Paper List
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A Theoretical Framework for the Formation of Large Animal Groups: Topological Coordination, Subgroup Merging, and Velocity Inheritance
This paper addresses the core problem of how large, coordinated animal groups form in nature, challenging the classical view of gradual aggregation by...
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CONFIDE: Hallucination Assessment for Reliable Biomolecular Structure Prediction and Design
This paper addresses the critical limitation of current protein structure prediction models (like AlphaFold3) where high-confidence scores (pLDDT) can...
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Generative design and validation of therapeutic peptides for glioblastoma based on a potential target ATP5A
This paper addresses the critical bottleneck in therapeutic peptide design: how to efficiently optimize lead peptides with geometric constraints while...
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Pharmacophore-based design by learning on voxel grids
This paper addresses the computational bottleneck and limited novelty in conventional pharmacophore-based virtual screening by introducing a voxel cap...
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Human-Centred Evaluation of Text-to-Image Generation Models for Self-expression of Mental Distress: A Dataset Based on GPT-4o
This paper addresses the critical gap in evaluating how AI-generated images can effectively support cross-cultural mental distress communication, part...
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ANNE Apnea Paper
This paper addresses the core challenge of achieving accurate, event-level sleep apnea detection and characterization using a non-intrusive, multimoda...
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DeeDeeExperiment: Building an infrastructure for integrating and managing omics data analysis results in R/Bioconductor
This paper addresses the critical bottleneck of managing and organizing the growing volume of differential expression and functional enrichment analys...
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Cross-Species Antimicrobial Resistance Prediction from Genomic Foundation Models
This paper addresses the core challenge of predicting antimicrobial resistance across phylogenetically distinct bacterial species, where traditional m...
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.