Related papers: What is Aperiodic Order?

This paper is simply a collection of process diagrams for further use and reference. These are diagrams about different approaches to research.

The natural order in the space of binary sequences permits to recover the $U$-sequence. Also the scaling laws of the period-doubling cascade and the intermittency route to chaos defined in that ordered set are explained. These arise as…

This is a review (in Italian) on aperiodic tilings of the plane intended for a general audience. First, we recall some basic results about lattices and periodic tilings. Then, we move on to one-dimensional (domino) tilings and Wang tilings.…

We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…

The characteristic feature of the adeles is that they involve localizations of products (or equivalently restricted products of localizations). The point of this paper is to introduce an adelic style cohomological invariant of a partially…

We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…

The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.

In directed graphs, a cycle can be seen as a structure that allows its vertices to loop back to themselves, or as a structure that allows pairs of vertices to reach each other through distinct paths. We extend these concepts to temporal…

We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite…

This report consists of two parts. The first part is a brief exposition of classical descriptive set theory. This part introduces some fundamental concepts, motivations and results from the classical theory and ends with a section on the…

A brief review of the history of the discovery of the deuteron in provided. The current status of both experiment and theory for the elastic electron scattering is then presented.

It is shown how simple assumptions lead to piecewise linear behavior, which is observed in certain phase transitions.

Various ideas associated with exotic hadrons, and hadronic structure in general, are briefly reviewed.

As a contribution to the inverse scattering problem for classical chaotic systems, we show that one can select sequences of intervals of continuity, each of which yields the information about period, eigenvalue and symmetry of one unstable…

Link prediction in graphs is a task that has been widely investigated. It has been applied in various domains such as knowledge graph completion, content/item recommendation, social network recommendations and so on. The initial focus of…

Physics of dielectric mixtures are presented to stimulate discussion and to provide information on the recent advances in this topic.

We introduce the concept of K-th order chaoticity of unitaries, and analyze it for the case of two-level quantum systems. This property is relevant in a certain quantum random number generation scheme. We show that no unitaries exist with…

This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.

We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1-D maps and possible relevance of…

This paper is an introduction to a series of papers in which we give combinatorial models for certain important operads (including A-infinity and E-infinity operads, the little n-cubes operads, and the framed little disks operad) and…