Applied Mathematics, Mathematical Modeling, Optimal Control & Numerical Analysis

1. A. K. Paul*, M. H. A. Biswas, "A Mathematical Theory for Studying and Controlling the Multi-Scale Dynamical Disinformation System", Contributory Talk at 2nd International Conference on Mathematical Analysis and Application in Modeling (ICMAAM-2023), October, 9-11 Jadavpur University, Kolkata, India. DOI: 10.13140/RG.2.2.29975.14243/1

A novel method is presented for identifying and classifying different types of disinformation using mathematical Modelling and an optimal control approach.  First, we formulated a mathematical model to represent the disinformation system including online and face-to-face contact, and then we performed the bifurcation analysis and examined the external rate-induced changes. We have analyzed rate-induced tipping points of the system to understand how the system actually evolves only for the external forces or how the system dynamics can be changed forcefully. Here a non-autonomous system of differential equations is used and we have determined how the optimal control strategies should be formulated. 

2. A. K. Paul*, M. S. Khatun and M. H. A. Biswas, "Modeling and Optimal Control Applied to Reduce the Effects of Greenhouse Gases Emitted from the Coal-based Power Plant in Bangladesh " Hellyon, July 2023. DOI : 10.1016/j.heliyon.2023.e18409

I first realized the necessity for this research and later I presented the entire system through a mathematical model. That research was previously presented at a conference and published as Proceedings. By extending the previous research. Later I provided an idea of how to control the whole system. I managed the design, analysis, numerical simulation and other technical aspects of the research. Prof. Haider Ali Biswas and Shanta Khatun also contributed to concepts of new analysis, validation, writing the paper, reviewing and revising the paper and others. 

3. A. K. Paul* and M. H. A. Biswas, "A Mathematical Study for Modeling the Dynamics of Violence Epidemic Spreading from Misinformation" in Mathematical and Computational Modelling of Covid-19 Transmission, Oxfordshire, England, UK, Routledge, 2023. Link to the publication. 

This publication is a part of my MSc thesis. There I studied the misinformation-spreading system and its control strategies mathematically. 

4. M. H. A. Biswas, M. A. Islam, S. Akter, S. Mandal, M. S. Khatun, S. A. Samad, A. K. Paul and M. R. Khatun, "Modelling the Effect of Self-Immunity and the Impacts of Asymptomatic and Symptomatic Individuals on COVID-19 Outbreak" Computer Modeling in Engineering & Sciences, vol. 125, no. 3, pp. 1133-1060, 2021. DOI : 10.32604/cmes.2020.012792

In the above study, I solved difficult and numerical simulation tasks. I also solved some analytical equations to perform the task.

5. A. K. Paul and M. H. A. Biswas, "A Mathematical Study for Modeling the Dynamics of Violence Epidemic Spreading from Misinformation" N. H. Shah and M. Mittal (Eds.), Mathematical and Computational Modelling of Covid-19 Transmission. River Publishers, Denmark.  2022 (in Press)

I carried out various simulations and analysis including conceptualization, problem identification, data collection and analysis, Mathematical model development and analysis of the above research. I then provide a practical solution by using optimal control theory to provide a precise solution on how to control the system. Prof. Haider Ali Biswas provided various guidance during the research and theoretical and mathematical ideas on how to make the research more practical.

6. M. H. A. Biswas, A. K. Paul*, M. S. Khatun, S. Manda, S. A. M. A. Islam, M. R. Khatun and S. A. Samad, "Modelling the Spread of COVID-19 Among Doctors From the Asymptomatic Individuals" in Mathematical Engineering, Springer, 02 April, 2021, pp. 39-60, DOI:   10.1007/978-981-33-6264-2_3

I presented the whole process mathematically, starting with the concern about how the healthcare system can break down during the coronavirus infection and developed the initial concept to all analytical and numerical analysis and solutions. Other authors handle the research paper writing, formatting, spotting and correcting various errors and other various activities. The entire research was conducted under the guidance of Prof. Haider Ali Biswas. 

7. M. Biswas, M.A.Islam, S.Akter, S. Mandal, M. S. Khatun, S.A.Samad, A. K. Paul and M. Khatun, "Modelling the Effect of Self-Immunity and the Impacts of Asymptomatic and Symptomatic Individuals on COVID-19 Outbreak" Computer Modeling in Engineering & Sciences, 2020.   

In the above study, I solved difficult and numerical simulation tasks. He also solves some analytical equations to perform the task.

8. A. K. Paul* and M. H. A. Biswas, "Modeling and Assessment of Carbon Dioxide Concentration Emitted from the Coal-based Power Plant in Bangladesh" in International Conference on Industrial Engineering and Operations Management, Bangkok, Thailand, March 5, 2019. Link : http://ieomsociety.org/ieom2019/papers/472.pdf

This study is the first to think mathematically about how air pollutants that will be emitted from the proposed Rampal power plant near the Sundarbans, the world's largest mangrove forest, could affect the surrounding environment and health. I conducted the whole study including expressing the process through mathematical models and documenting it through numerical simulations. I have done all the work myself including the mathematical model development, analysis, correction, and refinement. Prof. Haider Ali Biswas provided various mathematical concepts during the course of this work and provided guidance in all mathematical and technical matters to get the results of the research properly and supported the entire research.

