Explorations

research notes, experiments, and technical investigations.

Lacunae

Accelerated MRI Reconstruction from Undersampled K-Space via U-Net

U-Net that reconstructs full MRI scans from 25% of the frequency data.

artificial-intelligencemedicinemathematics

Random Cartesian UndersamplingK-Space Masking (4x Acceleration)U-Net with Skip ConnectionsL1 Reconstruction LossSSIM / PSNR EvaluationInverse FFT Baseline

PythonPyTorchfastMRIh5pyscikit-imagewandb

Github

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Precursor

Cross-Asset Momentum Spillover from Commodities to Sector Equities via Granger Causality

Tests whether commodity price momentum predicts sector equity moves 1–5 days ahead.

financeeconomicsmathematics

Granger Causality (F-test)Vector Autoregression (VAR)AIC Lag SelectionDirected Acyclic Graph (DAG)Long/Short BacktestSharpe Ratio & Max Drawdown

Pythonstatsmodelsnetworkxyfinancepandasmatplotlib

Github Paper

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Deadzones

Modeling the Seasonal Collapse and Recovery of Gulf Hypoxia from River Nutrient Loading

40-year model tracing Gulf of Mexico dead zones back to Midwest agricultural runoff.

climategeospatialmathematics

Random Forest RegressionLeave-One-Out Cross ValidationPearson Correlation AnalysisAnomaly DetectionTime Series Feature EngineeringNetCDF Oceanographic ProcessingGeospatial VisualizationSea Surface Temperature Analysis

Pythonxarraypandasscikit-learnmatplotlibcartopyNumPyJupyterNetCDF4

Github

Grokking

Reproducing Generalization Beyond Overfitting on Modular Arithmetic

Reproduces the phenomenon where a transformer memorizes first, then suddenly generalizes.

artificial-intelligencemathematics

Transformer (1-layer, 4-head)Modular Arithmetic ClassificationAdamW with High Weight DecayTrain/Val Loss & Accuracy TrackingGrokking Epoch Detection

PythonPyTorchmatplotlib

Github

Quantum Drug Binding

Predicting Small-Molecule Binding Affinity via Quantum Chemical Descriptors

Uses quantum mechanical molecular descriptors to predict how tightly a drug binds to its target.

artificial-intelligencemedicinemathematics

Density Functional Theory (DFT)HOMO/LUMO Energy ExtractionMolecular Electrostatic PotentialGradient Boosting RegressionPearson Correlation AnalysisIC50 Label Processing

PythonRDKitPySCFpandasscikit-learnmatplotlib

Github