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1. Realization of unpinned two-dimensional dirac states in antimony atomic layers

   https://doi.org/10.1038/s41467-022-32327-8  

   Lu, Qiangsheng ; Cook, Jacob ; Zhang, Xiaoqian ; Chen, Kyle Y. ; Snyder, Matthew ; Nguyen, Duy Tung ; Reddy, P. V. Sreenivasa ; Qin, Bingchao ; Zhan, Shaoping ; Zhao, Li-Dong ; et al ( August 2022 , Nature Communications)

   Two-dimensional (2D) Dirac states with linear dispersion have been observed in graphene and on the surface of topological insulators. 2D Dirac states discovered so far are exclusively pinned at high-symmetry points of the Brillouin zone, for example, surface Dirac states at$$\overline{{{\Gamma }}}$$$\overline{\Gamma }$in topological insulators Bi₂Se(Te)₃and Dirac cones atKand$$K^{\prime}$$$K^{\prime }$points in graphene. The low-energy dispersion of those Dirac states are isotropic due to the constraints of crystal symmetries. In this work, we report the observation of novel 2D Dirac states in antimony atomic layers with phosphorene structure. The Dirac states in the antimony films are located at generic momentum points. This unpinned nature enables versatile ways such as lattice strains to control the locations of the Dirac points in momentum space. In addition, dispersions around the unpinned Dirac points are highly anisotropic due to the reduced symmetry of generic momentum points. The exotic properties of unpinned Dirac states make antimony atomic layers a new type of 2D Dirac semimetals that are distinct from graphene.

    

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2. Curvature Sets Over Persistence Diagrams

   https://doi.org/10.1007/s00454-024-00634-0  

   Gómez, Mario ; Mémoli, Facundo ( April 2024 , Discrete & Computational Geometry)

   We study a family of invariants of compact metric spaces that combines the Curvature Sets defined by Gromov in the 1980 s with Vietoris–Rips Persistent Homology. For given integers$$k\ge 0$$$k\ge 0$and$$n\ge 1$$$n\ge 1$we consider the dimensionkVietoris–Rips persistence diagrams ofallsubsets of a given metric space with cardinality at mostn. We call these invariantspersistence setsand denote them as$${\textbf{D}}_{n,k}^{\textrm{VR}}$$$D_{n,k}^{\text{VR}}$. We first point out that this family encompasses the usual Vietoris–Rips diagrams. We then establish that (1) for certain range of values of the parametersnandk, computing these invariants is significantly more efficient than computing the usual Vietoris–Rips persistence diagrams, (2) these invariants have very good discriminating power and, in many cases, capture information that is imperceptible through standard Vietoris–Rips persistence diagrams, and (3) they enjoy stability properties analogous to those of the usual Vietoris–Rips persistence diagrams. We precisely characterize some of them in the case of spheres and surfaces with constant curvature using a generalization of Ptolemy’s inequality. We also identify a rich family of metric graphs for which$${\textbf{D}}_{4,1}^{\textrm{VR}}$$$D_{4,1}^{\text{VR}}$fully recovers their homotopy type by studying split-metric decompositions. Along the way we prove some useful properties of Vietoris–Rips persistence diagrams using Mayer–Vietoris sequences. These yield a geometric algorithm for computing the Vietoris–Rips persistence diagram of a spaceXwith cardinality$$2k+2$$$2k+2$with quadratic time complexity as opposed to the much higher cost incurred by the usual algebraic algorithms relying on matrix reduction.

    

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3. Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings

   https://doi.org/10.1007/s40993-022-00388-9  

   Adžaga, Nikola ; Chidambaram, Shiva ; Keller, Timo ; Padurariu, Oana ( October 2022 , Research in Number Theory)

   We complete the computation of all$$\mathbb {Q}$$$Q$-rational points on all the 64 maximal Atkin-Lehner quotients$$X_0(N)^*$$$X_0{\left(N\right)}^{\ast }$such that the quotient is hyperelliptic. To achieve this, we use a combination of various methods, namely the classical Chabauty–Coleman, elliptic curve Chabauty, quadratic Chabauty, and the bielliptic quadratic Chabauty method (from a forthcoming preprint of the fourth-named author) combined with the Mordell-Weil sieve. Additionally, for square-free levelsN, we classify all$$\mathbb {Q}$$$Q$-rational points as cusps, CM points (including their CM field andj-invariants) and exceptional ones. We further indicate how to use this to compute the$$\mathbb {Q}$$$Q$-rational points on all of their modular coverings.

