Department Seminars 2021

Abstract:
Before the scientific community, one of the most challenging problems is what sustains life or how living things originate from non-living things. A biological cell is assumed as the smallest unit of life. The multiple cellular processes are mainly controlled by tiny biological machines called motor proteins which move along macromolecular highways, namely microtubules, to transfer cargoes at distinct locations inside a cell. To get insight into the life-sustaining mechanism, it is necessary to understand the collective transport of motor proteins that fall into a specific category of the non-equilibrium system due to the presence of non-zero current governed by the continuous supply of energy. In recent decades, asymmetric simple exclusion process (TASEP), a Markov model which includes unidirectional particle hopping along a one-dimensional discrete lattice, has achieved the status of paradigm model to analyze stochastic non-equilibrium transport, including motor movement. The first part of the talk will be devoted to some beautiful results on the standard 1D TASEP model with fixed lattice size. Recent experimental observations suggest that the biological paths (microtubules) can polymerize or depolymerize under certain conditions, resulting in the growth or shrinkage of these paths. Modeling stochastic transport with dynamic microtubules will be explored in the second part of the talk, then validating theoretical results through experimental observations and extensively performed Monte Carlo simulations. Finally, challenges in modeling and analyzing intracellular transport will be discussed.

Biography:
I have completed BSc in Physics, Chemistry, Mathematics from CSJMU Kanpur (2012), followed by MSc in Industrial Mathematics & Informatics from IIT Roorkee (2014). I earned a Ph.D. on the topic "Mathematical Modelling of Driven Stochastic Transport Systems" from IIT Ropar (2019). After completing my Ph.D., I worked as Director's Fellow at IIT Ropar from Sep 2019 to May 2021. Since June 2021, I have been working as Assistant Professor at the Department of Mathematics, NIT Trichy, Tamil Nadu. I have published 9 research papers (all SCI) in international journals of repute like Physical Review E, Journal of Statistical Physics, Journal of Statistical Mechanics, etc.

Abstract:
The second order Partial differential equations (PDEs) are extremely important in both mathematics and physics. This talk provides a review on the nomenclature of the geometrical figures, if B2 - 4AC > 0 the partial differential equation is said to be hyperbolic; if B2 - 4AC = 0 the equation is parabolic, and if B2 - 4AC < 0 the equation is elliptic. Also, illustrate these on real life situational examples and its solution behaviour lucidly.

Biography:
I have studied all my education starting from 1st class to Ph. D in Government Schools/ Social Welfare Residential Hostels and Government Universities. I have completed my Ph.D in Mathematics from the Department of Mathematics, Central University of Pondicherry, Pondicherry India under the guidance of Prof. Rajeswari Seshadri.(Ph.D. from IISc Bangalore) in the areas of Solutions for nonlinear differential equations. Also, I have completed my one year Post Doctoral Fellow (PDF) research work in Applied Mathematics/Mechanics from School of Naval Architecture, Ocean and Civil Engineering(1st Rank in World by GLOBAL RANKING OF WORLD OF ACADEMIC SUBJECTS-2018), Shanghai Jiao Tong University, Shanghai in China under the guidance of senior Scientist and Distinguished Professor. Shi Jun Liao (HAM method Founder and 2016 Most Highly Cited Researchers in Global Mathematics).
I have "5 years" of teaching experience and “1 year” Post Doctoral fellow experience and Published 28(SCI/SCOPUS/UGC) international journal articles/conference proceedings and have communicated 4 more papers. I also presented 5 papers and gave 8 lectures at various conferences and seminars. I have participated in more than 74 Conferences / Seminars / Workshops and presented papers in some of them. I have received prestigious fellowship “Rajiv Gandhi National Fellowship(JRF & SRF) from UGC, New Delhi, Govt of India during my M.Phil and Ph.D. I have received renowned the SJTU Post Doctoral Fellowship from Shanghai Jiao Tong University, Shanghai, China in 2016 and Prof. Meenakshi Sundaram Memorial Best paper award in Applied Mathematics by APSMS in 2017. Also awarded QITCS Post Doctoral Scientist fellow from Shandong University, Govt of China-2020(Not availing due to Covid). Recently, I have received CONFIRMATION LETTER FOR HIGH LEVEL FOREIGN TALENTS from CHINA (i.e. prestigious “China Talent Visa(R)” i.e, Foreign High-Level Talents Fellow Researcher among all 100 International fellows from Government of China) for 2 years free VISA services for work as a Postdoctoral Scientist from 6th April, 2020 to 6th April, 2022 at Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, China under the supervision of Director, Prof. Wenjian Liu.

