Bibliographic record
Abstract
This article gives a brief overview of near sets. The proposed approach in introducing near sets is to consider a set theory-based form of nearness (proximity) called discrete proximity. There are two basic types of near sets, namely, spatially near sets and descriptively near sets. By endowing a nonempty set with some form of a nearness (proximity) relation, we obtain a structured set called a proximity spaces. Let $${\mathcal{P}(X)}$$ denote the set of all subsets of a nonempty set X. One of the oldest forms of nearness relations p (later denoted by δ) was introduced by E. Čech during the mid-1930s, which leads to the discovery of spatially near sets, i.e., those sets that have elements in common. That is, given a proximity space (X, δ), for any subset $${A \in \mathcal{P}(X)}$$ , one can discover nonempty nearness collections $${\xi(A) = \{B \in \mathcal{P}(X): A \, \delta \, B\} }$$ . Recently, descriptively near sets were introduced as a means of solving classification and pattern recognition problems arising from disjoint sets (i.e, sets with empty spatial intersections) that resemble each other. One discovers descriptively near sets by choosing a set of probe functions Φ that represent features of points in a set and endowing the set of points with a descriptive proximity relation δ Φ and obtaining a descriptively structured set (called descriptive proximity space). Given a descriptive proximity spaces (X, δ Φ), one can discover collections of subsets that resemble each other. This leads to the discovery of descriptive nearness collections $${\xi_{\Phi}(A) = \{B \in \mathcal{P}(X): A \,\delta_{\Phi} \, B\} }$$ . That is, if $${B \in \xi_{\Phi}(A)}$$ , then A δ Φ B (relative to the chosen features of points in X, A resembles B). The focus of this tutorial is on descriptively near sets.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.006 | 0.013 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.020 | 0.007 |
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".