Moduli Of Certain Wild Covers Of Curves

A fine moduli space (see Chapter~\ref{secn&t} Definition~\ref{finemdli}) is constructed, for cyclic-by-$\mathsf{p}$ covers of an affine curve over an algebraically closed field $k$ of characteristic $\mathsf{p}\u3e0$. An intersection (see Definition~\ref{M}) of finitely many fine moduli spaces for cyclic-by-$\mathsf{p}$ covers of affine curves gives a moduli space for $\mathsf{p}\u27$-by-$\mathsf{p}$ covers of an affine curve. A local moduli space is also constructed, for cyclic-by-$\mathsf{p}$ covers of $Spec(k((x)))$, which is the same as the global moduli space for cyclic-by-$\mathsf{p}$ covers of $\mathbb{P}^1-\{0\}$ tamely ramified over $\infty$ with the same Galois group. Then it is shown that a restriction morphism (see Lemma~\ref{res mor-2}) is finite with degrees on connected components $\textsf{p}$ powers: There are finitely many deleted points (see Figure 1) of an affine curve from its smooth completion. A cyclic-by-$\mathsf{p}$ cover of an affine curve gives a product of local covers with the same Galois group, of the punctured infinitesimal neighbourhoods of the deleted points. So there is a restriction morphism from the global moduli space to a product of local moduli spaces

FEND: A Future Enhanced Distribution-Aware Contrastive Learning Framework for Long-tail Trajectory Prediction

Predicting the future trajectories of the traffic agents is a gordian technique in autonomous driving. However, trajectory prediction suffers from data imbalance in the prevalent datasets, and the tailed data is often more complicated and safety-critical. In this paper, we focus on dealing with the long-tail phenomenon in trajectory prediction. Previous methods dealing with long-tail data did not take into account the variety of motion patterns in the tailed data. In this paper, we put forward a future enhanced contrastive learning framework to recognize tail trajectory patterns and form a feature space with separate pattern clusters. Furthermore, a distribution aware hyper predictor is brought up to better utilize the shaped feature space. Our method is a model-agnostic framework and can be plugged into many well-known baselines. Experimental results show that our framework outperforms the state-of-the-art long-tail prediction method on tailed samples by 9.5% on ADE and 8.5% on FDE, while maintaining or slightly improving the averaged performance. Our method also surpasses many long-tail techniques on trajectory prediction task.Comment: Accepted for publication at the IEEE/CVF Conference on Computer Vision and Pattern Recognition 2023 (CVPR 2023

Heterogeneous Trajectory Forecasting via Risk and Scene Graph Learning

Heterogeneous trajectory forecasting is critical for intelligent transportation systems, while it is challenging because of the difficulty for modeling the complex interaction relations among the heterogeneous road agents as well as their agent-environment constraint. In this work, we propose a risk and scene graph learning method for trajectory forecasting of heterogeneous road agents, which consists of a Heterogeneous Risk Graph (HRG) and a Hierarchical Scene Graph (HSG) from the aspects of agent category and their movable semantic regions. HRG groups each kind of road agents and calculates their interaction adjacency matrix based on an effective collision risk metric. HSG of driving scene is modeled by inferring the relationship between road agents and road semantic layout aligned by the road scene grammar. Based on this formulation, we can obtain an effective trajectory forecasting in driving situations, and superior performance to other state-of-the-art approaches is demonstrated by exhaustive experiments on the nuScenes, ApolloScape, and Argoverse datasets.Comment: Submitted to IEEE Transactions on Intelligent Transportation Systems, 202

Robust residual-guided iterative reconstruction for sparse-view CT in small animal imaging

Objective. We introduce a robust image reconstruction algorithm named residual-guided Golub–Kahan iterative reconstruction technique (RGIRT) designed for sparse-view computed tomography (CT), which aims at high-fidelity image reconstruction from a limited number of projection views. Approach. RGIRT utilizes an inner-outer dual iteration framework, with a flexible least square QR (FLSQR) algorithm implemented in the inner iteration and a restarted iterative scheme applied in the outer iteration. The inner FLSQR employs a flexible Golub–Kahan bidiagonalization method to reduce the size of the inverse problem, and a weighted generalized cross-validation method to adaptively estimate the regularization hyper-parameter. The inner iteration efficiently yields the intermediate reconstruction result, while the outer iteration minimizes the residual and refines the solution by using the result obtained from the inner iteration. Main results. The reconstruction performance of RGIRT is evaluated and compared to other reference methods (FBPConvNet, SART-TV, and FLSQR) using projection data from both numerical phantoms and real experimental Micro-CT data. The experimental findings, from testing various numbers of projection views and different noise levels, underscore the robustness of RGIRT. Meanwhile, theoretical analysis confirms the convergence of residual for our approach. Significance. We propose a robust iterative reconstruction algorithm for x-ray CT scans with sparse views, thereby shortening scanning time and mitigating excessive ionizing radiation exposure to small animals

Optimized operational approach for multi-type reactive power compensation to enhance the grid integration strength of new energy clusters

The insufficient system strength in the high-proportion new energy access area has gradually emerged as a crucial factor contributing to the transient overvoltage issue. Therefore, it is imperative to propose a reactive power optimization operation mode that takes into consideration both the power grid strength and system operating voltage of the new energy cluster system. Firstly, the relationship between the evaluation index of power grid strength and the performance of system voltage response is elucidated, while analyzing the influence mechanism of various reactive power compensation devices on the power grid strength of new energy cluster systems. Then, a reactive power operation optimization model is proposed to maximize the strength of the system grid and minimize the voltage deviation. To solve this problem, a hybrid approach combining genetic algorithm and CPLEX solver is employed. Finally, the effectiveness of the proposed method is validated through a typical simulation example

Non-invasive visualization of amyloid-beta deposits in Alzheimer amyloidosis mice using magnetic resonance imaging and fluorescence molecular tomography

Abnormal cerebral accumulation of amyloid-beta peptide (Aβ) is a major hallmark of Alzheimer's disease. Non-invasive monitoring of Aβ deposits enables assessing the disease burden in patients and animal models mimicking aspects of the human disease as well as evaluating the efficacy of Aβ-modulating therapies. Previous in vivo assessments of plaque load have been predominantly based on macroscopic fluorescence reflectance imaging (FRI) and confocal or two-photon microscopy using Aβ-specific imaging agents. However, the former method lacks depth resolution, whereas the latter is restricted by the limited field of view preventing a full coverage of the large brain region. Here, we utilized a fluorescence molecular tomography (FMT)-magnetic resonance imaging (MRI) pipeline with the curcumin derivative fluorescent probe CRANAD-2 to achieve full 3D brain coverage for detecting Aβ accumulation in the arcAβ mouse model of cerebral amyloidosis. A homebuilt FMT system was used for data acquisition, whereas a customized software platform enabled the integration of MRI-derived anatomical information as prior information for FMT image reconstruction. The results obtained from the FMT-MRI study were compared to those from conventional planar FRI recorded under similar physiological conditions, yielding comparable time courses of the fluorescence intensity following intravenous injection of CRANAD-2 in a region-of-interest comprising the brain. In conclusion, we have demonstrated the feasibility of visualizing Aβ deposition in 3D using a multimodal FMT-MRI strategy. This hybrid imaging method provides complementary anatomical, physiological and molecular information, thereby enabling the detailed characterization of the disease status in arcAβ mouse models, which can also facilitate monitoring the efficacy of putative treatments targeting Aβ