On a geometric approach to the segment sum problem and its generalization
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Bibliographic record
Abstract
Given a sequence of n real numbers a1,a2,a3,...,an, the maximum segment sum problem is that of determin- ing indices i and j (1 � ijn) such that the sum s(i,j) = ai + ai+1 + ... + aj is a maximum. Monotone matrices were shown to be remarkably effective in solv- ing several geometric optimization problems. The sur- prise is that it can also be applied to the above problem as we show here. Recently, there was a breakthrough in obtaining an O(nlogn) algorithm for the kth smallest segment sum problem by exploiting a connection of this problem to the well-known slope selection problem. In this paper we show that this problem can also be solved within the same time bounds in the simpler framework of expander graphs.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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