Paper List
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Translating Measures onto Mechanisms: The Cognitive Relevance of Higher-Order Information
This review addresses the core challenge of translating abstract higher-order information theory metrics (e.g., synergy, redundancy) into defensible, ...
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Emergent Bayesian Behaviour and Optimal Cue Combination in LLMs
This paper addresses the critical gap in understanding whether LLMs spontaneously develop human-like Bayesian strategies for processing uncertain info...
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Vessel Network Topology in Molecular Communication: Insights from Experiments and Theory
This work addresses the critical lack of experimentally validated channel models for molecular communication within complex vessel networks, which is ...
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Modulation of DNA rheology by a transcription factor that forms aging microgels
This work addresses the fundamental question of how the transcription factor NANOG, essential for embryonic stem cell pluripotency, physically regulat...
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Imperfect molecular detection renormalizes apparent kinetic rates in stochastic gene regulatory networks
This paper addresses the core challenge of distinguishing genuine stochastic dynamics of gene regulatory networks from artifacts introduced by imperfe...
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PanFoMa: A Lightweight Foundation Model and Benchmark for Pan-Cancer
This paper addresses the dual challenge of achieving computational efficiency without sacrificing accuracy in whole-transcriptome single-cell represen...
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Beyond Bayesian Inference: The Correlation Integral Likelihood Framework and Gradient Flow Methods for Deterministic Sampling
This paper addresses the core challenge of calibrating complex biological models (e.g., PDEs, agent-based models) with incomplete, noisy, or heterogen...
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Contrastive Deep Learning for Variant Detection in Wastewater Genomic Sequencing
This paper addresses the core challenge of detecting viral variants in wastewater sequencing data without reference genomes or labeled annotations, ov...
Social Distancing Equilibria in Games under Conventional SI Dynamics
Department of Mathematics, Pennsylvania State University | Huck Institute of Life Sciences, Pennsylvania State University
30秒速读
IN SHORT: This paper solves the core problem of proving the existence and uniqueness of Nash equilibria in finite-duration SI epidemic games, showing they are always bang-bang strategies.
核心创新
- Methodology Introduces a novel change of variables that simplifies the geometry and analysis of the SI social-distancing game, enabling explicit integration and closed-form solutions.
- Theory Proves that for the specified SI game with threshold-linear costs, the unique strategic equilibrium is always a time-dependent bang-bang strategy (wait-then-lockdown), with no singular solutions.
- Theory Demonstrates that in the restricted strategy space of two-phase (off-on) strategies, the bang-bang Nash equilibrium is also an Evolutionarily Stable Strategy (ESS), and that it coincides with the socially optimal policy, eliminating free-riding.
主要结论
- For all parameter tuples (m, I0, tf), there exists one and only one equilibrium point x* (Theorem 10), proving uniqueness in the SI game.
- The equilibrium strategy is explicitly given by x*(m, I0, tf) = m - 1 - W((1/I0 - 1)e^{m-1-tf}) for intermediate parameters, utilizing the Lambert W function (Eq. 13).
- The optimal public policy (minimizing population disutility ℰ(x̄)) exactly corresponds with the individual Nash equilibrium strategy (Eq. 18), showing no conflict between individual and social optima in this model.
摘要: The mathematical characterization of social-distancing games in classical epidemic theory remains an important question, for their applications to both infectious-disease theory and memetic theory. We consider a special case of the dynamic finite-duration SI social-distancing game where payoffs are accounted using Markov decision theory with zero-discounting, while distancing is constrained by threshold-linear running-costs, and the running-cost of perfect-distancing is finite. In this special case, we are able construct strategic equilibria satisfying the Nash best-response condition explicitly by integration. Our constructions are obtained using a new change of variables which simplifies the geometry and analysis. As it turns out, there are no singular solutions, and a time-dependent bang-bang strategy consisting of a wait-and-see phase followed by a lock-down phase is always the unique strategic equilibrium. We also show that in a restricted strategy space the bang-bang Nash equilibrium is an ESS, and that the optimal public policy exactly corresponds with the equilibrium strategy.