Modeling Network Contagion Via Interacting Finite Memory Pólya Urns
Bibliographic record
Abstract
We construct a system of interacting finite memory Pólya urns to model contagion spread in a network. The urns, which are composed of red and black balls (representing degrees of infection and healthiness, respectively) interact in the sense that the probability at any time instant of drawing a red ball for a given urn not only depends on that urn’s ratio of red balls, but also on the ratio of red balls in the other urns of the network, hence accounting for the effect of spatial contagion. The urns have a finite memory, M, in the sense that reinforcing (black or red) balls added to each urn at time t are only kept in that urn for M future time instants (until time t + M). The resulting vector of all urn drawing variables forms an Mth order time-invariant irreducible and aperiodic Markov chain. We analytically examine the properties of the underlying Markov process and derive its asymptotic behaviour for the case of homogeneous system parameters. We further use mean-field approximation to obtain a class of approximating linear and nonlinear dynamical systems for the non-homogeneous case. Finally, we present simulations to assess the quality of these mean-field approximations.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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, unvalidatedMachine predicted; a candidate call from one teacher head, 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".