Adam Murray - Research Explorations

Recent Posts

Research explorations in computational drug discovery, geometric deep learning, and mathematical theory—from rigorous frameworks to playful curiosities.

Soap Film Surface Analysis: A Theoretical Framework for Cyclic Peptide Conformational Analysis

A proposed mathematical framework that applies minimal surface theory to cyclic peptide conformational analysis, offering a novel geometric perspective through the lens of soap film physics.

differential-geometry minimal-surfaces cyclic-peptides conformational-analysis theoretical-chemistry

Parallel Chemical Hierarchies: A Multi-Perspective Embedding Strategy for Cyclic Peptide Drug Discovery

A theoretical framework for molecular embeddings that preserves both synthetic and biological organizational principles through parallel hierarchical decomposition, with applications to cyclic peptide permeability prediction.

molecular-embeddings cyclic-peptides drug-discovery graph-theory information-theory cell-permeability

Generalized Adduct Intervals Problem: A Formal Mathematical Proof

A rigorous mathematical framework establishing optimal mass spacing strategies for mass spectrometry-based detection of combinatorial cyclic peptide libraries, providing provable upper bounds for multi-objective evolutionary algorithms in drug discovery.

mathematics algorithms mass-spectrometry optimization drug-discovery

Information-Theoretic Limits and Phase Transitions in Combinatorial Library Sampling

A mathematical framework for optimal sampling strategies in massive combinatorial chemical spaces, establishing fundamental limits, phase transitions, and experimental design principles through quotient space theory and information geometry.

30 min read
information-theory phase-transitions combinatorial-chemistry experimental-design quotient-spaces

Cloth of Gold: Competitive Cellular Automata as a Strategy Game

A game-theoretic analysis of a modified Conway's Game of Life where two players compete for survival and territory through strategic pattern placement and cellular evolution.

cellular-automata game-theory competitive-dynamics complex-systems strategic-programming

Graph-Theoretic Validation of Combinatorial Synthesis via Signal Processing

A mathematically rigorous framework for validating DNA-encoded library synthesis using only one-dimensional chromatographic signals and graph-theoretic constraints, without requiring mass spectrometry or molecular structure information.

graph-theory signal-processing discrete-morse-theory combinatorial-chemistry poisson-statistics