Events
Department of Mathematics and Statistics
Texas Tech University
Mixed-norm spaces $H(p, q, a)$ are a family of spaces of analytic functions which generalize standard weighted Bergman spaces and, as a limit case, Hardy spaces. They were introduced by Flett, but some of their properties were deduced previously by Hardy and Littlewood. The possible inclusions between them are completely characterized, but the norms of these inclusions are unknown in general. These norms, in some cases, could be of interest for other fields of Mathematics as Mathematical Physics or Number Theory.
In this talk, based on a joint work with D. Vukotic, we will show some conditions under which we are able to prove the contractivity of the inclusion (that is, when the norm of the inclusion operator is exactly 1).
To join the talk on Zoom please click
here.
A mathematical model of tumor-immune system interactions with an oncolytic virus therapy for which the immune system plays a twofold role against cancer cells is derived. The immune cells can kill cancer cells but can also eliminate viruses from the therapy. In addition, immune cells can either be stimulated to proliferate or be impaired to reduce their growth by tumor cells. It is shown that if the tumor killing rate by immune cells is above a critical value, the tumor can be eradicated for all sizes, where the critical killing rate depends on whether the immune system is immunosuppressive or proliferative. For a reduced tumor killing rate with an immunosuppressive immune system, bistability exists in a large parameter space. The tumor can either be eradicated or grow near to its carrying capacity depending on the tumor size. However, reducing the viral killing rate by immune cells always increases the effectiveness of the viral therapy. This reduction may be achieved by manipulating certain genes of viruses via genetic engineering.
 | Tuesday
Sep. 28
3:30 PM
MATH 016
|
| Real-Algebraic Geometry
Etale Space
David Weinberg
Department of Mathematics and Statistics, Texas Tech University
|
N/A
Please virtually attend this week's Statistics group seminar at 3 PM (UT-5) Wednesday via this Zoom link.
Rapid advances in artificial neural network (ANN) technology have led to promising results in scientific applications. This introductory talk reviews the basics of ANNs with emphasis on architectures which are useful for high-dimensional function approximation and the reduced-order modeling of nonlinear PDEs. Current methods for accomplishing each of these tasks are surveyed, including some of the speaker's recent work.
Please virtually attend the Applied Math seminar via this Zoom link.
We discuss a homological method for transferring algebra structure on
complexes along suitably nice homotopy equivalences. As an application
which motivated this project, we discuss how to use this method to
build a concrete permutation invariant differential graded algebra
structure on a well-known resolution. This is joint work with Claudia
Miller
Join the seminar via this
Zoom link
We establish a uniqueness result for the $[\varphi,\vec{e}_{3}]$-catenary cylinders by their asymptotic behaviour.
Well known examples of such cylinders are the grim reaper translating solitons for the mean curvature flow. For such solitons,
F. Martín, J. Pérez-García, A. Savas-Halilaj and K. Smoczyk proved that, if $\Sigma$ is a properly embedded translating soliton with
locally bounded genus, and $\mathcal{C}^{\infty}$-asymptotic to two
vertical planes outside a cylinder, then $\Sigma$ must coincide with
some grim reaper translating soliton. In this talk, applying a strong
maximum principle for elliptic operators together with a compactness
result, we increase the family of $[\varphi,\vec{e}_{3}]$-minimal
graphs
where these types of results hold under different assumption of
asymptotic behaviour.
Watch online via this Zoom link.Abstract: We introduce two new high-frequency volatility estimators that account
for possible breakpoints in the spot volatility process.
They are $\ell_1$-penalized versions of classical estimators - quadratic variation
and jump robust bipower variation.
We show that in the presence of a mean-square error of order $o_P(1)$ achieved
by these classical estimators, detecting breakpoints using the volatility estimator
is asymptotically equivalent to detecting them using the infeasible (latent)
volatility path.
The proposed estimators are evaluated in simulations and on real data.
They are computationally efficient, and they accurately detect breakpoints even close
to the end of the sample. Both properties are very desirable for algorithmic trading firms.
In terms of out-of-sample volatility prediction, the new estimators outperform all
competitors at various frequencies and forecasting horizons.
In the last part of the talk, we discuss multivariate extensions of the proposed
estimators and their application and empirical performance in portfolio optimization.