Events
Department of Mathematics and Statistics
Texas Tech University
Abstract pdf
This Job Colloquium is sponsored by the Applied Math seminar group. Please virtually attend Wednesday the 13th at 4 PM CDT (UT-5) via this Zoom link.
We extend the Markov Decision Process setup to the cases of MFG and MFC problems and we generalize the optimality Bellman equation for Q-learning. By introducing two learning rates, one for the Q-matrix and one for the population distribution, we are able to design a single algorithm which learns the optimal policies for the MFG or for the MFC depending on the ratio of these two rates. Applications to problems in finance are also discussed.
This is joint work with Andrea Angiuli and Mathieu Laurière. Please virtually attend at 3:30 PM CDT (UT-5) via this Zoom link.
We consider the degenerate Einstein’s Brownian motion model for the case when the time interval (τ) of particle Jumps before collision (free jumps) reciprocal to the number of particles per unit volume u(x,t) >0 at the point of observation x at time t. The parameter 0 < τ ≤ C < ∞ , controls characteristic of the fluid "almost decreases" to 0 when u→ ∞. This degeneration leads to the localization of the spread of particle propagation in the media. In our report we will present a structural condition of the time interval of free jumps τ and the frequency of these free jumps φ as functions of u which guarantees the finite speed of propagation of u.
To join the talk on Zoom please click
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The limited supply of the COVID-19 vaccine and its inequitable distribution pose a public health concern contributing to worsening health disparity. This study explores the public health — and economic impact of four possible vaccination strategies — fixed-dose interval (S1), prioritization of the first dose (S2), and screen-and-vaccinate those with the COVID-19 infection history with fixed-dose interval (S3) or first-dose prioritization (S4). Using mathematical modelling, we quantified the number of quarantine and hospitalization days and deaths averted from each strategy, as well as the associated cost. The model parameters and initial conditions are based on Canada, and the simulation ran over 365 days starting from June 1st, 2021. Net monetary benefit (NMB) and incremental cost-effectiveness ratio were calculated from a societal perspective. In addition, sensitivity analysis explored how each strategy reacts to different conditions of daily vaccine supply, the initial proportion of the recovered, and the initial coverage of the first dose. The findings suggest the potential benefits of alternative vaccination strategies that can save lives and costs. Our study's framework and findings can inform policymakers to explore the optimal COVID-19 vaccination strategy under their unique settings.
Please virtually attend this week's Biomath seminar at 3:30 PM (UT-5) on Tuesday the 12th via this Zoom link. Meeting ID: 839 9465 7333 Passcode: BfriM6
This is joint work with T. Miura and F. Rupp.
In this talk we study the qualitative behavior of elastic flows of curves -- Can embedded curves develop self-intersections along the flow?
In general they can, as revealed by [S. Blatt (2010)], even for a larger class of higher order geometric flows. In a recent work we have observed that this loss of embeddedness may only occur only above a certain energy treshold, which can be quantified optimally.
My goal for this talk is to explain this optimal treshold geometrically. This discussion will lead us into the fabulous world of Euler's elastic curves.
Watch online via this Zoom link.Abstract: We extend the Markov Decision Process setup to the cases of MFG and MFC problems
and we generalize the optimality Bellman equation for Q-learning.
By introducing two learning rates, one for the Q-matrix and one for the population distribution,
we are able to design a single algorithm which learns the optimal policies for the MFG or for the MFC
depending on the ratio of these two rates.
Applications to problems in finance are also discussed.
This is joint work with Andrea Angiuli and Mathieu Laurière.
Brief Bio: Professor Fouque's research is in the domain of random media with applications
ranging from wave propagation phenomena to financial mathematics.
He has published over one hundred research articles and co-authored three books:
"Derivatives in Financial Markets with Stochastic Volatility" (Cambridge University Press, 2000),
"Wave Propagation and Time Reversal in Randomly Layered Media" (Springer, 2007), and
"Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives" (Cambridge University Press, 2011).
Jean-Pierre Fouque received his Ph.D. in Mathematics from the University Pierre et Marie Curie, Paris.
He held positions at the CNRS and at the Ecole Polytechique in France, before joining North Carolina State University
in 1998 where he started the Masters of Financial Mathematics.
In 2006, he joined the department of Statistics and Applied Probability at the University of California Santa Barbara
where he is a Distinguished Professor and Co-director of the Center for Financial Mathematics and Actuarial Research (CFMAR).
He is currently Editor-in-Chief of the SIAM Journal on Financial Mathematics and Past-President of the Bachelier Finance Society.
He is a Fellow of the Institute of Mathematical Statistics since 2009 and a SIAM Fellow since 2011.