Events
Department of Mathematics and Statistics
Texas Tech University
Progress continues in the unification and extension of discrete and continuous analysis since Stefan Hilger’s landmark paper in 1988. The general idea is to prove a result once for a dynamic equation where the unknown function’s domain is a time scale T, which is an arbitrary, nonempty, closed subset of the real numbers.
A few years ago, I changed the direction of my research, focusing on more applied problems instead of theoretical ones. Of particular interest are issues arising in mathematical biology. While infusing an introduction to the time scales theory, in this talk, we use dynamic equations on time scales to model intermittent androgen deprivation (IAD) therapy. Our approach is novel since time scales combine continuous and discrete time and have not been used to model IAD therapy. Traditionally, continuous ordinary differential equations are used to estimate prostate-specific antigen levels, which are used to determine the timing of a pause in IAD treatment. In this work, we use dynamic equations to estimate prostate-specific antigen levels and construct a time scale model to account for continuous and discrete time simultaneously. We discuss preliminary results on the development of specific models and present the next steps.
We conclude the talk with activities related to my service mission.
Dr. Raegan Higgins' Tenure and Promotion Colloquium has been archived in the Mediasite catalog.
Linear algebra plays a central role in scientific computing. My research in numerical linear algebra is centered around preconditioning, which is a key to the performance of iterative solvers for systems of linear equations. In this talk, I will discuss a few recent research projects. The first is in preconditioning for implicit Runge-Kutta (IRK) methods. IRK methods have attractive stability properties, but until recently have not been used frequently due to challenges in solving the resulting linear systems. I will present some recent results, an analysis of the preconditioners via eigenvalues and field of values and preliminary results from a new optimized preconditioner.
In addition, I will briefly describe two other projects. One is using machine learning algorithms to improve preconditioners, and the other is in simulation and machine learning for classification of skeletal trauma.
Dr. Victoria Howle's Tenure and Promotion Colloquium has been archived in the Mediasite catalog.
A classical result, at the interface between harmonic analysis and partial differential equations, asserts that the $L^p$-Dirichlet problem for the Laplacian is well posed in the upper half-space. In fact, the same is true for constant coefficient homogeneous second-order systems satisfying the Legendre-Hadamard
(strong) ellipticity condition. In my talk I will show that this well-posedness result may fail if the system in question is assumed to be only weakly elliptic (i.e., its characteristic matrix is merely invertible rather than strictly positive definite). In fact, the aforementioned failure is at a fundamental level, in the sense that there exist weakly elliptic systems for which the $L^p$-Dirichlet problem in the upper half-space is not even Fredholm solvable.
Ghost ideals were firstly introduced by Dan Christensen in the stable
homotopy category. We will present an abelian version of the ghost
ideal associated to a class of objects. Then we study powers of the
ghost ideal and show that, under mild assumptions, any (finite or
infinite) power of a ghost ideal appears as the half of a complete
ideal cotorsion pair, and in fact, it agrees with a nice complete
cotorsion pair of objects for some infinite inductive power.
Applications will be given in the category of modules and unbounded
chain complexes of modules.
The talk is based on a work in progress with XianHui Fu, Ivo Herzog
and Sinem Odabasi
Join Zoom Meeting https://texastech.zoom.us/j/91729629174?pwd=TFJHbDk1ZS9KeTBRaldNL1hUbVNlQT09
Meeting ID: 971 2962 9174
Passcode: 914040
Environmental, Social, and Governance (ESG) scores measure companies' performance
concerning sustainability and societal impact and are organized on three pillars:
Environmental (E), Social (S), and Governance (G).
These complementary non-financial ESG scores should provide information about the ESG performance and
risks of different companies.
However, the extent of not yet published ESG information makes the reliability of ESG scores questionable.
To explicitly denote the not yet published information on ESG category scores, a new pillar,
the so-called Missing (M) pillar, is formulated. Environmental, Social, Governance, and Missing (ESGM)
scores are introduced to consider the potential release of new information in the future.
Furthermore, an optimization scheme is proposed to compute ESGM scores, linking them to the companies'
riskiness.
By relying on the data provided by Refinitiv, we show that the ESGM scores strengthen the companies'
risk relationship.
These new scores could benefit investors and practitioners as ESG exclusion strategies using only
ESG scores might exclude assets with a low score solely because of their missing information and
not necessarily because of a low ESG merit.