Bibliographic record
Abstract
Logarithms log 2 (n) and exponentials 2 n arise often when analyzing algorithms. Uses: These are some of the places that you will see them. Divide a Logarithmic Number of Times: Many algorithms repeatedly cut the input instance in half. A classic example is binary search (Section 1.4): You take something of size n and you cut it in half, then you cut one of these halves in half, and one of these in half, and so on. Even for a very large initial object, it does not take very long until you get a piece of size below 1. The number of divisions required is about log 2 (n) . Here the base 2 is because you are cutting them in half. If you were to cut them into thirds, then the number of times to cut would be about log 3 (n) . A Logarithmic Number of Digits: Logarithms are also useful because writing down a given integer value n requires ｢log 10 (n + 1)｣ decimal digits. For example, suppose that n = 1,000,000 = 10 6 . You would have to divide this number by 10 six times to get to 1. Hence, by definition, log 10 (n) = 6. This, however, is the number of zeros, not the number of digits. We forgot the leading digit 1.
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.006 | 0.015 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.006 |
| Insufficient payload (model declined to judge) | 0.031 | 0.014 |
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".