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1. On the equivalence between weak BMO and the space of derivatives of the Zygmund class

   https://doi.org/10.1515/dema-2021-0013  

   Kwessi, Eddy (January 2021, Demonstratio Mathematica)

   Abstract In this paper, we will discuss the space of functions of weak bounded mean oscillation. In particular, we will show that this space is the dual space of the special atom space, whose dual space was already known to be the space of derivative of functions (in the sense of distribution) belonging to the Zygmund class of functions. We show, in particular, that this proves that the Hardy space H 1 {H}^{1} strictly contains the special atom space. 

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2. Interfacial adsorption and dynamics of fluorotelomers with soil minerals – mechanistic insights

   https://doi.org/10.1039/D4EN00465E  

   Loganathan, Narasimhan; Ashby, Libby; Schumm, Christina E; Wilson, Angela K (January 2025, Environmental Science: Nano)

   Following the global regulation of legacy PFAS molecules, fluorotelomer molecules have been widely employed as replacements to PFOS in aqueous film-forming foam (AFFF) and PFOA in other products. Recent field studies indicate that fluorotelomer molecules are increasingly identified in environmental settings including groundwater, soil and sediments. Consequently, gaining a comprehensive understanding of the fate and transport of fluorotelomers in soils and sedimentary environments is vital. In this study, the behavior of two different fluorotelomers, 6[thin space (1/6-em)]:[thin space (1/6-em)]2 FTS and 6[thin space (1/6-em)]:[thin space (1/6-em)]2 FTC, in three common soil minerals (kaolinite, montmorillonite and illite) having quite different interfacial properties are reported using molecular dynamics simulations. The interfacial adsorption and dynamical characteristics of 6[thin space (1/6-em)]:[thin space (1/6-em)]2 FTS and 6[thin space (1/6-em)]:[thin space (1/6-em)]2 FTC vary substantially between the three minerals. Irrespective of the mineral composition, 6[thin space (1/6-em)]:[thin space (1/6-em)]2 FTS exhibits surface complexation while 6[thin space (1/6-em)]:[thin space (1/6-em)]2 FTC coordinates only with neutral and low charged clay minerals. In addition, the fundamental interactions that dictate the adsorption, interfacial structure of 6[thin space (1/6-em)]:[thin space (1/6-em)]2 FTS and 6[thin space (1/6-em)]:[thin space (1/6-em)]2 FTC are completely different for the three minerals. The large, aggregated clusters of 6[thin space (1/6-em)]:[thin space (1/6-em)]2 FTS at the surface experienced greater stability for longer periods of time and restricted mobility than 6[thin space (1/6-em)]:[thin space (1/6-em)]2 FTC for all three clay minerals. Importantly, the current study provides cluster size dependent diffusion behavior of surface adsorbed fluorotelomer molecules in each clay mineral. Such detailed mechanistic insights are necessary to understand the environmental footprint of fluorotelomers around contaminated sites. 

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3. Stable Strata of Geodesics in Outer Space

   https://doi.org/10.1093/imrn/rnx269  

   Algom-Kfir, Yael; Kapovich, Ilya; Pfaff, Catherine (January 2018, International Mathematics Research Notices)

   Abstract In this article, we propose an Outer space analog for the principal stratum of the unit tangent bundle to the Teichmüller space $${\mathcal{T}}(S)$$ of a closed hyperbolic surface $$S$$. More specifically, we focus on properties of the geodesics in Teichmüller space determined by the principal stratum. We show that the analogous Outer space “principal” periodic geodesics share certain stability properties with the principal stratum geodesics of Teichmüller space. We also show that the stratification of periodic geodesics in Outer space exhibits some new pathological phenomena not present in the Teichmüller space context. 

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4. Diversity in the space physics community: an overview of collaborative efforts led by The University of Alabama in Huntsville

   https://doi.org/10.3389/fspas.2023.1155972  

   Yalim, Mehmet S.; Zank, Gary P.; Provenzani, Laura; Spencer, Douglas; Howatson, Katie (June 2023, Frontiers in Astronomy and Space Sciences)

   The field of Space Physics has significant recruitment potential. Almost everyone has been fascinated by space in one way or another since their early childhood. From this perspective, Space Physics might be expected to exhibit considerable diversity as a discipline. Regrettably, as in many STEM fields, the reality is quite different. Numerous reasons have been advanced about why the reality and the expectation diverge but one observation we have made over the years stands out, and, that is, that when students are given the opportunity, they are very eager to learn about Space Physics and enthusiastic about working on space physics projects. At The University of Alabama in Huntsville, we have developed a series of outreach programs, including summer programs, that are aimed at bringing students not typically exposed to space physics into the Space Physics community through working on real research projects that have the potential to produce journal publication results. These programs have been very effective in creating interest in Space Physics and have led to the recruitment of students that have been underrepresented historically into our research programs. In this paper, we summarize the various summer programs that the Center for Space Plasma and Aeronomic Research and Department of Space Science at The University of Alabama in Huntsville have been organizing in Space Physics for years and how these programs have contributed to increasing diversity in the field. 

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5. Using deep LSD to build operators in GANs latent space with meaning in real space

   https://doi.org/10.1371/journal.pone.0287736  

   Toledo-Marín, J. Quetzalcóatl; Glazier, James A. (June 2023, PLOS ONE)

   Liu, Jin (Ed.)

   Generative models rely on the idea that data can be represented in terms of latent variables which are uncorrelated by definition. Lack of correlation among the latent variable support is important because it suggests that the latent-space manifold is simpler to understand and manipulate than the real-space representation. Many types of generative model are used in deep learning,e.g., variational autoencoders (VAEs) and generative adversarial networks (GANs). Based on the idea that the latent space behaves like a vector space Radford et al. (2015), we ask whether we can expand the latent space representation of our data elements in terms of an orthonormal basis set. Here we propose a method to build a set of linearly independent vectors in the latent space of a trained GAN, which we call quasi-eigenvectors. These quasi-eigenvectors have two key properties: i) They span the latent space, ii) A set of these quasi-eigenvectors map to each of the labeled features one-to-one. We show that in the case of the MNIST image data set, while the number of dimensions in latent space is large by design, 98% of the data in real space map to a sub-domain of latent space of dimensionality equal to the number of labels. We then show how the quasi-eigenvectors can be used for Latent Spectral Decomposition (LSD). We apply LSD to denoise MNIST images. Finally, using the quasi-eigenvectors, we construct rotation matrices in latent space which map to feature transformations in real space. Overall, from quasi-eigenvectors we gain insight regarding the latent space topology. 

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