Identifiability of Linear Time-Invariant Differential-Algebraic Systems. 2. The Differential-Algebraic Approach
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Bibliographic record
Abstract
A mathematical model is identifiable if and only if there is a unique relationship between each parameter value and the input−output behavior of the model. If a model is not identifiable, there is no unique solution to the parameter estimation problem, regardless of the number and type of experiments that are performed. A method for testing the identifiability of linear time-invariant (LTI) differential-algebraic equation (DAE) systems, based on differential algebra, is presented. In the proposed approach, the LTI DAE system is treated as a set of linear mappings in the input, output, and state variables. The proposed treatment allows the input−output representation of the system to be obtained by combining and differentiating elements of this set. The identifiability of the system is tested by checking whether the relationship between the model parameters and the coefficients in the input−output representation of the system is one-to-one. One benefit of the proposed method is that it readily produces a simplified realization of the system that is identifiable even when the original LTI DAE model is not identifiable. Necessary and sufficient conditions for local and global identifiability are presented, and the application of the proposed method is illustrated using a simplified gas-phase reaction model.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it