Recovering the conductances on grids: A theoretical justification
Bibliographic record
Abstract
In this work, we present an overview of the work developed by the authors in the context of inverse problems on finite networks and moreover, we display the steps needed to recover the conductances in a 3–dimensional grid. This study performs an extension of the pioneer studies by E. B. Curtis and J. A. Morrow, and sets the theoretical basis for solving inverse problems on networks. We present just a glance of what we call overdetermined partial boundary value problems, in which any data are not prescribed on a part of the boundary, whereas in another part of the boundary both the values of the function and of its normal derivative are given. The resolvent kernels associated with these problems are described and they are the fundamental tool to perform an algorithm for the recovery of the conductance of a 3 3 –dimensional grid. We strongly believe that the columns of the overdetermined partial Poisson kernel are the discrete counterpart of the so–called CGO solutions (complex geometrical optic solutions) that, in their turn, are the key to solve inverse continuous problems on planar domains.
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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 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".