Investigations
These are working notes, not peer-reviewed papers. Each one starts with a concrete question, pulls from a public dataset, and shows the math behind the answer.
20
Investigations
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The Information Content of Earnings Call Language
A Sector-Level Sentiment Study of Predictive Signal in Management Discourse
Computational Approaches to Hindustani Raga Identification
Spectral Methods, Perceptual Timbre Spaces, and the Limits of Discrete Representation
The Three-Point Revolution and the Geometry of Efficient Offense
Expected Value, Shot Selection Optimization, and the Mathematics of Spacing
Mathematical Models of Growth and Spread
From Tumor Kinetics and Epidemic Dynamics to Predator-Prey Oscillation
Calibration, Bias, and Rational Belief Updating in Human Forecasting
Overconfidence, Bayesian Heuristics, and the Optimization of Risk and Reward
Can Earnings Call Language Predict Sector Rotation?
Does the sentiment and linguistic complexity of earnings call transcripts carry measurable predictive signal for subsequent sector-level capital flows?
What Makes a Stock More Volatile?
Which structural and market characteristics are the strongest predictors of realized volatility in large-cap U.S. equities?
Can Momentum Beat Buy-and-Hold?
Over rolling 20-year windows, does a time-series momentum strategy applied to U.S. equity sectors generate risk-adjusted excess returns over a passive index?
Can Fourier Analysis Distinguish Hindustani Ragas?
Do the frequency-domain characteristics of Hindustani classical performances contain sufficient structure to computationally distinguish between ragas, and which spectral features carry the most discriminative information?
The Mathematics of Musical Timbre
How do the overtone structures of different instruments create perceptually distinct timbres, and can multidimensional scaling of spectral features recover the perceptual timbre space established in psychoacoustic experiments?
Modeling Improvisation as a Dynamical System
Can the temporal evolution of jazz improvisation be characterized as a deterministic dynamical system, and what do measures of recurrence and Lyapunov stability reveal about improvisational structure?
Why Three-Point Shooting Changed Basketball
How did the rise of three-point shooting alter the spatial geometry and expected-value landscape of NBA offense, and what mathematical threshold drove its adoption?
Optimizing Shot Selection Using Expected Value
Across the full shot chart, what spatial regions and shot types maximize expected points per possession, and how does the efficient frontier of shot selection vary by player skill profile?
The Mathematics of Spacing
How does the spatial distribution of offensive players affect shot quality and scoring efficiency, and can convex hull area and entropy measures quantify offensive spacing?
Modeling Tumor Growth Using Differential Equations
How accurately do classical growth models (exponential, logistic, Gompertz, and von Bertalanffy) describe observed tumor volume trajectories, and which model best captures the deceleration of growth at large volumes?
Predicting Disease Spread: SIR and Beyond
How does the basic SIR model's prediction of epidemic trajectory compare to observed COVID-19 outbreak data, and what extensions are necessary to capture real-world dynamics?
Population Dynamics Simulations: Predator-Prey Systems
Do the oscillatory dynamics of predator-prey systems observed in the field conform to Lotka-Volterra predictions, and what parameter regimes produce stable limit cycles versus chaos?
Why Humans Systematically Misjudge Probability
What cognitive biases produce the most substantial and consistent deviations from Bayesian reasoning, and can simple debiasing interventions reduce overconfidence in probability judgments?
Bayesian Decision Making in Practice
In sequential decision problems with uncertain information, how large must the observed evidence be to rationally justify revising a prior belief, and what practical heuristics approximate Bayesian reasoning?
Risk vs. Reward: Optimization Under Uncertainty
How does mean-variance portfolio optimization translate to general decision problems, and does the Markowitz efficient frontier framework extend meaningfully to non-financial choice under uncertainty?
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