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Free, publiclyaccessible full text available May 1, 2023

Free, publiclyaccessible full text available January 1, 2023

Datasensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a datasensitive metric called the nearest neighbor metric. In fact, we prove the surprising result that a previously published 3approximation is an exact algorithm. The nearest neighbor metric can be viewed as a special case of a densitybased distance used in machine learning, or it can be seen as an example of a manifold metric. Previous computational research on such metrics despaired of computing exact distances on account of the apparent difficulty of minimizing over all continuous paths between a pair of points. We leverage the exact computation of the nearest neighbor metric to compute sparse spanners and persistent homology. We also explore the behavior of the metric built from point sets drawn from an underlying distribution and consider the more general case of inputs that are finite collections of pathconnected compact sets. The main results connect several classical theories such as the conformal change of Riemannian metrics, the theory of positive definite functions of Schoenberg, and screw function theory of Schoenberg and Von Neumann. We alsomore »

We present two graph quantities Psi(G, S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, Lambda(G, S) and Lambda_2(G), respectively. Our techniques make use of a discrete Hardytype inequality due to Muckenhoupt.

Abstract We present the results from the first two years of the Planet Hunters TESS citizen science project, which identifies planet candidates in the TESS data by engaging members of the general public. Over 22,000 citizen scientists from around the world visually inspected the first 26 Sectors of TESS data in order to help identify transitlike signals. We use a clustering algorithm to combine these classifications into a ranked list of events for each sector, the top 500 of which are then visually vetted by the science team. We assess the detection efficiency of this methodology by comparing our results to the list of TESS Objects of Interest (TOIs) and show that we recover 85 % of the TOIs with radii greater than 4 ⊕ and 51 % of those with radii between 3 and 4 R⊕. Additionally, we present our 90 most promising planet candidates that had not previously been identified by other teams, 73 of which exhibit only a single transit event in the TESS light curve, and outline our efforts to follow these candidates up using groundbased observatories. Finally, we present noteworthy stellar systems that were identified through the Planet Hunters TESS project.

ABSTRACT We report on the discovery and validation of a twoplanet system around a bright (V = 8.85 mag) early G dwarf (1.43 R⊙, 1.15 M⊙, TOI 2319) using data from NASA’s Transiting Exoplanet Survey Satellite (TESS). Three transit events from two planets were detected by citizen scientists in the monthlong TESS light curve (sector 25), as part of the Planet Hunters TESS project. Modelling of the transits yields an orbital period of $11.6264 _{  0.0025 } ^ { + 0.0022 }$ d and radius of $3.41 _{  0.12 } ^ { + 0.14 }$ R⊕ for the inner planet, and a period in the range 19.26–35 d and a radius of $5.83 _{  0.14 } ^ { + 0.14 }$ R⊕ for the outer planet, which was only seen to transit once. Each signal was independently statistically validated, taking into consideration the TESS light curve as well as the groundbased spectroscopic followup observations. Radial velocities from HARPSN and EXPRES yield a tentative detection of planet b, whose mass we estimate to be $11.56 _{  6.14 } ^ { + 6.58 }$ M⊕, and allow us to place an upper limit of 27.5 M⊕ (99 per cent confidence) on the mass of planet c. Due to the brightness ofmore »

ABSTRACT We report on the discovery and validation of TOI 813 b (TIC 55525572 b), a transiting exoplanet identified by citizen scientists in data from NASA’s Transiting Exoplanet Survey Satellite (TESS) and the first planet discovered by the Planet Hunters TESS project. The host star is a bright (V = 10.3 mag) subgiant ($R_\star =1.94\, R_\odot$, $M_\star =1.32\, M_\odot$). It was observed almost continuously by TESS during its first year of operations, during which time four individual transit events were detected. The candidate passed all the standard light curvebased vetting checks, and groundbased followup spectroscopy and speckle imaging enabled us to place an upper limit of $2\, M_{\rm Jup}$ (99 per cent confidence) on the mass of the companion, and to statistically validate its planetary nature. Detailed modelling of the transits yields a period of $83.8911 _{  0.0031 } ^ { + 0.0027 }$ d, a planet radius of 6.71 ± 0.38 R⊕ and a semimajor axis of $0.423 _{  0.037 } ^ { + 0.031 }$ AU. The planet’s orbital period combined with the evolved nature of the host star places this object in a relatively underexplored region of parameter space. We estimate that TOI 813 b induces a reflex motion in its host star with a semiamplitude of ∼6 m s−1, makingmore »