nauty and Traces: Graph Isomorphism Algorithms
An updated description of nauty and introduction of Traces, two programs for graph isomorphism testing and canonical labeling using the individualization-refinement paradigm.
Scientific Computing
Kabsch-Horn Cookbook: Differentiable Alignment
A differentiable point-set alignment library implementing N-dimensional Kabsch, Horn quaternion, and Umeyama scaling algorithms with per-point weights, batch dimensions, and custom autograd across NumPy, PyTorch, JAX, TensorFlow, and MLX.
Second-Order Langevin Equation for Field Simulations
Proposes the Hyperbolic Algorithm for Euclidean field theory simulations. By adding a second-order fictitious time derivative to the Langevin equation, the method reduces systematic errors from O(ε) down to O(ε²).
AI & Physical Sciences Taxonomy: A Seven-Vector Framework
Personal working taxonomy for categorizing papers as Method, Theory, Resource, Systematization, Position, Discovery, or Application contributions using a superposition model.
Molecular String Renderer: Robust Visualization Tool
A fault-tolerant RDKit wrapper treating molecular visualization as a software engineering problem, implementing strategy pattern for SVG generation with automatic raster fallback, native SELFIES support for generative AI workflows, and strict type safety for reliable batch processing of millions of molecules in training pipelines.
Exponential Random Numbers: Two Classic Algorithms
Explore two fundamental approaches to generating exponentially distributed random numbers: the modern inverse transform method using logarithms and von Neumann’s ingenious 1951 comparison-based algorithm that avoids transcendental functions entirely.
Modernizing Rahman''s 1964 Argon Simulation
A digital restoration of Rahman’s seminal 1964 molecular dynamics paper using LAMMPS and a production-grade Python analysis pipeline featuring intelligent decorator-based caching, fully vectorized NumPy computations for O(N^2) operations, and modern tooling (uv, type hints, Makefile automation) transforming academic scripts into reproducible research toolkit.
Modernizing Rahman's 1964 Argon Simulation
I replicated Rahman’s landmark 1964 liquid argon molecular dynamics simulation using modern tools, building a production-grade Python analysis pipeline with intelligent caching, vectorization, and type safety to bridge vintage science with contemporary software engineering.
Kabsch Algorithm: NumPy, PyTorch, TensorFlow, and JAX
Learn to align molecular structures and point clouds using the Kabsch algorithm, with differentiable implementations for modern ML frameworks.
Automated Adatom Diffusion Workflow
A complete input-to-analysis workflow for simulating adatom diffusion on FCC metal surfaces using LAMMPS and EAM potentials, providing comparative datasets for copper and platinum that demonstrate how atomic mass and bonding strength affect surface dynamics, with automated Python analysis generating publication-ready visualizations.
IQCRNN: Certified Stability for Neural Networks
A PyTorch implementation enforcing strict Lyapunov stability guarantees on recurrent neural network controllers through Integral Quadratic Constraints, bridging 1990s robust control theory with modern deep reinforcement learning by solving semidefinite programs inside the gradient descent loop to provide mathematical certificates of safety.
Cartesian Genetic Programming in Julia
A sophomore year exploration of evolutionary algorithms applied to Atari games, implementing NEAT-inspired speciation mechanisms for Cartesian Genetic Programming to protect topological innovation while introducing custom crossover operators (subgraph, aligned-node) for evolving neural network policies.