103 research outputs found

    On triangulations with fixed areas

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    We prove that the number of dissections of a given polygon into triangles with fixed areas of faces is finite and that an equidissection is algebraic as long as the vertices of the original polygon have algebraic coordinates.Comment: 3 pages, 1 figur

    New and interesting lichen records from the Ural Mountains, Russia

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    Ten species of lichenized ascomycetes are reported from the Urals. Aspicilia spermatomanes, Fuscidea praeruptorum, Lepra excludens, L. monogona, Metamelanea caesiella and Pertusaria amarescens are new to Russia while Bryobilimbia ahlesii, Lecanora orosthea, L. rouxii and Tephromela grumosa are new for the Urals. Our records considerably extend the ranges or fill gaps in the formerly disjunctive distributions of these species. The morphology, secondary chemistry and ecology of the species are discussed.

    Lichens and allied fungi from the Pechenga district and surroundings (Lapponia Petsamoënsis, Murmansk Region, Russia)

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    168 species of lichens are specified for the Pechenga district and surroundings. Microcalicium ahlneri and Placidium norvegicum are new for the Murmansk Region. 18 species are new for Lapponia Petsamoënsis. Stereocaulon dactylophyllum is included into the Red Data Book of the Russian Federation. Caloplaca diphyodes, Dermatocarpon meiophyllizum, Haematomma ochroleucum, Phlyctis argena and Stereocaulon dactylophyllum are included into the Red Data Book of the Murmansk Region

    Performance of Hyperbolic Geometry Models on Top-N Recommendation Tasks

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    We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably, even with such a minimalistic approach, we not only outperform the Euclidean counterpart but also achieve a competitive performance with respect to the current state-of-the-art. We additionally explore the effects of space curvature on the quality of hyperbolic models and propose an efficient data-driven method for estimating its optimal value.Comment: Accepted at ACM RecSys 2020; 7 page

    New crustose Teloschistaceae in Central Europe

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    Central Europe in general is poor in Teloschistaceae lichen crusts (Caloplaca s. lat.). Diversity of these lichens is increased by the occurrence of some Arctic, Mediterranean and continental species, which are here close to the limits of their range. Examples include: 1) Caloplaca interfulgens, previously known from arid territories of northern Africa and western Asia, is recorded, surprisingly, from Austria, Czech Republic, Germany, Slovakia and southern Russia. In Central Europe, it is restricted to scattered xerothermic limestone outcrops. 2) Caloplaca scabrosa, previously known only from Svalbard, is recorded from the Sudetes in the Czech Republic. It is similar to, but not conspecific with, C. furfuracea. Its diagnostic characters include a blastidiate thallus and the presence of atranorin. Our results show that atranorin is absent in the majority of taxa related to C. furfuracea with only two exceptions: the sample from Eastern Carpathians, here called C. aff. scabrosa, and in one Sudetan sample identified as C. crenularia. 3) Caloplaca emilii, newly described below, is closely related to the Mediterranean C. areolata. We consider C. emilii a Mediterranean species rarely occurring in higher latitudes in Austria, the Czech Republic and Germany. It is distinguished from C. areolata mainly by the presence of vegetative diaspores (blastidia); a possible role of blastidia in the distribution pattern of C. emilii is discussed below. Status of the names Caloplaca areolata, C. isidiigera and C. spalatensisis, formerly used for the new taxon, is clarified. 4) Caloplaca molariformis, newly described below, belongs to the Pyrenodesmia group (a lineage of Caloplaca without anthraquinones). It is a continental species, frequently collected on limestone or lime-rich tuffs in steppes or deserts in Turkey, Iran, western Kazakhstan and southern Russia, and is also known from eastern Ukraine and southern Slovakia. Caloplaca molariformis is characterized by its thick thallus with fungal and algal tissues arranged in high stacks. 5) Caloplaca substerilis, newly described below, is distinguished from the closely related C. ulcerosa by its endophloeodal or minutely squamulose thallus with soralia formed in bark crevices or on margins of squamules. While C. ulcerosa has a maritime distribution in Europe, C. substerilis is typically a continental species. North American continental lichens called "C. ulcerosa” are phylogenetically closer and more similar to C. substerilis. The positions within Teloschistaceae of the taxa considered are demonstrated by ITS phylogenies. The distributions of C. areolata, C. emilii and C. interfulgens are mapped. The new species are fully described using more than a hundred phenotype characters, and diagnostic characters are indicated separatel

    Development of conception of three-dimensional design of clothes

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    The concept of three-dimensional modeling of clothes has been further developed, information support of this process has been developed, the spatial position of the main anthropometric points and constructive lines on the virtual dummy has been determined, and their correspondence has been established in the "mannequin-clothing" system. A database of transformations of details of basic designs of female shoulder clothes is developed, rational values ​​of transformations are determined taking into account the properties of materials