    

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4. Sites of Planet Formation in Binary Systems. I. Evidence for Disk−Orbit Alignment in the Close Binary FO Tau

   https://doi.org/10.3847/1538-3881/ad354d  

   Tofflemire, Benjamin M. ; Prato, Lisa ; Kraus, Adam L. ; Segura-Cox, Dominique ; Schaefer, G. H. ; Akeson, Rachel ; Andrews, Sean ; Jensen, Eric L. N. ; Johns-Krull, Christopher M. ; Zanazzi, J. J. ; et al ( April 2024 , The Astronomical Journal)

   Close binary systems present challenges to planet formation. As binary separations decrease, so do the occurrence rates of protoplanetary disks in young systems and planets in mature systems. For systems that do retain disks, their disk masses and sizes are altered by the presence of the binary companion. Through the study of protoplanetary disks in binary systems with known orbital parameters, we seek to determine the properties that promote disk retention and therefore planet formation. In this work, we characterize the young binary−disk system FO Tau. We determine the first full orbital solution for the system, finding masses of${0.35}_{-0.05}^{+0.06}{M}_{\odot }$and 0.34 ± 0.05M_⊙for the stellar components, a semimajor axis of$22{(}_{-1}^{+2})$au, and an eccentricity of$0.21{(}_{-0.03}^{+0.04})$. With long-baseline Atacama Large Millimeter/submillimeter Array interferometry, we detect 1.3 mm continuum and¹²CO (J= 2–1) line emission toward each of the binary components; no circumbinary emission is detected. The protoplanetary disks are compact, consistent with being truncated by the binary orbit. The dust disks are unresolved in the image plane, and the more extended gas disks are only marginally resolved. Fitting the continuum and CO visibilities, we determine the inclination of each disk, finding evidence for alignment of the disk and binary orbital planes. This study is the first of its kind linking the properties of circumstellar protoplanetary disks to a precisely known binary orbit. In the case of FO Tau, we find a dynamically placid environment (coplanar, low eccentricity), which may foster its potential for planet formation.

    

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5. Dimensionally reduced machine learning model for predicting single component octanol–water partition coefficients

   https://doi.org/10.1186/s13321-022-00660-1  

   Kenney, David H. ; Paffenroth, Randy C. ; Timko, Michael T. ; Teixeira, Andrew R. ( January 2023 , Journal of Cheminformatics)

   MF-LOGP, a new method for determining a single component octanol–water partition coefficients ($$LogP$$$\mathrm{LogP}$) is presented which uses molecular formula as the only input. Octanol–water partition coefficients are useful in many applications, ranging from environmental fate and drug delivery. Currently, partition coefficients are either experimentally measured or predicted as a function of structural fragments, topological descriptors, or thermodynamic properties known or calculated from precise molecular structures. The MF-LOGP method presented here differs from classical methods as it does not require any structural information and uses molecular formula as the sole model input. MF-LOGP is therefore useful for situations in which the structure is unknown or where the use of a low dimensional, easily automatable, and computationally inexpensive calculations is required. MF-LOGP is a random forest algorithm that is trained and tested on 15,377 data points, using 10 features derived from the molecular formula to make$$LogP$$$\mathrm{LogP}$predictions. Using an independent validation set of 2713 data points, MF-LOGP was found to have an average$$RMSE$$$\mathrm{RMSE}$= 0.77 ± 0.007,$$MAE$$$\mathrm{MAE}$= 0.52 ± 0.003, and$${R}^{2}$$$R^2$= 0.83 ± 0.003. This performance fell within the spectrum of performances reported in the published literature for conventional higher dimensional models ($$RMSE$$$\mathrm{RMSE}$= 0.42–1.54,$$MAE$$$\mathrm{MAE}$= 0.09–1.07, and$${R}^{2}$$$R^2$= 0.32–0.95). Compared with existing models, MF-LOGP requires a maximum of ten features and no structural information, thereby providing a practical and yet predictive tool. The development of MF-LOGP provides the groundwork for development of more physical prediction models leveraging big data analytical methods or complex multicomponent mixtures.

   Graphical Abstract

    

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