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1. Analysis of signal-to-noise ratio of angle of polarization and degree of polarization

   https://doi.org/10.1364/OSAC.422541  

   Chen, Yingkai; Zhu, Zhongmin; Liang, Zuodong; Iannucci, Leanne_E; Lake, Spencer_P; Gruev, Viktor (April 2021, OSA Continuum)

   Recent advancements in nanofabrication technology has led to commercialization of single-chip polarization and color-polarization imaging sensors in the visible spectrum. Novel applications have arisen with the emergence of these sensors leading to questions about noise in the reconstructed polarization images. In this paper, we provide theoretical analysis for the input and output referred noise for the angle and degree of linear polarization information. We validated our theoretical model with experimental data collected from a division of focal plane polarization sensor. Our data indicates that the noise in the angle of polarization images depends on both incident light intensity and degree of linear polarization and is independent of the incident angle of polarization. However, noise in degree of linear polarization images depends on all three parameters: incident light intensity, angle and degree of linear polarization. This theoretical model can help guide the development of imaging setups to record optimal polarization information. 

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2. The size of the class of countable sequences of ordinals

   https://doi.org/10.1090/tran/8573  

   Chan, William; Jackson, Stephen; Trang, Nam (January 2021, Transactions of the American Mathematical Society)

   Assume . There is no injection of (the set of countable length sequences of countable ordinals) into (the class of length sequences of ordinals). There is no injection of (the powerset of ) into (the class of countable length sequences of ordinals). 

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3. 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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4. Classification of symplectic birational involutions of manifolds of OG10 type

   https://doi.org/10.1007/s00209-025-03697-8  

   Marquand, Lisa; Muller, Stevell (April 2025, Mathematische Zeitschrift)

   Abstract We give a complete classification of symplectic birational involutions of manifolds ofOG10 type. We approach this classification with three techniques—via involutions of the Leech lattice, via involutions of cubic fourfolds, and finally lattice enumeration via a modified Kneser’s neighbour algorithm. The classification consists of three involutions with an explicit geometric realisation via cubic fourfolds, and three exceptional involutions which cannot be obtained by any known construction. 

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5. Size of nodal domains of the eigenvectors of a graph

   https://doi.org/10.1002/rsa.20925  

   Huang, Han; Rudelson, Mark (April 2020, Random Structures & Algorithms)

   Consider an eigenvector of the adjacency matrix of aG(n,p) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two nodal domains for each eigenvector corresponding to a nonleading eigenvalue. We prove that with high probability, the sizes of these nodal domains are approximately equal to each other. 

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