Integer Hulls, Z-Polyhedra and Presburger Arithmetic in Action
Bibliographic record
Abstract
When solving systems of polynomial equations and inequalities, the task of computing their solutions with integer coordinates is a much harder problem than that of computing their real solutions or that of computing all their solutions. In fact, in the presence of non-linear constraints, this task may simply become an undecidable problem [12, 15]. However, studying the integer solutions of linear systems of equations and inequalities is of practical importance in various areas of scientific computing. Two such areas are combinatorial optimization (in particular, integer linear programming) and compiler optimization (in particular, the analysis, transformation, and scheduling of nested loops in computer programs), where a variety of algorithms solve questions related to the points with integer coordinates in a given polyhedron. Another area is at the crossroads of computer algebra and polyhedral geometry, with topics such as toric ideals and Hilbert bases, see [16], as well as the manipulation of Laurent series, see [1].
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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 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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".