Related papers: Bethe Ansatz in the Bernoulli Matching Model of Ra…
We study the Bethe ansatz equations for a generalized $XXZ$ model on a one-dimensional lattice. Assuming the string conjecture we propose an integer version for vacancy numbers and prove a combinatorial completeness of Bethe's states for a…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
In this paper we develop a Bethe approximation, based on the cluster variation method, which is apt to study lattice models of branched polymers. We show that the method is extremely accurate in cases where exact results are known as, for…
We reformulate the nested coordinate Bethe ansatz in terms of coproducts of Yangian symmetry generators. This allows us to derive the nested Bethe equations for the bound state string S-matrices. We find that they coincide with the Bethe…
We propose a novel combinatorial inference framework to conduct general uncertainty quantification in ranking problems. We consider the widely adopted Bradley-Terry-Luce (BTL) model, where each item is assigned a positive preference score…
I derived Bethe Ansatz equations for two model Periodic Quantum Circuits: 1) XXZ model; 2) Chiral Hubbard Model. I obtained explicit expressions for the spectra of the strings of any length. These analytic results may be useful for…
In this paper, we present a fast and strong neural approach for general purpose text matching applications. We explore what is sufficient to build a fast and well-performed text matching model and propose to keep three key features…
The nineteen-vertex models of Zamolodchikov-Fateev, Izergin-Korepin and the supersymmetric osp(1|2) with periodic boundary conditions are studied. We find the spectrum of these quantum spin chains using the Coordinate Bethe Ansatz. The…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes…
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…
Sentence Ordering refers to the task of rearranging a set of sentences into the appropriate coherent order. For this task, most previous approaches have explored global context-based end-to-end methods using Sequence Generation techniques.…
Molecular phylogenetic techniques do not generally account for such common evolutionary events as site insertions and deletions (known as indels). Instead tree building algorithms and ancestral state inference procedures typically rely on…
In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…
Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…
Tree-based ensemble methods such as random forests, gradient-boosted trees, and Bayesianadditive regression trees have been successfully used for regression problems in many applicationsand research studies. In this paper, we study ensemble…
Sentence ordering aims to arrange the sentences of a given text in the correct order. Recent work frames it as a ranking problem and applies deep neural networks to it. In this work, we propose a new method, named BERT4SO, by fine-tuning…
A common problem faced in statistical inference is drawing conclusions from paired comparisons, in which two objects compete and one is declared the victor. A probabilistic approach to such a problem is the Bradley-Terry model, first…
The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the $SU(2|2)$ vertex model with…
We compute the anomalous dimension for a short single-trace operator in planar ABJM theory at intermediate coupling. This is done by solving numerically the set of Thermodynamic Bethe Ansatz equations which are expected to describe the…