Dr. Sahaya Vijay Jeyaraj - Applied Mathematics & Chemical Reaction Networks

About Me

Dr. Sahaya Vijay Jeyaraj
Postdoctoral Researcher, NIMS

I am an interdisciplinary researcher with a strong background in applied mathematics, chemical kinetics, and chemical reaction networks. Currently, I am a postdoctoral researcher at the National Institute for Materials Science (NIMS), Japan, where I develop accurate mathematical models and analytical formulations to predict the properties and dynamics of complex, nonlinear chemical systems.

My doctoral research was in chemical graph theory, focusing on predicting the physicochemical properties of metamaterials and drug-related structures. The central contribution of that work was using regression analysis to evaluate a wide range of topological indices and identify those with the strongest predictive power for the physicochemical properties of several important classes of molecular structures.

Across both my doctoral and postdoctoral work, a single thread runs through everything: the analysis of chemical reaction networks. I am passionate about leveraging mathematical tools to gain deeper insight into chemical processes and to contribute to advances in materials science and related disciplines.

The greatest discoveries are made at the boundaries between disciplines, where different ways of thinking come together to reveal new understanding.

Research Interests

My current postdoctoral research concerns predicting the kinetic properties of chemical reaction networks in champion materials, using mathematical modelling based on ordinary differential equations (ODEs) and graph theory. Although the systems and fields differ, all of my projects rest on the same core framework: the analysis of chemical reaction networks.

Chemical Graph Theory

I represent molecules and crystals as graphs and design fast algorithms to describe their structure. These algorithms give counting polynomials and distance-based descriptors for boric acid, aluminophosphates and fullerene cages. I relate these descriptors to the NMR and ESR spectral patterns of boric acid nanosheets. I then use them in quantitative structure–property relationship (QSPR) and machine-learning models. These models predict the properties of drugs and graphene nanoribbons.

3D view of a hydrogen-bonded boric acid sheet with boron in green, oxygen in red and hydrogen in blue, and a log-log plot of its Wiener index against the number of atoms — A hydrogen-bonded boric acid sheet treated as a graph, with B, O and H atoms as vertices. (a) A 168-atom sheet, with boron in green, oxygen in red and hydrogen in blue. Solid lines are covalent bonds and dotted lines are hydrogen bonds. (b) The exact Wiener index for sheets of 42 to 6,048 atoms approaches a slope of 5/2.

Autocatalysis & the Origin of Life

How did the first chemical networks begin to amplify themselves? I study this by writing protometabolism in an open system as a reaction network of ordinary differential equations (ODEs). From this model I derived the rate at which autocatalysis amplifies itself in linear networks. This rate shows when a catalytic network grows and keeps itself alive, and when it fades away. A manuscript on this result is under minor revision at Physical Review E. This gives a clear kinetic test for self-sustaining chemistry.

Simulated autocatalytic cycle shown in 3D, with a plot of total amount against time at three loss rates — A simulated six-species autocatalytic cycle with illustrative rates. (a) Sphere size shows each species' share of the growing mode, and the last step doubles X₁. (b) The total amount grows, holds or decays as the loss rate d passes the threshold d*. Dots are numerical integration and dashed lines are the exact growth rate.

Mathematical & Computational Modelling

Across all my projects, I turn a reaction network into equations that I can solve and interpret. I developed methods that estimate how long an autocatalytic network survives. I also separate the dynamics of linear networks into their individual timescales. These methods rest on linear algebra, stability analysis and timescale analysis. I implement and test them in Python and Mathematica, and apply them to the origin of life and electrochemistry. These tools let me compare different systems in one framework.

3D plot of trajectories reaching one steady state, with a plot of the distance from steady state showing two timescales — A simulated three-species linear network with illustrative rates. (a) Trajectories from five starting compositions reach one steady state. (b) The distance from steady state follows two timescales, which come from the eigenvalues of the rate matrix.

Electrochemical Impedance Spectroscopy

An impedance spectrum carries the kinetics of every step in a catalytic reaction. I build analytical microkinetic models that read this kinetic information for multi-step reactions. By solving the kinetic ODEs, I obtained a formula for the surface coverage. From it I derived a new equation for fitting electrochemical impedance spectroscopy (EIS) data. The resulting impedance spectra and Bode plots connect directly to the kinetic timescales of a catalyst. I also simulate and fit spectra numerically.

3D plot of impedance against frequency, with a Nyquist plot comparing the simulation and the linearised model — Impedance simulated in the time domain for a textbook Volmer–Heyrovsky reaction with illustrative rate constants. (a) Impedance against frequency in 3D. (b) The Nyquist plot, where dots are the simulation and the line is the linearised model. Their largest relative difference is 5 × 10⁻⁵.

