Paper List
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STAR-GO: Improving Protein Function Prediction by Learning to Hierarchically Integrate Ontology-Informed Semantic Embeddings
This paper addresses the core challenge of generalizing protein function prediction to unseen or newly introduced Gene Ontology (GO) terms by overcomi...
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Incorporating indel channels into average-case analysis of seed-chain-extend
This paper addresses the core pain point of bridging the theoretical gap for the widely used seed-chain-extend heuristic by providing the first rigoro...
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Competition, stability, and functionality in excitatory-inhibitory neural circuits
This paper addresses the core challenge of extending interpretable energy-based frameworks to biologically realistic asymmetric neural networks, where...
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Enhancing Clinical Note Generation with ICD-10, Clinical Ontology Knowledge Graphs, and Chain-of-Thought Prompting Using GPT-4
This paper addresses the core challenge of generating accurate and clinically relevant patient notes from sparse inputs (ICD codes and basic demograph...
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Learning From Limited Data and Feedback for Cell Culture Process Monitoring: A Comparative Study
This paper addresses the core challenge of developing accurate real-time bioprocess monitoring soft sensors under severe data constraints: limited his...
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Cell-cell communication inference and analysis: biological mechanisms, computational approaches, and future opportunities
This review addresses the critical need for a systematic framework to navigate the rapidly expanding landscape of computational methods for inferring ...
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Generating a Contact Matrix for Aged Care Settings in Australia: an agent-based model study
This study addresses the critical gap in understanding heterogeneous contact patterns within aged care facilities, where existing population-level con...
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Emergent Spatiotemporal Dynamics in Large-Scale Brain Networks with Next Generation Neural Mass Models
This work addresses the core challenge of understanding how complex, brain-wide spatiotemporal patterns emerge from the interaction of biophysically d...
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.