Towards a Universal Semantic Dictionary

[EN] A novel method for finding linear mappings among word embeddings for several languages, taking as pivot a shared, multilingual embedding space, is proposed in this paper. Previous approaches learned translation matrices between two specific languages, while this method learns translation matrices between a given language and a shared, multilingual space. The system was first trained on bilingual, and later on multilingual corpora as well. In the first case, two different training data were applied: Dinu¿s English¿Italian benchmark data, and English¿Italian translation pairs extracted from the PanLex database. In the second case, only the PanLex database was used. The system performs on English¿Italian languages with the best setting significantly better than the baseline system given by Mikolov, and it provides a comparable performance with more sophisticated systems. Exploiting the richness of the PanLex database, the proposed method makes it possible to learn linear mappings among an arbitrary number of languages.This research was funded by Spanish MINECO and FEDER grant number TIN2017-85854-C4-2-R.Castro-Bleda, MJ.; Iklódi, E.; Recski, G.; Borbély, G. (2019). Towards a Universal Semantic Dictionary. Applied Sciences. 9(19):1-14. https://doi.org/10.3390/app9194060S114919Youn, H., Sutton, L., Smith, E., Moore, C., Wilkins, J. F., Maddieson, I., … Bhattacharya, T. (2016). On the universal structure of human lexical semantics. Proceedings of the National Academy of Sciences, 113(7), 1766-1771. doi:10.1073/pnas.1520752113Ruder, S., Vulić, I., & Søgaard, A. (2019). A Survey of Cross-lingual Word Embedding Models. Journal of Artificial Intelligence Research, 65, 569-631. doi:10.1613/jair.1.11640Bojanowski, P., Grave, E., Joulin, A., & Mikolov, T. (2017). Enriching Word Vectors with Subword Information. Transactions of the Association for Computational Linguistics, 5, 135-146. doi:10.1162/tacl_a_0005

Stressed backbone and elasticity of random central-force systems

We use a new algorithm to find the stress-carrying backbone of ``generic'' site-diluted triangular lattices of up to 10^6 sites. Generic lattices can be made by randomly displacing the sites of a regular lattice. The percolation threshold is Pc=0.6975 +/- 0.0003, the correlation length exponent \nu =1.16 +/- 0.03 and the fractal dimension of the backbone Db=1.78 +/- 0.02. The number of ``critical bonds'' (if you remove them rigidity is lost) on the backbone scales as L^{x}, with x=0.85 +/- 0.05. The Young's modulus is also calculated.Comment: 5 pages, 5 figures, uses epsfi

2nd European Congress of Mathematics

This is the second volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua

Des édifices d’un étage comme charpentes de tenségrité

Bolker et Crapo [l] ont fourni une solution matroïdale au problème du contreventement d’un édifice d’un étage. Un des objectifs de la présente note est de résumer leurs résultats en utilisant seulement la thèorie des graphes. Puis, la 2e partie présente des résultats analogues pour des charpentes de tenségrité spéciales (où les arêtes de la grille carrée sont encore des tiges, mais les diagonales sont des câbles). Comme il fallait s’y attendre, il suffira d’utiliser des graphes orientés, bien que l’étude des charpentes de tenségrité, en général, puisse nécessiter le recours aux matroïdes orientées.Bolker & Crapo [l] gave a matroidal solution to decide how to brace a one-story building. One of the aims of the present note is to summarize their results using graph theory only. Then, in Part 2, we present analogous results for special tensegrity frameworks (where the edges of the square grid are still rods but the diagonals are cables). As one can expect, directed graphs will be required only, although the study of tensegrity frameworks, in general, might need oriented matroids.Peer Reviewe

Des édifices d’un étage comme charpentes de tenségrité

Bolker et Crapo [l] ont fourni une solution matroïdale au problème du contreventement d’un édifice d’un étage. Un des objectifs de la présente note est de résumer leurs résultats en utilisant seulement la thèorie des graphes. Puis, la 2e partie présente des résultats analogues pour des charpentes de tenségrité spéciales (où les arêtes de la grille carrée sont encore des tiges, mais les diagonales sont des câbles). Comme il fallait s’y attendre, il suffira d’utiliser des graphes orientés, bien que l’étude des charpentes de tenségrité, en général, puisse nécessiter le recours aux matroïdes orientées.Bolker & Crapo [l] gave a matroidal solution to decide how to brace a one-story building. One of the aims of the present note is to summarize their results using graph theory only. Then, in Part 2, we present analogous results for special tensegrity frameworks (where the edges of the square grid are still rods but the diagonals are cables). As one can expect, directed graphs will be required only, although the study of tensegrity frameworks, in general, might need oriented matroids.Peer Reviewe