Efficient Method for Estimating Globally Optimal Simple Vertical Curves
Why this work is in the frame
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Bibliographic record
Abstract
Different methods for estimating simple vertical curves that optimally fit observed profile data have been developed. In 1999, the author developed a linear programming (LP) method for estimating simple vertical curves using LINGO optimization software. To obtain the global optimal solution, the LP formulation was manually solved for different combinations of the two unknown nonlinear variables (using 5m increments). In 2004, an improved method that automates the iterations using Visual-Basic in Excel Solver was published. The global optimal solution required 10h for an increment of 0.1m. This technical note presents an extension of the previously developed LP formulation that converges to the global optimal solution in a minute. The formulation involves no iterations of the nonlinear variables. Instead, the start and end points of the parabolic curve were modeled using three binary variables, and the resulting mixed-integer nonlinear model was solved using LINGO global option that has been recently developed. The proposed method, which is applicable to both crest and sag vertical curves, should be of interest to surveying professionals.
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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it