An algorithm for three‐dimensional Voronoi S‐network
Bibliographic record
Abstract
The paper presents an algorithm for calculating the three-dimensional Voronoi-Delaunay tessellation for an ensemble of spheres of different radii (additively-weighted Voronoi diagram). Data structure and output of the algorithm is oriented toward the exploration of the voids between the spheres. The main geometric construct that we develop is the Voronoi S-network (the network of vertices and edges of the Voronoi regions determined in relation to the surfaces of the spheres). General scheme of the algorithm and the key points of its realization are discussed. The principle of the algorithm is that for each determined site of the network we find its neighbor sites. Thus, starting from a known site of the network, we sequentially find the whole network. The starting site of the network is easily determined based on certain considerations. Geometric properties of ensembles of spheres of different radii are discussed, the conditions of applicability and limitations of the algorithm are indicated. The algorithm is capable of working with a wide variety of physical models, which may be represented as sets of spheres, including computer models of complex molecular systems. Emphasis was placed on the issue of increasing the efficiency of algorithm to work with large models (tens of thousands of atoms). It was demonstrated that the experimental CPU time increases linearly with the number of atoms in the system, O(n).
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 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".