On vertex-vertex systems and their use in geometric and biological modelling
Bibliographic record
Abstract
In the areas of geometry and biology, there are a number of modelling problems that require the creation and manipulation of discrete surfaces that behave dynamically. For example, in geometric modelling there are surface subdivision algorithms that require the repeated insertion of vertices into a polygon mesh. In biological modelling there is the question of modelling growing surfaces, such as a growing flower or a growing tissue of cells. In these cases, there is the open question of how to model dynamical systems with a dynamical structure of a 2-manifold topology, discrete surfaces that have components that change in character, connectivity and number over time. However, the selection of available tools for modelling dynamical surfaces is limited. There have been some proposed solutions for limited cases, such as cell systems for modelling cells. But there is still a need for a methodology and tools for dealing with dynamical surfaces in general. In this dissertation, I present a methodology for modelling dynamical systems with a dynamical structure of a 2-manifold topology. This methodology is comprised of the vertex-vertex data structure and algebra and is implemented in the vertex-vertex software environment. I also demonstrate its application with examples in the domains of geometric and biological modelling.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.006 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".