Editorial “Symmetries and differential equations”
Bibliographic record
Abstract
completed his PhD thesis, "Construction of Solutions to Partial Differential Equations by the Use of Transformation Groups".Since then, this subject and the broader field of symmetry methods applied to differential equations have been his main academic interest.Outside of research and teaching are his activities in university administration, in school mathematics education, and in Jewish Canadian culture and history (his parents were saved by the heroic Japanese consul Chiune Sempo Sugihara during the second world war).Among George's approximately 100 scientific publications, there are well-recognized and pioneering advances in the theory and applications of Lie symmetry reduction methods, their extensions to nonclassical symmetries and potential symmetries, and the construction of associated conservation laws.In addition, George has written four books on these subjects, and each of them has been a must-read item in the education of several generations of early-career researchers, including 20 of his own graduate students, many close collaborators, and many more interested students and researchers around the world.This special issue called for contributions within these aforementioned areas of interest by his research colleagues ( * ) and leading researchers.Symmetries are an intrinsic (coordinate-free) feature of a given differential equation.They can be computed in an algorithmic way and provide a powerful tool for many purposes:
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 | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.007 | 0.009 |
| Insufficient payload (model declined to judge) | 0.017 | 0.008 |
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".