Semidefinite Programming and Graph Partitioning with Preferences Suely Oliveira
Bibliographic record
Abstract
this paper, is to use an SDP relaxation. 3 Graph Patitioning and Semidefinite Programming Like combinatorial methods, spectral methods have proven to be e#ective for large graphs arising from FEM discretizations [31]. Software packages that use spectral methods combined with combinatorial algorithms include METIS [23], Chaco [17], JOSTLE [42], PARTY [32], and SCOTCH [29]. The spectral algorithms which are used in these packages are based on models that partition a graph by finding an eigenvector associated with the second smallest eigenvalue of its graph Laplacian matrix using an iterative method. Mathematically, the problem can be formulated as follows. Let the graph be given by its weighted adjacency matrix A. Define the matrix L = diag(Ae) -A, where e is the vector of all ones. The matrix L is called the Laplacian matrix associated with the graph. If a partition is represented by a vector x where 1} depending on whether x i belongs to set P 1 or P 2 , we get the following formulation for the min-cut problem
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".