Adam Murray - Research Explorations
2026·06·142025·06·052025·05·282025·04·232025·03·102025·02·272024·10·13

Recent Posts

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

  1. 2026·06·14 Light at the Specimen Surface: Geometric Optics of Petri Dish Imaging A geometric optics framework for predicting and avoiding specular artifacts in routine biological photography, derived from first principles and illustrated through an interactive ray-tracing simulation of a layered petri dish system. OpticsOpticsphysics.opticsAdaptive optics. Astronomical optics. Atmospheric optics. Biomedical optics. Cardinal points. Collimation. Doppler effect. Fiber optics. Fourier optics. Geometrical optics (Gradient index optics. Holography. Infrared optics. Integrated optics. Laser applications. Laser optical systems. Lasers. Light amplification. Light diffraction. Luminescence. Microoptics. Nano optics. Ocean optics. Optical computing. Optical devices. Optical imaging. Optical materials. Optical metrology. Optical microscopy. Optical properties. Optical signal processing. Optical testing techniques. Optical wave propagation. Paraxial optics. Photoabsorption. Photoexcitations. Physical optics. Physiological optics. Quantum optics. Segmented optics. Spectra. Statistical optics. Surface optics. Ultrafast optics. Wave optics. X-ray optics.Medical PhysicsMedical Physicsphysics.med-phRadiation therapy. Radiation dosimetry. Biomedical imaging modelling. Reconstruction, processing, and analysis. Biomedical system modelling and analysis. Health physics. New imaging or therapy modalities.Quantitative MethodsQuantitative Methodsq-bio.QMAll experimental, numerical, statistical and mathematical contributions of value to biologyImage and Video ProcessingImage and Video Processingeess.IVTheory, algorithms, and architectures for the formation, capture, processing, communication, analysis, and display of images, video, and multidimensional signals in a wide variety of applications. Topics of interest include: mathematical, statistical, and perceptual image and video modeling and representation; linear and nonlinear filtering, de-blurring, enhancement, restoration, and reconstruction from degraded, low-resolution or tomographic data; lossless and lossy compression and coding; segmentation, alignment, and recognition; image rendering, visualization, and printing; computational imaging, including ultrasound, tomographic and magnetic resonance imaging; and image and video analysis, synthesis, storage, search and retrieval.Biological PhysicsBiological Physicsphysics.bio-phMolecular biophysics, cellular biophysics, neurological biophysics, membrane biophysics, single-molecule biophysics, ecological biophysics, quantum phenomena in biological systems (quantum biophysics), theoretical biophysics, molecular dynamics/modeling and simulation, game theory, biomechanics, bioinformatics, microorganisms, virology, evolution, biophysical methods.
  2. 2025·06·05 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. BiomoleculesBiomoleculesq-bio.BMDNA, RNA, proteins, lipids, etc.; molecular structures and folding kinetics; molecular interactions; single-molecule manipulation.Differential GeometryDifferential Geometrymath.DGComplex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysisMetric GeometryMetric Geometrymath.MGEuclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spacesBiological PhysicsBiological Physicsphysics.bio-phMolecular biophysics, cellular biophysics, neurological biophysics, membrane biophysics, single-molecule biophysics, ecological biophysics, quantum phenomena in biological systems (quantum biophysics), theoretical biophysics, molecular dynamics/modeling and simulation, game theory, biomechanics, bioinformatics, microorganisms, virology, evolution, biophysical methods.Quantitative MethodsQuantitative Methodsq-bio.QMAll experimental, numerical, statistical and mathematical contributions of value to biology
  3. 2025·05·28 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. BiomoleculesBiomoleculesq-bio.BMDNA, RNA, proteins, lipids, etc.; molecular structures and folding kinetics; molecular interactions; single-molecule manipulation.Machine LearningMachine Learningcs.LGPapers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.Information TheoryInformation Theorycs.ITCovers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.Quantitative MethodsQuantitative Methodsq-bio.QMAll experimental, numerical, statistical and mathematical contributions of value to biology
  4. 2025·04·23 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. Data Structures and AlgorithmsData Structures and Algorithmscs.DSCovers data structures and analysis of algorithms. Roughly includes material in ACM Subject Classes E.1, E.2, F.2.1, and F.2.2.Optimization and ControlOptimization and Controlmath.OCOperations research, linear programming, control theory, systems theory, optimal control, game theoryQuantitative MethodsQuantitative Methodsq-bio.QMAll experimental, numerical, statistical and mathematical contributions of value to biologyComputational GeometryComputational Geometrycs.CGRoughly includes material in ACM Subject Classes I.3.5 and F.2.2.Neural and Evolutionary ComputingNeural and Evolutionary Computingcs.NECovers neural networks, connectionism, genetic algorithms, artificial life, adaptive behavior. Roughly includes some material in ACM Subject Class C.1.3, I.2.6, I.5.
  5. 2025·03·10 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. Information TheoryInformation Theorycs.ITCovers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.ProbabilityProbabilitymath.PRTheory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theoryStatistical MechanicsStatistical Mechanicscond-mat.stat-mechPhase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulenceOptimization and ControlOptimization and Controlmath.OCOperations research, linear programming, control theory, systems theory, optimal control, game theoryMethodologyMethodologystat.MEDesign, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods 30 min
  6. 2025·02·27 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 and Lattice GasesCellular Automata and Lattice Gasesnlin.CGComputational methods, time series analysis, signal processing, wavelets, lattice gasesComputer Science and Game TheoryComputer Science and Game Theorycs.GTCovers all theoretical and applied aspects at the intersection of computer science and game theory, including work in mechanism design, learning in games (which may overlap with Learning), foundations of agent modeling in games (which may overlap with Multiagent systems), coordination, specification and formal methods for non-cooperative computational environments. The area also deals with applications of game theory to areas such as electronic commerce.Dynamical SystemsDynamical Systemsmath.DSDynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equationsComputational ComplexityComputational Complexitycs.CCCovers models of computation, complexity classes, structural complexity, complexity tradeoffs, upper and lower bounds. Roughly includes material in ACM Subject Classes F.1 (computation by abstract devices), F.2.3 (tradeoffs among complexity measures), and F.4.3 (formal languages), although some material in formal languages may be more appropriate for Logic in Computer Science. Some material in F.2.1 and F.2.2, may also be appropriate here, but is more likely to have Data Structures and Algorithms as the primary subject area.Adaptation and Self-Organizing SystemsAdaptation and Self-Organizing Systemsnlin.AOAdaptation, self-organizing systems, statistical physics, fluctuating systems, stochastic processes, interacting particle systems, machine learning
  7. 2024·10·13 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. Quantitative MethodsQuantitative Methodsq-bio.QMAll experimental, numerical, statistical and mathematical contributions of value to biologySignal ProcessingSignal Processingeess.SPTheory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.CombinatoricsCombinatoricsmath.CODiscrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theoryData Structures and AlgorithmsData Structures and Algorithmscs.DSCovers data structures and analysis of algorithms. Roughly includes material in ACM Subject Classes E.1, E.2, F.2.1, and F.2.2.ApplicationsApplicationsstat.APBiology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences