Calculating the meeting point of scattered robots on weighted terrain surfaces
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Bibliographic record
Abstract
In this paper we discuss the problem of determining a meeting point of a set of scattered robots R = {r1,r2,...,rs} in a weighted terrain P which has n> s triangular faces. Our algorithmic approach is to produce a discretization of P by producing a graph G = {V G,E G} which lies on the surface of P. For a chosen vertex p ′ ∈ V G, we define ‖Π(ri,p ′)‖ as the minimum weight cost of traveling from ri to p ′. We show that minp ′ ∈V G{max1≤i≤s{‖Π(ri,p ′)‖}} ≤ minp∗∈P{max1≤i≤s{‖Π(ri,p ∗)‖}} + W |L | where L is the longest edge of P, W is the maximum cost weight of a face of P, and p ∗ is the optimal solution. Our algorithm requires O(snmlog(snm)+snm 2) time to run, where m = n in the Euclidean metric and m = n2 in the weighted metric. However, we show through experimentation that only a constant value of m is required (e.g., m=8) in order to produce very accurate solutions (< 1 % error). Hence, for typical terrain data, the expected running time of our algorithm is O(snlog(sn)). Also, as part of our experiments we show that by using geometrical subsets (i.e., 2D/3D convex hulls, 2D/3D bounding boxes and random selection) of the robots we can improve the running time for finding p ′, with minimal or no additional accuracy error when comparing p ′ to p ∗. 1
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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 | 0.000 | 0.000 |
| 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