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Abstract In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints which here we call poles. We define generalised knotoids to allow arbitrarily many poles, intervals and circles, each pole corresponding to any number of interval endpoints, including zero. This theory subsumes a variety of other related topological objects and introduces some particularly interesting new cases. We explore various analogs of knotoid invariants, including height, index polynomials, bracket polynomials and hyperbolicity. We further generalise to knotoidal graphs, which are a natural extension of spatial graphs that allow both poles and vertices. 

We improve the upper bound on superbridge index [Formula: see text] in terms of bridge index [Formula: see text] from [Formula: see text] to [Formula: see text]. 

We present a catalog of results of gamma-ray observations made by VERITAS, published from 2008 to 2020. VERITAS is a ground based imaging atmospheric Cherenkov telescope observatory located at the Fred Lawrence Whipple Observatory (FLWO) in southern Arizona, sensitive to gamma-ray photons with energies in the range of ∼ 100 GeV - 30 TeV. Its observation targets include galactic sources such as binary star systems, pulsar wind nebulae, and supernova remnants, extragalactic sources like active galactic nuclei, star forming galaxies, and gamma-ray bursts, and some unidentified objects. The catalog includes in digital form all of the high-level science results published in 112 papers using VERITAS data and currently contains data on 57 sources. The catalog has been made accessible via GitHub and at NASA's HEASARC. 

ABSTRACT A major goal of evolutionary science is to understand how biological diversity is generated and altered. Despite considerable advances, we still have limited insight into how phenotypic variation arises and is sorted by natural selection. Here we argue that an integrated view, which merges ecology, evolution and developmental biology (eco evo devo) on an equal footing, is needed to understand the multifaceted role of the environment in simultaneously determining the development of the phenotype and the nature of the selective environment, and how organisms in turn affect the environment through eco evo and eco devo feedbacks. To illustrate the usefulness of an integrated eco evo devo perspective, we connect it with the theory of resource polymorphism (i.e. the phenotypic and genetic diversification that occurs in response to variation in available resources). In so doing, we highlight fishes from recently glaciated freshwater systems as exceptionally well‐suited model systems for testing predictions of an eco evo devo framework in studies of diversification. Studies on these fishes show that intraspecific diversity can evolve rapidly, and that this process is jointly facilitated by (i) the availability of diverse environments promoting divergent natural selection; (ii) dynamic developmental processes sensitive to environmental and genetic signals; and (iii) eco evo and eco devo feedbacks influencing the selective and developmental environments of the phenotype. We highlight empirical examples and present a conceptual model for the generation of resource polymorphism – emphasizing eco evo devo, and identify current gaps in knowledge. 

The Cherenkov Telescope Array (CTA) is the next-generation ground-based observatory for very-high-energy gamma rays. One candidate design for CTA's medium-sized telescopes consists of the Schwarzschild-Couder Telescope (SCT), featuring innovative dual-mirror optics. The SCT project has built and is currently operating a 9.7-m prototype SCT (pSCT) at the Fred Lawrence Whipple Observatory (FLWO); such optical design enables the use of a compact camera with state-of-the art silicon photomultiplier detectors. A partially-equipped camera has recently successfully detected the Crab Nebula with a statistical significance of 8.6 standard deviations. A funded upgrade of the pSCT focal plane sensors and electronics is currently ongoing, which will bring the total number of channels from 1600 to 11328 and the telescope field of view from about 2.7° to 8° . In this work, we will describe the technical and scientific performance of the pSCT. 

For the first time in the history of ground-based x-ray astronomy, the on-axis performance of the dual mirror, aspheric, aplanatic Schwarzschild-Couder optical system has been demonstrated in a 9:7-m aperture imaging atmospheric Cherenkov telescope. The novel design of the prototype Schwarzschild-Couder Telescope (pSCT) is motivated by the need of the next-generation Cherenkov Telescope Array (CTA) observatory to have the ability to perform wide (>=8°) field-of-view observations simultaneously with superior imaging of atmospheric cascades (resolution of 0:067 per pixel or better). The pSCT design, if implemented in the CTA installation, has the potential to improve significantly both the x-ray angular resolution and the off-axis sensitivity of the observatory, reaching nearly the theoretical limit of the technique and thereby making a major impact on the CTA observatory sky survey programs, follow-up observations of multi-messenger transients with poorly known initial localization, as well as on the spatially resolved spectroscopic studies of extended x-ray sources. This contribution reports on the initial alignment procedures and point-spread-function results for the challenging segmented aspheric primary and secondary mirrors of the pSCT.