean-field method with a scaling scheme. We find that quantum fluctuations break up the nontrivial continuous dege...

In this paper, we use the multitype mean field voter model as a model of species interaction, to obtain results about species abundance. Briefly, we start with the complete graph on n vertices, Cn, with each site occupied by a particle. Particles are represented by a value in (0, 1), where distinct values represent different species. Particles then undergo mutation at rate α, and are relabelled...

In this paper, we derive a model for analyzing the innuence of local cortical connections on the activities of neurons in V1. A set of orientation columns is arranged according to a measured orientation map. Orientation columns are connected by local excitatory and slightly more distributed inhibitory bers. Based on this geometrical model we demonstrate that (i) sharp and contrast{invariant ori...

Exact solutions are obtained for the mean-field spherical model, with or without an external magnetic field, for any finite or infinite number N of degrees of freedom, both in the microcanonical and in the canonical ensemble. The canonical result allows for an exact discussion of the loci of the Fisher zeros of the canonical partition function. The microcanonical entropy is found to be nonanaly...

Large systems of interacting objects are highly prevalent in today’s world. Such system usually consist of a large number of relatively simple identical objects, and can be observed in many different field as, e.g., physics (interactions of molecules in gas), chemistry (chemical reactions), epidemiology (spread of the infection), etc. In this thesis we primarily address large systems of interac...

A model of hybridized bosons and fermions is studied beyond the mean field approximation. The divergent boson self-energy at zero temperature makes the Cooper pairing of fermions impossible. The frequency and momentum dependence of the self-energy and the condensation temperature T c of initially localized bosons are calculated analytically. The value of the boson condensation temperature T c i...

I use a previously introduced mapping between the continuum percolation model and the Potts fluid to derive a mean field theory of continuum percolation systems. This is done by introducing a new variational principle, the basis of which has to be taken, for now, as heuristic. The critical exponents obtained are β = 1, γ = 1 and ν = 0.5, which are identical with the mean field exponents of latt...