Events
Department of Mathematics and Statistics
Texas Tech University
Breast cancer is the second most commonly diagnosed cancer in women worldwide. MCF-7 cell line is an extensively studied human breast cancer cell line. This cell line expresses estrogen receptors, and the growth of MCF-7 cells is hormone dependent. In this talk, I will propose a mathematical model which governs MCF-7 cell growth with interaction among tumor cells, estradiol, natural killer (NK) cells, cytotoxic T lymphocytes (CTLs) or CD8+ T cells, and white blood cells (WBCs). Experimental data are used to determine functional forms and parameter values. Breast tumor growth is then studied using the mathematical model. The results obtained from numerical simulation are compared with those from clinical and experimental studies. The system has three coexisting stable equilibria representing the tumor-free state, a microscopic tumor, and a large tumor. These three equilibrium states are similar to the three phases of immunoediting. Numerical simulation shows that a healthy immune system is able to effectively eliminate a small tumor or produce long-term dormancy. The cytotoxicity of CTLs plays an important role in immune surveillance. The association between the circulating estradiol level and cancer risk is not significant.
This Biomath seminar may be attended Monday the 21st at 4:00 PM CST (UT-6) via this Zoom link. Meeting ID: 839 9465 7333 Passcode: BfriM6
We study the generalized Forchheimer flows of slightly compressible fluids in rotating
porous media. In the problem's model, the varying density in the Coriolis force is fully
accounted for without any simplifications. It results in a doubly nonlinear parabolic
equation for the density. We derive a priori estimates for the solutions in terms of the
initial, boundary data and physical parameters, emphasizing on the case of unbounded data.
Weighted Poincaré-Sobolev inequalities suitable to the equation's nonlinearity, adapted
Moser's iteration and maximum principle are used and combined to obtain different types
of estimates. This is joint work with Emine Celik and Thinh Kieu.
To join the talk on Zoom please click
here.
Algebraic quantum field theory (AQFT) is a time-honoured axiomatic approach to describe and study QFTs on Lorentzian manifolds. In this talk I will try to summarize some of our main insights and results about “levelling up” traditional AQFT to the higher categorical world, which leads to a refined framework that I believe is suitable for quantum gauge theories. I will focus on both the underlying higher algebraic structures, i.e., the question “What does an ∞-AQFT assign? And why?”, and on concrete examples (mostly toy-models) that one can construct through methods from derived algebraic geometry. This talk is based on a long-term research program with Marco Benini.Fifty years ago Blaine Lawson constructed the first examples, beyond geodesic spheres and Clifford tori, of closed minimal surfaces embedded in the round 3-sphere. I will review some natural questions (and a few answers) concerning the space of such surfaces, with a focus on results recently obtained for the Lawsons in collaboration with Nicos Kapouleas: namely a characterization by their topology and symmetries and, for an infinite subfamily, the computation of their Morse index and nullity.
Please watch online via this Zoom link.
In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. Based on the framework of strong stability-preserving Runge-Kutta approach, we propose two high-order multirate explicit time-stepping schemes (SSPRK2-SE and SSPRK3-SE) for the resulting split system in this paper. The proposed schemes allow for a large time step to be used for the three-dimensional baroclinic (slow) mode and a small time step for the two-dimensional barotropic (fast) mode, in which each of the two mode solves just need to satisfy their respective CFL conditions for numerical stability. Specifically, at each time step, the baroclinic velocity is first computed by advancing the baroclinic mode and fluid thickness of the system with the large time-step and the assistance of some intermediate approximations of the baroctropic mode obtained by substepping with the small time step; then the barotropic velocity is corrected by using the small time step to re-advance the barotropic mode under an improved barotropic forcing produced by interpolation of the forcing terms from the preceding baroclinic mode solves; lastly, the fluid thickness is updated by coupling the baroclinic and barotropic velocities. Additionally, numerical inconsistencies on the discretized sea surface height caused by the mode splitting are relieved via a reconciliation process with carefully calculated flux deficits. Two benchmark tests from the ``MPAS-Ocean" platform are carried out to numerically demonstrate the performance and parallel scalability of the proposed SSPRK-SE schemes.
Please virtually attend the Applied Math seminar via this Zoom link Wednesday the 2nd at 4 PM (UT-5) -- meeting ID: 937 2431 1192
The cotangent complex is an important but difficult to understand
object in commutative algebra. For a homomorphism $\varphi: R\to S$ of
commutative noetherian rings, this is a complex $L_{\varphi} =
L_0\rightarrow L_1\rightarrow \cdots $ of free $S$-modules. To start
with I'll connect this back to some more familiar commutative algebra
invariants by explaining how you can see the module of differentials,
the conormal module, and the Koszul homology as syzygies inside
$L_{\varphi}$.
When the cotangent complex was introduced by Quillen, he conjectured
(for maps of finite flat dimension) that if $\varphi$ is not complete
intersection then $L_{\varphi}$ must go on forever. This was proven by
Avramov in 1999. I will explain how to get a new proof (of a stronger
result) by paying attention to the $syzygies of L_{\varphi}$. This is
all joint work with Srikanth Iyengar.
Join Zoom Meeting https://texastech.zoom.us/j/97115201141?pwd=N0YwcDkzTDc4bC9JYS9kVFQ1bFh2UT09
Meeting ID: 971 1520 1141
Passcode: 900450
The growing interest for sustainable investing calls for an axiomatic approach to characterize risk
and reward measures for investors that do not focus uniquely on financial returns,
but also for environmental and social sustainability.
We propose definitions of ESG-coherent risk and reward measures, as well as ESG risk-reward ratios.
Such measures are defined as functions of bivariate random variables:
the financial returns, and ESG scores (a proxy for sustainability).
We provide examples of such functions, describing families of measures that can be derived from
traditional univariate risk and reward measures.
We then show an empirical example in which we use an ESG-adjusted CVaR in portfolio optimization.