Chemical Graph Theory
To study the physicochemical, biological, and pharmaceutical properties of chemical compounds, a lot of laboratory equipment is required. Since these experiments are time-consuming and expensive, an alternative method has been proposed to get rid of these constraints. The proposed method of predicting the required properties is nothing but finding the topological indices and performing QSAR/QSPR analysis. The study of the topological indices helps us understand the physicochemical and biomedical properties of many chemical compounds. This research is mainly focused on predicting the physical, chemical, and biological properties of phytochemicals using topological indices. QSAR (Qualitative Structure-Activity Relationships) and QSPR (Qualitative Structure-Property Relationships) analysis will be carried out to study the physicochemical properties and bioactivity of the chemical structures and molecules using topological indices. This research outcome contributes to the Department of Medicine and Pharmacology. The predicted properties and correlation coefficients might help them in designing new antiviral drugs, composite drugs, and drug delivery systems.
Research Areas
Fractal Geometry, Fractal Interpolation and Approximation, Fractal Applications
Fractal geometry and fractal analysis have a wide range of applications in complex analysis (for example Julia and Fatou sets), dynamical systems, economics, mathematical finance (for example modelling stock prices through fractal times series), mathematical biology, computational biology (for instance Feigenbaum attractor, Lorenz attractor, Henon map), number theory (for example Fibonacci sequence), stochastics and many more scientific and engineering branches. Fractal interpolation is the generalised spline interpolation technique and also the most advanced interpolation technique which attracts researchers for the approximation of rough functions and interpolating certain data generated by a function whose certain derivatives are irregular in nature. The presence of the scaling factors in the structure of a fractal interpolant provides a large flexibility to its shape. Using fractal interpolation, one can produce not only irregular objects but also smooth curves by choosing the appropriate IFS and its parameters (scaling factors and shape parameters) on suitable compact spaces. The research in fractal applications includes Solutions of BVPs, Graph Directed Fractal Interpolation, Fractal Image Compression, Fractals and Biology, Scattered Data Interpolation, etc.
Fluid flow, heat, and mass transfer
Fluid mechanics is the study of fluid behaviour (liquids, gases, blood, and plasmas) at rest and in motion. Fluid mechanics has a wide range of applications in mechanical and chemical engineering, in biological systems, and in astrophysics. The transport of heat and mass are fundamental features of fluid flows. As such, thermal-fluid-mass transfer processes are essential to addressing energy problems of conserving energy, enhancing energy efficiency and the overall energy crises. Research focuses on thermal management and thermal control for industrial applications, from the study of high performance heat transfer surfaces. And also extended to fluid boundary layers, which continues to be useful in understanding the characteristics of fluid flow that are pivotal to reducing energy consumption.
A Commutative Algebraic Approach to Generating Functions
The research explores connections between algebraic tools and number thirty, particularly focusing on generating functions and trigonometric sums. A novel approach using commutative algebra has been introduced to simplify and generalize established results, revealing intriguing parallels between reciprocity laws and partial fraction identities. The exploration extends to degenerative Bernoulli and Euler numbers, Umbral Calculus, and Hypergeometric Functions, supported by efficient algorithms in Computer Algebra systems. Current investigations concentrate on the geometric connections between partial fractions and reciprocity laws, the establishment of an algebraic Mittag-Leffler Theorem, and algebraic generalizations of Ramanujan sums with applications to deletion correction codes.
Microlocal Analysis, Pseudodifferential Operators, and Hyperbolic Operators
We are interested in performing a singularity analysis of hyperbolic operators with singular and oscillatory coefficients in this area. It is well-known that these operators exhibit a loss of regularity. Using microlocal techniques (specifically, space-frequency techniques), we capture this loss of regularity by tracking changes in the underlying symplectic geometry. We are also interested in cases where coefficients degenerate, vanishing at certain points, known as Fuchsian operators. For these problems, we have demonstrated a propagation of singularities.
AI-ML and Deep Learning Methods in Medical Diagnostics and State of Art Health care with reference to Coronary Artery Disease, Tuberculosis, Cancer
Recommend the drug and dosage to be prescribed to meet targeted cholesterol level.
Study of Patient Specific Three-Dimensional Left Ventricular Dynamics
To predict Treatment Outcome and Loss to Follow Up at Scale in Tuberculosis using Machine learning with reference to Karnataka state TB Data.
