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Articles 1 - 9 of 9
Full-Text Articles in Other Mathematics
An Explicit Construction Of Sheaves In Context, Tyler A. Bryson
An Explicit Construction Of Sheaves In Context, Tyler A. Bryson
Dissertations, Theses, and Capstone Projects
This document details the body of theory necessary to explicitly construct sheaves of sets on a site together with the development of supporting material necessary to connect sheaf theory with the wider mathematical contexts in which it is applied. Of particular interest is a novel presentation of the plus construction suitable for direct application to a site without first passing to the generated grothendieck topology.
Sl(2,Z) Representations And 2-Semiregular Modular Categories, Samuel Nathan Wilson
Sl(2,Z) Representations And 2-Semiregular Modular Categories, Samuel Nathan Wilson
LSU Doctoral Dissertations
We address the open question of which representations of the modular group SL(2,Z) can be realized by a modular category. In order to investigate this problem, we introduce the concept of a symmetrizable representation of SL(2,Z) and show that this property is necessary for the representation to be realized. We then prove that all congruence representations of SL(2,Z) are symmetrizable. The proof involves constructing a symmetric basis, which greatly aids in further calculation. We apply this result to the reconstruction of modular category data from representations, as well as to the classification of semiregular categories, which are defined via an …
Categorical Aspects Of Graphs, Jacob D. Ender
Categorical Aspects Of Graphs, Jacob D. Ender
Undergraduate Student Research Internships Conference
In this article, we introduce a categorical characterization of directed and undirected graphs, and explore subcategories of reflexive and simple graphs. We show that there are a number of adjunctions between such subcategories, exploring varying combinations of graph types.
At The Interface Of Algebra And Statistics, Tai-Danae Bradley
At The Interface Of Algebra And Statistics, Tai-Danae Bradley
Dissertations, Theses, and Capstone Projects
This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals …
Logic -> Proof -> Rest, Maxwell Taylor
Logic -> Proof -> Rest, Maxwell Taylor
Senior Independent Study Theses
REST is a common architecture for networked applications. Applications that adhere to the REST constraints enjoy significant scaling advantages over other architectures. But REST is not a panacea for the task of building correct software. Algebraic models of computation, particularly CSP, prove useful to describe the composition of applications using REST. CSP enables us to describe and verify the behavior of RESTful systems. The descriptions of each component can be used independently to verify that a system behaves as expected. This thesis demonstrates and develops CSP methodology to verify the behavior of RESTful applications.
Mathematical Frameworks For Consciousness, Menas C. Kafatos, Ashok Narasimhan
Mathematical Frameworks For Consciousness, Menas C. Kafatos, Ashok Narasimhan
Mathematics, Physics, and Computer Science Faculty Articles and Research
If Awareness is fundamental in the universe, mathematical frameworks are better suited to reveal its fundamental aspects than physical models. Awareness operates through three fundamental laws which apply at all levels of reality and is characterized by three universal powers. We explore and summarize in general terms mathematical formalisms that may take us as close as possible to conscious awareness, beginning with the primary relationships between the observer with the observed, using a Hilbert space approach. We also examine insights from category theory, and the calculus of indications or laws of forms. Mathematical frameworks as fundamental languages of our interaction …
Coalgebraic Semantics Of Reflexive Economics (Dagstuhl Seminar 15042), Samson Abramsky, Alexander Kurz, Pierre Lescanne, Viktor Winschel
Coalgebraic Semantics Of Reflexive Economics (Dagstuhl Seminar 15042), Samson Abramsky, Alexander Kurz, Pierre Lescanne, Viktor Winschel
Engineering Faculty Articles and Research
This report documents the program and the outcomes of Dagstuhl Seminar 15042 “Coalgebraic Semantics of Reflexive Economics”.
Diamond Semiotic Short Studies, Rudolf Kaehr
Diamond Semiotic Short Studies, Rudolf Kaehr
Rudolf Kaehr
A collection of papers on semiotics, polycontexturality and diamond theory
Double Cross Playing Diamonds, Rudolf Kaehr
Double Cross Playing Diamonds, Rudolf Kaehr
Rudolf Kaehr
Understanding interactivity in/between bigraphs and diamonds Grammatologically, the Western notational system is not offering space in itself to place sameness and otherness necessary to realize interaction/ality. Alphabetism is not prepared to challenge the dynamics of interaction directly. The Chinese writing system in its scriptural structuration, is able to place complex differences into itself, necessary for the development and design of formal systems and programming languages of interaction. The challenge of interactionality to Western thinking, modeling and design interactivity has to be confronted with the decline of the scientific power of alpha-numeric notational systems as media of living in a complex …