Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Algorithm (1)
- Automatic calculation (1)
- Biophysics (1)
- Category theory (1)
- Causal inference (1)
-
- Complexity (1)
- Composition identities (1)
- Computation of coefficient (1)
- Diffeological spaces (1)
- Differential equation (1)
- Functional connectivity (1)
- Gauss composition (1)
- Generating function (1)
- Geometry (1)
- Higher composition laws (1)
- Identity proof (1)
- Integral equation (1)
- Large cardinals (1)
- Maximality principle (1)
- Neuroscience (1)
- Parabolicity (1)
- Polynomial (1)
- Problem solving (1)
- Quadratic rings (1)
- Root-finding (1)
- Spike trains (1)
- Subdivision (1)
- Sumudu transform (1)
- Surfaces (1)
- Publication Type
Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Higher Diffeology Theory, Emilio Minichiello
Higher Diffeology Theory, Emilio Minichiello
Dissertations, Theses, and Capstone Projects
Finite dimensional smooth manifolds have been studied for hundreds of years, and a massive theory has been built around them. However, modern mathematicians and physicists are commonly dealing with objects outside the purview of classical differential geometry, such as orbifolds and loop spaces. Diffeology is a new framework for dealing with such generalized smooth spaces. This theory (whose development started in earnest in the 1980s) has started to catch on amongst the wider mathematical community, thanks to its simplicity and power, but it is not the only approach to dealing with generalized smooth spaces. Higher topos theory is another such …
Bifurcations And Resultants For Rational Maps And Dynatomic Modular Curves In Positive Characteristic, Colette Lapointe
Bifurcations And Resultants For Rational Maps And Dynatomic Modular Curves In Positive Characteristic, Colette Lapointe
Dissertations, Theses, and Capstone Projects
No abstract provided.
Sigma_N-Correct Forcing Axioms, Benjamin P. Goodman
Sigma_N-Correct Forcing Axioms, Benjamin P. Goodman
Dissertations, Theses, and Capstone Projects
I introduce a new family of axioms extending ZFC set theory, the Sigma_n-correct forcing axioms. These assert roughly that whenever a forcing name a' can be forced by a poset in some forcing class Gamma to have some Sigma_n property phi which is provably preserved by all further forcing in Gamma, then a' reflects to some small name such that there is already in V a filter which interprets that small name so that phi holds. Sigma_1-correct forcing axioms turn out to be equivalent to classical forcing axioms, while Sigma_2-correct forcing axioms for Sigma_2-definable forcing classes are consistent relative to …
Explicit Composition Identities For Higher Composition Laws In The Quadratic Case, Ajith A. Nair
Explicit Composition Identities For Higher Composition Laws In The Quadratic Case, Ajith A. Nair
Dissertations, Theses, and Capstone Projects
The theory of Gauss composition of integer binary quadratic forms provides a very useful way to compute the structure of ideal class groups in quadratic number fields. In addition to that, Gauss composition is also important in the problem of representations of integers by binary quadratic forms. In 2001, Bhargava discovered a new approach to Gauss composition which uses 2x2x2 integer cubes, and he proved a composition law for such cubes. Furthermore, from the higher composition law on cubes, he derived four new higher composition laws on the following spaces - 1) binary cubic forms, 2) pairs of binary quadratic …
Parabolic And Non-Parabolic Surfaces With Small Or Large End Spaces Via Fenchel-Nielsen Parameters, Michael Antony Pandazis
Parabolic And Non-Parabolic Surfaces With Small Or Large End Spaces Via Fenchel-Nielsen Parameters, Michael Antony Pandazis
Dissertations, Theses, and Capstone Projects
We consider conditions on the Fenchel-Nielsen parameters of a Riemann surface X that determine whether or not a surface X is parabolic. Fix a geodesic pants decomposition of a surface and call the boundary geodesics in the decomposition cuffs. For a zero or half-twist flute surface, we prove that parabolicity is equivalent to the surface having a covering group of the first kind. Using that result, we give necessary and sufficient conditions on the Fenchel-Nielsen parameters of a half-twist flute surface X with increasing cuff lengths such that X is parabolic. As an application, we determine whether or not each …
Me And Mathematics: “Doing What You’Re Talking About”: In Dialogue With My Family, Eden Morris
Me And Mathematics: “Doing What You’Re Talking About”: In Dialogue With My Family, Eden Morris
Dissertations, Theses, and Capstone Projects
This paper is a philosophically oriented accompaniment to my audio project (accessible through the following link: https://cuny.manifoldapp.org/projects/me-and-mathematics). Working together, the paper and audio collages form a call to action and a resource. My primary finding is the importance of doing what you’re talking about or exploring and implementing your ideas experientially. Doing what you’re talking about is important for effective teaching/learning and feeling in line with oneself. This working concept came to my attention during my research conversation with my oldest living relative, and then, again, with my youngest (non-baby) relative. This doing what you’re talking about is a way …
New Effective Transformational Computational Methods, Jun Zhang, Ruzong Fan, Fangyang Shen, Junyi Tu
New Effective Transformational Computational Methods, Jun Zhang, Ruzong Fan, Fangyang Shen, Junyi Tu
Publications and Research
Mathematics serves as a fundamental intelligent theoretic basis for computation, and mathematical analysis is very useful to develop computational methods to solve various problems in science and engineering. Integral transforms such as Laplace Transform have been playing an important role in computational methods. In this paper, we will introduce Sumudu Transform in a new computational approach, in which effective computational methods will be developed and implemented. Such computational methods are straightforward to understand, but powerful to incorporate into computational science to solve different problems automatically. We will provide computational analysis and essentiality by surveying and summarizing some related recent works, …
New Algorithmic Support For The Fundamental Theorem Of Algebra, Vitaly Zaderman
New Algorithmic Support For The Fundamental Theorem Of Algebra, Vitaly Zaderman
Dissertations, Theses, and Capstone Projects
Univariate polynomial root-finding is a venerated subjects of Mathematics and Computational Mathematics studied for four millenia. In 1924 Herman Weyl published a seminal root-finder and called it an algorithmic proof of the Fundamental Theorem of Algebra. Steve Smale in 1981 and Arnold Schonhage in 1982 proposed to classify such algorithmic proofs in terms of their computational complexity. This prompted extensive research in 1980s and 1990s, culminated in a divide-and-conquer polynomial root-finder by Victor Pan at ACM STOC 1995, which used a near optimal number of bit-operations. The algorithm approximates all roots of a polynomial p almost as fast as one …
A Causal Inference Approach For Spike Train Interactions, Zach Saccomano
A Causal Inference Approach For Spike Train Interactions, Zach Saccomano
Dissertations, Theses, and Capstone Projects
Since the 1960s, neuroscientists have worked on the problem of estimating synaptic properties, such as connectivity and strength, from simultaneously recorded spike trains. Recent years have seen renewed interest in the problem coinciding with rapid advances in experimental technologies, including an approximate exponential increase in the number of neurons that can be recorded in parallel and perturbation techniques such as optogenetics that can be used to calibrate and validate causal hypotheses about functional connectivity. This thesis presents a mathematical examination of synaptic inference from two perspectives: (1) using in vivo data and biophysical models, we ask in what cases the …