Related papers: A Commentary on "Breaking Row and Column Symmetrie…

We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…

We study symmetry breaking in $Z_2$ symmetric large $N$ matrix models. In the planar approximation for both the symmetric double-well $\phi^4$ model and the symmetric Penner model, we find there is an infinite family of broken symmetry…

The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs…

We study the rank of complex sparse matrices in which the supports of different columns have small intersections. The rank of these matrices, called design matrices, was the focus of a recent work by Barak et. al. (BDWY11) in which they…

The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…

The planar grasshopper problem, originally introduced in (Goulko & Kent 2017 Proc. R. Soc. A 473, 20170494), is a striking example of a model with long-range isotropic interactions whose ground states break rotational symmetry. In this work…

In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov's regularization. In the regularization process, we convert the ill-posed system to a well-posed system. The…

This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…

The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case,…

The special features of CP violation in the Standard Model are presented. The significance of measuring CP violation in B, K and D decays is explained. The predictions of the Standard Model for CP asymmetries in B decays are analyzed in…

Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…

We present a pedagogical introduction to supersymmetry and supersymmetric models and give an overview of the potential of the linear collider for studying them. If supersymmetry is found, its discovery will bring with it many more questions…

This paper proposes a Matrix Error Correction Model to identify cointegration relations in matrix-valued time series. We hereby allow separate cointegrating relations along the rows and columns of the matrix-valued time series and use…

We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two…

In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.

We report here an extension of a previous work in which we have shown that matrix models provide a tool to compute the intersection numbers of p-spin curves. We discuss further an extension to half-integer p, and in more details for p=1/2…

In this paper, we study pattern matching in the set F_{n,k} of fillings of the k x n rectangle with the integers 1,...,kn such that the elements in any column increase from bottom to top. Let P be a column strict tableau of shape 2^k. We…

The cutting plane approach to optimal matchings has been discussed by several authors over the past decades (e.g., Padberg and Rao '82, Grotschel and Holland '85, Lovasz and Plummer '86, Trick '87, Fischetti and Lodi '07) and its…

In constraint programming and related paradigms, a modeller specifies their problem in a modelling language for a solver to search and return its solution(s). Using high-level modelling languages such as Essence, a modeller may express…