21,064 research outputs found

    Symmetries and Lie algebra of the differential-difference Kadomstev-Petviashvili hierarchy

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    By introducing suitable non-isospectral flows we construct two sets of symmetries for the isospectral differential-difference Kadomstev-Petviashvili hierarchy. The symmetries form an infinite dimensional Lie algebra.Comment: 9 page

    Landau-Zener-Stuckelberg interference in a multi-anticrossing system

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    We propose a universal analytical method to study the dynamics of a multi-anticrossing system subject to driving by one single large-amplitude triangle pulse, within its time scales smaller than the dephasing time. Our approach can explain the main features of the Landau-Zener-Stuckelberg interference patterns recently observed in a tripartite system [Nature Communications 1:51 (2010)]. In particular, we focus on the effects of the size of anticrossings on interference and compare the calculated interference patterns with numerical simulations. In addition, Fourier transform of the patterns can extract information on the energy level spectrum.Comment: 6 pages, 5 figure

    SU(3)FSU(3)_F Meson Mass Formula from Random Phase Approximation

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    We present a SU(3)FSU(3)_F meson mass formula from random phase approximation (RPA). Both the mesons of ground-state pseudoscalar octet and the ground-state vector octet are described quite well in this mass formula. We also estimate the current and constituent quark masses from the na\"{\i}ve quark model with the PCAC relation

    5-Hydr­oxy-1-(3-hydr­oxy-2-naphtho­yl)-3,5-dimethyl-2-pyrazoline

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    In the title mol­ecule, C16H16N2O3, intra­molecular O—H⋯O hydrogen bonds influence the mol­ecular conformation. Inter­molecular O—H⋯O hydrogen bonds [O⋯O = 2.922 (2) Å] link the mol­ecules into centrosymmetric dimers. Weak inter­molecular C—H⋯O inter­actions assemble these dimers into layers parallel to the bc plane

    COCO-O: A Benchmark for Object Detectors under Natural Distribution Shifts

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    Practical object detection application can lose its effectiveness on image inputs with natural distribution shifts. This problem leads the research community to pay more attention on the robustness of detectors under Out-Of-Distribution (OOD) inputs. Existing works construct datasets to benchmark the detector's OOD robustness for a specific application scenario, e.g., Autonomous Driving. However, these datasets lack universality and are hard to benchmark general detectors built on common tasks such as COCO. To give a more comprehensive robustness assessment, we introduce COCO-O(ut-of-distribution), a test dataset based on COCO with 6 types of natural distribution shifts. COCO-O has a large distribution gap with training data and results in a significant 55.7% relative performance drop on a Faster R-CNN detector. We leverage COCO-O to conduct experiments on more than 100 modern object detectors to investigate if their improvements are credible or just over-fitting to the COCO test set. Unfortunately, most classic detectors in early years do not exhibit strong OOD generalization. We further study the robustness effect on recent breakthroughs of detector's architecture design, augmentation and pre-training techniques. Some empirical findings are revealed: 1) Compared with detection head or neck, backbone is the most important part for robustness; 2) An end-to-end detection transformer design brings no enhancement, and may even reduce robustness; 3) Large-scale foundation models have made a great leap on robust object detection. We hope our COCO-O could provide a rich testbed for robustness study of object detection. The dataset will be available at \url{https://github.com/alibaba/easyrobust/tree/main/benchmarks/coco_o}.Comment: To appear in ICCV2023, https://github.com/alibaba/easyrobust/tree/main/benchmarks/coco_
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