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We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all vertices have degree at least d, for a certain…

Combinatorics · Mathematics 2009-06-18 Olivier Bernardi

We develop a nonstandard approach to exploring polynomials associated with peaks and runs of permutations. With the aid of a context-free grammar, or a set of substitution rules, one can perform a symbolic calculus, and the computation…

Combinatorics · Mathematics 2023-02-02 William Y. C. Chen , Amy M. Fu

In this paper we resolve the degree-2 Abel map for nodal curves. Our results are based on a previous work of the authors reducing the problem of the resolution of the Abel map to a combinatorial problem via tropical geometry. As an…

Algebraic Geometry · Mathematics 2022-01-28 Alex Abreu , Sally Andria , Marco Pacini

The note introduces a novel concept of non-Abelian patchworking arising as real locus of non-Abelian complex-phase tropical hypersurfaces, the theory of which is now developed enough to allow the proposed spin-off. Although, non-Abelian…

Algebraic Geometry · Mathematics 2026-03-10 Turgay Akyar , Mikhail Shkolnikov

Automatic Multi-Word Term (MWT) extraction is a very important issue to many applications, such as information retrieval, question answering, and text categorization. Although many methods have been used for MWT extraction in English and…

Computation and Language · Computer Science 2014-09-11 Abdelkader El Mahdaouy , Saïd EL Alaoui Ouatik , Eric Gaussier

A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…

Logic in Computer Science · Computer Science 2023-06-22 Denisa Diaconescu , George Metcalfe , Laura Schnüriger

Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…

Geometric Topology · Mathematics 2021-12-30 Christoph Dorn , Christopher L. Douglas

Inspired by Morse theory, we introduce a topological stack Broken, which we refer to as the moduli stack of broken lines. We show that Broken can be presented as a Lie groupoid with corners and provide a combinatorial description of sheaves…

Algebraic Topology · Mathematics 2018-05-25 Jacob Lurie , Hiro Lee Tanaka

In spite of its robust syntax, semantic cohesion, and less ambiguity, lemma level analysis and generation does not yet focused in Arabic NLP literatures. In the current research, we propose the first non-statistical accurate Arabic…

Computation and Language · Computer Science 2012-03-19 Tarek El-Shishtawy , Fatma El-Ghannam

Visual question answering (VQA) in medical imaging aims to support clinical diagnosis by automatically interpreting complex imaging data in response to natural language queries. Existing studies typically rely on distinct visual and textual…

Computer Vision and Pattern Recognition · Computer Science 2025-07-08 Yuanhe Tian , Chen Su , Junwen Duan , Yan Song

Scattering amplitudes at loop level can be reduced to a basis of linearly independent Feynman integrals. The integral coefficients are extracted from generalized unitarity cuts which define algebraic varieties. The topology of an algebraic…

High Energy Physics - Theory · Physics 2015-06-03 Mads Sogaard , Yang Zhang

Diacritization process attempt to restore the short vowels in Arabic written text; which typically are omitted. This process is essential for applications such as Text-to-Speech (TTS). While diacritization of Modern Standard Arabic (MSA)…

Computation and Language · Computer Science 2019-06-03 Ahmed Abdelali , Mohammed Attia , Younes Samih , Kareem Darwish , Hamdy Mubarak

We introduce Morse, a recurrent encoder-decoder model that produces morphological analyses of each word in a sentence. The encoder turns the relevant information about the word and its context into a fixed size vector representation and the…

Computation and Language · Computer Science 2019-09-25 Ekin Akyürek , Erenay Dayanık , Deniz Yuret

This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…

Computational Complexity · Computer Science 2016-02-02 Jaroslav Horáček , Milan Hladík , Michal Černý

The Linguistic Data Consortium (LDC) has developed hundreds of data corpora for natural language processing (NLP) research. Among these are a number of annotated treebank corpora for Arabic. Typically, these corpora consist of a single…

Computation and Language · Computer Science 2013-09-24 Mona Diab , Nizar Habash , Owen Rambow , Ryan Roth

To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…

Geometric Topology · Mathematics 2014-07-25 Benjamin A. Burton , William Pettersson

This demo paper presents a Google Docs add-on for automatic Arabic word-level readability visualization. The add-on includes a lemmatization component that is connected to a five-level readability lexicon and Arabic WordNet-based…

Computation and Language · Computer Science 2022-10-20 Reem Hazim , Hind Saddiki , Bashar Alhafni , Muhamed Al Khalil , Nizar Habash

Multimodal LLMs can accurately perceive numerical content across modalities yet fail to perform exact multi-digit multiplication when the identical underlying arithmetic problem is presented as numerals, number words, images, or in audio…

Computation and Language · Computer Science 2026-04-21 Samuel G. Balter , Ethan Jerzak , Connor T. Jerzak

Morphological parsing is the task of decomposing words into morphemes, the smallest units of meaning in a language, and labelling their grammatical roles. It is a particularly challenging task for agglutinative languages, such as the Nguni…

Computation and Language · Computer Science 2025-05-20 Cael Marquard , Simbarashe Mawere , Francois Meyer

We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in…

Computational Geometry · Computer Science 2012-01-13 Eric Berberich , Pavel Emeliyanenko , Alexander Kobel , Michael Sagraloff
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