Abstract Pott’s disease is a form of extrapulmonary tuberculosis (TB) affecting the spine. Approximately 10% individuals with TB will have skeletal manifestations most common area affected being spine, followed by hip and knee. Within has predilection for thoraco-lumbar region, cervical spine least affected. Here, we report case in 16-year-old child, no risk factors TB, presenting neck pain sti...

In Exact Real Arithmetic, real numbers are represented as potentially infinite streams of information units, called digits. In this paper, we work in the framework of Linear Fractional Transformations (LFT’s, also known as Möbius transformations) that provide an elegant approach to real number arithmetic (Gosper 1972, Vuillemin 1990, Nielsen and Kornerup 1995, Potts and Edalat 1996, Edalat and ...

In this report, we present a systematical account of the descending procedure from six-vertex model to the N -state chiral Potts model through fusion relations of τ -operators, following the works of Bazhanov-Stroganov and Baxter-Bazhanov-Perk. A careful analysis of the descending process leads to appearance of the high genus curve as rapidities’ constraint for the chiral Potts models. Full sym...

The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On L × L self-dual lattices studied (L ≤ 8), no Fisher zero lies on the unit circle p0 = e iθ in the complex p = (e − 1)/√Q plane for Q < 1, while some of the Fisher zeros lie on the unit circle for Q > 1 and the number ...

We address the continuous problem of assigning multiple (unordered) labels with the minimum perimeter. The corresponding discrete Potts model is typically addressed with a-expansion which can generate metrication artifacts. Existing convex continuous formulations of the Potts model use TV-based functionals directly encoding perimeter costs. Such formulations are analogous to ’min-cut’ problems ...

We consider a gas of classical particles in R having q distinct colours, interacting via a mean-field Potts potential and subject to an external field; a colour-independent molecular interaction of a mean-field type is also admitted. In contrast to the usual lattice Potts model, the Potts gas exhibits the specific volume v as a parameter, in addition to colour-ordering. The v-dependence of the ...

We comment on the article by Fujimoto (1997 J. Phys. A: Math. Gen. 30 3779) where the exact equilibrium crystal shape (ECS) in the critical Q-state Potts model on the square lattice was calculated, and its equivalence with ECS in the Ising model was established. We confirm these results, giving their alternative derivation applying the transformation properties of the one-particle dispersion re...

We analyse in this article the critical behavior of M q1-state Potts models coupled to N q2-state Potts models (q1, q2 ∈ [2..4]) with and without disorder. The technics we use are based on perturbed conformal theories. Calculations have been performed at two loops. We already find some interesting situations in the pure case for some peculiar values of M and N with new tricritical points. When ...

We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition function). We focus on the behavior of the number of points over finite fields for these hypersurfaces, in comparison with the graph hypersurfaces of perturbative quantum field theory defined by the Kirchhoff graph polynomial. We give a very simple example of the failure of the “f...

Existence of global classical solutions of a class of reaction–diffusion systems with chemotactic terms is demonstrated. This class contains a system of equations derived recently as a continuous limit of the stochastic discrete cellular Potts model. This provides mathematical justification for using numerical solutions of this system for modeling cellular motion in a chemotactic field. © 2009 ...