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  1. Abstract

    This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are nonlinear power flow equations, or an abstract one that represents constraint couplings between decision variables of different agents. Despite the recent development of distributed algorithms for nonconvex programs, highly complicated constraints still pose a significant challenge in theory and practice. We first identify some difficulties with the existing algorithms based on the alternating direction method of multipliers (ADMM) for dealing with such problems. We then propose a reformulation that enables us to design a two-level algorithm, which embeds a specially structured three-block ADMM at the inner level in an augmented Lagrangian method framework. Furthermore, we prove the global and local convergence as well as iteration complexity of this new scheme for general nonconvex constrained programs, and show that our analysis can be extended to handle more complicated multi-block inner-level problems. Finally, we demonstrate with computation that the new scheme provides convergent and parallelizable algorithms for various nonconvex applications, and is able to complement the performance of the state-of-the-art distributed algorithms in practice by achievingmore »either faster convergence in optimality gap or in feasibility or both.

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  2. Supervised training of optical flow predictors generally yields better accuracy than unsupervised training. However, the improved performance comes at an often high annotation cost. Semi-supervised training trades off accuracy against annotation cost. We use a simple yet effective semi-supervised training method to show that even a small fraction of labels can improve flow accuracy by a significant margin over unsupervised training. In addition, we propose active learning methods based on simple heuristics to further reduce the number of labels required to achieve the same target accuracy. Our experiments on both synthetic and real optical flow datasets show that our semi-supervised networks generally need around 50% of the labels to achieve close to full-label accuracy, and only around 20% with active learning on Sintel. We also analyze and show insights on the factors that may influence active learning performance. Code is available at https://github.com/duke-vision/ optical-flow-active-learning-release.
    Free, publicly-accessible full text available October 23, 2023
  3. Abstract

    Understanding the magnetic structure of filament channels is difficult but essential for identifying the mechanism (s) responsible for solar eruptions. In this paper we characterize the magnetic field in a well-observed filament channel with two independent methods, prominence seismology and magnetohydrodynamics flux-rope modeling, and compare the results. In 2014 May and June, active region 12076 exhibited a complex of filaments undergoing repeated oscillations over the course of 12 days. We measure the oscillation periods in the region with both Global Oscillation Network Group Hαand Solar Dynamics Observatory (SDO) Advanced Imaging Assembly EUV images, and then utilize the pendulum model of large-amplitude longitudinal oscillations to calculate the radius of curvature of the fields supporting the oscillating plasma from the derived periods. We also employ the regularized Biot–Savart laws formalism to construct a flux-rope model of the field of the central filament in the region based on an SDO Helioseismic and Magnetic Imager magnetogram. We compare the estimated radius of curvature, location, and angle of the magnetic field in the plane of the sky derived from the observed oscillations with the corresponding magnetic-field properties extracted from the flux-rope model. We find that the two models are broadly consistent, but detailed comparisonsmore »of the model and specific oscillations often differ. Model observation comparisons such as these are important for advancing our understanding of the structure of filament channels.

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  4. Hydraulic fracture (or hydrofracture) can promote the propagation of meltwater-filled surface crevasses in glaciers and, in some cases, lead to full-depth penetration that can enhance basal sliding and iceberg calving. Here, we propose a novel poro-damage phase field model for hydrofracturing of glacier crevasses, wherein the crevasse is represented by a nonlocal damage zone and the effect of hydrostatic pressure due to surface meltwater is incorporated based on Biot’s poroelasticity theory. We find that the elastic strain energy decomposition scheme of Lo et al. (2019) with an appropriate fracture energy threshold can adequately represent the asymmetric tensile–compressive fracture behavior of glacier ice subjected to self-gravity loading. We assessed the performance of the model against analytical linear elastic fracture mechanics solutions by comparing their predictions of maximum crevasse penetration depth. The model simulates both surface crevasse propagation in the interior region of the glacier, as well as cliff failure in the terminus region. The excellent performance of the proposed model for air/water-filled surface crevasses in idealized land- and marine-terminating grounded glaciers illustrates its applicability to studying the dynamic response of glaciers to atmospheric warming.
  5. Abstract A recent focus of quantum spin liquid (QSL) studies is how disorder/randomness in a QSL candidate affects its true magnetic ground state. The ultimate question is whether the QSL survives disorder or the disorder leads to a “spin-liquid-like” state, such as the proposed random-singlet (RS) state. Since disorder is a standard feature of most QSL candidates, this question represents a major challenge for QSL candidates. YbMgGaO 4 , a triangular lattice antiferromagnet with effective spin-1/2 Yb 3+ ions, is an ideal system to address this question, since it shows no long-range magnetic ordering with Mg/Ga site disorder. Despite the intensive study, it remains unresolved as to whether YbMgGaO 4 is a QSL or in the RS state. Here, through ultralow-temperature thermal conductivity and magnetic torque measurements, plus specific heat and DC magnetization data, we observed a residual κ 0 / T term and series of quantum spin state transitions in the zero temperature limit for YbMgGaO 4 . These observations strongly suggest that a QSL state with itinerant excitations and quantum spin fluctuations survives disorder in YbMgGaO 4 .
    Free, publicly-accessible full text available December 1, 2022
  6. Aims. We study the relative helicity of active region (AR) NOAA 12673 during a ten-hour time interval centered around a preceding X2.2 flare (SOL2017-09-06T08:57) and also including an eruptive X9.3 flare that occurred three hours later (SOL2017-09-06T11:53). In particular, we aim for a reliable estimate of the normalized self-helicity of the current-carrying magnetic field, the so-called helicity ratio, | H J |/| H 𝒱 |, a promising candidate to quantity the eruptive potential of solar ARs. Methods. Using Solar Dynamics Observatory Helioseismic and Magnetic Imager vector magnetic field data as an input, we employ nonlinear force-free (NLFF) coronal magnetic field models using an optimization approach. The corresponding relative helicity, and related quantities, are computed using a finite-volume method. From multiple time series of NLFF models based on different choices of free model parameters, we are able to assess the spread of | H J |/| H 𝒱 |, and to estimate its uncertainty. Results. In comparison to earlier works, which identified the non-solenoidal contribution to the total magnetic energy, E div / E , as selection criterion regarding the required solenoidal quality of magnetic field models for subsequent relative helicity analysis, we propose to use in addition the non-solenoidal contributionmore »to the free magnetic energy, | E mix |/ E J , s . As a recipe for a reliable estimate of the relative magnetic helicity (and related quantities), we recommend to employ multiple NLFF models based on different combinations of free model parameters, to retain only those that exhibit smallest values of both E div / E and | E mix |/ E J , s at a certain time instant, to subsequently compute mean estimates, and to use the spread of the individually contributing values as an indication for the uncertainty.« less