835,296 research outputs found
Genetic algorithm for line labeling of diagrams having drawing cues
Drawings are an integral part of the design process, helping designers communicate abstract concepts to others. In this paper we propose a genetic algorithm that successfully exploits cues present in drawings in a line labeling algorithm for sketches.peer-reviewe
PaL Diagrams: A Linear Diagram-Based Visual Language
Linear diagrams have recently been shown to be
more effective than Euler diagrams when used
for set-based reasoning. However, unlike the
growing corpus of knowledge about formal aspects
of Euler and Venn diagrams, there has been no
formalisation of linear diagrams. To fill this
knowledge gap, we present and formalise Point
and Line (PaL) diagrams, an extension of simple
linear diagrams containing points, thus providing
a formal foundation for an effective visual
language.We prove that PaL diagrams are exactly
as expressive as monadic first-order logic with
equality, gaining, as a corollary, an equivalence
with the Euler diagram extension called spider
diagrams. The method of proof provides translations
between PaL diagrams and sentences of monadic
first-order logic
Reasoning with Spider Diagrams
Spider diagrams combine and extend Venn diagrams and Euler circles to express constraints on sets and their relationships with other sets. These diagrams can usefully be used in conjunction with object-oriented modelling notations such as the Unified Modelling Language. This paper summarises the main syntax and semantics of spider diagrams and introduces four inference rules for reasoning with spider diagrams and a rule governing the equivalence of Venn and Euler forms of spider diagrams. This paper also details rules for combining two spider diagrams to produce a single diagram which retains as much of their combined semantic information as possible and discusses disjunctive diagrams as one possible way of enriching the system in order to combine spider diagrams so that no semantic information is lost
Tree Diagrams for String Links II: Determining Chord Diagrams
In previous work, we defined the intersection graph of a chord diagram
associated with a string link (as in the theory of finite type invariants). In
this paper, we look at the case when this graph is a tree, and we show that in
many cases these trees determine the chord diagram (modulo the usual 1-term and
4-term relations).Comment: 14 pages, many figure
The cone of Betti diagrams over a hypersurface ring of low embedding dimension
We give a complete description of the cone of Betti diagrams over a standard
graded hypersurface ring of the form k[x,y]/, where q is a homogeneous
quadric. We also provide a finite algorithm for decomposing Betti diagrams,
including diagrams of infinite projective dimension, into pure diagrams.
Boij--Soederberg theory completely describes the cone of Betti diagrams over a
standard graded polynomial ring; our result provides the first example of
another graded ring for which the cone of Betti diagrams is entirely
understood.Comment: Minor edits, references update
Linkable Dynkin Diagrams
In this article we develop some aspects of the construction of new Hopf
algebras found recently by Andruskiewitsch and Schneider. There the authors
classified (under some slight restrictions) all pointed finite dimensional Hopf
algebras with coradical (Z/p)^s. We contribute to this work by giving a closer
description of the possible ``exotic'' linkings.Comment: 20 pages, 7 figures, submitted to Journal of Algebr
A Diagram Is Worth A Dozen Images
Diagrams are common tools for representing complex concepts, relationships
and events, often when it would be difficult to portray the same information
with natural images. Understanding natural images has been extensively studied
in computer vision, while diagram understanding has received little attention.
In this paper, we study the problem of diagram interpretation and reasoning,
the challenging task of identifying the structure of a diagram and the
semantics of its constituents and their relationships. We introduce Diagram
Parse Graphs (DPG) as our representation to model the structure of diagrams. We
define syntactic parsing of diagrams as learning to infer DPGs for diagrams and
study semantic interpretation and reasoning of diagrams in the context of
diagram question answering. We devise an LSTM-based method for syntactic
parsing of diagrams and introduce a DPG-based attention model for diagram
question answering. We compile a new dataset of diagrams with exhaustive
annotations of constituents and relationships for over 5,000 diagrams and
15,000 questions and answers. Our results show the significance of our models
for syntactic parsing and question answering in diagrams using DPGs
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