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Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design for GNNs remains impoverished. In this paper, we consider the benefits of architectures that maintain and update edge embeddings. On the theoretical front, under a suitable computational abstraction for a layer in the model, as well as memory constraints on the embeddings, we show that there are natural tasks on graphical models for which architectures leveraging edge embeddings can be much shallower. Our techniques are inspired by results on time-space tradeoffs in theoretical computer science. Empirically, we show architectures that maintain edge embeddings almost always improve on their node-based counterparts—frequently significantly so in topologies that have “hub” nodes. 

Abstract Studies commonly assumed that variations in ionospheric conductance were insignificant and proposed that vorticities can be a reliable proxy or diagnostic for ionospheric field‐aligned currents (FACs). We propose a complete method for measuring FACs using data from the Super Dual Auroral Radar Network radar and the Defense Meteorological Satellite Program. In our method, the FACs are determined by three terms. The first term is referred to as magnetospheric‐origin FACs, while the second and third terms are known as ionospheric‐origin FACs. This method incorporates height‐integrated conductances based on observational data, thereby addressing the limitation of assuming uniform conductances. Different from previous works, we can calculate FACs at a low altitude of 250 km and obtain high‐resolution measurements within observable areas. Another advantage of this method lies in its ability to directly calculate and analyze the impact of ionospheric vorticity and conductance on FACs. We apply this method to obtain FACs in the Northern Hemisphere from 2010 to 2016 and analyze the distributions of height‐integrated conductances and total FACs. Our analysis reveals that the average FACs clearly exhibit the large‐scale R1 and R2 FAC systems. We conduct statistical analysis on magnetospheric‐origin FACs and ionospheric‐origin FACs. Our findings show that within the auroral oval, ionospheric‐origin FACs reach a comparable level to magnetospheric‐origin FACs. However, ionospheric‐origin FACs are significantly minor and almost negligible in other regions. This implies that height‐integrated conductance gradients and vorticities play equally significant roles within the auroral oval, whereas vorticities dominate in other regions. 

Abstract We present a JWST MIRI medium-resolution spectrometer spectrum (5–27μm) of the Type Ia supernova (SN Ia) SN 2021aefx at +415 days pastB-band maximum. The spectrum, which was obtained during the iron-dominated nebular phase, has been analyzed in combination with previous JWST observations of SN 2021aefx to provide the first JWST time series analysis of an SN Ia. We find that the temporal evolution of the [Coiii] 11.888μm feature directly traces the decay of⁵⁶Co. The spectra, line profiles, and their evolution are analyzed with off-center delayed-detonation models. Best fits were obtained with white dwarf (WD) central densities ofρ_c= 0.9−1.1 × 10⁹g cm⁻³, a WD mass ofM_WD= 1.33–1.35M_⊙, a WD magnetic field of ≈10⁶G, and an off-center deflagration-to-detonation transition at ≈0.5M_⊙seen opposite to the line of sight of the observer (−30°). The inner electron capture core is dominated by energy deposition fromγ-rays, whereas a broader region is dominated by positron deposition, placing SN 2021aefx at +415 days in the transitional phase of the evolution to the positron-dominated regime. The formerly “flat-tilted” profile at 9μm now has a significant contribution from [Niiv], [Feii], and [Feiii] and less from [Ariii], which alters the shape of the feature as positrons mostly excite the low-velocity Ar. Overall, the strength of the stable Ni features in the spectrum is dominated by positron transport rather than the Ni mass. Based on multidimensional models, our analysis is consistent with a single-spot, close-to-central ignition with an indication of a preexisting turbulent velocity field and excludes a multiple-spot, off-center ignition. 

In this work, we propose a novel approach for the real-time estimation of chip-level spatial power maps for commercial Google Coral M.2 TPU chips based on a machine-learning technique for the first time. The new method can enable the development of more robust runtime power and thermal control schemes to take advantage of spatial power information such as hot spots that are otherwise not available. Different from the existing commercial multi-core processors in which real-time performance-related utilization information is available, the TPU from Google does not have such information. To mitigate this problem, we propose to use features that are related to the workloads of running different deep neural networks (DNN) such as the hyperparameters of DNN and TPU resource information generated by the TPU compiler. The new approach involves the offline acquisition of accurate spatial and temporal temperature maps captured from an external infrared thermal imaging camera under nominal working conditions of a chip. To build the dynamic power density map model, we apply generative adversarial networks (GAN) based on the workload-related features. Our study shows that the estimated total powers match the manufacturer's total power measurements extremely well. Experimental results further show that the predictions of power maps are quite accurate, with the RMSE of only 4.98\rm mW/mm^2, or 2.6\% of the full-scale error. The speed of deploying the proposed approach on an Intel Core i7-10710U is as fast as 6.9ms, which is suitable for real-time estimation.