Gene clusters as intersections of powers of paths
Bibliographic record
Abstract
Abstract There are various definitions of a gene cluster determined by two genomes and methods for finding these clusters. However, there is little work on characterizing configurations of genes that are eligible to be a cluster according to a given definition. For example, given a set of genes in a genome, is it always possible to find two genomes such that their intersection is exactly this cluster? In one version of this problem, we make use of the graph theory to reformulated it as follows: Given a graph G with n vertices, do there exist two θ-powers of paths G S =(V S ,E S ) and G T =(V T ,E T ) such that G S ∩G T contains G as an induced subgraph? In this work, we divide the problem in two cases, depending on whether or not G is an induced subgraph of G S or G T . We show an $\mathcal{O}(n^{2})$ time algorithm that generates the smallest θ-powers of paths G S and G T (with respect to and the number of vertices) that contains G as an induced subgraph. Finally, we discuss the problem when G is an induced subgraph neither of G S nor of G T and we present a method of finding the smallest power of a path when graph G is a cycle C 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 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".