Two lower bounds for self-assemblies at temperature 1
Bibliographic record
Abstract
Self-assembly is an autonomous process by which small simple parts assemble into larger and more complex objects. Self-assembly occurs in nature, for example, when atoms combine to form molecules, and molecules combine to form crystals. It has been suggested that intricate self-assembly schemes will ultimately be useful for circuit fabrication, nanorobotics, DNA computing, and amorphous computing [2, 7]. To study the process of self-assembly we use the Tile Assembly Model proposed by Rothemund and Winfree [5]. This model considers the assembly of square blocks called "tiles" and a set of glues called "binding domains". Each binding domain has a strength. Each of the four sides of a tile can have a glue on it that determines interactions with neighbouring tiles. The two neighbouring tiles form a bond if the binding domains on the touching sides are the same. The strength of this bond is the strength of the matching binding domain. The process of self-assembly is initiated by a single seed tile and proceeds by attaching tiles one by one. A tile can only attach to the growing complex if it binds strongly enough, i.e., if the sum of the strengths of its bonds to the existing complex is at least the temperature τ. It is assumed that there is an infinite supply of tiles of each tile type. When this growing process stops, i.e., no tile can be attached to the existing complex, we say that the tile system has assembled this shape. A tile system is specified by the seed tile, the set of tile types, the strengths of glues and the temperature.
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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 | 0.003 | 0.021 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.005 | 0.010 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.005 | 0.008 |
| Insufficient payload (model declined to judge) | 0.022 | 0.007 |
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".