Related papers: A Chomsky-Sch\"utzenberger representation for weig…

The commutative ambiguity of a context-free grammar G assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newton's method to…

We introduce weighted regular tree grammars with storage as combination of (a) regular tree grammars with storage and (b) weighted tree automata over multioperator monoids. Each weighted regular tree grammar with storage generates a…

We give a new proof of Salvati's theorem that the group language $O_2$ is $2$ multiple context free. Unlike Salvati's proof, our arguments do not use any idea specific to two-dimensions. This raises the possibility that the argument might…

We show that it is decidable in exponential time whether the lexicographic ordering of a context-free language is scattered, or a well-ordering.

Let $G$ be an almost linear Nash group, namely, a Nash group which admits a Nash homomorphism with finite kernel to some $\GL_k(\mathbb R)$. A homology theory (the Schwartz homology) is established for the category of smooth \Fre…

We show that the language equivalence problem for regular and context-free commutative grammars is coNEXP-complete. In addition, our lower bound immediately yields further coNEXP-completeness results for equivalence problems for…

We survey recent results on the topological complexity of context-free omega-languages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge…

We present an approach to learning multi-sense word embeddings relying both on monolingual and bilingual information. Our model consists of an encoder, which uses monolingual and bilingual context (i.e. a parallel sentence) to choose a…

We consider the quantum-mechanical algebra of observables generated by canonical quantization of $SL(2,R)$ Chern-Simons theory with rational charge on a space manifold with torus topology. We produce modular representations generalizing the…

We introduce the notion of weighted singular vectors and weighted uniform exponent with respect to a set of weights. We prove invariance of these exponents for affine subspaces and submanifolds inside those affine subspaces. For certain…

We study unitarity of lowest weight irreducible representations of rational Cherednik algebras. We prove several general results, and use them to determine which lowest weight representations are unitary in a number of cases. In particular,…

We prove an easy but interesting result about the linear independence of multiple zeta values of different weights.

Recent work on learning multilingual word representations usually relies on the use of word-level alignements (e.g. infered with the help of GIZA++) between translated sentences, in order to align the word embeddings in different languages.…

We establish the characterizations of commutators of several versions of maximal functions on spaces of homogeneous type. In addition, with the aid of interpolation theory, we provide weighted version of the commutator theorems by…

We study the full language of quasigeodesics in Cayley graphs, with fixed error constants. We show that, given a non-virtually-cyclic nilpotent group or Baumslag--Solitar group, and any finite generating set, such languages fail to be…

We introduce a novel method for multilingual transfer that utilizes deep contextual embeddings, pretrained in an unsupervised fashion. While contextual embeddings have been shown to yield richer representations of meaning compared to their…

The problem of determining the representation type of the full transformation monoid was resolved by Ponizovskii, Putcha, and Ringel. In this paper, we present a similar result for the monoid of binary relations, a partial result for the…

Recently, in weighted automata theory the weight structure of strong bimonoids has found much interest; they form a generalization of semirings and are closely related to near-semirings studied in algebra. Here, we define polynomials over a…

This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…

In this paper, we propose a multilingual encoder-decoder architecture capable of obtaining multilingual sentence representations by means of incorporating an intermediate {\em attention bridge} that is shared across all languages. That is,…