Application of Ant Colony Programming Approach for Solving Systems of Stochastic Differential Equations
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Bibliographic record
Abstract
Stochastic differential equations (SDE) have wide applications in natural phenomena, engineering, finance, and biological models. Obtaining analytic solutions for an SDE is often complex, and the complexity increases for an SDE system. The paper introduces ant colony programming (ACP) as a novel approach for solving SDE system. Ant colony programming was developed in two directions, the first is to add the Wiener process as a variable to the terminals and functions, and the second is to construct the appropriate fitness function . ACP constructs mathematical expressions and evaluates them using the fitness function . The ACP proposed effectiveness has been demonstrated by applying to 2,3 and 4-dimensional SDE systems. The most important finding of this work is that ACP generates symbolic stochastic processes that represent solutions for SDE system. Methods for solving SDE systems are important tools for study phenomena that involve noise or randomness.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 it