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The use of stone hammers to produce sharp stone flakes—knapping—is thought to represent a significant stage in hominin technological evolution because it facilitated the exploitation of novel resources, including meat obtained from medium‐to‐large‐sized vertebrates. The invention of knapping may have occurred via an additive (i.e., cumulative) process that combined several innovative stages. Here, we propose that one of these stages was the hominin use of ‘naturaliths,’ which we define as naturally produced sharp stone fragments that could be used as cutting tools. Based on a review of the literature and our own research, we first suggest that the ‘typical’ view, namely that sharp‐edged stones are seldom produced by nonprimate processes, is likely incorrect. Instead, naturaliths can be, and are being, endlessly produced in a wide range of settings and thus may occur on the landscape in far greater numbers than archaeologists currently understand or acknowledge. We then explore the potential role this ‘naturalith prevalence’ may have played in the origin of hominin stone knapping. Our hypothesis suggests that the origin of knapping was not a ‘Eureka!’ moment whereby hominins first made a sharp flake by intention or by accident and then sought something to cut, but instead was an emulative process by hominins aiming to reproduce the sharp tools furnished by mother nature and already in demand. We conclude with a discussion of several corollaries our proposal prompts, and several avenues of future research that can support or question our proposal. 

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. 

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. 

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. 

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.