||Title and Abstract
||No Talk this Friday!
Gilberto Gonzalez Parra (NMT)
Different topics in applied mathematics
In this talk I will discuss different topics in the field of applied mathematics, and mainly mathe- matical models in infectious diseases.
First I will introduce the most important mathematical mod- els in infectious disease such as Susceptible-Infected-Recovered (SIR) and
Susceptible-Exposed- Infected-Recovered (SEIR) models. Secondly, I will do a brief description of other models that depend on processes
at scales ranging from cellular to environmental. In addition, I will show some aspects regarding the mathematical modeling process and
some numerical and statistical methods related to it. I will point out the most important challenges and perspectives. An introduction to the
modeling of social behaviors is also included. Different mathematical tools such stochastic, delay or fractional differential equations used in
applied mathematics are presented in order to show a va- riety of options. Through the talk I will remark why the choice of the theoretical
framework from the mathematical point of view is important since this aspect allows a better approximation to the real phenomenon.
In addition, different perspectives to extend some mathematical models and their paradigms are introduced.
||Oleg Makhnin (NMT)
testing for genetics applications: the next step
Bioinformatics applications (microarrays, RNA-seq) require in gene expression studies, two or more groups are simultaneous testing of
multiple quantitative traits. For example, compared, and we wish to identify which genes are expressed differently in these groups.
Based on a Bayesian framework developed earlier, I propose extensions for testing with correlated data, and for multi-level testing. Additionally, I present some opportunities for students to get involved.
||Anwar Hossain (NMT)||Title: Bayesian estimation and
prediction for the Maxwell Failure distribution based on
Type II censored data
We present Bayes estimators, highest posterior density (HPD) intervals, and maximum likelihood estimators (MLEs), for the Maxwell failure distribution based on Type II censored data, i.e. using the first r lifetimes from a group of n components under test. Reliability/Hazard function estimates, Bayes predictive distributions and highest posterior density prediction intervals for a future observation are also considered. Two data examples and a Monte Carlo simulation study are used to illustrate the results and compare the performances of the different methods.
||Mingji Zhang (NMT)||Title: Qualitative
properties of ionic flows via Poisson-Nernst-Planck
models: Selectivity of cations
Abstract: We study a quasi-one-dimensional PNP model with three ion species, two positively charged and one negatively charged with zero permanent charge. Of particular interest is the selectivity of cations, such as K^+ and Na^+ due to boundary conditions. Nonlinear interplays among physical parameters are carefully characterized, which provide useful and deep insights for further studies.