Andreev's Theorem on hyperbolic polyhedra

In 1970, E. M. Andreev published a classification of all three-dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, $C$, Andreev's Theorem provides five classes of linear inequalities, depending on $C$, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing $C$ with the assigned dihedral angles. Andreev's Theorem also shows that the resulting polyhedron is unique, up to hyperbolic isometry. Andreev's Theorem is both an interesting statement about the geometry of hyperbolic 3-dimensional space, as well as a fundamental tool used in the proof for Thurston's Hyperbolization Theorem for 3-dimensional Haken manifolds. It is also remarkable to what level the proof of Andreev's Theorem resembles (in a simpler way) the proof of Thurston. We correct a fundamental error in Andreev's proof of existence and also provide a readable new proof of the other parts of the proof of Andreev's Theorem, because Andreev's paper has the reputation of being ``unreadable''.Comment: To appear les Annales de l'Institut Fourier. 47 pages and many figures. Revision includes significant modification to section 4, making it shorter and more rigorous. Many new references include

Type determination in an optimizing compiler for APL

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New record of the pavement ant, Tetramorium immigrans (Hymenoptera: Formicidae), in South Dakota with notes on its thermal tolerance and geographic distribution

The pavement ant, Tetramorium immigrans, is an abundant and widespread species across large portions of the United States. Yet despite its current distribution in Northeastern, Midwestern, Pacific, and Western states, there is a surprising lack of records from the Great Plains. Here we present an updated county list of T. immigrans from museum collections and research grade observations (459 counties; ~15% of US counties), highlighting the first records from one Great Plains state—South Dakota. Observations on community science platforms since 2006 have undoubtedly increased the awareness of T. immigrans (+329 counties; ~72% of all county records), however we posit that such platforms may also highlight the dispersal limitations of this species into the less urban, colder Northern Great Plains states of Montana, Nebraska, North Dakota, South Dakota, and Wyoming (~5% of 291 counties). As such, we offer novel information on T. immigrans’ thermal biology including measurements of critical thermal limits, knock-down resistance, and chill coma recovery. While T. immigrans can likely tolerate the warm summer temperatures found in South Dakota due to its heat tolerance hovering around 46°C, its lower ability to tolerate cold winter conditions may be a possible mechanism for its limited dispersal

Future research to underpin successful peste des petits ruminants virus (PPRV) eradication

Peste des petits ruminants virus (PPRV) is a significant pathogen of small ruminants and is prevalent in much of Africa, the Near and Middle East and Asia. Despite the availability of an efficacious and cheap live-attenuated vaccine, the virus has continued to spread, with its range stretching from Morocco in the west to China and Mongolia in the east. Some of the world’s poorest communities rely on small ruminant farming for subsistence and the continued endemicity of PPRV is a constant threat to their livelihoods. Moreover, PPRV’s effects on the world’s population are felt broadly across many economic, agricultural and social situations. This far-reaching impact has prompted the Food and Agriculture Organization of the United Nations (FAO) and the World Organisation for Animal Health (OIE) to develop a global strategy for the eradication of this virus and its disease. PPRV is a morbillivirus and, given the experience of these organizations in eradicating the related rinderpest virus, the eradication of PPRV should be feasible. However, there are many critical areas where basic and applied virological research concerning PPRV is lacking. The purpose of this review is to highlight areas where new research could be performed in order to guide and facilitate the eradication programme. These areas include studies on disease transmission and epidemiology, the existence of wildlife reservoirs and the development of next-generation vaccines and diagnostics. With the support of the international virology community, the successful eradication of PPRV can be achieved

Tessellations and Pattern Formation in Plant Growth and Development

The shoot apical meristem (SAM) is a dome-shaped collection of cells at the apex of growing plants from which all above-ground tissue ultimately derives. In Arabidopsis thaliana (thale cress), a small flowering weed of the Brassicaceae family (related to mustard and cabbage), the SAM typically contains some three to five hundred cells that range from five to ten microns in diameter. These cells are organized into several distinct zones that maintain their topological and functional relationships throughout the life of the plant. As the plant grows, organs (primordia) form on its surface flanks in a phyllotactic pattern that develop into new shoots, leaves, and flowers. Cross-sections through the meristem reveal a pattern of polygonal tessellation that is suggestive of Voronoi diagrams derived from the centroids of cellular nuclei. In this chapter we explore some of the properties of these patterns within the meristem and explore the applicability of simple, standard mathematical models of their geometry.Comment: Originally presented at: "The World is a Jigsaw: Tessellations in the Sciences," Lorentz Center, Leiden, The Netherlands, March 200