On triangulations with fixed areas

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

A Simple and Accurate Syntax-Agnostic Neural Model for Dependency-based Semantic Role Labeling

We introduce a simple and accurate neural model for dependency-based semantic role labeling. Our model predicts predicate-argument dependencies relying on states of a bidirectional LSTM encoder. The semantic role labeler achieves competitive performance on English, even without any kind of syntactic information and only using local inference. However, when automatically predicted part-of-speech tags are provided as input, it substantially outperforms all previous local models and approaches the best reported results on the English CoNLL-2009 dataset. We also consider Chinese, Czech and Spanish where our approach also achieves competitive results. Syntactic parsers are unreliable on out-of-domain data, so standard (i.e., syntactically-informed) SRL models are hindered when tested in this setting. Our syntax-agnostic model appears more robust, resulting in the best reported results on standard out-of-domain test sets.Comment: To appear in CoNLL 201

New and interesting lichen records from the Ural Mountains, Russia

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)

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

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

Surface modes and chiral symmetry (Wilson Fermions in a box)

We give a Hamiltonian discussion of surface states in an extra dimension as a basis for chiral fermions in lattice models. Such modes appear with the Wilson fermion action when the hopping parameter exceeds a critical value. The association of such states with the closing and reopening of a band gap was noted by Shockley in 1939. Poster presented by Michael Creutz at Lattice 93. Uuencoded compressed postscript file.Comment: 4 pages, BNL-4978