Bibliographic record
Abstract
In this thesis, we present a construction of a spanner on a set of $n$ points in $\R^d$ that we call a heavy path WSPD spanner. The construction is parameterized by a constant $s>2$. The size of the graph is $O(s^dn)$ and the spanning ratio is at most $1+2/s+2/(s-1)$. We also show that this graph has a hop spanning ratio of at most $2\lg{n}+1$. We present a memoryless local routing algorithm for heavy path WSPD spanners. A vertex $v$ of the graph stores $O(\deg(v)\log{n})$ bits of information. The routing ratio is at most $1+4/s+1/(s-1)$ and at least $1+4/s$. The number of edges on the routing path is bounded by $2\lg{n}+1$. We then show that the construction and routing algorithm can be generalized to metric spaces of bounded doubling dimension. The spanning and hop spanning ratios are unchanged. The routing ratio becomes at most $1+(2+\frac{\tau}{\tau-1})/s+1/(s-1)$, where $\tau\ge11$ is a constant.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 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".