We apply a replica inference based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of “community detection” and its phase diagram. Specifically, the problem is cast as identifying tightly bound clusters (“communities” or “solutes”) against a background or “solvent”. Within our multiresolution approach, we ...

Using suitable Monte Carlo methods and finite-size scaling, we investigate critical and tricritical surface phenomena of two-dimensional Potts models. For the critical two- and three-state models, we determine a surface scaling dimension describing percolation properties of the so-called Potts clusters near the edges. On this basis, we propose an exact expression describing this exponent for th...

We investigate the evolution of the random interfaces in a two dimensional Potts model at zero temperature under Glauber dynamics for some particular initial conditions. We prove that under space-time diffusive scaling the shape of the interfaces converges in probability to the solution of a non-linear parabolic equation. This Law of Large Numbers is obtained from the Hydrodynamic limit of a co...

We have considered clusters of like spin in the Q-Potts model, Potts clusters. Using Monte Carlo simulations, we studied these on a square lattice with periodic boundary conditions for values Q [1,4]. continue work initiated Delfino and Viti (2013) by measuring universal finite size corrections two-point connectivity. The numerical data are perfectly compatible CFT prediction, thus supporting e...

A Potts associative memory network has been proposed as a simplified model of macroscopic cortical dynamics, in which each Potts unit stands for a patch of cortex, which can be activated in one of S local attractor states. The internal neuronal dynamics of the patch is not described by the model, rather it is subsumed into an effective description in terms of graded Potts units, with adaptation...

We demonstrate that the transfer matrix of the inhomogeneous N -state chiral Potts model with two vertical superintegrable rapidities serves as the Q-operator of XXZ chain model for a cyclic representation of Uq(sl2) with Nth root-of-unity q and representation-parameter. The symmetry problem of XXZ chain with a general cyclic Uq(sl2)-representation is mapped onto the problem of studying Q-opera...

Monte Carlo (MC) simulations and series expansions (SE) data for the energy, specific heat, magnetization, and susceptibility of the three-state and four-state Potts model and Baxter-Wu model on the square lattice are analyzed in the vicinity of the critical point in order to estimate universal combinations of critical amplitudes. We also form effective ratios of the observables close to the cr...

This commentary on Potts et al provides a critical view on their thesis that increasing the level of education among women is likely to reduce terrorism. Presence of a strong family planning program enables women to control family size resulting in women’s public participation more likely and facilitating the emergence of small birth cohorts who are less likely to become unemployed. In spite of...

This thesis studies statistical image processing of high frequency ultrasound imaging, with application to in-vivo exploration of human skin and noninvasive lesion assessment. More precisely, Bayesian methods are considered in order to perform tissue segmentation in ultrasound images of skin. It is established that ultrasound signals backscattered from skin tissues converge to a complex Levy Fl...

Potts, Deborah. 2020: Broken Cities: Inside the Global Housing Crisis. Zed Press. 319 pp. £70.00 hardcover, £18.99 paperback. ISBN: 1786990547.