相关论文: Media theory: representations and examples

We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute…

Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…

We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making…

Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…

We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of $U(1)$ groups and look for representations by probability distributions on the…

We consider the description of the fractal media that uses the fractional integrals. We derive the fractional generalizations of the equation that defines the medium mass. We prove that the fractional integrals can be used to describe the…

We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb…

This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple…

We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing…

In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…

These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…

As the world's democratic institutions are challenged by dissatisfied citizens, political scientists and also computer scientists have proposed and analyzed various (innovative) methods to select representative bodies, a crucial task in…

This work analyses main features that should be present in knowledge representation. It suggests a model for representation and a way to implement this model in software. Representation takes care of both low-level sensor information and…

Adaptive behavior often requires predicting future events. The theory of reinforcement learning prescribes what kinds of predictive representations are useful and how to compute them. This paper integrates these theoretical ideas with work…

As the intermediate-level representations bridging the two levels, structured representations of visual scenes, such as visual relationships between pairwise objects, have been shown to not only benefit compositional models in learning to…

News entities must select and filter the coverage they broadcast through their respective channels since the set of world events is too large to be treated exhaustively. The subjective nature of this filtering induces biases due to, among…

Few, if any, applications of quantum technology are as widely known as the quantum simulation of quantum matter. Consequently, many interesting questions have been sparked at the intersection of condensed matter, quantum chemistry, and…

The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…

Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00] (which correspond to the case where H is…

This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…