Zeros of Reliability Polynomials and <i>f</i>-vectors of Matroids
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
For a finite multigraph G , the reliability function of G is the probability R G ( q ) that if each edge of G is deleted independently with probability q then the remaining edges of G induce a connected spanning subgraph of G ; this is a polynomial function of q . In 1992, Brown and Colbourn conjectured that, for any connected multigraph G , if q ∈ [Copf ] is such that R G ( q ) = 0 then [mid ] q [mid ] [les ] 1. We verify that this conjectured property of R G ( q ) holds if G is a series-parallel network. The proof is by an application of the Hermite–Biehler theorem and development of a theory of higher-order interlacing for polynomials with only real nonpositive zeros. We conclude by establishing some new inequalities which are satisfied by the f -vector of any matroid without coloops, and by discussing some stronger inequalities which would follow (in the cographic case) from the Brown–Colbourn conjecture, and are hence true for cographic matroids of series-parallel networks.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it