Fisher information and Shannon entropy calculations for two-electron systems
Bibliographic record
Abstract
Fisher information is calculated for the ground state of He-isoelectronic series, in position ([Formula: see text]) space. The results are given and discussed as a function of the nuclear charge (Z) and the screening parameter (λ) in the case study of Yukawa potential. Simple and explicit one-, two-, and three-correlated terms of Hylleraas wave function are used to focus on extracting the most characteristic physical features of the results. The numerical values of Fisher information are given in 1- and 2-electron charge densities, and their ratio of 2- to 1-electron densities results are defined and analyzed. To enable a comparison with others, the Fisher–Shannon information products, which measure the electron–electron correlation strength, are calculated in 1-electron density. The calculations of Fisher information, the ratio, and the Shannon-information products for two-electron systems in the presence of Yukawa potential are carried out for the first time in this study.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".