Research & Patents

One thread runs through twenty-five years of work: identify what a measurement is telling you, and quantify how certain you should be. From knot theory and dynamical systems to the algorithms that became the US government's standard for hyperspectral identification.

The core invention

Detection → Identification → Ranking

Detection asks a yes/no question about one material at a time — and drowns analysts in false alarms. Identification asks the richer question: which materials, in what mixture, best explain the light in this pixel? My 2008 insight was to fuse them: detect across the full image, automatically identify every candidate against a large spectral library using Bayesian Model Averaging (producing honest probabilities, not brittle labels), remove background signatures, and present a single ranked list.

Deployed operationally from 2010, the method inverted the economics of an entire intelligence discipline: roughly 99% of false alarms eliminated, collection-to-decision time cut from more than 8 hours to under 10 minutes, and one analyst doing work that had required two hundred. One airborne program grew from 1 to 10 aircraft and processed approximately 25 million images with ~18,000 confirmed successes. The methods spread to more than twenty US government organizations and established new terminology in the field — target-identification, confusers.

Patents

Current research

Fast-BMA: unmixing the whole planet

Conventional unmixing tools map 5–10 minerals per scene, chosen in advance. Fast-BMA evaluates a library of 1,000+ minerals for every pixel — no prior target list — distinguishing mineral variants down to roughly 2% abundance, with a posterior probability attached to every identification. Peer-reviewed at IGARSS 2025 and validated against classic ground-truth sites (Cuprite, NV) and public data over major deposits, including lepidolite detection at Thacker Pass, NV — the largest measured lithium resource in the United States.

The research frontier: extending probabilistic mineral maps upward through the geological inference chain — from minerals to alteration zones, from alteration zones to deposit-model classification, and from deposit models to evidence-based inference about ore and structure at depth, with quantified uncertainty at every step.

Foundations

Mathematics: topology & dynamical systems

My mathematical work spans minimal flows, global cross sections, knots and topologically transitive flows on 3-manifolds — and the discovery that topology solves practical problems: the Topological Anomaly Detector (TAD), developed during my NGA sabbatical, applied graph theory to anomaly detection in imagery and transitioned to operational use.

I wrote Topology and Its Applications (Wiley, 2006), used in courses internationally.

With population dynamics I've modeled the ecological collapse of Easter Island (SIAM J. Applied Math; covered by USA Today), and with J.C. Sanford proved an extension of Fisher's Fundamental Theorem of Natural Selection incorporating mutations (J. Mathematical Biology, 57 citations).

Recent work applies dynamical systems and index theory to understanding deep learning itself.

Funded research

Selected grants