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1. Models of G–spectra as presheaves of spectra

   https://doi.org/10.2140/agt.2024.24.1225  

   Guillou, Bertrand J; May, J Peter (January 2024, Algebraic & Geometric Topology)

   Greenlees, John (Ed.)

   Let G be a finite group. We give Quillen equivalent models for the category of G–spectra as categories of spectrally enriched functors from explicitly described domain categories to nonequivariant spectra. Our preferred model is based on equivariant infinite loop space theory applied to elementary categorical data. It recasts equivariant stable homotopy theory in terms of point–set-level categories of G–spans and nonequivariant spectra. We also give a more topologically grounded model based on equivariant Atiyah duality. 

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2. Alphabet Projection of Spectra

   https://doi.org/https://doi.org/10.1021/acs.jproteome.9b00216  

   Kreitzberg, Patrick; Bern, Marshall; Shu, Qingbo; Yang, Fuquan; Serang, Oliver (July 2019, Journal of proteome research)

   In the metabolomics, glycomics, and mass spectrometry of structured small molecules, the combinatoric nature of the problem renders a database impossibly large, and thus de novo analysis is necessary. De novo analysis requires an alphabet of mass difference values used to link peaks in fragmentation spectra when they are different by a mass in the alphabet divided by a charge. Often, this alphabet is not known, prohibiting de novo analysis. A method is proposed that, given fragmentation mass spectra, identifies an alphabet of m/z differences that can build large connected graphs from many intense peaks in each spectrum from a collection. We then introduce a novel approach to efficiently find recurring substructures in the de novo graph results. 

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3. Photothermal Spectra of Semiconductors

   Marcano, Aristides; Luna, Jose; Tan, Songjian; Zhang, Tianyao. (September 2020, FiOS Conference 2020, Washington DC, OSA)

   null (Ed.)

   We measure and calibrate the photothermal spectra of Gallium Arsenide and Cadmium Telluride in the 400-800 nm spectral region using a white light source. The spectra yield the photothermal quantum yields of the materials. 

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4. Spectra of products of digraphs

   https://doi.org/10.13001/ela.2020.5243  

   Catral, Minerva; Ciardo, Lorenzo; Hogben, Leslie; Reinhart, Carolyn (January 2020, The Electronic Journal of Linear Algebra)

   null (Ed.)

   A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the new distance matrix, with natural extensions to the distance Laplacian and distance signless Laplacian, in addition to the new adjacency matrix, with natural extensions to the Laplacian and signless Laplacian. Various sums of Kronecker products of nonnegative matrices are introduced to model the Cartesian and lexicographic products of digraphs. The Jordan canonical form is applied extensively to the analysis of spectra and eigenvectors. The analysis shows that Cartesian products provide a method for building infinite families of transmission regular digraphs with few distinct distance eigenvalues. 

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5. Spectra of Random Regular Hypergraphs

   https://doi.org/10.37236/8741  

   Dumitriu, Ioana; Zhu, Yizhe (July 2021, The Electronic Journal of Combinatorics)

   In this paper, we study the spectra of regular hypergraphs following the definitions from Feng and Li (1996). Our main result is an analog of Alon's conjecture for the spectral gap of the random regular hypergraphs. We then relate the second eigenvalues to both its expansion property and the mixing rate of the non-backtracking random walk on regular hypergraphs. We also prove the spectral gap for the non-backtracking operator of a random regular hypergraph introduced in Angelini et al. (2015). Finally, we obtain the convergence of the empirical spectral distribution (ESD) for random regular hypergraphs in different regimes. Under certain conditions, we can show a local law for the ESD. 

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