Paper List
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Developing the PsyCogMetrics™ AI Lab to Evaluate Large Language Models and Advance Cognitive Science
This paper addresses the critical gap between sophisticated LLM evaluation needs and the lack of accessible, scientifically rigorous platforms that in...
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Equivalence of approximation by networks of single- and multi-spike neurons
This paper resolves the fundamental question of whether single-spike spiking neural networks (SNNs) are inherently less expressive than multi-spike SN...
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The neuroscience of transformers
提出了Transformer架构与皮层柱微环路之间的新颖计算映射，连接了现代AI与神经科学。
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Framing local structural identifiability and observability in terms of parameter-state symmetries
This paper addresses the core challenge of systematically determining which parameters and states in a mechanistic ODE model can be uniquely inferred ...
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Leveraging Phytolith Research using Artificial Intelligence
This paper addresses the critical bottleneck in phytolith research by automating the labor-intensive manual microscopy process through a multimodal AI...
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Neural network-based encoding in free-viewing fMRI with gaze-aware models
This paper addresses the core challenge of building computationally efficient and ecologically valid brain encoding models for naturalistic vision by ...
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Scalable DNA Ternary Full Adder Enabled by a Competitive Blocking Circuit
This paper addresses the core bottleneck of carry information attenuation and limited computational scale in DNA binary adders by introducing a scalab...
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ELISA: An Interpretable Hybrid Generative AI Agent for Expression-Grounded Discovery in Single-Cell Genomics
This paper addresses the critical bottleneck of translating high-dimensional single-cell transcriptomic data into interpretable biological hypotheses ...
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.