Two models of sparse and clustered dynamic networks
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Bibliographic record
Abstract
Abstract We present two models of sparse dynamic networks that display transitivity—the tendency for nodes sharing a common neighbour to be neighbours of one another. Our first network is a continuous time Markov chain $ G=\{G_{t}=(V, E_{t}),t\geq 0\} $ whose states are graphs with the common set of nodes $ V=\{1 , \dots, n\} $. The transitions are defined as follows. Given $ t $, the node pairs $ \{i, j\}\subset V $ are assigned independent exponential waiting times $ A_{ij} $. At time $ t+\min_{ij}A_{ij} $ the pair $ \{i_{0},j_{0}\} $ with $ A_{i_{0}j_{0}}=\min_{ij}A_{ij} $ toggles its adjacency status. To mimic clustering patterns of sparse real networks we set intensities $ a_{ij} $ of exponential times $ A_{ij} $ to be decreasing functions of the degrees of common neighbours of nodes $ i $ and $ j $ in $ G_{t} $. Our second network $ G^{\prime}=\{G^{\prime}_{t}=(E^{\prime}_{t},V),t\geq 0\} $ is the affiliation network based on a latent Markov chain $ H=\{H_{t}=(V\cup W, E_{t}),t\geq 0\} $ whose states are bipartite graphs with the bipartition $ V\cup W $, where $ W=\{1 , \dots, m\} $ is an auxiliary set of attributes/affiliations. Nodes $ i_{1},i_{2}\in V $ are adjacent in $ G^{\prime}_{t} $ whenever $ i_{1} $ and $ i_{2} $ have a common neighbour in $ H_{t} $. We analyse geometric properties of both dynamic networks at stationarity and show that networks possess high clustering. They admit tunable degree distribution and clustering coefficients.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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