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1. Shadow Removal Refinement via Material-Consistent Shadow Edges

   https://doi.org/10.1109/WACV61041.2025.00261  

   Hu, Shilin; Le, Hieu; Athar, ShahRukh; Das, Sagnik; Samaras, Dimitris (February 2025, Proceedings)
2. Shadow line distributions

   https://doi.org/10.1090/mcom/4110  

   Balakrishnan, Jennifer; Çiperiani, Mirela; Mazur, Barry; Rubin, Karl (July 2025, Mathematics of Computation)

   Let $E$be an elliptic curve over $\mathbb{Q}$with Mordell–Weil rank $2$and $p$be an odd prime of good ordinary reduction. For every imaginary quadratic field $K$satisfying the Heegner hypothesis, there is (subject to the Shafarevich–Tate conjecture) a line, i.e., a free ${\mathbb{Z}}_p$-submodule of rank $1$, in $E\left(K\right)\otimes <\#comment/>{\mathbb{Z}}_p$given by universal norms coming from the Mordell–Weil groups of subfields of the anticyclotomic ${\mathbb{Z}}_p$-extension of $K$; we call it theshadow line. When the twist of $E$by $K$has analytic rank $1$, the shadow line is conjectured to lie in $E\left(\mathbb{Q}\right)\otimes <\#comment/>{\mathbb{Z}}_p$; we verify this computationally in all our examples. We study the distribution of shadow lines in $E\left(\mathbb{Q}\right)\otimes <\#comment/>{\mathbb{Z}}_p$as $K$varies, framing conjectures based on the computations we have made. 

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3. Optimal high-precision shadow estimation

   Chen, Sitan; Li, Jerry; Liu, Allen (July 2024, https://doi.org/10.48550/arXiv.2407.13874)

   The authors provide the first tight sample complexity bounds for shadow tomography and classical shadows in the regime where the target error is below some sufficiently small inverse polynomial in the dimension of the Hilbert space. Specifically, they present a protocol that, given any 𝑚 ∈ 𝑁 m∈N and 𝜖 ≤ 𝑂 ( 𝑑 − 1 / 2 ) ϵ≤O(d −1/2 ), measures 𝑂 ( log ⁡ ( 𝑚 ) / 𝜖 2 ) O(log(m)/ϵ 2 ) copies of an unknown mixed state 𝜌 ∈ 𝐶 𝑑 × 𝑑 ρ∈C d×d and outputs a classical description of 𝜌 ρ. This description can then be used to estimate any collection of 𝑚 m observables to within additive accuracy 𝜖 ϵ. Previously, even for the simpler case of shadow tomography where observables are known in advance, the best known rates either scaled benignly but suboptimally in all of 𝑚 , 𝑑 , 𝜖 m,d,ϵ, or scaled optimally in 𝜖 , 𝑚 ϵ,m but included additional polynomial factors in 𝑑 d. Interestingly, the authors also show via dimensionality reduction that one can rescale 𝜖 ϵ and 𝑑 d to reduce to the regime where 𝜖 ≤ 𝑂 ( 𝑑 − 1 / 2 ) ϵ≤O(d −1/2 ). Their algorithm draws on representation-theoretic tools developed in the context of full state tomography. 

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4. Shadow Geometry of Kerr Naked Singularities

   https://doi.org/10.3847/1538-4357/ace697  

   Nguyen, Bao; Christian, Pierre; Chan, Chi-kwan (August 2023, The Astrophysical Journal)

   Abstract Direct imaging of supermassive black holes (SMBHs) at event horizon-scale resolutions, as recently done by the Event Horizon Telescope, allows for testing alternative models to SMBHs such as Kerr naked singularities (KNSs). We demonstrate that the KNS shadow can be closed, open, or vanishing, depending on the spins and observational inclination angles. We study the critical parameters where the KNS shadow opens a gap, a distinctive phenomenon that does not happen with the black hole shadow. We show that the KNS shadow can only be closed for dimensionless spina≲ 1.18 and vanishing fora≳ 1.18 for certain ranges of inclination angles. We further analyze the effective angular momentum of photon orbits to demonstrate the fundamental connections between light geodesics and the KNS shadow geometry. We also perform numerical general relativistic ray-tracing calculations, which reproduce the analytical topological change in the KNS shadow, and illustrate other observational features within the shadow due to the lack of an event horizon. By comparing the geometric features of the KNS shadow with black hole shadow observations, the topological change in the shadow of KNSs can be used to test the cosmic censorship hypothesis and KNSs as alternative models to SMBHs. 

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5. Io’s Optical Aurorae in Jupiter’s Shadow

   https://doi.org/10.3847/PSJ/ac85b0  

   Schmidt, Carl; Sharov, Mikhail; de Kleer, Katherine; Schneider, Nick; de Pater, Imke; Phipps, Phillip H.; Conrad, Albert; Moore, Luke; Withers, Paul; Spencer, John; et al (February 2023, The Planetary Science Journal)

   Abstract Decline and recovery timescales surrounding eclipse are indicative of the controlling physical processes in Io’s atmosphere. Recent studies have established that the majority of Io’s molecular atmosphere, SO 2 and SO, condenses during its passage through Jupiter’s shadow. The eclipse response of Io’s atomic atmosphere is less certain, having been characterized solely by ultraviolet aurorae. Here we explore the response of optical aurorae for the first time. We find oxygen to be indifferent to the changing illumination, with [O i ] brightness merely tracking the plasma density at Io’s position in the torus. In shadow, line ratios confirm sparse SO 2 coverage relative to O, since their collisions would otherwise quench the emission. Io’s sodium aurora mostly disappears in eclipse and e-folding timescales, for decline and recovery differ sharply: ∼10 minutes at ingress and nearly 2 hr at egress. Only ion chemistry can produce such a disparity; Io’s molecular ionosphere is weaker at egress due to rapid recombination. Interruption of a NaCl + photochemical pathway best explains Na behavior surrounding eclipse, implying that the role of electron impact ionization is minor relative to photons. Auroral emission is also evident from potassium, confirming K as the major source of far red emissions seen with spacecraft imaging at Jupiter. In all cases, direct electron impact on atomic gas is sufficient to explain the brightness without invoking significant dissociative excitation of molecules. Surprisingly, the nonresponse of O and rapid depletion of Na is opposite the temporal behavior of their SO 2 and NaCl parent molecules during Io’s eclipse phase. 

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