AI-Assisted Research & Development

I use AI tools as a regular part of my research and software work. I direct agentic coding tools such as Claude Code to build programs from specifications that I write. I built a no-code graphical tool this way, and it is now under peer review. I defined every algorithm and feature in it myself. I also use AI assistants to draft and review code, derivations and manuscripts. I never accept an output unchecked. I validate each one against analytical results, numerical tests or known reference values.

3D plot of solver error against tolerance and cycle length with a pass limit, and a parity plot of computed against exact growth rates — Validation tests on a numerical solver. (a) Relative error of the computed growth rate in 30 tests, where the plane marks the 10⁻⁶ pass limit. (b) Computed against exact growth rates for 40 random networks.

Scientific Computing & Open Tools

I build open software that makes molecular descriptors easy to compute and check. PyTIE is a Python program of four packages. It calculates degree-based topological descriptors and molecular entropy from molecular graphs, and its code is on GitHub. The method is described in an arXiv preprint. PyTIE automates calculations that are slow and error-prone by hand, so large sets of molecules can be analysed quickly. Because the code is open, other researchers can reuse it, check it and extend it.

3D view of a graphene nanoribbon coloured by vertex degree, with a plot of three topological descriptors against the number of atoms — Degree-based descriptors computed for armchair graphene nanoribbons, with carbon atoms as vertices. (a) A 94-atom ribbon, coloured by vertex degree. (b) The first Zagreb (M₁), Randić (R) and atom-bond connectivity (ABC) indices grow linearly with size.

Skills & Expertise

Each card uses a simple picture and a plain-language note, so the tools and methods make sense even to readers outside my field.

A short Python function and the value it prints

Programming

I write computer programs that run the mathematical models and simulations behind my research.

Python · C++ · Java · HTML · CSS

A rate equation and its solution, typeset

Scientific Software

Specialised tools for heavy calculation, symbolic mathematics, and preparing scientific documents.

MATLAB · Mathematica · Chemcraft · LaTeX · Flash8

Amount of A falling and amount of B rising over time

Research Methods

The mathematical techniques I use to describe how chemicals react and change over time.

ODE modelling · reaction networks · graph theory · QSPR · machine learning · impedance analysis

Naphthalene drawn as a graph, with each atom labelled by its degree

Software I Built

Open-source Python tools (PyTIE) I developed that measure the structure of molecules automatically.

PyTIE_D · PyTIE_DS · PyTIE_SMS_DE · PyTIE_SMS_DSE — GitHub ↗

Two groups of points separated by a line learned from the data

Certifications

Certified training in using Python for machine learning.

Python Programming for Machine Learning (Certificate No. 1BHGBFVZ)

The word for hello in Tamil and in English

Languages

Languages I read, write, and speak fluently.

English · Tamil

Talks & Presentations

Invited lectures, keynote addresses, and conference presentations on chemical reaction networks, mathematical biology, and chemical graph theory.

Invited & Keynote Talks

Resource Person

Mathematical Tools and Modern Techniques for Research, Thesis Writing and Scholarly Publication

Dhanalakshmi Srinivasan University, Tiruchirappalli, India · 8 September 2026

Invited Speaker

International Faculty Development Programme: Enhancing Research Capacity - Publication, Grants and Research Impact

Dhanalakshmi Srinivasan University, Tiruchirappalli, India · 27 August 2026

Keynote

3rd International Conference on Recent Trends in Data Science (ICRTDS-2026)

St. Xavier's College (Autonomous), Palayamkottai, India · 5-6 March 2026

Keynote

3rd International Conference on Innovation in Science and Humanities (ICISH-2025)

Saveetha Engineering College, Chennai, India · 19-20 August 2025

Conference & Symposium Presentations

Poster Presentation

Microkinetic from the Analytical Impedance of the Heyrovsky-Volmer-Tafel Mechanism

NIMS Award Symposium 2026, Tsukuba International Congress Center, Tsukuba, Japan · 10 November 2026

Presentation

Calculating the Lifetime of Autocatalytic Networks

Joint Conference of the Asian Conference on Mathematical Biology & Annual Meeting of the Japanese Society for Mathematical Biology, Kyoto Terrsa, Kyoto, Japan · 11-17 July 2025

Presentation

Timescale Decomposition of Linear Chemical Reaction Networks

Asian Conference for Mathematical Biology, Kyoto Terrsa, Kyoto, Japan · 11-17 July 2025

Presentation

Analyzing the Stability of Autocatalytic Chemical Reaction Networks Based on their Amplification Rate

Japan Geoscience Union Meeting 2025, Makuhari Messe, Chiba, Japan · 29 May 2025

Presentation

Calculating the Lifetime of Autocatalytic Chemical Reaction Networks

CSRS Interim Progress Report Meeting, RIKEN Yokohama Campus, Yokohama, Japan · 17 November 2025

