Bibliographic record
Abstract
A number of recent works have used a variety of combinatorial constructions to derive Tanner graphs for LDPC codes and some of these LDPC codes have been shown to perform well in terms of their probability of errors and error floors. Such graphs are bipartite and many of these constructions yield biregular graphs, where the degree of left vertices is a constant c + 1 and that of the right vertices is a constant d + 1. Such graphs are termed (c+1, d +1) biregular bipartite graphs. Two properties of interest in such work is the girth of the graph and the number of short cycles in the graph, cycles of length either the girth or slightly larger. Such numbers have been shown to be related to the error floor of the probability of error curve of the related LDPC code. Using known results of graph theory, it is shown how the girth and the number of cycles of length equal to the girth may be computed for these (c + 1, d + 1) biregular bipartite graphs knowing only the parameters c and d and the numbers of left and right vertices. While numerous algorithms to determine the number of short cycles in arbitrary graphs exist, the reduction of the problem from an algorithm to a computation for these biregular bipartite graphs is of interest.
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.
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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".