Related papers: A graph-based mathematical morphology reader
Readability criteria have been addressed as a measurement of the quality of graph visualizations. In this paper, we argue that readability criteria are necessary but not sufficient. We propose a new kind of criteria, namely faithfulness, to…
A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…
Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods,…
The aim of this paper is to derive on the basis of the Euler's formula several analytical relations which hold for certain classes of planar graphs and which can be useful in algorithmic graph theory.
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
This paper provides an overview of the morphology and syntax of the Tamil language, focusing on its contemporary usage. The paper also highlights the complexity and richness of Tamil in terms of its morphological and syntactic features,…
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…
Discovering and making sense of relevant literature is fundamental in any scientific field. Node-link diagram-based visualization tools can aid this process; however, existing tools have been evaluated only on small scales. This paper…
As part of the NLP Scholar project, we created a single unified dataset of NLP papers and their meta-information (including citation numbers), by extracting and aligning information from the ACL Anthology and Google Scholar. In this paper,…
Graph-structured data arise naturally in many different application domains. By representing data as graphs, we can capture entities (i.e., nodes) as well as their relationships (i.e., edges) with each other. Many useful insights can be…
This is a draft of a textbook on differential forms. The primary target audience is sophmore level undergraduates enrolled in what would traditionally be a course in vector calculus. Later chapters will be of interest to advaced…
Our goal is to use formal methods to analyse normative documents written in English, such as privacy policies and service-level agreements. This requires the combination of a number of different elements, including information extraction…
This document describes the Gloss Ontology. The ontology and associated class model are organised into several packages. Section 2 describes each package in detail, while Section 3 contains a summary of the whole ontology.
We study the notion of hierarchy in the context of visualizing textual data and navigating text collections. A formal framework for ``hierarchy'' is given by an ultrametric topology. This provides us with a theoretical foundation for…
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…
In this era of information technology, abundant information is available on the internet in the form of web pages and documents on any given topic. Finding the most relevant and informative content out of these huge number of documents,…
Query-based text summarization is an important real world problem that requires to condense the prolix text data into a summary under the guidance of the query information provided by users. The topic has been studied for a long time and…
Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…