Related papers: Reconstruction of symmetric Potts Models
We study the phase diagram of the ferromagnetic $q$-state Potts model on the various three-dimensional lattices for integer and non-integer values of $q>1$. Our approach is based on a thermodynamically self-consistent Ornstein-Zernike…
The Potts conformal field theory is an analytic continuation in the central charge of conformal field theory describing the critical two-dimensional $Q$-state Potts model. Four-point functions of the Potts conformal field theory are…
The tree-metric theorem provides a necessary and sufficient condition for a dissimilarity matrix to be a tree metric, and has served as the foundation for numerous distance-based reconstruction methods in phylogenetics. Our main result is…
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described…
We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…
In this paper we are concerned with the stabilization of MUSCL-type finite volume schemes in arbitrary space dimensions. We consider a number of limited reconstruction techniques which are defined in terms inequality-constrained linear or…
Ancestral state reconstruction is one of the most important tasks in evolutionary biology. Conditions under which we can reliably reconstruct the ancestral state have been studied for both discrete and continuous traits. However, the…
The problem of reconstructing evolutionary trees or phylogenies is of great interest in computational biology. A popular model for this problem assumes that we are given the set of leaves (current species) of an unknown binary tree and the…
Generative models for networks with communities have been studied extensively for being a fertile ground to establish information-theoretic and computational thresholds. In this paper we propose a new toy model for planted generative models…
In this paper the bootstrap conditions that follow from the general postulates of effective scattering theory (EST) are checked in the strange sector. We construct the system of tree level bootstrap constraints for the renormalization…
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically,…
It is a classical result that any finite tree with positively weighted edges, and without vertices of degree 2, is uniquely determined by the weighted path distance between each pair of leaves. Moreover, it is possible for a (small) strict…
Reconstruction problems have been studied in a number of contexts including biology, information theory and and statistical physics. We consider the reconstruction problem for random $k$-colourings on the $\Delta$-ary tree for large $k$.…
In this article, we prove that finite (weakly) systolic and Helly complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). Furthermore, Helly complexes and 2-dimensional systolic complexes can be…
We have simulated, by using cluster algorithm, the $q=8$ state Potts model in two-dimension with varying amount of quenched bond randomness. We have shown that there exist a finite size dependent threshold value of the introduced quenched…
We discuss the q-state Potts models for q<=4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions…
Pemantle and Steif provided a sharp threshold for the existence of a RPT (robust phase transition) for the continuous rotator model and the Potts model in terms of the branching number and the second eigenvalue of the transfer operator,…
Multinomial processing tree (MPT) models are tools for disentangling the contributions of latent cognitive processes in a given experimental paradigm. The present note analyzes MPT models subject to order constraints on subsets of its…
Numerical simulations on the total mass, the numbers of bonds on the hull, external perimeter, singly connected bonds and gates into large fjords of the Fortuin-Kasteleyn clusters for two-dimensional q-state Potts models at criticality are…
A central theme in phylogenetics is the reconstruction and analysis of evolutionary trees from a given set of data. To determine the optimal search methods for reconstructing trees, it is crucial to understand the size and structure of the…