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Abstract Both ground based magnetometers and ionospheric radars at Earth have frequently detected Ultra Low Frequency (ULF) fluctuations at discrete frequencies extending below one mHz‐range. Many dayside solar wind drivers have been convincingly demonstrated as driver mechanisms. In this paper we investigate and propose an additional, nightside generation mechanism of a low frequency magnetic field fluctuation. We propose that the Moon may excite a magnetic field perturbation of the order of 1 nT at discrete frequencies when it travels through the Earth's magnetotail 4–5 days every month. Our theoretical prediction is supported by a case study of ARTEMIS magnetic field measurements at the lunar orbit in the Earth's magnetotail. ARTEMIS detects statistically significant peaks in magnetic field fluctuation power at frequencies of 0.37–0.47 mHz that are not present in the solar wind. 

The Magnetospheric Multi-scale Mission has frequently observed periodic bursts of counterstreaming electrons with energies ranging from ≈ 30 to 500 keV at the Earth's magnetospheric boundary layers, termed “microinjections.” Recently, a source region for microinjections was discovered at the high-latitude magnetosphere where microinjections showed up simultaneously at all energy channels and were organized by magnetic field variation associated with ultra low frequency mirror mode waves (MMWs) with ≈ 5 min periodicity. These MMWs were associated with strong higher frequency electromagnetic wave activity. Here, we have identified some of these waves as electromagnetic ion cyclotron (EMIC) waves. EMIC waves and parallel electric fields often lead to the radiation belt electron losses due to pitch-angle scattering. We show that, for the present event, the EMIC waves are not responsible for scattering electrons into a loss cone, and thus, they are unlikely to be responsible for the observed microinjection signature. We also find that the parallel electric field potentials within the waves are not adequate to explain the observed electrons with >90 keV energies. While whistler waves may contribute to the electron scattering and may exist during this event, there was no burst mode data available to verify this. 

A flag is a nested sequence of vector spaces. The type of the flag encodes the sequence of dimensions of the vector spaces making up the flag. A flag manifold is a manifold whose points parameterize all flags of a fixed type in a fixed vector space. This paper provides the mathematical framework necessary for implementing self-organizing mappings on flag manifolds. Flags arise implicitly in many data analysis contexts including wavelet, Fourier, and singular value decompositions. The proposed geometric framework in this paper enables the computation of distances between flags, the computation of geodesics between flags, and the ability to move one flag a prescribed distance in the direction of another flag. Using these operations as building blocks, we implement the SOM algorithm on a flag manifold. The basic algorithm is applied to the problem of parameterizing a set of flags of a fixed type. 

Latent space Energy-Based Models (EBMs), also known as energy-based priors, have drawn growing interests in generative modeling. Fueled by its flexibility in the formulation and strong modeling power of the latent space, recent works built upon it have made interesting attempts aiming at the interpretability of text modeling. However, latent space EBMs also inherit some flaws from EBMs in data space; the degenerate MCMC sampling quality in practice can lead to poor generation quality and instability in training, especially on data with complex latent structures. Inspired by the recent efforts that leverage diffusion recovery likelihood learning as a cure for the sampling issue, we introduce a novel symbiosis between the diffusion models and latent space EBMs in a variational learning framework, coined as the latent diffusion energy-based model. We develop a geometric clustering-based regularization jointly with the information bottleneck to further improve the quality of the learned latent space. Experiments on several challenging tasks demonstrate the superior performance of our model on interpretable text modeling over strong counterparts.