Related papers: A panorama of specification-like properties and th…

Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the…

Shape is an important feature of physical systems although very seldom it is addressed in the framework of a quantitative description approach. In this paper we propose to interpret the shape of things as a physical manifestation of the…

This paper presents an observation that under reasonable conditions, many partial differential equations from mathematical physics possess three structural properties. One of them can be understand as a variant of the celebrated Onsager…

In the context of studying string backgrounds, much work has been devoted to the question of how similar a general quantum field theory (specifically, a two-dimensional superconformal theory) is to a sigma model. Put differently, one would…

Compositionality is a widely discussed property of natural languages, although its exact definition has been elusive. We focus on the proposal that compositionality can be assessed by measuring meaning-form correlation. We analyze…

We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give…

Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of…

The Shannon entropy of a random variable has much behaviour analogous to a signed measure. Previous work has explored this connection by defining a signed measure on abstract sets, which are taken to represent the information that different…

We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a…

The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…

We introduce pointwise measure expansivity for bi-measurable maps. We show through examples that this notion is weaker than measure expansivity. In spite of this fact, we show that many results for measure expansive systems hold true for…

As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…

This lecture provides an overview of the principles and methodologies involved in linear optics design. It aims to introduce key concepts such as the matrix formalism, the symplecticity, the quantities that are preserved in the single…

This paper addresses how to construct features for the problem of image correspondence, in particular, the paper addresses how to construct features so as to maintain the right level of invariance versus discriminability. We show that…

This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…

The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers two related notions---$\epsilon$-approximations and…

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…

The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…

We give a notion of entropy for general gemetric structures, which generalizes well-known notions of topological entropy of vector fields and geometric entropy of foliations, and which can also be applied to singular objects, e.g. singular…

Given a feature set for the shape of a closed loop, it is natural to ask which features in that set do not change when the starting point of the path is moved. For example, in two dimensions, the area enclosed by the path does not depend on…