ITERATED FUNCTION SYSTEMS WITH PLACE-DEPENDENT PROBABILITIES AND THE INVERSE PROBLEM OF MEASURE APPROXIMATION USING MOMENTS
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Bibliographic record
Abstract
We are concerned with the approximation of probability measures on a compact metric space [Formula: see text] by invariant measures of iterated function systems with place-dependent probabilities (IFSPDPs). The approximation is performed by moment matching. Associated with an IFSPDP is a linear operator [Formula: see text], where [Formula: see text] denotes the set of all infinite moment vectors of probability measures on [Formula: see text]. Let [Formula: see text] be a probability measure that we desire to approximate, with moment vector [Formula: see text]. We then look for an IFSPDP which maps [Formula: see text] as close to itself as possible in terms of an appropriate metric on [Formula: see text]. Some computational results are presented.
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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 | 0.000 | 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)
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