Related papers: A graph-based mathematical morphology reader
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Morphological tasks use large multi-lingual datasets that organize words into inflection tables, which then serve as training and evaluation data for various tasks. However, a closer inspection of these data reveals profound…
Graph covers are a way to describe continuous maps (and homeomorphisms) of a Cantor set, more generally than e.g.\ Bratteli-Vershik systems. Every continuous map on a zero-dimensional compact set can be expressed by a graph cover (e.g.\…
Lexical semantic typology has identified important cross-linguistic generalizations about the variation and commonalities in polysemy patterns---how languages package up meanings into words. Recent computational research has enabled…
Graph-structured data are the commonly used and have wide application scenarios in the real world. For these diverse applications, the vast variety of learning tasks, graph domains, and complex graph learning procedures present challenges…
In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data,…
The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…
This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely…
Because most of the scientific literature data is unmarked, it makes semantic representation learning based on unsupervised graph become crucial. At the same time, in order to enrich the features of scientific literature, a learning method…
Iconology is a branch of art history that investigates the meaning of artworks in relation to their social and cultural background. Nowadays, several interdisciplinary research fields leverage theoretical frameworks close to iconology to…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
This paper is simply a collection of process diagrams for further use and reference. These are diagrams about different approaches to research.
We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…
The paper approaches to the reader to topology with a curious example of topological classification by homeomorphisms applied to the letters of the alphabet viewed as subsets of Euclidean plane.
Is it possible to specify a grammatical representation (descriptors and their application guidelines) to such a degree that it can be consistently applied by different grammarians e.g. for producing a benchmark corpus for parser evaluation?…
This paper describes an ongoing multi-scale visual analytics approach for exploring and analyzing biomedical knowledge at scale.We utilize global and local views, hierarchical and flow-based graph layouts, multi-faceted search, neighborhood…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…
Large graphs can be found in a wide array of scientific fields ranging from sociology and biology to scientometrics and computer science. Their analysis is by no means a trivial task due to their sheer size and complex structure. Such…
Ontologies present an attractive technology for describing bio-medicine, because they can be shared, and have rich computational properties. However, they lack the rich expressivity of English and fit poorly with the current scientific…