Bibliographic record
Abstract
In this work, we focus on two kinds of problems involving the proximity of geometric objects.The first part revolves around intersection detection problems.In this setting, we are given two (or more) geometric objects, and we are allowed to preprocess them separately.Then, the objects are translated and rotated within a geometric space, and we need to e ciently test if they intersect in these new positions.We develop representations of convex polytopes in any (constant) dimension that allow us to perform this intersection test in logarithmic time.In the second part of this work, we turn our attention to facility location problems.In this setting, we are given a set of sites in a geometric space and we want to place a facility at a specific place in such a way that the distance between the facility and its farthest site is minimized.We study first the constrained version of the problem, in which the facility can only be placed within a given geometric domain.We then study the facility location problem under the geodesic metric.In this setting, we consider a di↵erent way to measure distances: Given a simple polygon, we say that the distance between two points is the length of the shortest path that connects them while staying within the given polygon.In both cases, we present algorithms to find the optimal location of the facility.In the process of solving facility location problems, we rely heavily on geometric structures called Voronoi diagrams.These structures summarize the proximity information of a set of "simple" geometric objects in the plane and encode it as a decomposition of the plane into interior disjoint regions whose boundaries define a plane graph.We study the problem of constructing Voronoi diagrams incrementally by analyzing the number of edge insertions and deletions needed to maintain its combinatorial structure as new sites are added.vi
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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 | 0.021 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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".