Bibliographic record
Abstract
This appendix reviews in a very compact form the basic concepts of random variables and random processes for the purpose of understanding jitter and phase noise. The goal is not to provide a thorough treatment, but rather to help the reader in recalling the definitions and the meanings of some of the most useful and common concepts. It is assumed that the reader is familiar with the basic concepts of probability. Although not strictly necessary, it is beneficial that the reader has been previously exposed to the theory of random variables and random processes, as can be found in a typical graduate university class. For further reading, or an in-depth analysis of the concepts, such specialized textbooks as [1], [13], [129], and [105] can be consulted. Random Variables Definition Given an experiment with many possible outcomes, a random variable X is defined as a function that assigns a real number to each outcome of this experiment. In order to be called a random variable, the function must satisfy the following condition: the set of outcomes for which X is smaller than or equal to a given real number a , has a given, well-defined probability for any a . As an example, let's take as an experiment the toss of a dice. The possible outcomes are each of the six faces of the dice. We can associate with each face the integer numbers 1 to 6, even if there are no numbers (or dots) on the faces of the dice (assuming that we can distinguish each of the faces of the dice somehow). This rule of association can be formalized as a function X which can assume the values 1, 2, 3, 4, 5, 6. Given any real number a , the probability that X < a is always well defined. For instance, the probability that X ≤ 3.4567 is equal to the probability that the dice shows one of the faces associated with the numbers 1 to 3. The probability that X ≤ -1 is obviously zero, since there is no possible outcome associated to numbers below 1. Since the condition stated in the above paragraph is satisfied, X can be called a random variable. Note that the name “random variable” is, strictly speaking, a misnomer, since it refers to a function, not to a variable.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.011 | 0.008 |
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".