Related papers: Complete integrability versus symmetry

Ichikawa et al. [Phys. Rev. A 78, 052105 (2008)] showed that exchange symmetry gives rise to simple characterization of whether multipartite pure quantum states being either globally entangled or fully separable. In this Brief Report, we…

We give an elementary and constructive proof for a theorem of de Smit et Lenstra. Note: In version 1, was missing the proof that "completely secant" implies "1-secant"

We give a definition of thickness in $\mathbb{R}^d$ that is useful even for totally disconnected sets, and prove a Gap Lemma type result. We also guarantee an interval of distances in any direction in thick compact sets, relate thick sets…

The results of this paper have been greatly superseded by those in the paper "Contact geometry and isosystolic inequalities" (arXiv:1109.4253) by the same authors.

We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might…

The goal of this survey is to give a list of resent results about topology of manifolds admitting different metrics with the same geodesics. We emphasize the role of the theory of integrable systems in obtaining these results.

We address a problem posed in [1] by demonstrating through an example that, in the absence of separability, the property of sequential cone compactness does not generally imply cone compactness.

The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.

A ring with a test module of finite upper complete intersection dimension is complete intersection.

Enforcing exact symmetry in machine learning models often yields significant gains in scientific applications, serving as a powerful inductive bias. However, recent work suggests that relying on approximate symmetry can offer greater…

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.

The regular autonomous asynchronous systems are the non-deterministic Boolean dynamical systems and universality means the greatest in the sense of the inclusion. The paper gives four definitions of symmetry of these systems in a slightly…

We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…

In this paper we solve in the positive the question of whether any finite set of integers, containing the zero, is the mapping degree set between two oriented closed connected manifolds of the same dimension. We extend this question to the…

We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…

In this paper we give a generalization of the normal holomorphic frames in the symplectic manifolds and find conditions for the integrability of complex structures.

We construct a De Morgan algebra-valued logic with quantifiers, where the truth values are in a finite De Morgan algebra, We show that there is a representation theorem of the cylindric algebra of this logic from which a completeness…

In this paper, we explore the relationship between integrability and the discrete holomorphicity of a class of complex lattice observables in the context of the Potts dense loop model and the O(n) dilute loop model. It is shown that the…

Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer…

In this paper we investigate possible extensions of the idea of geodesic completeness in complex manifolds, following two directions: metrics are somewhere allowed not to be of maximum rank, or to have 'poles' somewhere else. Geodesics are…