Events
Department of Mathematics and Statistics
Texas Tech University
A semidualizing module is a generalization of Grothendieck's dualizing
module. For a local Cohen-Macaulay ring \(R\), the ring itself and its
canonical module are always realized as (trivial) semidualizing
modules. In this talk, we discuss the existence of nontrivial
semidualizing modules over numerical semigroup rings. We review the
techniques that allow us to completely classify which of these rings,
up to multiplicity 9, possess a nontrivial semidualizing module. We
will end with a construction that allows us to extend our results to
higher multiplicity. This is joint work with Ela Celikbas (West
Virginia University) and Toshinori Kobayashi (Meiji University).
Follow the talk via this Zoom link
Meeting ID: 913 0074 4693
Passcode: 586188
The assumption of second-order stationarity is important in time series modeling. A new method is proposed to check whether a nonlinear time series is second-order stationary. The new test relies on blocks-of-blocks bootstrap covariance matrix estimates and Walsh transformations to capture the nonlinear features of time series data. The asymptotic normality of the Walsh coefficients and their asymptotic covariance matrix under the null hypothesis is derived for nonlinear processes. Additionally, the asymptotic covariance matrix in an increasing dimension is consistently estimated using a blocks-of-blocks bootstrap procedure. In the framework of locally stationary nonlinear processes, it is demonstrated that the proposed test remains consistent under a sequence of local alternatives. A simulation study is conducted to examine the finite sample performance of the procedure. For many nonlinear time series, the proposed test performs well, whereas existing methods may exhibit highly inflated type I error rates. The proposed test is applied to an analysis of a financial data set.
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday the 2nd via this Zoom link.
Meeting ID: 984 8380 7557
Passcode: 363729
This is part 1 of a 2-part talk. The task of modelling and forecasting a dynamical system is one of the oldest problems. Broadly, this task has two subtasks- extracting the full dynamical information from a partial observation; and then explicitly learning the dynamics from this information. These two subtasks can be combined into a single mathematical framework using the language of spaces, maps, and commutations. The framework also unifies two of the most common learning paradigms- delay coordinates and reservoir computing. This framework provides a platform for two other investigations of the reconstructed system- its dynamical stability; and the growth of error under iterations. We show that these questions are deeply tied to more fundamental properties of the underlying system the behavior of matrix cocycles over the base dynamics, its non-uniform hyperbolic behavior, and properties of its Koopman operator. Co-author : Tyrus Berry, George Mason University Paper.
Tables, Arrays, and Matrices are useful in data storage and manipulation, employing operations and methods from Numerical Linear Algebra for computer algorithm development. Recent advances in computer hardware and high performance computing invite us to explore more advanced data structures, such as sheaves and the use of sheaf operations for more sophisticated computations. Abstractly, Mathematical Sheaves can be used to track data associated to the open sets of a topological space; practically, sheaves as an advanced data structure provide a framework for the manipulation and optimization of complex systems of interrelated information. Do we ever really get to see a concrete example? I will point to several recent examples of (1) the use of sheaves as a tool for data organization, and (2) the use of sheaves to gain additional information about a system.Abstract. During this talk I will introduce and compare several finite element numerical schemes to approximate a chemo-attraction model with consumption effects, which is a nonlinear parabolic system for two variables; the cell density and the concentration of the chemical signal that the cell feel attracted to. I will detail the main properties of each scheme, such as conservation of cells, energy-stability and approximated positivity. Moreover, I will present numerical results to illustrate the efficiency of each of the schemes and to compare them with others classical schemes. This contribution is based on a joint work with Francisco Guillén-Gonzaléz (Universidad de Sevilla,
Spain).
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 968 6501 7586
* Passcode: Applied
 | Wednesday
Oct. 4
7 PM
MA 108
|
| Mathematics Education
Math Circle
Aaron Tyrrell
Department of Mathematics and Statistics, Texas Tech University
|
Math Circle Fall Poster
The word “Topology”, best known for its association to the study of invariants of an abstract space, is a branch of Pure Mathematics whose best known applications are found in Physics (Quantum Mechanics, Quantum Field Theory). Very rarely does a Pure Math Field find such as Topology find relevance in a world of Big Data and computer automation. Data Science utilizes these powerful topological invariants to quickly gather information about complex data spaces in a brave new area of study called “Topological Data Analysis” or TDA. Given a set of data points, the nerve construction produces a simplicial complex that can be analyzed to understand important characteristics of the data. I will provide an introduction to TDA and a few examples of surprising Data Science applications.We continue our discussion with an example of “Path-Optimization Sheaves” (https://arxiv.org/abs/2012.05974); an alternative approach to classical Dijkstra’s Algorithm, paths from a source vertex to sink vertex in a graph are revealed as Sections of the Path-finding Sheaf.Quasiperiodically driven dynamical systems are nonlinear systems which are driven by some periodic source with multiple base-frequencies. Such systems abound in nature, and are present in data collected from sources such as astronomy and traffic data. Such dynamics decomposes into two components - the driving quasiperiodic source with generating frequencies; and the driven nonlinear dynamics. Analysis of the quasiperiodic part presents the same challenges as classical Harmonic analyis. On the other hand, the nonlinear part bears all the aspects of chaotic dynamics, and possibly carry stochastic perturbations. We present a kernel-based method which provides a robust means to learn both these components. It uses a combination of a kernel based Harmonic analysis and kernel based interpolation technique, to discover these two parts. The technique performs reliably in several real world systems, ranging from analyzing the human heart to traffic data.
abstract 2 PM CDT (UT-5)