Bibliographic record
Abstract
A single change covering design (SCCD) is a sequence of b k-sets, called blocks, of a V -set in which exactly one element differs between consecutive blocks and every s-set of V is in some block.We will review the literature and discuss several recursive constructions which completely solve the existence of SCCD for k = 3, 4 and partially for k = 5.We will examine optimizations on exhaustive search techniques.We determined that there are 313 unique circular SCCD (12,4,2,22).We determine a recursion for s = 3 and general k using expansion sets.A double change covering design (DCCD) is similarly defined but consecutive blocks differ by two elements.We will completely solve the existence of tight DCCD k = 3, s = 2.We give several constructions using recursion and algebraic difference methods.This provides us with constructions for circular DCCD(4k -2, 2k, 2, 2k -1), circular DCCD(4k -1, 2k + 1, 2, 2k -1) and circular DCCD(4k -5k, 2, 4k -2) exists.We also find some other circular DCCD with given v and k.I would first like to thank my supervisor, Brett Stevens, for providing guidance, feedback and support though out my Master's degree.I am so grateful that when I started this journey in my undergraduate years he introduced me to single change covering designs.I am also very thankful that we started this journey pre-Covid-19 and that video conferencing allowed us to continue meeting virtually.I would also like to thank my committee members Steven Wang, Michael Newman, and Root Gorelick and chair, Saban Alaca, for their time.Heartfelt thanks to my parents, siblings and relatives for supporting me through this academic journey and encouraging me to pursue what I love.Also, thanks for letting me take over the games table at the cottage all last summer.I am truly blessed to have such an amazing family.
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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 | 0.000 | 0.001 |
| 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 | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".