Elementary Statistical Models for Vector Collision-Sequence Interference Effects with Poisson-Distributed Collision Times
Bibliographic record
Abstract
In a recent paper (Lewis, 2008) a class of models suitable for application to collision-sequence interference was introduced. In these models velocities are assumed to be completely randomized in each collision. The distribution of velocities was assumed to be Gaussian. The integrated induced dipole moment <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>μ</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math>, for vector interference, or the scalar modulation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>μ</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math>, for scalar interference, was assumed to be a function of the impulse (integrated force) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="bold">f</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math>, or its magnitude <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math>, experienced by the molecule in a collision. For most of (Lewis, 2008) it was assumed that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>μ</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>∝</mml:mo><mml:msub><mml:mi mathvariant="bold">f</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>μ</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>∝</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math>, but it proved to be possible to extend the models, so that the magnitude of the induced dipole moment is equal to an arbitrary power or sum of powers of the intermolecular force. This allows estimates of the infilling of the interference dip by the disproportionality of the induced dipole moment and force. One particular such model, using data from (Herman and Lewis, 2006), leads to the most realistic estimate for the infilling of the vector interference dip yet obtained. In (Lewis, 2008) the drastic assumption was made that collision times occurred at equal intervals. In the present paper that assumption is removed: the collision times are taken to form a Poisson process. This is much more realistic than the equal-intervals assumption. The interference dip is found to be a Lorentzian in this model.
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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 | 0.000 | 0.001 |
| 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 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".