Research Interest: Quantization: Theory and Applications, Fractal Geometry and Dynamical Systems.

Short Description: Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the constraint of the constrained quantization. A quantization without a constraint is known as an unconstrained quantization, which traditionally in the literature is known as quantization. Constrained quantization has recently been introduced by Pandey and Roychowdhury. With the introduction of constrained quantization, quantization now has two classifications: constrained quantization and unconstrained quantization. Constrained quantization is greatly useful in radiation therapy of cancer treatment. In radiation therapy, to make sure that the radiation does not directly hit the region of good cells one can use the constrained quantization technique. Constrained quantization is extensively useful in national security, for example, to install missile stations targeting another country in an efficient way the technique of constrained quantization can be used. Constrained quantization is also useful in sending and getting signals from a certain region with minimum distortion using a fixed number of towers installed in a different region. Further, we have introduced another new idea in quantization which is known as conditional quantization in both constrained and unconstrained cases. Conditional quantization has also significant interdisciplinary applications: for example, in radiation therapy of cancer treatment to find the optimal locations of n centers of radiation, where k centers for some k<n of radiation are preselected, the conditional quantization technique can be used. After the introduction of constrained quantization, and then conditional quantization, the quantization theory is now much more enriched with huge applications in our real world. For more details one can consult my preprints and publications. 

Some interesting links:

• Talk slides of Professor Karoly Simon: Quantization dimension for fractals of overlapping construction. 
  
• YouTube Video uploaded by Sergio Soto Quintero: https://youtu.be/V0QjrSV-8OM

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Research Grant:

• Faculty Seed Research Grant from the University of Texas Rio Grande Valley, Texas, USA, May 2022, PI.  
  
• U.S. National Security Agency (NSA), Grant #H98230-14-1-0320, Award Period: 09/12/2014 - 09/11/2016, PI.
  

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Editorial Service:

• AMS Contemporary Mathematics, Volume 797, Recent Developments in Fractal Geometry and Dynamical Systems, edited by: Sangita Jha, Mrinal Kanti Roychowdhury, and Saurabh Verma, ISBN: 978-1-4704-7216-0. 
  
• Special issue on fractal geometry, dynamical systems, and their applications, edited by: Michael Barnsley, James Keesling, and Mrinal Kanti Roychowdhury, published: 01 January 2019 in Discrete & Continuous Dynamical Systems-S. 
  

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