Bibliographic record
Abstract
The h-index is a single-number metric that combines the effect of a researcher’s productivity and impact to measure her research ‘excellence.’ Google Scholar offers a free service where authors can check their record of citations, h-index and i10-index values. This paper employs dynamic analysis and attempts to shed some light on the reasons why h-index grows slowly. We first present a deterministic model where a closed-form expression of the h-index is found as a function of the rate of citations received, and the time since the author’s first publication. Next, we present a stochastic model where the rate of citations is a discrete random variable. For this case, we determine the probability density function of the random h-index using probability generating functions. We show that when the citation arrival rate is an affine linear function of time, the h-index always grows linearly in time. Finally, we consider the more general case of citation arrivals varying over time. For this case, simulation analysis demonstrates that as the variability increases, we find a decline in the h-index. We also find that when variability is low, the simulated h-index values move in parallel with the theoretical results.
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How this classification was reachedexpand
Direct model labels (unvalidated)
Per-model category and study-design labels from the labeling rounds. They are machine output, unvalidated, and the disagreement between models ships as data. No study design here is MEDLINE-validated yet.
| Model arm | Categories | Study design | Confidence |
|---|---|---|---|
| gemma | Bibliometrics Domain: not available · Genre: Empirical About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | low |
| gpt | BibliometricsMetaresearch Domain: Evaluation · Genre: Empirical About the Canadian research system: no · About a Canadian topic: no | Observational | high |
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 | 0.027 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.039 | 0.107 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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 itClassification
machine, unvalidatedLabeled directly by 2 models reading the full record.
The models disagree on parts of this classification; every voice is preserved in the section at the end of the page.
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".