Probability and Statistics Seminar
Speaker: Dr. Parichoy Pal Choudhury, KCDH, IIT Bombay
Host: Siuli Mukhopadhyay
Title: Statistical approaches to disease risk prediction with applications in risk-stratified disease prevention
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, October 07
Venue: Ramanujan Hall
Abstract: Risk-stratified disease prevention involves tailoring of health decisions about screening and prevention based on the individualized risk predictions. This requires a comprehensive understanding of the risk factors, including genetic variants, biomarkers, lifestyle/behavioral and environmental factors leading to the development of a model for predicting absolute risk of a disease of interest. Absolute risk model development requires information on relative risks of the risk factors, population-based age-specific disease incidence rates and competing event rates and population distributions of the risk factors. Such a model needs to be validated ideally in independent prospective cohorts before clinical applications. In this talk, I will describe the Individualized Coherent Absolute Risk Estimator (iCARE) software tool for implementing absolute risk estimation of a disease integrating multiple data sources leveraging the best information available for each of the input parameters and standardized approaches for risk model validation. I will describe multiple recent applications of this tool in the risk prediction of breast, bladder and ovarian cancers. Model validation in two-phase study settings often involve scenarios where expensive biomarkers (e.g., polygenic risk score) are measured in smaller subsample of a prospective cohort and subjects may be selected in the sub-sample using complex sampling designs. I will describe a simple partial risk score-based method for improving precision of model validation statistics (e.g., AUC) using the partial risk factors from the full cohort and complete risk factors from the subsample. I will show two applications of this method: (1) in lung cancer risk prediction with questionnaire-based risk factors and inflammation biomarkers and (2) in breast cancer risk prediction with questionnaire-based risk factors and PRS. If time permits, I will briefly discuss additional ongoing projects.

Geometric Analysis Talk
Speaker: Dr. Ramesh Mete, IIT Bombay
Host: Saikat Mazumdar
Title: On the existence of coupled extremal Kähler metrics on ruled surfaces.
Time, day and date: 3:00:00 PM – 4:00:00 PM, Wednesday, October 07
Venue: Ramanujan Hall
Abstract: We investigate the existence conditions for coupled extremal Kähler metrics on minimal ruled surfaces over a genus 2 Riemann surface. Using the Calabi ansatz to reduce the coupled extremal equations to ordinary differential equations, we prove that a pair of coupled extremal metrics exists for normalized Kähler classes $\Omega_a$ and $\Omega_b$ if and only if their parameters $(a,b)$ belong to an explicitly defined open region $\mathcal{S}_{ext}$ in the positive real quadrant. Furthermore, we show that this existence region inherently contains the diagonal segment corresponding to classical extremal Kähler metrics.

Ph.D. Defence
Speaker: Mr. Rishi Das, IIT Bombay
Host: Harsha Hutridurga
Title: Robust Mathematical Analysis and Numerical Methods for Flow-Transport Problems
Time, day and date: 4:00:00 PM – 5:00:00 PM, Wednesday, October 07
Venue: Ramanujan Hall (https://zoom.us/j/92827897299?pwd=55qKZRjyi6JM8dPTupMAGekskLkkk3.1)
Abstract: Mixed finite element methods naturally give rise to saddle-point structures. We exploit this intrinsic structure to construct parameter-dependent weighted spaces and establish robust well-posedness for three models arising in fluid flow and transport through porous media: the Darcy system, the Darcy—Forchheimer system, and the coupled Darcy--Forchheimer and advection-diffusion-reaction system. For each model, we develop parameter-robust discretization, derive a priori error estimates with constants independent of the physical parameters, and construct robust block-diagonal preconditioners within the operator preconditioning framework. Numerical results illustrate the robustness of the proposed methods across a wide range of physically relevant parameter regimes.