Epithelial to mesenchymal transition (EMT) is a fundamental process during development and disease, including development of the heart valves and tumour metastases. An extended cellular Potts model was implemented to represent the behaviour emerging from autonomous cell morphology, labile adhesion, junctional coupling and cell motility. Computer simulations normally focus on these functional ch...

Actinomvcosis seldom involves the vertebral column. Only four out of 670 patients with actinomycosis reviewed by Sanford and Voelker (1925) had rib or vertebral involvement. It is clear that in the past the diagnosis has been difficult and that tile condition has often been mistaken for Potts disease. Among the reports of sixty cases of mycosis of the vertebral column Meyer and Gall (1935) foun...

We consider a directed compact site lattice animal problem on the d-dimensional hypercubic lattice, and establish its equivalence with (i) the infinite-state Potts model and (ii) the enumeration of sd 2 1ddimensional restricted partitions of an integer. The directed compact lattice animal problem is solved exactly in d ­ 2, 3 using known solutions of the enumeration problem. The maximum number ...

Ii is shown that trie cavity method developed to describe equilibrium states in trie mean-field Ising spin glass model con be generalized to describe metastable stores in trie mean-field Potts glass. Trie crucial input is trie existence of an extensive number of statistically similar but incongruent metastable states with a weighted Gaussian free energy distribution. It is argued that the inher...

The critical points of the two-layer Ising and Potts models for square lattice have been calculated with high precision using probabilistic cellular automata (PCA) with Glauber alghorithm. The critical temperature is calculated for the isotropic and symmetric case (Kx=Ky=Kz=K), where Kx and Ky are the nearest-neighbor interactions within each layer in the x and y directions, respectively, and K...

In a recent paper [1] we investigated Potts models on “thin” random graphs – generic Feynman diagrams, using the idea that such models may be expressed as the N → 1 limit of a matrix model. The models displayed first order transitions for all q > 2, giving identical behaviour to the corresponding Bethe lattice. We use here one of the results of [1] namely a general saddle point solution for a q...

In this paper, correlation inequalities which have been considered on Ising model are extended to q-Potts model. It is considered on generalized Potts model with interaction of any number of spins. We replace the set of spin values F = {1, 2, · · · , q} by the centered set F = {−(q−1)/2,−(q−3)/2, · · · , (q−3)/2, (q−1)/2}. Let N be the subset of one-dimensional lattice with n vertices, γ = (σ1,...

These notes give examples of how suitably defined geometrical objects encode in their fractal structure thermal critical behavior. The emphasis is on the two-dimensional Potts model for which two types of spin clusters can be defined. Whereas the Fortuin-Kasteleyn clusters describe the standard critical behavior, the geometrical clusters describe the tricritical behavior that arises when includ...