Events
Department of Mathematics and Statistics
Texas Tech University
The theory of kernel integral operators lies at the intersection of diverse fields such as Operator theory, Harmonic analysis, Geometric analysis, and even Dynamical systems theory. Kernels used in Analysis are usually equipped with a bandwidth parameter ϵ controlling the decay of tails. There are various results, theoretical and empirical - about such integral operators revealing the local geometry as ϵ→0, such as curvature, the Laplace and advection operators. However, little is known about the limiting behavior of these operators in non-smooth surfaces, such as fractals. I shall present to you an axiomatic framework which proves existing results on the asymptotic behavior of kernel integral operators. It also established spectral convergence, an elusive property in operator theory. This framework also provides directions in which one can generalize these results to non-smooth manifolds.
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday the 10th via this Zoom link.
Meeting ID: 948 7629 6935
Passcode: 602422
Drug resistance is a common phenomenon in the treatment of cancer. As with other cancer therapies, treatment failure due to resistance also occurs for the oncolytic viral therapy (OVT). In this talk, we introduce mathematical models of tumor-virus interaction to investigate OVT resistance. The free oncolytic viruses are modeled explicitly as one compartment and the tumor cells are classified as either susceptible, resistant, or infected. Since there is a time delay from the initial viral infection to the time when infected cells are able to infect other tumor cells, we also consider a model of delay differential equations. It is shown that the OVT fails no matter how large the viral dose is if no treatment upon the resistant tumor cells is applied. When the treatment for resistance is adopted, the delay has no effect on the stability of the OVT escaped equilibrium and the model can have a unique positive equilibrium. A critical delay is derived under which a Hopf bifurcation occurs for the positive equilibrium. The critical delay, however, depends on several model parameters. We conclude that combined therapy is essential for the control of the tumor, and as delay is a characteristic of the virus, the virus should be engineered carefully to avoid tumor oscillations.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
 | Wednesday
Oct. 12
|
| Algebra and Number Theory
No Seminar
|
Self-similar solutions and translating solitons are not only special solutions of mean curvature flow (MCF) but a key role in the study of singularities of MCF. They have received a lot of attention. We introduce some examples of self-similar solutions and translating solitons for the mean curvature flow (MCF) and give rigidity results of some of them. We also investigate self-similar solutions and translating solitons to the inverse mean curvature flow (IMCF) in Euclidean space.
Watch online via this Zoom link.
The behaviour of a person is dominated by their ability to process uncertain information
available to them.
When there is a range of alternatives to choose from, the likelihoods assigned by the person
to these different alternatives determine the state of their mind in relation to that
particular choice.
When new information arrives, the person’s perspective changes, generating behavioural dynamics.
To model this behaviour, it is highly effective to use the mathematics of signal processing.
In this scheme, it is then possible to represent (i) reliable information, (ii) noise,
and (iii) disinformation in a unified framework.
Because the approach is designed to characterise the dynamics of the behaviour of people,
it is possible to quantify the impact of information control, including those resulting
from the dissemination of disinformation.
It can be shown that if a decision maker assigns an exceptionally high weight on one of
the alternative realities, then under the Bayesian logic their perception hardly changes
in time even if evidences presented indicate that this alternative corresponds to a false reality.
Thus confirmation bias need not be incompatible with Bayesian updating;
contrary to what is widely believed in psychology.
The information-based approach, originated in financial modelling, when applied to psychology,
also poses new challenges in stochastic analysis, which will be discussed briefly.
The talk will be an extended version of an informal article in:
https://theconversation.com/the-mathematics-of-human-behaviour-how-my-new-model-can-spot-liars-and-counter-disinformation-185309