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Record W3192628405 · doi:10.51201/jusst/21/07285

Some Recent Developments in theory of Metric Spaces

2021· article· en· W3192628405 on OpenAlex
Parveen Sheoran

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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueJournal of University of Shanghai for Science and Technology · 2021
Typearticle
Languageen
FieldComputer Science
TopicDigital Image Processing Techniques
Canadian institutionsToronto Metropolitan University
Fundersnot available
KeywordsTopology (electrical circuits)Metric spaceMathematicsMetric (unit)Space (punctuation)Set (abstract data type)Topological spaceFunction (biology)Hausdorff spaceComputer sciencePure mathematicsCombinatorics

Abstract

fetched live from OpenAlex

The topology on a set X is formed by a non-negative real valued scalar function called metric, which may be understood as measuring some quantity. Because some of the set’s attributes are similar, there’s a distance between any two elements, or points. Quite evocative of the common concept of distance that we come across in our daily lives. Because its topology is entirely defined by a scalar distance function, this sort of topological space has a distinct advantage over all others. We may reasonably assume that we are familiar with the qualities of such a function and are capable of dealing with it successfully. Instead, a generic topology is frequently dictated by a set of perhaps abstract rules. Frecklet initially proposed the concept of a metric space in 1906, but it was Hausdorff who coined the phrase metric space a few years later.

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 imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.682
Threshold uncertainty score0.208

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.003
Science and technology studies0.0000.001
Scholarly communication0.0000.001
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.017
GPT teacher head0.250
Teacher spread0.233 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it