Bibliographic record
Abstract
Shuffle on trajectories was introduced by Mateescu et al. [147] as a method of generalizing several studied operations on words, such as the shuffle, concatenation and insertion operations. This natural construction has received significant and varied attention in the literature. In this thesis, we consider several unexamined areas related to shuffle on trajectories. We first examine the state complexity of the shuffle on trajectories. We find that the density of the set of trajectories is an appropriate measure of the complexity of the associated operation, since low density sets of trajectories yield less complex operations. We introduce the operation of deletion along trajectories, which serves as an inverse to shuffle on trajectories. The operation is also of independent interest, and we examine its closure properties. The study of deletion along trajectories also leads to the study of language equations and systems of language equations with shuffle on trajectories. The notion of shuffle on trajectories also has applications to the theory of codes. Each shuffle on trajectories operation defines a class of languages. Several of these language classes are important in the theory of codes, including the prefix-, suffix-, biprefix-codes and the hypercodes. We investigate these classes of languages, decidability questions, and related binary relations. We conclude with results relating to iteration of shuffle and deletion on trajectories. We characterize the smallest language closed under shuffle on trajectories or deletion along trajectories, as well as generalize the notion of primitive words and primitive roots. Further examination of language equations are also possible with the iterated counterparts of shuffle and deletion along trajectories.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.005 | 0.011 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.016 | 0.003 |
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".