Events
Department of Mathematics and Statistics
Texas Tech University
We formulate and analyze a differential equation model for the population dynamics of feral cats. The model includes three categories: kittens, adult females, and adult males. Feral cats are subject to various animal control measures including impounding, adoption, and euthanasia. The feral cat population also interacts with a fixed population of domestic house cats, some of which experience abandonment. We attempt to classify all equilibrium points and describe their stability.
The Biomath seminar may be attended Monday the 4th at 4:00 PM CDT (UT-5) via this Zoom link. Meeting ID: 839 9465 7333 Passcode: BfriM6
Nematic liquid crystals consist of aggregates of rodlike molecules with orientational ordering, that is described through a unit vector n, called the director. In statics, the typical problem for nematics is to determine the vector field n in a spatial domain, which can be affected by either external actions or boundary conditions. Within the variational approach an energy functional, dependent on n and on its gradient, is minimized according to the boundary conditions. When nematics are confined on curved surfaces, the director field is influenced by both geometrical and topological constraints. To determine the nematic alignment on a surface it is more convenient to deal with an effective functional defined on the surface itself rather than in a spatial domain.
In this talk we will discuss how, naively (but not too naively), this effective functional can be obtained. We will compare the classical two-dimensional model with our revised one and show how the nematic texture is affected by both intrinsic and extrinsic surface curvature. We will illustrate both examples where the surface is fixed and others where the surface is deformable.
With reference to deformable surfaces, we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive.
Watch online via this Zoom link.
Let $\mathfrak{p}$ be a prime ideal in a commutative noetherian ring
$R$. We show that if an $R$-module $M$ satisfies
$\mathrm{Ext}_R^{n+1}(k(\mathfrak{p}),M)=0$ for some
$n\geq\mathrm{dim}\;R$, where $k(\mathfrak{p})$ is the residue field
at $\mathfrak{p}$, then $\mathrm{Ext}^i_R(k(\mathfrak{p}),M)=0$ holds
for all $i>n$. This is an improvement of a result of Christensen,
Iyengar and Marley. Similar improvements concerning homological
dimensions and the rigidity of Tors are proved. The main tool that we
use to provide these improvements is the existence of minimal
semi-flat-cotorsion replacements.
Join Zoom Meeting https://texastech.zoom.us/j/97115201141?pwd=N0YwcDkzTDc4bC9JYS9kVFQ1bFh2UT09
Meeting ID: 971 1520 1141
Passcode: 900450
We will discuss how to define the AKSZ theory as a fully extended functorial field theory using the geometric cobordism hypothesis.Asset-specific factors have been widely used to explain financial returns and measure asset-specific risk premia.
We employ these factors in various machine learning models to measure sector risk premia.
First, we make a comparison of the prediction of different models and demonstrate large economic gains from
using machine learning for sector forecasting.
Second, we develop an ensemble algorithm that combines different models based on the history of their risk premia
prediction performance, and we prove that the prediction accuracy of the resulting meta-algorithm is not much
worse than the prediction accuracy of an infeasible optimal ensemble.
The proposed ensemble achieves out-of-sample R2 of 1.54%, and the resulting meta-prediction is used in a sector
rotation investment strategy that substantially outperforms the market, individual models, and other naive ensembles.
The annual Sharpe ratio of the proposed long-short sector rotation strategy is 1.83,
and the portfolio performance survives many robustness checks against other factors and subperiods,
it does not die out in more recent years, and the strategy is profitable even at very conservative transaction cost levels.
Our results show that individual stock characteristics, when used in a well designed ensemble of machine learning algorithms,
are highly relevant for the prediction of sector risk premia, and for the construction of profitable sector rotation strategy.