This paper reviews the Bethe/gauge correspondence and its relation with geometric representation theory. The Bethe/gauge correspondence, first introduced by Nekrasov and Shatashvili, connects an N = (2, 2) supersymmetric gauge theory in two dimensions with an integrable system solvable by the Bethe ansatz. Both sides of the correspondence are discussed and then the Bethe/gauge correspondence is...

In [4, Theorem X7.11 it is shown that if a partial function can be realized by a (nondeterministic) finite state a-transducer, then it can also be realized by a (deterministic) generalized bimachine (introduced in [l 11). Thus the generalized bimachines compute precisely all partial functions which are realizable by a-transducers. It can easily be shown that instead of a generalized bimachine (...

We define and study an inference algorithm based on“belief propagation” (BP) and the Bethe approximation. The idea is to encode into a graph an a priori information composed of correlations or marginal probabilities of variables, and to use a message passing procedure to estimate the actual state from some extra realtime information. This method is originally designed for traffic prediction and...

We show that every regular Bethe ansatz eigenstate of the XXZ spin chain at roots of unity is a highest weight vector of the sl2 loop algebra and discuss whether it generates an irreducible representation or not. We show it in some sectors with respect to eigenvalues of the total spin operator SZ . The parameter q is given by a root of unity, q2N 0 = 1, for an integer N . Here, q is related to ...

We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of empirical marginals where such Bethe learning will fail. By failure we mean that the empirical marginals cannot be recovered from the approximated maximum likel...

Abstract In this paper, we describe a certain kind of q -connections on projective line, namely Z -twisted ( G , q stretchy="false">) {(G,q)} -opers with regular singularities using the language generalized minors. part one explored corre...

A detailed study of an S = 1 2 spin ladder model is given. The ladder consists of plaquettes formed by nearest neighbor rungs with all possible SU(2)-invariant interactions. For properly chosen coupling constants, the model is shown to be integrable in the sense that the quantum YangBaxter equation holds and one has an infinite number of conserved quantities. The R-matrix and L-operator associa...