Presentation

A Cut-Method Technique Used on Topological Descriptors of Melamine Cyanuric Acid

International Conference on Mathematics and Its Applications (ICMA-2024), Sacred Heart College (Autonomous), Tirupattur, India · 15-16 February 2024

Presentation

Topological Properties and Entropy Calculations of Aluminophosphates

International Conference on Modelling, Simulation and Optimization of Energy Systems (MSOES-2023), Canadian University Dubai, UAE · 17-18 June 2023

Presentation

Computation of Wiener Descriptor for Melamine Cyanuric Acid Structure

International Conference on Recent Developments in Mathematics (ICRDM-2022), Canadian University Dubai, UAE · 24-26 August 2022

Publications

Peer-reviewed research in mathematical modelling, topological analysis, molecular descriptors, and computational science.

16Publications

2023-26Active Years

-Citations

-h-index

View on Google Scholar ↗

1. Kinetic Boundary between Autocatalysis and Diffusion in the Origin of Life

Sahaya Vijay Jeyaraj, Hirokazu Komatsu, Tomoharu Suda, Ryuhei Nakamuram, Hideshi Ooka

Chemrxiv(2026)

View Publication

2. Anticancer Activity with Physical Property Analysis of Mollugo Cerviana (L.) Ser. Whole Plant Extract on Hepatocellular Carcinomic Cell Lines - HEPG2

F. Sherin Rebecca, R. Sharmila, Sahaya Vijay Jeyaraj, Fikadu Tesgera Tolasa, Rajamanickam Pon Nivedha, Janani Ezhilan, Tony Augustine

Scientific Reports (2026)

View Publication

3. Topological, Graph-Spectral Properties, NMR and ESR Spectral Patterns of Hydrogen-Bonded Nanosheets of Boric Acid

S. Prabhu, Sahaya Vijay Jeyaraj, V. Manimozhi, Micheal Arockiaraj, Roy Santiago, J. Celin Fiona, Krishna Balasubramanian

Journal of Cluster Science (2026)

View Publication

4. Machine Learning Approach on Topological Features of Bottom-up Synthesized Graphene Nanoribbons Using Valency-Based Descriptors

K. Jyothish, S. Roy, P. Chandra Sekar, K. B. Gayathri, Sahaya Vijay Jeyaraj, T. Augustine

Frontiers in Chemistry (2026)

View Publication

5. PyTIE: A Python Program for the Evaluation of Degree-Based Topological Descriptors and Molecular Entropy

Sahaya Vijay Jeyaraj, S. Roy, S. Govardhan, Tony Augustine, K. Jyothish

arXiv (2025)

View Publication

6. Machine Learning Approach on Degree-Sum-Based Topological Indices of Bottom-up-Synthesized Graphene Nanoribbons

K. B. Gayathri, S. Roy, Sahaya Vijay Jeyaraj, P. Chandra Sekar, Tony Augustine

Nano (2025)

View Publication

7. Graph-Theoretical Approach to Topological Features of Zeolitic Tetrahedral Imidazolate Framework-3

Abdelli Fathi, Tony Augustine, Mohamad Nazri Husin, Sahaya Vijay Jeyaraj, Jain Maria Thomas, Santiago Roy

Malaysian Journal of Fundamental and Applied Sciences (MJFAS) (2025)

View Publication

8. Efficient Generation of Specific Counting Polynomials and Its Subsequent Indices of Complex Boric Acid Structure

Sahaya Vijay Jeyaraj, Roy Santiago, Chandra Sekar Ponnusamy, Jain Maria Thomas, Mohamad Husin, Abdelli Fathi

Current Organic Synthesis (2025)

View Publication

9. Exploring Neighborhood Topological Descriptors for QSPR Analysis and Entropy Measures of Some Anti-cancer Drugs

Tony Augustine, Roy Santiago, Sahaya Vijay Jeyaraj, Mohamad Azeem

Current Organic Synthesis (2025)

View Publication

10. QSPR Modeling of Central Nervous System (CNS) Drug Activity Using Molecular Descriptors

Sahaya Vijay Jeyaraj, R. Santiago, M. Azeem, T. Augustine, M. N. Husin

Current Organic Synthesis (2024)

View Publication

11. Valency-Based Molecular Descriptor on Structural-Property Relationship of Ni Tetrathiafulvalene Tetrathionate

A. Fathi, Sahaya Vijay Jeyaraj, M. N. Husin, Tony Augustine

Malaysian Journal of Fundamental and Applied Sciences (MJFAS) (2024)

View Publication

12. In Silico Rationalization of Piperidin-4-One Analogs as Anaplastic Lymphoma Kinase Inhibitors: DFT, Topological Descriptor, Molecular Docking and Pharmacological Feature Profiling

