Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Institution
- Publication
- Publication Type
Articles 1 - 6 of 6
Full-Text Articles in Algebraic Geometry
From Mathematics To Medicine: A Practical Primer On Topological Data Analysis (Tda) And The Development Of Related Analytic Tools For The Functional Discovery Of Latent Structure In Fmri Data, Andrew Salch, Adam Regalski, Hassan Abdallah, Raviteja Suryadevara, Michael J. Catanzaro, Vaibhav A. Diwadkar
From Mathematics To Medicine: A Practical Primer On Topological Data Analysis (Tda) And The Development Of Related Analytic Tools For The Functional Discovery Of Latent Structure In Fmri Data, Andrew Salch, Adam Regalski, Hassan Abdallah, Raviteja Suryadevara, Michael J. Catanzaro, Vaibhav A. Diwadkar
Mathematics Faculty Research Publications
fMRI is the preeminent method for collecting signals from the human brain in vivo, for using these signals in the service of functional discovery, and relating these discoveries to anatomical structure. Numerous computational and mathematical techniques have been deployed to extract information from the fMRI signal. Yet, the application of Topological Data Analyses (TDA) remain limited to certain sub-areas such as connectomics (that is, with summarized versions of fMRI data). While connectomics is a natural and important area of application of TDA, applications of TDA in the service of extracting structure from the (non-summarized) fMRI data itself are heretofore nonexistent. …
The Adams Spectral Sequence For Topological Modular Forms, Robert Bruner, John Rognes
The Adams Spectral Sequence For Topological Modular Forms, Robert Bruner, John Rognes
Mathematics Faculty Research Publications
The connective topological modular forms spectrum, 𝑡𝑚𝑓, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of 𝑡𝑚𝑓 and several 𝑡𝑚𝑓-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account …
Integer Optimization And Computational Algebraic Topology, Bala Krishnamoorthy
Integer Optimization And Computational Algebraic Topology, Bala Krishnamoorthy
Systems Science Friday Noon Seminar Series
We present recently discovered connections between integer optimization, or integer programming (IP), and homology. Under reasonable assumptions, these results lead to efficient solutions of several otherwise hard-to-solve problems from computational topology and geometric analysis. The main result equates the total unimodularity of the boundary matrix of a simplicial complex to an algebraic topological condition on the complex (absence of relative torsion), which is often satisfied in real-life applications . When the boundary matrix is totally unimodular, the problem of finding the shortest chain homologous under Z (ring of integers) to a given chain, which is inherently an integer program, can …
An Investigation Of Kurosh's Theorem, Keith Anthony Earl
An Investigation Of Kurosh's Theorem, Keith Anthony Earl
Theses Digitization Project
The purpose of this project will be an exposition of the Kurosh Theorem and the necessary and suffcient condition that A must be algebraic and satisfy a P.I. to be locally finite.
The Fundamental Group And Van Kampen's Theorem, Aaron Christopher Thomas
The Fundamental Group And Van Kampen's Theorem, Aaron Christopher Thomas
Theses Digitization Project
This thesis deals with the field of algebraic topology. Basic topological facts are addressed including open and closed sets, continuity, homeomorphisms, and path connectedness as well as discussing Van Kampen's Theorem in detail.
The Universal Coefficient Theorem For Cohomology, Michael Anthony Rosas
The Universal Coefficient Theorem For Cohomology, Michael Anthony Rosas
Theses Digitization Project
This project is an expository survey of the Universal Coefficient Theorem for Cohomology. Algebraic preliminaries, homology, and cohomology are discussed prior to the proof of the theorem.