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Record W3196171449 · doi:10.1016/j.aim.2021.107956

The Calder\'{o}n inverse problem for isotropic quasilinear conductivities

2021· article· en· W3196171449 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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenuearXiv (Cornell University) · 2021
Typearticle
Languageen
FieldMathematics
TopicNumerical methods in inverse problems
Canadian institutionsFields Institute for Research in Mathematical Sciences
FundersNational Natural Science Foundation of ChinaFields Institute for Research in Mathematical SciencesIowa Academy of ScienceAgence Nationale de la RechercheNational Science Foundation
KeywordsMathematicsUniquenessIsotropyMathematical analysisBounded functionOpen setCompleteness (order theory)InverseDirichlet distributionAnisotropyBoundary value problemBoundary (topology)Neumann boundary conditionNonlinear systemPure mathematicsGeometry

Abstract

fetched live from OpenAlex

We prove a global uniqueness result for the Calder\'{o}n inverse problem for a general quasilinear isotropic conductivity equation on a bounded open set with smooth boundary in dimension $n\ge 3$. Performing higher order linearizations of the nonlinear Dirichlet--to--Neumann map, we reduce the problem of the recovery of the differentials of the quasilinear conductivity, which are symmetric tensors, to a completeness property for certain anisotropic products of solutions to the linearized equation. The completeness property is established using complex geometric optics solutions to the linearized conductivity equation, whose amplitudes concentrate near suitable two dimensional planes.

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)0.001
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: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.389
Threshold uncertainty score0.736

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.001
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 head0.234
GPT teacher head0.268
Teacher spread0.034 · 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