January 2, 2017 - January 6, 2017
Public Access Category: All |
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
- Time:
- 3:00pm-4:00pm
- Location:
- Room No. 216
- Description:
- Title: Estimating parameters of directional distributions
Abstract: Data related to spread of disease bacteria, wind directions, seasonal variations etc. can be represented by directional distributions. Langevin distribution is one of most commonly used directional distributions. We unify the results on admissibility, minimaxity and best equivariance of MLE of direction parameter. Various other estimators of direction parameter are compared with respect to robustness and asymptotic efficiency. Methods of improving estimators for spherical location are developed. Special applications to problems in restricted parameter spaces are given.
- Time:
- 3:30pm-4:30pm
- Location:
- Mini conference room, Mathematics department
- Description:
- Title: Study of a nonlinear renewal equation with diffusion
Abstract: We consider a nonlinear age structured McKendrick-von Foerster
population model with diffusion term (MV-D). We prove the existence and
uniqueness of solution of the MV-D equation. We also prove the convergence
of the solution to its steady state as time tends to infinity using the generalized relative entropy inequality and Poincare Writinger type inequality.
We propose a numerical scheme for the linear MV-D equation. We discretize
the time variable to get a system of second order ordinary differential
equations. Convergence of the scheme is established using the stability
estimates by introducing Rothe’s function.
- Time:
- 4:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Prof. Dinakar Ramakrishnan
Title: Rational Points
Abstract: Since time immemorial, people have been trying to understand the rational number solutions of systems of homogeneous polynomial equations with integer coefficients (called a Diophantine system). It is more convenient to think of them as rational points on associated projective varieties X, which we wll take to be smooth. This talk will introduce the various questions of this topic, and briefly review the reasonably well understood one-dimensional situation. But then the focus will be on dimension 2, and some progress for those covered by the unit ball will be discussed. The talk will end with a program (joint with Mladen Dimitrov) to establish an analogue of a result of Mazur.
- Time:
- 11:00am-12:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Dr. Samiran Ghosh,
Associate Professor of Biostatistics
Department of Family Medicine and Public Health Sciences,
Wayne State University School of Medicine
Title: “ON THE ESTIMATION OF THE INCIDENCE AND PREVALENCE RATE IN A TWO-PHASE LONGITUDINAL SAMPLING DESIGN”
Abstract:
Two-phase sampling design is a common practice in many medical studies with rare disorders. Generally, the first-phase classification is fallible but relatively cheap, while the accurate second-phase state of-the-art medical diagnosis is complex and rather expensive to perform. When constructed efficiently it offers great potential for higher true case detection as well as for higher precision. In this talk, we consider epidemiological studies with two-phase sampling design. However, instead of a single two-phase study we consider a scenario where a series of two-phase studies are done in longitudinal fashion. Efficient and simultaneous estimation of prevalence as well incidence rate are being considered at multiple time points from a sampling design perspective. Simulation study is presented to measure accuracy of the proposed estimation technique under many different circumstances. Finally, proposed method is applied to a population of elderly adults for the prognosis of major depressive disorder.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Rost nilpotence
Abstract:The Rost nilpotence principle is an important tool in the study of motivic decompositions of smooth projective varieties over a field. We will introduce this principle and briefly survey the cases in which it is known to hold. We will then outline a new approach to the question using etale motivic cohomology, which helps us to give a simpler and more conceptual proof of Rost nilpotence for surfaces, generalize the known results over one-dimensional bases and sheds more light on the situation in higher dimensions. The talk is based on joint work with Andreas Rosenschon.