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Full-Text Articles in Physical Sciences and Mathematics
Geometry In Spectral Triples: Immersions And Fermionic Fuzzy Geometries, Luuk S. Verhoeven
Geometry In Spectral Triples: Immersions And Fermionic Fuzzy Geometries, Luuk S. Verhoeven
Electronic Thesis and Dissertation Repository
We investigate the metric nature of spectral triples in two ways.
Given an oriented Riemannian embedding i:X->Y of codimension 1 we construct a family of unbounded KK-cycles i!(epsilon), each of which represents the shriek class of i in KK-theory. These unbounded KK-cycles are further equipped with connections, allowing for the explicit computation of the products of i! with the spectral triple of Y at the unbounded level. In the limit epsilon to 0 the product of these unbounded KK-cycles with the canonical spectral triple for Y admits an asymptotic expansion. The divergent part of this expansion is known and …
Generating Polynomials Of Exponential Random Graphs, Mohabat Tarkeshian
Generating Polynomials Of Exponential Random Graphs, Mohabat Tarkeshian
Electronic Thesis and Dissertation Repository
The theory of random graphs describes the interplay between probability and graph theory: it is the study of the stochastic process by which graphs form and evolve. In 1959, Erdős and Rényi defined the foundational model of random graphs on n vertices, denoted G(n, p) ([ER84]). Subsequently, Frank and Strauss (1986) added a Markov twist to this story by describing a topological structure on random graphs that encodes dependencies between local pairs of vertices ([FS86]). The general model that describes this framework is called the exponential random graph model (ERGM).
In the past, determining when a probability distribution has strong …
Internal Yoneda Ext Groups, Central H-Spaces, And Banded Types, Jarl Gunnar Taxerås Flaten
Internal Yoneda Ext Groups, Central H-Spaces, And Banded Types, Jarl Gunnar Taxerås Flaten
Electronic Thesis and Dissertation Repository
We develop topics in synthetic homotopy theory using the language of homotopy type theory, and study their semantic counterparts in an ∞-topos. Specifically, we study Grothendieck categories and Yoneda Ext groups in this setting, as well as a novel class of central H-spaces along with their associated bands. The former are fundamental notions from homological algebra that support important computations in traditional homotopy theory. We develop these tools with the goal of supporting similar computations in our setting. In contrast, our results about central H-spaces and bands are new, even when interpreted into the ∞-topos of spaces.
In Chapter …