102 research outputs found

    A PEL-type Igusa Stack and the pp-adic Geometry of Shimura Varieties

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    Let (G,X)(G,X) be a PEL-Shimura datum of type AC in Kottwitz's classification. Assume GQpG_{\mathbf{Q}_p} is unramified. We show that the good reduction locus of the infinite pp-level Shimura variety attached to this datum, considered as a diamond, can be described as the fiber product of a certain v-stack (which we call ``Igusa stack") with a Schubert cell of the corresponding BdR+B_{dR}^+-affine Grassmannian, over the stack of GQpG_{\mathbf{Q}_p}-torsors on the Fargues-Fontaine curve. We also construct a minimal compactification of the Igusa stack and show that this fiber product structure extends to the minimal compactification of the Shimura variety. When the Schubert cell of the affine Grassmannian is replaced by a bounded substack of G\mathcal{G}-shtukas, where G\mathcal{G} is a reductive model of GQpG_{\mathbf{Q}_p} over Zp\mathbf{Z}_p, we show that this fiber product recovers the integral model of the Shimura variety. This result on integral models, if specialized to a Newton polygon stratum, recovers the fiber product formula of Mantovan. Similar fiber product structures are conjectured by Scholze to exist on general Shimura varieties.Comment: Comments welcome

    Evolutionary Reinforcement Learning via Cooperative Coevolutionary Negatively Correlated Search

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    Evolutionary algorithms (EAs) have been successfully applied to optimize the policies for Reinforcement Learning (RL) tasks due to their exploration ability. The recently proposed Negatively Correlated Search (NCS) provides a distinct parallel exploration search behavior and is expected to facilitate RL more effectively. Considering that the commonly adopted neural policies usually involves millions of parameters to be optimized, the direct application of NCS to RL may face a great challenge of the large-scale search space. To address this issue, this paper presents an NCS-friendly Cooperative Coevolution (CC) framework to scale-up NCS while largely preserving its parallel exploration search behavior. The issue of traditional CC that can deteriorate NCS is also discussed. Empirical studies on 10 popular Atari games show that the proposed method can significantly outperform three state-of-the-art deep RL methods with 50% less computational time by effectively exploring a 1.7 million-dimensional search space

    Cellulase Recycling after High-Solids Simultaneous Saccharification and Fermentation of Combined Pretreated Corncob

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    Despite the advantageous prospect of second-generation bioethanol, its final commercialization must overcome the primary cost impediment due to enzyme assumption. To solve this problem, this work achieves high-concentration ethanol fermentation and multi-round cellulase recycling through process integration. The optimal time and temperature of the re-adsorption process were determined by monitoring the adsorption kinetics of cellulases. Both glucose and cellobiose inhibited cellulase adsorption. After 96 h of ethanol fermentation, 40% of the initial cellulase remained in the broth, from which 62.5% of the cellulase can be recycled and reused in fresh substrate re-adsorption for 90 min. Under optimum conditions, i.e., pH 5.0, dry matter loading of 15 wt%, cellulase loading of 45 FPU/g glucan, two cycles of fermentation and re-adsorption can yield two-fold increased ethanol outputs and reduce enzyme costs by over 50%. The ethanol concentration in each cycle can be achieved at levels greater than 40 g/L

    PRIOR: Personalized Prior for Reactivating the Information Overlooked in Federated Learning

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    Classical federated learning (FL) enables training machine learning models without sharing data for privacy preservation, but heterogeneous data characteristic degrades the performance of the localized model. Personalized FL (PFL) addresses this by synthesizing personalized models from a global model via training on local data. Such a global model may overlook the specific information that the clients have been sampled. In this paper, we propose a novel scheme to inject personalized prior knowledge into the global model in each client, which attempts to mitigate the introduced incomplete information problem in PFL. At the heart of our proposed approach is a framework, the PFL with Bregman Divergence (pFedBreD), decoupling the personalized prior from the local objective function regularized by Bregman divergence for greater adaptability in personalized scenarios. We also relax the mirror descent (RMD) to extract the prior explicitly to provide optional strategies. Additionally, our pFedBreD is backed up by a convergence analysis. Sufficient experiments demonstrate that our method reaches the state-of-the-art performances on 5 datasets and outperforms other methods by up to 3.5% across 8 benchmarks. Extensive analyses verify the robustness and necessity of proposed designs.Comment: Accepted by NeurIPS 202

    Geometry of the Wiman Pencil, I: Algebro-Geometric Aspects

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    In 1981 W.L. Edge discovered and studied a pencil C\mathcal{C} of highly symmetric genus 66 projective curves with remarkable properties. Edge's work was based on an 1895 paper of A. Wiman. Both papers were written in the satisfying style of 19th century algebraic geometry. In this paper and its sequel [FL], we consider C\mathcal{C} from a more modern, conceptual perspective, whereby explicit equations are reincarnated as geometric objects.Comment: Minor revisions. Now 49 pages, 4 figures. To appear in European Journal of Mathematics, special issue in memory of W.L. Edg
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