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   https://doi.org/10.51387/23-NEJSDS31  

   Prothero, Jack; Hannig, Jan; Marron, J.S. (April 2023, The New England Journal of Statistics in Data Science)

   Data matrix centering is an ever-present yet under-examined aspect of data analysis. Functional data analysis (FDA) often operates with a default of centering such that the vectors in one dimension have mean zero. We find that centering along the other dimension identifies a novel useful mode of variation beyond those familiar in FDA. We explore ambiguities in both matrix orientation and nomenclature. Differences between centerings and their potential interaction can be easily misunderstood. We propose a unified framework and new terminology for centering operations. We clearly demonstrate the intuition behind and consequences of each centering choice with informative graphics. We also propose a new direction energy hypothesis test as part of a series of diagnostics for determining which choice of centering is best for a data set. We explore the application of these diagnostics in several FDA settings. 

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2. New results on orbital resonances

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   Malhotra, Renu (September 2022, Proceedings of the International Astronomical Union)

   Celletti, Alessandra; Beaugé, Cristian; Galeş, Cătălin; Lemaître, Anne (Ed.)

   Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called ``low-eccentricity resonant bridges" connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some -- though not necessarily entire -- resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase space structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances. 

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3. New perspectives on Fourier matrices

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   Li, Weilin (July 2025, IEEE)
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   Wong, Michael H.; Tollefson, Joshua; Hsu, Andrew I.; Pater, Imke de; Simon, Amy A.; Hueso, Ricardo; Sánchez-Lavega, Agustín; Sromovsky, Lawrence; Fry, Patrick; Luszcz-Cook, Statia; et al (March 2018, The Astronomical Journal)
5. New bounds on the minimal dispersion

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   Litvak, A.E.; Livshyts, G.V. (January 2022, Journal of Complexity)