Bibliographic record
Abstract
Nonlinear dynamics shape the world around us, from the harmonious movements of celestial bodies, via the swirling motions in fluid flows, to the complicated biochemistry in the living cell.Mathematically these beautiful phenomena are modeled by nonlinear dynamical systems, mainly in the form of ordinary differential equations (ODEs), partial differential equations (PDEs) and delay differential equations (DDEs).The presence of nonlinearities severely complicates the mathematical analysis of these dynamical systems, and the difficulties are even greater for PDEs and DDEs, which are naturally defined on infinite-dimensional function spaces.With the availability of powerful computers and sophisticated software, numerical simulations have quickly become the primary tool to study the models.However, while the pace of progress increases, one may ask: just how reliable are our computations?Even for finite-dimensional ODEs, this question naturally arises if the system under study is chaotic, as small differences in initial conditions (such as those due to rounding errors in numerical computations) yield wildly diverging outcomes.These issues have motivated the development of the field of rigorous numerics in dynamics.Rigorous numerics draws inspiration from the ideas in scientific computing, numerical analysis,
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 | 0.006 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".