Secured 1st rank in All India Entrance (PU CET) for M.Phill. in Mathematics at Pondichetty University ( A Central University), Pondicherry in 2009.
Secured 1st rank, All India Selections for Ph.D. in Mathematics at University of Hyderabad in 2011.
Secured 1st rank in All Andhra Pradesh state Entrance (KU CET) for M. Sc in Mathematics, Kakatiya University (State University), Warangal in 2005.

My research area is on application of approximate

Abstract:
Continued and remarkable empirical successes of increasingly complicated machine learning models such as neural networks without a sound theoretical understanding of success and failure conditions can leave a practitioner blind-sided and vulnerable, especially in critical applications such as self-driving cars and medical diagnosis. As such, there has been an enhanced interest in recent times in research on building interpretable models as well as interpreting model predictions. In this talk, I will discuss various theoretical and practical aspects of interpretability in machine learning along both these directions through the lenses of feature attribution and example-based learning. In the first part of the talk, I will present novel theoretical results to bridge the gap in theory and practice for interpretable dimensionality reduction aka feature selection. Specifically, I will show that feature selection satisfies a weaker form of submodularity. Because of this connection, for any function, one can provide constant factor approximation guarantees that are solely dependent on the condition number of the function. Moreover, I will discuss that the cost of interpretability accrued because of selecting features as opposed to principal components is not as high as was previously thought to be.
In the second part of the talk, I will discuss the development of a probabilistic framework for example-based machine learning to address ``which training data points are responsible for making given test predictions?“. This framework generalizes the classical influence functions. I will also present an application of this framework to understanding the transfer of adversarially trained neural network models.

Short Biography:
Dr. Rajiv Khanna is currently a Visiting Faculty Researcher at Google Research, and an incoming Assistant Professor at the Department of Computer Science at Purdue University. Previously, he was a postdoc at the Department of Statistics at UC Berkeley and was also associated with the Foundations of Data Analytics Institute (FODA) at UC Berkeley. Before that, he was a Research Fellow in the program of Foundations of Data Science at the Simons Institute for the Theory of Computing, also at UC Berkeley.
His research is focussed on elucidating mechanisms of success/failure conditions of machine learning through optimization, learning theory and interpretability. His work on beyond worst-case analysis on the Column Subset Selection won the best paper award at NeurIPS 2020. He earned his PhD in Electrical and Computer Engineering at UT Austin.

Abstract:
Algorithmic scalability is a challenge in many complex systems and machine learning applications. Inexact computing is one solution to this scalability challenge. With the focus on the problem of efficiently reducing large-scale dynamical systems, we propose the use of approximate (and hence, faster) linear solves in a set of model reducing algorithms. Theoretically, we prove that under mild conditions (easily satisfiable), these algorithms are backward stable with respect to the error introduced by inexact linear solves. Experimentally, we demonstrate that while reducing an industrial disk-brake model of size 1.2 million, one of our approximate algorithms leads to relative savings of up to 64% in the total computation time (when compared with the corresponding exact algorithm). In absolute terms, this leads to a saving of 5 days.
Another solution to this scalability challenge is sampling, which leads to a reduction in the problem size. With the focus on the problem of efficiently grouping plant species, we propose a class of probabilistically-sampled spectrally-clustered algorithms. Using experiments on multiple Soybean datasets comprising of thousands of species, we demonstrate the superiority of our approach over the current standard in-terms of both the cluster quality (up to 45% better) as well as the time complexity (an order-of-magnitude lesser).

Short Biography:
With Master’s and Ph.D. degrees in Mathematics and Computer Science (from Virginia Tech), Dr. Kapil Ahuja has a strong interdisciplinary focus. After graduating from VT, he received his postdoctoral training from the Max Planck Institute in Magdeburg. Since then, he has established his independent research program in Mathematics of Data Science and Simulation (MODSS) at IIT Indore, where he is currently working as an Associate Professor. In the recent past, he has also held visiting professor positions at TU Braunschweig, TU Dresden, and Sandia National Labs.
Dr. Ahuja’s core research interests are in Machine Learning, Optimization, Game Theory, and Numerical Methods. Dr. Ahuja's research output includes external funding worth more than half-a-million USD and over forty high-quality publications. While achieving this, he has graduated 4 PhD students with 1 more to graduate soon. On the teaching end, Dr. Ahuja has received the best teacher award four times at IIT Indore, and administratively, recently, he headed International Affairs at IIT Indore as its founding Dean.