CASCADE DECOMPOSITION WITH CANONICAL SCATTERING POLYNOMIALS
Bibliographic record
Abstract
Abstract — The decomposition of the transfer matrix T into a product of two simpler transfer matrices T a and T b, i.e., T = T a T b is discussed. Where T a corresponds to one of the elementary sections which are organized as a table in this paper and that T b has the same properties as T except a lower degree is proved rigorously in Theorems 1 and 2. Replacing T with T b, the decomposed procedure can be repeated until all elementary sections are extracted. Following Theorems 1 and 2, one necessary and sufficient condition for the cascade synthesis of a lossless, passive, two-port network from a given canonic set of scattering polynomials is obtained. Finally, based on the decomposition, a synthesis algorithm is presented for the realization of a lossless, passive, two-port network. REFERENCE [Jarm90] M. R. Jarmasz “A simplified synthesis of lossless two-port wave digital and analog fil ters,” Ph.D. Thesis, University. of Manitoba, Winnipeg,1990. [Fett70] A. Fettweis “Factorization of transfer matrices of lossless two-ports, ” IEE Trans. Circuit Theory,”
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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 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".