Events
Department of Mathematics and Statistics
Texas Tech University
The use of mathematical models to make predictions about tumor growth and response to treatment has become increasingly prevalent in the clinical setting. The level of complexity within these models ranges broadly, and the calibration of more complex models requires detailed clinical data. This raises questions about how much data should be collected and when, in order to minimize the total amount of data used and the time until a model can be calibrated accurately. To address these questions, we propose a Bayesian information-theoretic calibration protocol for experimental design, using a gradient-based score function to identify optimal times at which to collect data for informing treatment parameters. We illustrate this framework by calibrating a simple ordinary differential equation model of tumor response to radiotherapy to a set of synthetic data.
This Biomath seminar may be attended Monday the 28th at 4:00 PM CST (UT-6) via this Zoom link. Meeting ID: 839 9465 7333 Passcode: BfriM6
Since Hausdorff dimension was first introduced in 1918, many different notions of
dimension have been defined and used throughout many areas of Mathematics. An interesting
topic has always been the distortion of said dimensions of a given set under a specific
class of mappings. More specifically, Gehring and Väisälä proved in 1973 a theorem
concerning the distortion of Hausdorff dimension under quasiconformal maps, while Kaufman
in 2000 proved the analogous result for Box-counting dimension. In this talk, an introduction
to the different types of dimensions will be presented, along with the results of of Gehring,
Väisälä and Kaufman. We will then proceed to discuss analogous theorems we proved for
the Assouad dimension and spectrum, which describe how K-quasiconformal maps change these
notions of a given subset of $\mathbb{R}^n$. We will conclude the talk by demonstrating how
said theorems can be applied to fully classify polynomial spirals up to quasiconformal equivalence.
To join the talk on Zoom please click
here.
Please virtually attend this week's Statistics seminar at 4:00 PM Monday the 28th via this zoom link
Meeting ID: 930 3148 4740
Passcode: 852313
 | Wednesday
Mar. 2
|
| Algebra and Number Theory
No Seminar
|
A Riemannian metric on a closed manifold is called Zoll when all of its geodesics are closed and have the same period. Zoll metrics on the two-sphere were constructed by Zoll in the beginning of the nineteen hundreds, but many questions about them are still open. In this talk, I will explain my motivation to look for higher dimensional analogues of Zoll metrics, where closed geodesics are replaced by closed embedded minimal hypersurfaces. Then, I will discuss some recent results about the construction and geometric understanding of these new geometries. This is a joint project with F. Marques (Princeton) and A. Neves (UChicago).
Watch online via this Zoom link.
An abstract indefinite least squares problem with a quadratic constraint is considered. This is a quadratic programming problem with one quadratic equality constraint, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are found for the existence of solutions.
Please virtually attend the Applied Math seminar via this Zoom link Wednesday the 2nd at 4 PM (UT-6) -- meeting ID: 937 2431 1192
This talk will cover the Bachelier model of asset pricing, its extensions and option pricing.
Note: The Bachelier model uses a normal price distribution rather than the Black-Scholes
log-normal distribution and has applications when option prices can be negative.