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Following are broad areas of research.

My research is focused in

Mathematical and probabilistic methods and models, complex analysis, harmonic analysis, ODE/PDE, Stochastic Processes etc.

Methodologies in Machine Learning and Artificial Intelligence Algorithms in Medicine, biology. I also do biostatistical consulting for various projects.

 

Research Highlights

 

2022-GIAN Lecture Series Foreign Expert by MHRD, Government of India (Maharshi Dayanand University, Rohtak)

2022– Proof of a special form of Jordan Curve Theorem (with S.G. Krantz) to appear in Geometry and Statistics, Elsevier

2022-Invited Talk at “John Conway Lecture Series

2022- A partition Theorem for a Randomly selected Large Population (ACTA Biotheoretica)

2021– Rao distances and conformal mapping (Dedicated C.R. Rao’s Birth centenary)

2021-Multilevel Contours and bundle of complex planes (Dedicated to Steven G. Krantz’s 70th Birthday)

2021-Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods

2021-Topology of SARS-CoV-2

2021– Exact Deep Learning Machines

2020-Designing and Developing Mathematical Modeling and Methods for COVID-19 in collaboration with Dr. Steven G. Krantz, Washington University in St. Louis.

2020- Designed and Developed first AI Model for identification of COVID-19 through mobile phone Apps. This was the first article on COVID-19 identification and contact tracing strategy. Working on practical implementation of the same through hospital systems. See for example, Campus Technology TOIThe ETFastCompany, etc., See media page for more details.

2018—Designed and Developed Hybrid Models that use blockchain technology for healthcare.  Provisional patent obtained.

See Media & Press Coverage on our research work at the Media Coverage page.

2014- We formally stated and proved a fundamental theorem in the stationary population processes which was an open problem in the literature.  This is a joint work with J.R. Carey, also termed as Rao-Carey Fundamental Theorem in stationary population models. See a report on this work at MBI, Ohio’s success stories. Click here.  This work will appear in Journal of Mathematical Biology (Springer). One referee wrote “..In a very original and unusual way the authors 'trace' the formation of this equality "understanding the role of each captive subject, and their corresponding follow-up duration in a stationary population. This is indeed very interesting and unusually innovative...” Another referee wrote “..It's hard to write down such a proof any more simply than as given here. This proof should also be really useful in making extensions to other captive cohort situations…” A clarifications file for demographers is available here.

 

2014– Population stability theory through momentum was described in a research article is appeared in the prestigious journal Notices of the American Mathematical Society in October 2014. This article was dedicated to  Alfred J Lotka.

 

2014– Our work on mathematical modeling of epidemics which I led at Oxford during 2005-2007 was selected by the Mathematical Institute at the Oxford University as one of the selected works spanning in last ten years  -as a case study to show how their research had attained significant impact outside academia. They have submitted this to the nationwide government assessment of university departments in the UK (See REF2014 report).

 

2012- Our research in mathematical biology has contributed in Three Important National Policies in India. I had served as a member of  committees including NACPIV. Our research article on modeling ART appeared in prestigious Notices of the American Mathematical Society in April issue of 2012.

 

2012- One referee while reviewing my recent article in JTB has commented-

The question concerned here is of great importance to public health because effective Control policies depend on knowing true incidence or prevalence. Also authors approach for understanding reporting errors is novel and has a potential for becoming a tool that can be used in designing of control programs.

 

2010-We have initiated RRM related thinking in 2006 and started understanding SLE and its development. Tulasiram Reddy in his masters project (2010) gave a configuration for a 3D roter walk which inspired to obtain complete solution by Angel and Holroyd to an open problem in the area.

 

See arXiv for few working papers and See publications page for recent papers.

 

In addition to the above activities, I have been actively engaged in developing exercise solutions to the following two books:

Apostol Tom A. Mathematical Analysis.

Ahlfors Lars V. Complex Analysis. An Introduction to the theory of analytic functions of one complex variable.

Research

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DMS-2140493