Davis Geometric
Computational research

Geometry belongs in the computation.

I’m Bee Rosa Davis, a NASA systems engineer with over 28 years of experience in building infrastructure for high volume, high velocity, mission critical systems. My research investigates the hidden structure of data using computational analysis and topology—the mathematics of shape and connection. The goal is to understand which relationships matter, and how to carry them into the way we compute.

Exact unit-circle construction: directions 350 and 10 degrees are separated by a 20-degree arc, while their coordinates on a straight number line differ by 340 degrees.
A coordinate seam can separate numbers that describe nearby states. The research begins with the relationships a representation needs to preserve. Explore the figure and its evidence → Read the mathematical idea

A compass offers a simple example: 350° and 10° are only 20° apart. Subtracting the numbers gives 340°. To measure a meaningful change, the calculation has to account for the shape of what we are measuring.

This question grew from building machine-learning systems at Pandora and working with engineering teams at NASA. My project work explores it through data systems, algorithms, and applications across the physical and life sciences.

Through my work as a systems engineer with NASA and as an independent researcher, I’ve had the privilege of collaborating across aerospace, guidance, navigation and control, the physical sciences, medicine, and atmospheric modeling.

Each domain has its own relationships, scales, and context. A table can organize measurements, but it does not automatically preserve the connections that give them meaning. When we force every domain into the same fixed structure, we risk losing what makes its data distinctive.

My goal is to give each domain’s data and its context a chance to reveal their structure—and to build computational tools that can preserve it. The representation should grow out of the problem we are studying.

Bee Rosa Davis Systems engineer & independent researcher

02 / Featured study

Sequential shortest paths

Working paper · Experimental companion · September 2026

Bucket Width, Duplicate Work, and Local Lookahead in Sequential Shortest Paths

Research settingIndependent

A controlled comparison of bucket-based solvers and binary-heap Dijkstra, examining where duplicate suppression helps and where the tested methods lose.

Explore the companion → Paper (PDF) Reproduction artifact
Recorded SSSP density sweep and a matrix of implementation ratios across sparse, million-vertex, road, dense and grid inputs. Both faster and slower cases are shown.
SSSP · Reported timing ratios from the September 2026 companion. The density sweep and cross-input comparison include cases favoring the heap. A dash means the summary does not report that comparison. Single machine, sequential execution; no benchmarks rerun. Explore the figure and its evidence → Recorded data
Selected results reported in the SSSP companion. Ratio = standard-heap time / method time; greater than 1 favors the tested method.
Input Method Reported ratio
Sparse graphs · 1 million vertices Deduplicated cyclic buckets 1.82
Three DIMACS road networks Deduplicated cyclic buckets 1.51–1.64
Dense graphs · 5,000 vertices Deduplicated map buckets 0.564

Study scope: one machine, sequential execution, and the linked implementations. The table reproduces the companion results; full methodology and limitations accompany the paper.

From the working record

Inspect the structure. Read the evidence.

Figure sources ↗

Published measurements and computational studies, with their context, uncertainty, and source records.

Biochar · Fit quality and phosphorus capture

Independent · Awaiting external review
All 16 retained biochar capacity estimates with published standard errors, plus a complete count of retained fits, excluded fits and net-release labels across four Mg activation levels.
Independent research note · Awaiting external review. A secondary analysis of 36 published formulations: 16 pass the chosen R² > 0.80 screen. Capacity error bars are published parameter SE; the shortlist identifies candidates for further testing. Explore the figure and its evidence → Read the paper (PDF)

The Geometry of War · Connection under strain

CrowdStrike · Collaboration with Dr. Paolo Di Prodi

What happens when economic ties persist while trust breaks down? From the Helicity project and the Psychohistory paper to The Geometry of War, this work examines integration, diplomatic capacity and the structure of relationships.

Contours of the Psychohistory model ratio. Integration stays fixed while diplomatic capacity falls in an explicitly assumed scenario, with the component measurements kept separate.
A model of connection and diplomatic capacity, drawn from the paper’s stated formula. The full study traces the project’s origins, opens the book, and works through a checked network example. Explore the figure and its evidence → Read the book →

CHIHIRO · Shape, equilibrium & plasma stability

Independent · Computational plasma research

How does changing a plasma’s shape change its stability? CHIHIRO follows that question from shaped ballooning calculations and equilibrium studies to external-kink analysis and a Rust implementation with distinct instability diagnostics.

Four plasma geometry classes and all 40 saved ballooning-model ratios across magnetic shear. Circular, elongated, D-shaped and negative-triangularity cases retain their distinct curves.
The same stability calculation responds differently to four geometry classes. Dots show all 40 saved model evaluations; lines join sampled points. The full study opens the boundary calculations, plateau checks and separate diagnostic channels. Explore the figure and its evidence → Open CHIHIRO ↗

PHAETHON · IEEE 39-bus comparison

SOURCE DATA / REDRAWN FIGURE
All 39 buses and source network branches from the PHAETHON fixture, with generating buses marked, and a comparison of saved reduced effective and classical undamped spectra.
PHAETHON · The source IEEE 39-bus topology and saved base-case spectral comparison. Node placement is a visualization layout, not geography. The fixture agreement is a numerical consistency check, not a guarantee of grid stability. Explore the figure and its evidence → Saved spectral fixture

OSHUN · Measurements and model error

SOURCE DATA / REDRAWN FIGURE
534 measured skin permeability observations against the published Potts–Guy equation, plus context-stratified error estimates showing retained and excluded sample counts.
OSHUN · 534 public permeability observations and the companion’s reported error estimates. Context-stratified rows retain different subsets, so the apparent error reduction is not a paired improvement estimate. Data: huskinDB, Stepanov, Canipa & Wolber (2020), CC BY. Explore the figure and its evidence → Measurements & estimates

04 / Research areas

Questions across disciplines

View full catalog →

Explore the research by subject, from mathematical foundations to domain studies and engineering systems. Follow the links to papers, technical specifications, research accounts and books.

01Algorithms & computing

02Physical sciences

03Earth & energy systems

04Life sciences

05Engineering systems

06Economic & social systems

07Mathematical foundations

05 / Selected reading

Models, measurements, and their limits

Preprint + artifact

Power-system stability

PHAETHON studies how generators stay in step and what changes as a disturbance pushes them toward a pole slip. It connects oscillation modes, winding history and energy barriers, with a public reproduction kit.

Read scope & sources →
Study manuscript

Permeability & ingredient science

OSHUN asks how measured hair geometry can inform ingredient modeling. A skin-data study and interactive ingredient checker explore the role of context, explain when predictions are refused, and define the next hair-fiber experiment.

Read scope & sources →

06 / Engineering origins

From musical fingerprints to mission telemetry.

At Pandora, Bee Rosa Davis learned to treat the careful description of data as part of machine learning itself. At NASA, preparing roughly two terabytes of daily telemetry for AI led her to develop Adaptive Multi-Vector Correlation (AMC). Working with those adaptive vectors brought the topology of the data into view and shaped the questions she would pursue mathematically.

That question became Davis Geometric’s research direction: carrying the relationships in a measured system into the mathematics used to compute with it.

The journey behind the research → Research approach →

07 / Inside the research

Follow the reasoning.