A Peaceman-Rachford Splitting Method for the Protein Side-Chain Positioning Problem
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Bibliographic record
Abstract
This paper considers the NP-hard protein side-chain positioning (SCP) problem, an important final task of protein structure prediction. We formulate the SCP as an integer quadratic program and derive its doubly nonnegative (DNN) (convex) relaxation. Strict feasibility fails for this DNN relaxation. We apply facial reduction to regularize the problem. This gives rise to a natural splitting of the variables. We then use a variation of the Peaceman-Rachford splitting method to solve the DNN relaxation. The resulting relaxation and rounding procedures provide strong approximate solutions. Empirical evidence shows that almost all our instances of this NP-hard SCP problem, taken from the Protein Data Bank, are solved to provable optimality. Our large problems correspond to solving a DNN relaxation with 2,883,601 binary variables to provable optimality. History: Accepted by Paul Brooks, Area Editor for Applications in Biology, Medicine, & Healthcare. Funding: This research was supported by the Natural Sciences and Engineering Research Council of Canada [Grants 50503-10827 and RGPIN-2016-04660]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0094 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0094 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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