Predicting Metastasis in Cancer Patients Using Machine Learning: A Comparative Analysis of Models
AI-Development, Deployment, and Interpretation with High Performance Computing and Big Data Computing
Web3-based Decentralized MLOps: Empowering Transparency, Control, and Collaboration in AI Development
Evaluating Large Language Models for Structured Data Tasks: Scalability, Efficiency, and ROI in Text-to-SQL Conversion and Beyond
Enhancing AI Interpretability with Formal Concept Lattices: Local, Global, and Contrastive Explanations for Trustworthy Models
Computer Vision and Image Processing with applications in Health care
Patient Specific Three-Dimensional Left Ventricular Fluid Dynamic Analysis using Cardiac Ultrasound
Automatic Segmentation and Learning of the Distribution of White Matter Hyperintensities from 3D Neuro MRI for a Longitudinal Study
Use of Artificial Intelligence based technique for the retrieval of Atmospheric Motion Winds
Feature tracking algorithms find widespread application in various image processing domains. Meteorological departments, specifically concerned with determining horizontal winds, commonly employ these algorithms to track cloud features or changes in moisture images. This tracking process is often referred to as Atmospheric Motion Vectors (AMVs). AMVs find versatile applications, ranging from enhancing the assimilation of Numerical Weather Prediction (NWP) data for improved forecasting accuracy to facilitating super resolution techniques for satellite images, thereby elevating the quality of meteorological analysis
Privacy Preserving Machine Learning
The world generated 2.5 exabytes of data per day in 2018. With the widespread adoption of IoT, this number is expected to cross a hundredfold by 2025. All these data collected are sent to the cloud for storage and analysis. The data is nevertheless encrypted on its transmission. However, the machine learning models for data analysis is built on the decrypted data at the cloud servers. Thus, the data is exposed to the ML service providers. This poses a serious hindrance due to the strict privacy laws by countries, the rigorous data policies of companies, and growing privacy concerns among users.
Infectious Disease Modeling with reference to translational research
To model within-host and study the disease spread and behaviour dynamics and patterns with reference to diseases such as Dengue, COVID-19, Tuberculosis and Hansen’s Disease
To model vector-host and study the disease spread and behaviour dynamics and patterns with reference to diseases such as Dengue, COVID-19, Tuberculosis and Hansen’s Disease
Multiscale modelling studies with reference to diseases such as Dengue, COVID-19, Tuberculosis and Hansen’s Disease
Cryptography and Information Security: IoT/Blockchain based Security Systems
The research explores in developing novel proxy re-encryption (PRE) schemes with enhanced security and efficiency properties, by advancing the state-of-the-art in secure decentralized data-sharing technologies in cloud environments. Exploring the applications of PRE schemes in practical data-sharing scenarios, such as Healthcare data, Finance applications, with secure and privacy-preserving file sharing, identity, encrypted messaging, collaborative data analytics, ensuring end-to-end data confidentiality and access control. Exploration extends to enhance the computation and communication cost of the designed schemes using Lightweight Cryptography.
Social Security Data Mining
Social security schemes are the provisions and funding of various benefits by the Government for its citizens or beneficiaries. The major facilities provided by the Government include access to health care, income security, unemployment, work injury and insurance, mother and child care, etc. The research explores beneficiary, payment, policy, fraud, process, dialog, feedback and service-delivery centric analysis using various data mining techniques that includes AI/ML/DL and latest technology trends.
Computational Graph Theory
Graph theory is a rich and versatile field of mathematics that explores the properties and applications of graphs, which are structures made up of nodes (or vertices) connected by edges. One intriguing concept within graph theory is graceful labelling, where the vertices of a graph are assigned unique labels such that the absolute differences of the labels at the endpoints of each edge are distinct. Another important area of graph theory is the study of metric dimensions, which involves finding the minimum number of vertices required to uniquely determine all other vertices based on their distances to the selected set. This concept has practical applications in network navigation, robotic path planning, and sensor placement. Additionally, graph theoretical concepts play a crucial role in cryptography and authentication techniques, providing robust methods for securing data, ensuring privacy, and verifying identities through the use of complex graph structures and algorithms. These applications demonstrate the broad utility of graph theory in solving real-world problems across various domains.
SOCIETY OF ACTUARIES (SOA) RESEARCH PROJECTS
Using Interpretable Machine Learning Methods
This project endeavors to deliver a comprehensive research paper outlining a framework for interpretable machine learning algorithms tailored for fraud detection in health insurance. Machine learning algorithms excel at constructing intricate models by discerning patterns in data, yet the risk of overfitting to training data necessitates rigorous testing by modellers and users. While certain validation practices for linear models apply to machine learning, the challenge of interpretability remains pronounced.
Crop Insurance Revenue Protection
This research delves into the design and actuarial pricing of a specialized crop insurance product for farmers, utilizing actuarial data science and derivatives. It includes key features of the crop insurance product such as coverage, target market, and unique selling points. The research also examines the current state of crop insurance risk management and the crop reinsurance industry in the U.S., as well as the use of derivatives to hedge crop revenue protection risks. Considerations for designing the product for the Indian market, including regulatory, market, and cultural aspects will be looked into as part of the project.
A Framework to Integrate Artificial Intelligence and Machine Learning for Next Generation Hybrid Educational System
The main objective of this research is to bridge the gap between integrating AI and ML into the current educational system, facilitating growth in the sector. It aims to find an easily adoptable solution for educators, provide a scalable implementation for institutions, and create a dashboard for administration performance monitoring. The study’s outcome will be a generic framework for integrating AI and ML into hybrid education, addressing current challenges.
