Bibliographic record
Abstract
We consider a system of particles undergoing the branching and annihilating reactions $\stackrel{\ensuremath{\rightarrow}}{A}(m+1)A$ and $A+\stackrel{\ensuremath{\rightarrow}}{A}\ensuremath{\emptyset},$ with m even. The particles move via long-range L\'evy flights, where the probability of moving a distance r decays as ${r}^{\ensuremath{-}d\ensuremath{-}\ensuremath{\sigma}}.$ We analyze this system of branching and annihilating L\'evy flights using field theoretic renormalization group techniques close to the upper critical dimension ${d}_{c}=\ensuremath{\sigma}$ with $\ensuremath{\sigma}<2.$ These results are then compared with Monte Carlo simulations in $d=1.$ For $\ensuremath{\sigma}$ close to unity in $d=1,$ the critical point for the transition from an absorbing to an active phase occurs at zero branching. However, for $\ensuremath{\sigma}$ bigger than about $3/2$ in $d=1,$ the critical branching rate moves away from zero with increasing $\ensuremath{\sigma},$ and the transition lies in a different universality class, inaccessible to controlled perturbative expansions. We measure the exponents in both universality classes and examine their behavior as a function of $\ensuremath{\sigma}.$
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".