Related papers: Euclidean lattices: theory and applications

This talk is a brief summary of some theoretical issues in the field of hot and dense QCD matter and ultra-relativistic heavy ion collisions.

This article examines recent research in molecular communications from a telecommunications system design perspective. In particular, it focuses on channel models and state-of-the-art physical layer techniques. The goal is to provide a…

Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…

Objective: Translational science aims at "translating" basic scientific discoveries into clinical applications. The identification of translational science has practicality such as evaluating the effectiveness of investments made into large…

The present article studies combinatorial tilings of Euclidean or spherical spaces by polytopes, serving two main purposes: first, to survey some of the main developments in combinatorial space tiling; and second, to highlight some new and…

This is the first paper in a series in which we lay down the foundations of the theory of interpretations. We systematically study different types of interpretations and their properties. Some of these interpretations are known, while…

Lattices and periodic point sets are well known objects from discrete geometry. They are also used in crystallography as one of the models of atomic structure of periodic crystals. In this paper we study the embedding properties of spaces…

We review some of the recent progress in our understanding of the physics of ultrarelativistic heavy ion collisions due to applications of AdS/CFT correspondence.

Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…

This article is devoted to the tactical game theoretical interpretation of dialectics. Dialectical games are considered as abstractly as well as models of the internal dialogue and reflection. The models related to the representation theory…

We show that the transition laws for a 2-connection can be recovered by discretizing the base 2-space of a 2-bundle into an Euclidean hypercubic lattice. The aim of this work is to serve as an example of how important results in higher…

This paper investigates the theory of lattices, focusing on extending lattices relative to abstract classes, modular lattices, and torsion lattices. Definitions of type-1 and type-2 extending lattices are provided, along with their weakly…

Finite fields form an important chapter in abstract algebra, and mathematics in general. We aim to provide a geometric and intuitive model for finite fields, involving algebraic numbers, in order to make them accessible and interesting to a…

The aims of this letter are three-fold: First is to show that nonlinear generalizations of electrodynamics support various types of knotted solutions in vacuum. The solutions are universal in the sense that they do not depend on the…

This work analyzes the difficulties in learning and teaching Einstein's theory of special relativity. An extensive bibliographic review has been performed, considering articles published in the most relevant journals on science education,…

We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…

This paper fires the opening salvo in the systematic construction of the lattice-continuum correspondence, a precise dictionary that describes the emergence of continuum quantum theories from finite, nonperturbatively defined models…

These lectures about lattice field theory were written for, and given at, TASI 2019, ``The many dimensions of quantum field theory.'' The students at this TASI were mostly interested in formal things, and so these are slightly unusual…

The objective of this work is to provide a general introduction into the symmetry analysis of the rachet effect using a simple, non-interacting one-particle dynamics. Despite its simplicity, this model contains all the basic aspects of…

This article gives a brief survey of the theory and applications of anomalies.