Bibliographic record
Abstract
Our main aim in this thesis is to study and search for orthogonal matrices which have a certain kind of block structure.The most desirable class of matrices for our purpose are orthogonal designs constructible from 16 circulant matrices.In studying these ma trices, we show that the OD(l2; 1,1,1, 9) is the only orthogonal design constructible from 16 circulant matrices of type OD(4n; 1,1, l,4n -3), whenever n > 1 is an odd integer.We then use an exhaustive search to show that the only orthogonal design con structible from 16 circulant matrices of order 12 on 4 variables is the OD(12; 1,1,1, 9).It is known that by using of T-matrices and orthogonal designs constructible from 16 circulant matrices one can produce an infinite family of orthogonal designs.To com plement our studies we reproduce an important recent construction of T-matrices by Xia and Xia.We then turn our attention to the applications of orthogonal matrices.In some recent works productive regular Hadamard matrices are used to construct many new infinite families of symmetric designs.We show that for each integer n for which 4n is the order of a Hadamard matrix and 8n 2 -1 is a prime, there is a productive regular Hadamard matrix of order 16n 2 (8n 2 -l) 2 .As a corollary, we get many new infinite classes of symmetric designs whenever either of 4n(8n 2 -1) -1, 4n(8n 2 -1) + 1 is a prime power.We also review some other constructions of productive regular Hadamard matrices which are related to our work.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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 teacher head, 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".