A Finite Memory Interacting P\\'{o}lya Contagion Network and its\n Approximating Dynamical Systems
Bibliographic record
Abstract
We introduce a new model for contagion spread using a network of interacting\nfinite memory two-color P\\'{o}lya urns, which we refer to as the finite memory\ninteracting P\\'{o}lya contagion network. The urns interact in the sense that\nthe probability of drawing a red ball (which represents an infection state) for\na given urn, not only depends on the ratio of red balls in that urn but also on\nthe ratio of red balls in the other urns in the network, hence accounting for\nthe effect of spatial contagion. The resulting network-wide contagion process\nis a discrete-time finite-memory ($M$th order) Markov process, whose transition\nprobability matrix is determined. The stochastic properties of the network\ncontagion Markov process are analytically examined, and for homogeneous system\nparameters, we characterize the limiting state of infection in each urn. For\nthe non-homogeneous case, given the complexity of the stochastic process, and\nin the same spirit as the well-studied SIS models, we use a mean-field type\napproximation to obtain a discrete-time dynamical system for the finite memory\ninteracting P\\'{o}lya contagion network. Interestingly, for $M=1$, we obtain a\nlinear dynamical system which exactly represents the corresponding Markov\nprocess. For $M>1$, we use mean-field approximation to obtain a nonlinear\ndynamical system. Furthermore, noting that the latter dynamical system admits a\nlinear variant (realized by retaining its leading linear terms), we study the\nasymptotic behavior of the linear systems for both memory modes and\ncharacterize their equilibrium. Finally, we present simulation studies to\nassess the quality of the approximation purveyed by the linear and non-linear\ndynamical systems.\n
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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, 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".