Talk

A statistical model typically can be defined as a collection of probability measures on some outcome space. All, except perhaps one of these measures are ‘wrong’. Traditionally, the selection of a model is done based on certain fit criteria (via some loss function such as least squares, maximum likelihood etc.), that is, the distance from the data to the model. Usually, these include AIC, AICC, BIC, DIC, HQC among others. ‘Focused Information Criterion’ is comparatively a new model selection approach, which is getting popularized nowadays.

In this talk, we first introduce the basic principles of mathematical modelling. We then understand the basic SIR model for spread of diseases. The talk introduces population growth models based on the ODE approach and relates these to tumor growth. Consequently, the PDE approach will be introduced for a single species and multiple species within a tumor environment. These are coupled PDEs which can be treated via mathematical analysis, analytical techniques or numerical simulations. Some test cases will be shown.

In this talk I will discuss some of the problems in Semiconductor Device research I pursued, focussing on the insights gained. The first example would be a critical question I asked which led to the transformation of minority carrier transport equations. I explain how they can be used to solve a variety of problems, including non-quasi-static problems. Two insightful dimensionless constants were introduced. The first one is the Ki number which embeds all the essential bulk transport properties and the second one is the Sf number which embeds all the essential surface transport properties.

Abstract: Hemodynamic monitoring involves measuring cardiovascular parameters like blood pressure, perfusion pressure, cardiac output, and vascular resistance to assess circulatory system function. Recent advances in wearable hemodynamic monitoring technologies enable earlier disease diagnosis by detecting subtle anomalies in cardiovascular dynamics before outward symptoms manifest. This talk will briefly describe a technology to measure blood pressure via smartphone-based devices with a single press on the sensor.

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