Degeneracy in negative feedback (NFBL) and incoherent feedforward (IFFL) loops: Adaptation and resonance
Bibliographic record
Abstract
Abstract Degeneracy in dynamic models refers to these situations where multiple combinations of parameter values produce identical patterns for the observable variable. We investigate this phenomenon in two qualitatively different adaptive circuit mechanisms: nonlinear feedback loop (NFBL) and incoherent feedback loop (IFFL). We use minimal models of these circuit types together with analytical calculations, regular perturbation analysis, dynamical systems tools and numerical simulations. In response to constant (or step-constant) inputs, NFBLs and IFFLs produce and overshoot allowing the observable variable to return to a value closer to baseline than the peak (adaptation). We identify the dynamic principles underlying the emergence of degeneracy in adaptive patterns both within and across circuit types in representative NFBL and IFFL models in terms of biologically plausible parameters. We identify the conditions under which degeneracy persists in response to oscillatory inputs with arbitrary frequencies, giving rise to resonance and phasonance degeneracy. This naturally extends to the response of adaptive systems to time-dependent inputs within a relatively large class. By using phase-plane analysis, we provide a mechanistic, dynamical systems-based interpretation of degeneracy. Our results have implication for the understanding of adaptive systems, for the relationship between adaptive and resonant/phasonant systems, for the understanding of complex biochemical circuits, for neuronal computation, and for the development of methods for circuit and dynamical systems reconstruction based on experimental or observational data.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| 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 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".