Spatial Separability in Hub Location Problems with an Application to Brain Connectivity Networks
Bibliographic record
Abstract
Motivated by the need to solve large hub location problems efficiently and accurately, we discover an important characteristic of optimal solutions to p-hub median problems that we call spatial separability. It refers to the partitioning of the network into allocation clusters with nonoverlapping convex hulls. We illustrate numerically that the property persists over a wide range of randomly generated instances and propose a data-driven approach based on an insight from the property to tackle very large problem sizes. Computational experiments corroborate the effectiveness of the proposed approach in generating high-quality solutions within reasonable computational times. We then explore a new application area of hub location problems in brain connectivity networks and introduce the largest and the first set of three-dimensional instances in the literature. Computational results demonstrate the capability of hub location models in successfully depicting the hub organization of the human brain, as validated by the medical literature, thus revealing that hub location models can play an important role in investigating the intricate connectivity of the human brain.
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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 | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".