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1. A Mock Catalog of Gravitationally-lensed Quasars for the LSST Survey

   https://doi.org/10.3847/1538-3881/ac4cb0  

   Yue, Minghao; Fan, Xiaohui; Yang, Jinyi; Wang, Feige (February 2022, The Astronomical Journal)

   Abstract We present a mock catalog of gravitationally-lensed quasars atz_qso< 7.5 with simulated images for the Rubin Observatory Legacy Survey of Space and Time (LSST). We adopt recent measurements of quasar-luminosity functions to model the quasar population, and use the CosmoDC2 mock galaxy catalog to model the deflector galaxies, which successfully reproduces the observed galaxy-velocity dispersion functions up toz_d∼ 1.5. The mock catalog is highly complete for lensed quasars with Einstein radiusθ_E> 0.″07 and quasar absolute magnitudeM_i< − 20. We estimate that there are ∼10³lensed quasars discoverable in current imaging surveys, and LSST will increase this number to ∼ 2.4 × 10³. Most of the lensed quasars have image separation Δθ> 0.″5, which will at least be marginally resolved in LSST images with seeing of ∼0.″7. There will be ∼200 quadruply-lensed quasars discoverable in the LSST. The fraction of quad lenses among all discoverable lensed quasars is about ∼10%–15%, and this fraction decreases with survey depth. This mock catalog shows a large diversity in the observational features of lensed quasars, in terms of lensing separation and quasar-to-deflector flux ratio. We discuss possible strategies for a complete search of lensed quasars in the LSST era. 

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2. Shapes of hyperbolic triangles and once-punctured torus groups

   https://doi.org/10.1007/s00209-021-02745-3  

   Kim, Sang-hyun; Koberda, Thomas; Lee, Jaejeong; Ohshika, Ken’ichi; Tan, Ser Peow; Gao, Xinghua (January 2021, Mathematische Zeitschrift)

   null (Ed.)

   Abstract Let $$\Delta $$ Δ be a hyperbolic triangle with a fixed area $$\varphi $$ φ . We prove that for all but countably many $$\varphi $$ φ , generic choices of $$\Delta $$ Δ have the property that the group generated by the $$\pi $$ π -rotations about the midpoints of the sides of the triangle admits no nontrivial relations. By contrast, we show for all $$\varphi \in (0,\pi ){\setminus }\mathbb {Q}\pi $$ φ ∈ ( 0 , π ) \ Q π , a dense set of triangles does afford nontrivial relations, which in the generic case map to hyperbolic translations. To establish this fact, we study the deformation space $$\mathfrak {C}_\theta $$ C θ of singular hyperbolic metrics on a torus with a single cone point of angle $$\theta =2(\pi -\varphi )$$ θ = 2 ( π - φ ) , and answer an analogous question for the holonomy map $$\rho _\xi $$ ρ ξ of such a hyperbolic structure $$\xi $$ ξ . In an appendix by Gao, concrete examples of $$\theta $$ θ and $$\xi \in \mathfrak {C}_\theta $$ ξ ∈ C θ are given where the image of each $$\rho _\xi $$ ρ ξ is finitely presented, non-free and torsion-free; in fact, those images will be isomorphic to the fundamental groups of closed hyperbolic 3-manifolds. 

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3. The solution surface of the Li-Stephens haplotype copying model

   https://doi.org/10.1186/s13015-023-00237-z  

   Jin, Yifan; Terhorst, Jonathan (August 2023, Algorithms for Molecular Biology)

   Abstract The Li-Stephens (LS) haplotype copying model forms the basis of a number of important statistical inference procedures in genetics. LS is a probabilistic generative model which supposes that a sampled chromosome is an imperfect mosaic of other chromosomes found in a population. In the frequentist setting which is the focus of this paper, the output of LS is a “copying path” through chromosome space. The behavior of LS depends crucially on two user-specified parameters,$$\theta $$ $\theta$and$$\rho $$ $\rho$, which are respectively interpreted as the rates of mutation and recombination. However, because LS is not based on a realistic model of ancestry, the precise connection between these parameters and the biological phenomena they represent is unclear. Here, we offer an alternative perspective, which considers$$\theta $$ $\theta$and$$\rho $$ $\rho$as tuning parameters, and seeks to understand their impact on the LS output. We derive an algorithm which, for a given dataset, efficiently partitions the$$(\theta ,\rho )$$ $(\theta ,\rho )$plane into regions where the output of the algorithm is constant, thereby enumerating all possible solutions to the LS model in one go. We extend this approach to the “diploid LS” model commonly used for phasing. We demonstrate the usefulness of our method by studying the effects of changing$$\theta $$ $\theta$and$$\rho $$ $\rho$when using LS for common bioinformatic tasks. Our findings indicate that using the conventional (i.e., population-scaled) values for$$\theta $$ $\theta$and$$\rho $$ $\rho$produces near optimal results for imputation, but may systematically inflate switch error in the case of phasing diploid genotypes. 

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4. Optimal adaptive algorithms for estimating mixtures of unknown coins.

   Lee, Jasper CH; Valiant, Paul (January 2021, Proceedings of the 2021 ACM- SIAM Symposium on Discrete Algorithms (SODA), pages 414–433.)

   null (Ed.)

   Given a mixture between two populations of coins, “positive” coins that each have unknown and potentially different—bias ≥ 1 + ∆ and “negative” coins with bias ≤ 2 − ∆, we consider the task of estimating the fraction ρ of positive coins to within additive error E. We achieve an upper and lower bound of Θ( ρ log 1 ) samples for a 1 −δ probability of success, where crucially, our lower bound applies to all fully-adaptive algorithms. Thus, our sample complexity bounds have tight dependence for every relevant problem parameter. A crucial component of our lower bound proof is a decomposition lemma (Lemma 5.2) showing how to assemble partially-adaptive bounds into a fully-adaptive bound, which may be of independent interest: though we invoke it for the special case of Bernoulli random variables (coins), it applies to general distributions. We present sim- ulation results to demonstrate the practical efficacy of our approach for realistic problem parameters for crowdsourcing applications, focusing on the “rare events” regime where ρ is small. The fine-grained adaptive flavor of both our algo- rithm and lower bound contrasts with much previous workin distributional testing and learning. 

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5. Digitization, Measurement, and Analysis of a 1905 Barnard Atlas Photographic Plate

   https://doi.org/10.1088/1538-3873/ac87cf  

   Glusman, Rowen; Boegen, Lauren; Cerny, William; Chapman, Ali; Escapa, Isaiah; Kron, Richard G.; Martinez, Michael N.; Muratore, Amanda; Scott, Audrey P. (September 2022, Publications of the Astronomical Society of the Pacific)

   Abstract In the second paper in this series, we improve on our previous demonstration of the ability of a commercially available graphic arts scanner and cost-effective analysis tools to produce scientifically useful scans of astronomical photographic plates. We describe a method using freely available tools to extract magnitude measurements from the star images on sky-survey plates, such as are stored in observatory archives around the world. We detail the use of this method on one plate in particular, Plate 8 in E. E. Barnard’s A Photographic Atlas of Selected Regions of the Milky Way , examine the effects of our scanning method on our magnitude measurements, discuss the difficulties encountered when measuring the magnitudes of stars in crowded fields, and present a case study of red supergiant stars appearing within the field. Our work results in a catalog of more than 66,000 measurements of stellar positions and magnitudes in the central 6.°8 × 6.°8 field of view. 

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