Applying math to real-world systems
I started this because I wanted to find ways to apply math to things in my real-life that I enjoyed. So I dug into public datasets, analyzed the data, did the math, and wrote it all up.
Disclaimer: These have NOT been peer reviewed and thus should not be considered as scientific fact. They are my interpretations and analysis of available data.
These are the longest and most impressive papers (at least to me) from each domain.
Finance
Does the aggregate linguistic tone of management discourse across a GICS sector carry predictive signal for subsequent sector-level returns?
Sector tone explains roughly 12 to 18 percent of subsequent quarter returns in Technology and Healthcare. Uncertainty language predicts 30-day realized volatility with an R-squared of 0.24, leading by two to three weeks.
Read the full thing →Music
Is the auditory distinctiveness of Hindustani ragas computationally accessible from the raw audio signal, and which spectral features carry the most discriminative information?
Chroma-CQT features achieve about 71 percent accuracy in 10-class raga identification. Multidimensional scaling of spectral features recovers the perceptual timbre space, and experienced jazz improvisers show higher recurrence determinism.
Read the full thing →Basketball
How did the rise of three-point shooting alter the spatial geometry and expected-value landscape of NBA offense, and what drove its adoption?
Expected points per attempt from three first durably exceeded mid-range in 2010-11, with mass adoption following a two to three year lag. The optimal shot mix is approximately 35 percent corner threes, 45 percent restricted area, and 20 percent all else.
Read the full thing →Biology
How accurately do classical differential equation models describe tumor growth, epidemic spread, and predator-prey oscillation, and what do their failures reveal?
The Gompertz model achieves the lowest AICc in roughly 67 percent of tumor series. The SIR model predicts peak timing within 8 days but overestimates peak height by 40 to 120 percent until corrected by time-varying transmission.
Read the full thing →Decision Science
How far from optimal is human decision under uncertainty, what produces the gap, and how much can be recovered by simple corrections?
Median forecasters exhibit substantial overconfidence: events assigned 90 percent probability occur roughly 76 percent of the time. Superforecasters are near-perfectly calibrated with a slope of 0.96. A simple rounding heuristic recovers most of the accuracy lost to base-rate neglect.
Read the full thing →These are the 5 areas I found most interesting to apply math to.
Markets, earnings, portfolio theory, prediction, and risk. We investigate how mathematical models explain price formation, volatility clustering, and the limits of forecastability in financial time series.
Signal processing, acoustics, Fourier analysis, and harmonic structure. We treat music as a mathematical object: sequences, spectral functions, and dynamical systems that encode cultural meaning in physical form.
Shot optimization, efficiency metrics, lineup analysis, and game theory. Basketball has become one of the most data-rich sports, offering a real-time laboratory for optimization and spatial statistics.
Tumor growth modeling, population dynamics, genetics, and epidemiology. Mathematical biology has moved from metaphor to mechanism. We show how differential equations govern living systems.
Behavioral economics, probability, forecasting, and optimization. We study how humans actually make decisions, where they systematically deviate from rationality, and what mathematics prescribes instead.
Some of these started as side projects for the investigations while others were built solely for this project. They should help visualize what is written in the investigations.
Backtest equity portfolios using historical SPDR sector ETF returns (2000 to 2023). Adjust weights, compute Sharpe ratios, run Monte Carlo projections.
Explore harmonic decomposition and spectral features using reference data from University of Iowa instrument recordings. Compare piano and violin overtone structures.
Compare exponential, logistic, Gompertz, and linear growth models with adjustable parameters. Relevant to tumor dynamics, population growth, and product adoption.
Explore NBA shot efficiency by zone, compute expected value landscapes, and analyze how shot selection changes impact scoring.
Interactive tools for Bayesian reasoning, expected value calculations, calibration training, and risk-reward optimization.
Everything uses public data: SEC EDGAR, FRED, JHU CSSE, NBA Stats, Compmusic, and peer-reviewed publications. If I couldn't find a real dataset for something, I didn't write about it.
See all 15 datasets →