相关论文: Breaking Symmetry with Different Orderings

Modeling symmetry breaking is essential for understanding the fundamental changes in the behaviors and properties of physical systems, from microscopic particle interactions to macroscopic phenomena like fluid dynamics and cosmic…

A growing body of experimental work suggests that magic angle twisted bilayer graphene exhibits a "cascade" of spontaneous symmetry breaking transitions, sparking interest in the potential relationship between symmetry-breaking and…

Whether language models can systematically generalize remains actively debated. Yet empirical performance is jointly shaped by multiple factors such as training data, training paradigms, and inference-time strategies, making failures…

We define a new lattice structure on the elements of a finite Coxeter group W. This lattice, called the shard intersection order, is weaker than the weak order and has the noncrossing partition lattice NC(W) as a sublattice. The new…

In this paper two important aspects related to Caputo fractional-order discrete variant of a class of maps defined on the complex plane, are analytically and numerically revealed: attractors symmetry-broken induced by the fractional-order…

Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables. An "optimal (or simplest) canonical form" of linear…

The study of linear codes over a finite field of odd cardinality, derived from determinantal varieties obtained from symmetric matrices of bounded rank, was initiated in a recent paper by the authors. There, one found the minimum distance…

Symmetry in integer programming causes redundant search and is often handled with symmetry breaking constraints that remove as many equivalent solutions as possible. We propose an algebraic method which allows to generate a random family of…

We consider the ground state of a one-dimensional critical quantum system carrying a global symmetry in the bulk, which is explicitly broken by its boundary conditions. We probe the system via a string-order parameter, showing how it…

The supersymmetry preserving mu parameter in SUSY theories is naively expected to be of order the Planck scale while phenomenology requires it to be of order the weak scale. This is the famous SUSY mu problem. Its solution involves two…

A Locally Checkable Labeling (LCL) is a specification describing a set of labels that are valid with respect to a set of conditions that characterize a local part of a solution to a global problem. Conditions can only refer to nodes and…

The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…

We investigate supersymmetry (SUSY) breaking scenarios where both SUSY and Lorentz symmetry are broken spontaneously. For concreteness, we propose models in which scalar fluid or vector condensation breaks Lorentz symmetry and accordingly…

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum…

We consider the problem of optimally insulating a given domain $\Omega$ of ${\mathbb{R}}^d$; this amounts to solve a nonlinear variational problem, where the optimal thickness of the insulator is obtained as the boundary trace of the…

Lexicographical sorting is a fundamental problem with applications to contingency tables, databases, Bayesian networks, and more. A standard method to lexicographically sort general data is to iteratively use a stable sort -- a sort which…

Spontaneous symmetry breaking in nonlinear systems provides a unified method to understand vastly different phenomena, ranging from Higgs mechanism [1] and superconductivity [2] to ecological stability [3] and genome generation [4].…

An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…

The Szemer\'edi Regularity Lemma, in combination with the Blow-up Lemma, form the Regularity Method, a fundamental tool in graph embeddings, albeit restricted to very large and dense graphs. We propose an alternative vertex-partitioning…

Our topic is the use of machine learning to improve software by making choices which do not compromise the correctness of the output, but do affect the time taken to produce such output. We are particularly concerned with computer algebra…