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Record W4301953555 · doi:10.4171/owr/2006/12

Discrete Differential Geometry

2006· article· en· W4301953555 on OpenAlex

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.

aboutThe title or abstract carries a Canadian signal from the geographic lexicon.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueOberwolfach Reports · 2006
Typearticle
Languageen
FieldEngineering
TopicAdvanced Numerical Analysis Techniques
Canadian institutionsnot available
Fundersnot available
KeywordsGeometryDifferential geometryDifferential (mechanical device)Discrete geometryMathematicsPhysicsThermodynamics

Abstract

fetched live from OpenAlex

The workshop Discrete Differential Geometry , organized by Alexander I. Bobenko (Berlin), Richard W. Kenyon (Vancouver), John M. Sullivan (Berlin) and Günter M. Ziegler (Berlin), was held March 5th to March 11th, 2006. The meeting was very well attended, with almost 50 participants, from as far away as Australia and China. Discrete differential geometry is a new and active mathematical terrain where differential geometry (providing the classical theory for smooth manifolds) and discrete geometry (concerned with polytopes, simplicial complexes, etc.) meet and interact. Problems of discrete differential geometry also naturally appear in (and are relevant for) other areas of mathematics. Moreover, the process of discretizing notions, problems and methods from the smooth theory often brings out new connections and interrelations between different areas. The workshop at Oberwolfach brought together researchers with a wide variety of backgrounds, including of course discrete geometry and differential geometry, but also integrable systems, combinatorics, mathematical physics and geometry processing. The exchange of ideas among different subfields helped to build new bridges between these mathematical communities. Discrete differential geometry can be said to have arisen from the observation that when a notion from smooth geometry (such as the notion of a minimal surface) is discretized “properly”, the discrete objects are not merely approximations of the smooth ones, but have special properties of their own which make them form in some sense a coherent entity by themselves. The discrete theory would seem to be the more fundamental one: The smooth theory can always be recovered as a limit, while there seems to be no natural way to predict from the smooth theory which discretizations will have the nicest properties. One case where these ideas seem particularly well-developed is for geometries described by integrable systems. The notion of a discrete integrable system as given by consistency on a cubic lattice has already shed new light on classical, smooth integrable systems. Another theme which arose repeatedly during the workshop was that of circle patterns and sphere packings. These can be used to discretize conformal maps, isothermic surfaces, and elastic bending energy. Since a computer works with discrete representations of data, it is no surprise that many of the applications of discrete differential geometry are found within computer science, particularly in the areas of computational geometry, graphics and geometry processing. The workshop brought theoreticians together with people interested in these and other applications.

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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Bench or experimental · Consensus signal: Bench or experimental
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.386
Threshold uncertainty score0.661

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
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 head0.003
GPT teacher head0.204
Teacher spread0.201 · 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