A multipartite approach for the self-assembly of DNA graph structures
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Bibliographic record
Abstract
Abstract We consider a graph theory problem motivated by the self-assembly of DNA graph structures using branched junction molecules with flexible arms (called ‘tiles’ in the combinatorial model). More precisely, we want to determine a set of tiles that realizes a target graph G using the minimum number of bond-edge types so that no graph with order smaller than $$\vert V(G)\vert$$ can be realized; the parameter of interest is denoted by $$B_2(G)$$ . We present an approach that provides an upper bound for $$B_2(G)$$ using certain multipartite subgraphs of G . We provide some numerical conditions characterizing such multipartite graphs in terms of the degree of their vertices. Then, we apply our method to the graphs corresponding to the Platonic solids.
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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 | 0.000 | 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