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  1. Data-sensitive 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 data-sensitive metric called the nearest neighbor metric. In fact, we prove the surprising result that a previously published 3-approximation is an exact algorithm. The nearest neighbor metric can be viewed as a special case of a density-based 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 path-connected 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 also develop some novel proof techniques based on the combination of screw functions and Lipschitz extensions that may be of independent interest. 
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    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 Hardy-type inequality due to Muckenhoupt. 
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    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 transit-like 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 ground-based observatories. Finally, we present noteworthy stellar systems that were identified through the Planet Hunters TESS project. 
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    ABSTRACT We report on the discovery and validation of a two-planet 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 month-long 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 ground-based spectroscopic follow-up observations. Radial velocities from HARPS-N 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 of the host star and the strong likelihood of an extended H/He atmosphere on both planets, this system offers excellent prospects for atmospheric characterization and comparative planetology. 
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  6. Abstract

    Lacustrine δ2H and δ18O isotope proxies are powerful tools for reconstructing past climate and precipitation changes in the Arctic. However, robust paleoclimate record interpretations depend on site‐specific lake water isotope systematics, which are poorly described in the eastern Canadian Arctic due to insufficient modern lake water isotope data. We use modern lake water isotopes (δ18O and δ2H) collected between 1994–1997 and 2017–2021 from a transect of sites spanning a Québec‐to‐Ellesmere Island gradient to evaluate the effects of inflow seasonality and evaporative enrichment on the δ2H and δ18O composition of lake water. Four lakes near Iqaluit, Nunavut sampled biweekly through three ice‐free seasons reflect mean annual precipitation isotopes with slight evaporative enrichment. In a 23° latitudinal transect of 181 lakes, through‐flowing lake water δ2H and δ18O fall along local meteoric water lines. Despite variability within each region, we observe a latitudinal pattern: southern lakes reflect mean annual precipitation isotopes, whereas northern lakes reflect summer‐biased precipitation isotopes. This pattern suggests that northern lakes are more fully flushed with summer precipitation, and we hypothesize that this occurs because the ratio of runoff to precipitation increases with latitude as vegetation cover decreases. Therefore, proxy records from through‐flowing lakes in this region should reflect precipitation isotopes with minimal influence of evaporation, but vegetation changes in lake catchments across a latitudinal transect and through geologic time may influence the seasonality of lake water isotopic compositions. Thus, we recommend that future lake water isotope proxy records are considered in context with temperature and ecological proxy records.

     
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  7. Abstract

    The past 2,000 years provide a critical context for understanding twentieth century climate change. Due to the Past Global Changes 2k initiative, an extensive proxy database provides opportunities to assess regional climate change that have stronger ecological and societal implications than global‐mean temperature changes alone. However, the various sources of paleoclimate reconstruction poses serious challenges to scientifically and statistically sound inference within a unified framework. Here we show results from the first transient simulation for the past 2,000 years with the Community Earth System Model, called past2k, and use data‐model comparison to refine the interpretation of the proxy data. Our results indicate that the Atlantic Arctic was cooling at a faster rate than the Pacific Arctic over the past two millennia, in both proxy data and models. The model shows that this cooling pattern was dynamically supported by both a weakening of North Atlantic subpolar gyre and a stronger Aleutian Low.

     
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