9. M. H. A. Biswas*, M. S. Khatun, M. A. Islam, S. Mandal, A. K. Paul and A. Ali, "Optimal control strategy to combat the spread of covid-19 in absence of effective vaccine" Journal of Applied Mathematics & Informatics, vol. 40, no. 4, pp. 633-656, 2022. DOI : 10.14317/jami.2022.633

10. A. K. Paul* and M. H. A. Biswas, "Modeling the Dynamics of Spreading Rumors and Fake News through Online and Social Media" in Proceedings of the 2nd International Conference on Industrial and Mechanical Engineering and Operations Management (IMEOM), Dhaka, 2019.  Link : http://www.ieomsociety.org/imeom/60.pdf

I got the idea from a previously studied research article and I modified it considering some extra aspects of the situation. I represented it at a conference and got the best paper award for that presentation.

Data Science, Machine Learning and Others

1. A. K. Paul*, L. Devnath and M. R. Islam, "A Highly Secured Mathematical Model for Data EncryptionUsing Fingerprint Data," International Journal on Data Science and Technology, vol. 2, no. 4, pp. 46-50, 2016.

2. A. K. Paul*. L. Devnath and M. R. Islam, "An Approach To Prove The Existence Of After Life By Analyzing Near Death Experience's Data With Mathematical Logic," Academic Research International, vol. 7, no. 4, pp. 1-8, 2016.

It was one of my most passionate works about Mathematics. I tried to model the parapsychological concept using mathematics to prove the existence of the Afterlife. I used the concept of time delusion, the brain working mechanism, and Near Death experience data for gathering evidence and building a mathematical model. Liton Devnath helps writing the paper and publishing as well. 

3. L. Devnath, A. K. Paul and M. R. Islam, "A Study on Binary Number of Gender Identification Based on Fingerprints," International Journal of Scientific & Engineering Research, vol. 7, no. 2, pp. 338-342, 2016.

4. B. Madhu, A. K. Paul and R. Roy, "Performance Comparison of Various Kernels of Support Vector Regression for Predicting Option Price," International Journal of Discrete Mathematics, vol. 4, no. 1, pp. 21-31, 2019. DOI : 10.11648/j.dmath.20190401.14

I did the whole analysis, computation, visualization and other technical works alone during my BSC in mathematics final project. In this project, I learned a lot about Machine learning, data science, visualization, optimization and etc. I was supervised by Raju Roy and my partner was B. Modhu. 

5. A. K. Paul*, P. K. Boni and M. Z. Islam, "A Data-Driven Study to Investigate the Causes of Severity of Road Accidents," 2022 13th International Conference on Computing Communication and Networking Technologies (ICCCNT), Kharagpur, India, 2022, pp. 1-7, doi: 10.1109/ICCCNT54827.2022.9984499.

In the above study, I started an investigation and presented a theoretical model. Later, I provided guidance on how to conduct the entire study and provided training and other software along with the necessary code for various analyses and calculations.

6. A. K. Paul* and M.H. A. Biswas, "Violence Detection: Introducing a Machine Learning Based Novel Method," 3rd International Conference on Industrial and Mechanical Engineering and Operations Management (IMEOM), Dhaka, Bangladesh, Dhaka, February 08, 2021. Link : Presentation Detail

In this study, I found that it is very critical to predict violent activities from the image of videos of human beings and for solving this problem I found a socio-behavioral theory and collected all the data according to that theory. Then for validating my newly invented method, I tested those data with a convolutional neural network model and predicted the new outcome by a 96% accuracy.

7. A. K. Paul*, M. M. Hasan and M. D. Hosen, "A New Data-Driven Method to Identify Violent Facial Expression," Preprint in Arxiv, 2023.  DOI: 10.48550/arXiv.2308.08658.

In this study, I found that it is very critical to predict violent activities from the image of videos of human beings and for solving this problem I found a socio-behavioral theory and collected all the data according to that theory. Then for validating my newly invented method, I tested those data with a convolutional neural network model and predicted the new outcome by a 96% accuracy.

1. Probabilistic Record Linkage Library,  MATLAB.

The first library in MATLAB for solving problems related to Probabilistic Record Linkage (written in MATLAB)

2. Analytical Analysis of an OCP with System of ODEs in MATLAB

A graphical interface for solving an Optimal Control Problem and performing other analyses. 

3. Image Detective: An Application for Identifying manipulated Images.

 An open-source application developed by me to identify the manipulations and edits in Images using different  image processing techniques in Javascript. 

4. Covid and Non-Covid Visualization with Histogram Oriented Gradient Features.

 Analysing the covid infected and healthy lung images to understand the differences visually in Python.

5. Bengali Handwritten Digit Recognition Applying Various Learning Algorithms with Image Processing and CNN.

 A comparison of different Deep learning and machine learning algorithms with features for Bengali Handwritten Digits Recognition in Python.