Bibliographic record
Abstract
This article optimizes a continuous area cartogram algorithm published in The Professional Geographer by Dougenik, Chrisman, and Niemeyer (DCN) in 1985. The DCN algorithm simulates a rubber sheet and is an iterative and approximate solution of cartogram construction. Although it remains popular because of its conceptual simplicity and cartographic quality, the DCN algorithm cannot completely preserve topology and its mathematical properties are inadequately explained. This article presents an optimization to the DCN algorithm, named Opti-DCN, with three improvements. First, it provides a mathematical condition for topology preservation. Second, new transformation equations that meet this condition are deduced from mathematics, which simultaneously optimize the global elasticity coefficient, a key parameter that greatly impacts the convergence rate of the rubber-sheet algorithm and the topological integrity of its generated cartograms. Last, the new algorithm simplifies the way of generating transforming forces in DCN and improves its efficiency of geometric transformation. Comparison shows that Opti-DCN is significantly faster to converge to equal-density cartograms and can mathematically and practically eliminate topological errors.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| 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".