Paper List
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Macroscopic Dominance from Microscopic Extremes: Symmetry Breaking in Spatial Competition
This paper addresses the fundamental question of how microscopic stochastic advantages in spatial exploration translate into macroscopic resource domi...
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Linear Readout of Neural Manifolds with Continuous Variables
This paper addresses the core challenge of quantifying how the geometric structure of high-dimensional neural population activity (neural manifolds) d...
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Theory of Cell Body Lensing and Phototaxis Sign Reversal in “Eyeless” Mutants of Chlamydomonas
This paper solves the core puzzle of how eyeless mutants of Chlamydomonas exhibit reversed phototaxis by quantitatively modeling the competition betwe...
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Cross-Species Transfer Learning for Electrophysiology-to-Transcriptomics Mapping in Cortical GABAergic Interneurons
This paper addresses the challenge of predicting transcriptomic identity from electrophysiological recordings in human cortical interneurons, where li...
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Uncovering statistical structure in large-scale neural activity with Restricted Boltzmann Machines
This paper addresses the core challenge of modeling large-scale neural population activity (1500-2000 neurons) with interpretable higher-order interac...
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Realizing Common Random Numbers: Event-Keyed Hashing for Causally Valid Stochastic Models
This paper addresses the critical problem that standard stateful PRNG implementations in agent-based models violate causal validity by making random d...
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A Standardized Framework for Evaluating Gene Expression Generative Models
This paper addresses the critical lack of standardized evaluation protocols for single-cell gene expression generative models, where inconsistent metr...
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Single Molecule Localization Microscopy Challenge: A Biologically Inspired Benchmark for Long-Sequence Modeling
This paper addresses the core challenge of evaluating state-space models on biologically realistic, sparse, and stochastic temporal processes, which a...
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.