Inverse Laplace Transform Approaches to βNMR Relaxation
Bibliographic record
Abstract
Abstract Spin lattice relaxation is the simplest type of βNMR measurement. The usual approach is to implant a pulse of hyperpolarized nuclei and monitor the time-resolved β-decay asymmetry, yielding the ensemble average spin-lattice relaxation. In the simplest case, the asymmetry decays exponentially with a characteristic time constant T 1, but this ideal is rarely obtained in practice. In most data, the relaxation is more complicated. This can be the result of multiple crystallographic sites for the implanted probe each having a distinct T 1. The sample may also be inhomogeneous due to: impurities or defects (including interfaces that are particularly important for thin films), intrinsic phase separation, or, if it is a glass. There may also be a background signal from probe ions that stop outside the sample. The general approach to this problem has been the ad hoc development of an appropriate relaxation model that avoids overparametrization. Given the prevalence of more complicated relaxation, it is crucial to develop a systematic approach to relaxation modelling. The decomposition of a relaxing signal into exponentials is, however, a mathematically ill-posed problem[1]. This feature is intrinsic and unavoidable, but there are a number of methods to accommodate it for noisy real-world data, including nuclear spin relaxation[2, 3, 4]. Here we demonstrate one of the best and most commonly used methods, Tikhonov regularization for the inverse Laplace transform, implemented for the particular features of βNMR relaxation data, most importantly the strong time dependence of the statistical uncertainty stemming from the radioactive lifetime of the probe.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".