The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles
Why this work is in the frame
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Bibliographic record
Abstract
Abstract This book is an account of the theory and mathematical approaches in polymer entropy, with particular emphasis on mathematical approaches to directed and undirected lattice models. Results in the scaling and critical behaviour of models of directed and undirected models of self-avoiding walks, paths, polygons, animals and networks are presented. The general theory of tricritical scaling is reviewed in the context of models of lattice clusters, and the existence of a thermodynamic limit in these models is discussed in general and for particular models. Mathematical approaches based on subadditive and convex functions, generating function methods and percolation theory are used to analyse models of adsorbing, collapsing and pulled walks and polygons in the hypercubic and in the hexagonal lattice. These methods show the existence of thermodynamic limits, pattern theorems, phase diagrams and critical points and give results on topological properties such as knotting and writhing in models of lattice polygons. The use of generating function methods and scaling in directed models is comprehensively reviewed in relation to scaling and phase behaviour in models of directed paths and polygons, including Dyck paths and models of convex polygons. Monte Carlo methods for the self-avoiding walk are discussed, with particular emphasis on dynamic algorithms such as the pivot and BFACF algorithms, and on kinetic growth algorithms such as the Rosenbluth algorithms and its variants, including the PERM, GARM and GAS algorithms.
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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