Cyclic Behavior of Optimal Trajectories in Growth Models**The research is supported by the Russian Science Foundation (Project No. 15-11-10018).
Bibliographic record
Abstract
This paper estimates the accuracy of an algorithm for constructing optimal solutions of optimization resource productivity problem within the framework of economic growth modeling. The problem is investigated using the generalized Pontryagin maximum principle for infinite time interval problems. Qualitative analysis of the Hamiltonian system reveals that optimal trajectories have a cyclic behavior at a steady state neighborhood. This means that the Jacobian evaluated at a steady state has complex eigenvalues. A nonlinear stabilizer, constructed for saddle steady state, does not exist in this case. In the paper, we generalize the structure of a nonlinear stabilizer for the case of a focal steady state. Applying the stabilizer to the Hamiltonian system obtained from the Pontryagin maximum principle in the case of complex eigenvalues, one can derive a closed-loop system which has spiral-formed solutions converging to the steady state over time. Optimal trajectories in a steady state vicinity have similar behavior and infinitesimal closeness of high order to trajectories generated by the proposed nonlinear stabilizer. This observation provides the basis of the algorithm for constructing solutions of the considered class of optimal control problems. Estimation of the algorithm accuracy and performance time is provided in terms of the utility function of the optimal control problem.
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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".