Mathematical foundations of the TC-method for computing multiple DC-operating points
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Bibliographic record
Abstract
In this paper, we present a detailed mathematical analysis of nonlinear resistive networks with multiple dc-operating points. In our approach, we use elementary set theoretical principles of network theory. We propose two new approaches: the TC-method (transfer-characteristic method) and the DPC-method (driving-point characteristic method). We use the TC-method to reduce the computation of dc-operating points of a given nonlinear resistive network to the computation of crossing points between transfer characteristics of associated modified resistive networks with a straight line. It can be proved that at least one operating point of the given network corresponds to each such crossing point. We show that the proposed approaches lead to continuation methods for the finding dc-operating points of resistive networks. These continuation methods can be readily used in standard SPICE-like circuit simulators.
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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 | 0.000 | 0.000 |
| 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 | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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