Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Dedicated to Lucio Russo, on the occasion of his 70th birthdayIn many applications, it is of great importance to handle random closed sets of different (even though integer) Hausdorff dimensions, including local information about initial conditions and growth parameters.Following a standard approach in geometric measure theory, such sets may be described in terms of suitable measures.For a random closed set of lower dimension with respect to the environment space, the relevant measures induced by its realizations are singular with respect to the Lebesgue measure, and so their usual Radon-Nikodym derivatives are zero almost everywhere.In this paper, how to cope with these difficulties has been suggested by introducing random generalized densities (distributions) á la Dirac-Schwarz, for both the deterministic case and the stochastic case.For the last one, mean generalized densities are analyzed, and they have been related to densities of the expected values of the relevant measures.Actually, distributions are a subclass of the larger class of currents; in the usual Euclidean space of dimension d, currents of any order k ∈ {0, 1, . . ., d} or kcurrents may be introduced.In this paper, the cases of 0-currents (distributions), 1-currents, and their stochastic counterparts are analyzed.Of particular interest in applications is the case in which a 1-current is associated with a path (curve).The existence of mean values has been discussed for currents too.In the case of 1-currents associated with random paths, two cases are of interest: when the path is differentiable, and also when it is the path of a Brownian motion or (more generally) of a diffusion.Differences between the two cases have been discussed, and nontrivial problems are mentioned which arise in the case of diffusions.Two significant applications to real problems have been presented too: tumor driven angiogenesis, and turbulence.
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.
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 | 0.000 |
| 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 it