11,097 research outputs found

    Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity

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    Between Snyder's quantized space-time model in de Sitter space of momenta and the \dS special relativity on \dS-spacetime of radius RR with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with Planck length P\ell_P, R(3/Λ)1/2R\simeq (3/\Lambda)^{1/2} should be a fundamental constant. They lead to a dimensionless constant gPR1=(Gc3Λ/3)1/21061g{\sim\ell_PR^{-1}}=(G\hbar c^{-3}\Lambda/3)^{1/2}\sim 10^{-61}. These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local \dS-invariance characterized by gg. A simple model of \dS-gravity with a gauge-like action on umbilical manifolds may show these characters. It can pass the observation tests and support the duality.Comment: 32 page

    Newton-Hooke Limit of Beltrami-de Sitter Spacetime, Principles of Galilei-Hooke's Relativity and Postulate on Newton-Hooke Universal Time

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    Based on the Beltrami-de Sitter spacetime, we present the Newton-Hooke model under the Newton-Hooke contraction of the BdSBdS spacetime with respect to the transformation group, algebra and geometry. It is shown that in Newton-Hooke space-time, there are inertial-type coordinate systems and inertial-type observers, which move along straight lines with uniform velocity. And they are invariant under the Newton-Hooke group. In order to determine uniquely the Newton-Hooke limit, we propose the Galilei-Hooke's relativity principle as well as the postulate on Newton-Hooke universal time. All results are readily extended to the Newton-Hooke model as a contraction of Beltrami-anti-de Sitter spacetime with negative cosmological constant.Comment: 25 pages, 3 figures; some misprints correcte

    Advantage Actor-Critic with Reasoner: Explaining the Agent's Behavior from an Exploratory Perspective

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    Reinforcement learning (RL) is a powerful tool for solving complex decision-making problems, but its lack of transparency and interpretability has been a major challenge in domains where decisions have significant real-world consequences. In this paper, we propose a novel Advantage Actor-Critic with Reasoner (A2CR), which can be easily applied to Actor-Critic-based RL models and make them interpretable. A2CR consists of three interconnected networks: the Policy Network, the Value Network, and the Reasoner Network. By predefining and classifying the underlying purpose of the actor's actions, A2CR automatically generates a more comprehensive and interpretable paradigm for understanding the agent's decision-making process. It offers a range of functionalities such as purpose-based saliency, early failure detection, and model supervision, thereby promoting responsible and trustworthy RL. Evaluations conducted in action-rich Super Mario Bros environments yield intriguing findings: Reasoner-predicted label proportions decrease for ``Breakout" and increase for ``Hovering" as the exploration level of the RL algorithm intensifies. Additionally, purpose-based saliencies are more focused and comprehensible
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