S. Sonadevi, D. Rajaraman, D. Periyasamy, Sahaya Vijay Jeyaraj, Tony Augustine, Roy Santiago, M. Saritha, L. Athishu Anthony

Journal of Molecular Structure (2024)

View Publication

13. A Study on Efficient Technique for Generating Vertex-Based Topological Characterization of Boric Acid 2D Structure

Sahaya Vijay Jeyaraj, Roy Santiago

ACS Omega (2023)

View Publication

14. Topological Properties and Entropy Calculations of Aluminophosphates

Sahaya Vijay Jeyaraj, Santiago Roy, Bheeter Charles Beromeo, Mohamad Nazri Husin, Tony Augustine, R. U. Gobithaasan, Michael Easuraja

Mathematics (2023)

View Publication

15. Computation of Wiener Descriptor for Melamine Cyanuric Acid Structure

Sahaya Vijay Jeyaraj, S. Roy

Polycyclic Aromatic Compounds (2023)

View Publication

16. Topological Study on Degree-Based Molecular Descriptors of Fullerene Cages

T. Augustine, S. Roy, Sahaya Vijay Jeyaraj, J. Maria Thomas, P. Shanmugam

Molecular Physics (2023)

View Publication

About Me

Research Interests

Chemical Graph Theory

Autocatalysis & the Origin of Life

Mathematical & Computational Modelling

Electrochemical Impedance Spectroscopy

AI-Assisted Research & Development

Scientific Computing & Open Tools

Skills & Expertise

Programming

Scientific Software

Research Methods

Software I Built

Certifications

Languages

Talks & Presentations

Invited & Keynote Talks

Mathematical Tools and Modern Techniques for Research, Thesis Writing and Scholarly Publication

International Faculty Development Programme: Enhancing Research Capacity - Publication, Grants and Research Impact

3rd International Conference on Recent Trends in Data Science (ICRTDS-2026)

3rd International Conference on Innovation in Science and Humanities (ICISH-2025)

Conference & Symposium Presentations

Microkinetic from the Analytical Impedance of the Heyrovsky-Volmer-Tafel Mechanism

Calculating the Lifetime of Autocatalytic Networks

Timescale Decomposition of Linear Chemical Reaction Networks

Analyzing the Stability of Autocatalytic Chemical Reaction Networks Based on their Amplification Rate

Calculating the Lifetime of Autocatalytic Chemical Reaction Networks

A Cut-Method Technique Used on Topological Descriptors of Melamine Cyanuric Acid

Topological Properties and Entropy Calculations of Aluminophosphates

Computation of Wiener Descriptor for Melamine Cyanuric Acid Structure

Publications

1. Kinetic Boundary between Autocatalysis and Diffusion in the Origin of Life

2. Anticancer Activity with Physical Property Analysis of Mollugo Cerviana (L.) Ser. Whole Plant Extract on Hepatocellular Carcinomic Cell Lines - HEPG2

3. Topological, Graph-Spectral Properties, NMR and ESR Spectral Patterns of Hydrogen-Bonded Nanosheets of Boric Acid

4. Machine Learning Approach on Topological Features of Bottom-up Synthesized Graphene Nanoribbons Using Valency-Based Descriptors

5. PyTIE: A Python Program for the Evaluation of Degree-Based Topological Descriptors and Molecular Entropy

6. Machine Learning Approach on Degree-Sum-Based Topological Indices of Bottom-up-Synthesized Graphene Nanoribbons

7. Graph-Theoretical Approach to Topological Features of Zeolitic Tetrahedral Imidazolate Framework-3

8. Efficient Generation of Specific Counting Polynomials and Its Subsequent Indices of Complex Boric Acid Structure

9. Exploring Neighborhood Topological Descriptors for QSPR Analysis and Entropy Measures of Some Anti-cancer Drugs

10. QSPR Modeling of Central Nervous System (CNS) Drug Activity Using Molecular Descriptors

11. Valency-Based Molecular Descriptor on Structural-Property Relationship of Ni Tetrathiafulvalene Tetrathionate

12. In Silico Rationalization of Piperidin-4-One Analogs as Anaplastic Lymphoma Kinase Inhibitors: DFT, Topological Descriptor, Molecular Docking and Pharmacological Feature Profiling

13. A Study on Efficient Technique for Generating Vertex-Based Topological Characterization of Boric Acid 2D Structure

14. Topological Properties and Entropy Calculations of Aluminophosphates

15. Computation of Wiener Descriptor for Melamine Cyanuric Acid Structure

16. Topological Study on Degree-Based Molecular Descriptors of Fullerene Cages

Contact

Email

Postal Address

Academic Profiles