60,361 research outputs found
Drawing Order Diagrams Through Two-Dimension Extension
Order diagrams are an important tool to visualize the complex structure of
ordered sets. Favorable drawings of order diagrams, i.e., easily readable for
humans, are hard to come by, even for small ordered sets. Many attempts were
made to transfer classical graph drawing approaches to order diagrams. Although
these methods produce satisfying results for some ordered sets, they
unfortunately perform poorly in general. In this work we present the novel
algorithm DimDraw to draw order diagrams. This algorithm is based on a relation
between the dimension of an ordered set and the bipartiteness of a
corresponding graph.Comment: 16 pages, 12 Figure
Three Dimensional Software Modelling
Traditionally, diagrams used in software systems modelling have been two dimensional (2D). This is probably because graphical notations, such as those used in object-oriented and structured systems modelling, draw upon the topological graph metaphor, which, at its basic form, receives little benefit from three dimensional (3D) rendering. This paper presents a series of 3D graphical notations demonstrating effective use of the third dimension in modelling. This is done by e.g., connecting several graphs together, or in using the Z co-ordinate to show special kinds of edges. Each notation combines several familiar 2D diagrams, which can be reproduced from 2D projections of the 3D model. 3D models are useful even in the absence of a powerful graphical workstation: even 2D stereoscopic projections can expose more information than a plain planar diagram
Tree-width and dimension
Over the last 30 years, researchers have investigated connections between
dimension for posets and planarity for graphs. Here we extend this line of
research to the structural graph theory parameter tree-width by proving that
the dimension of a finite poset is bounded in terms of its height and the
tree-width of its cover graph.Comment: Updates on solutions of problems and on bibliograph
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CHREST+: A simulation of how humans learn to solve problems using diagrams.
This paper describes the underlying principles of a computer model, CHREST+, which learns to solve problems using diagrammatic representations. Although earlier work has determined that experts store domain-specific information within schemata, no substantive model has been proposed for learning such representations. We describe the different strategies used by subjects in constructing a diagrammatic representation of an electric circuit known as an AVOW diagram, and explain how these strategies fit a theory for the learnt representations. Then we describe CHREST+, an extended version of an established model of human perceptual memory. The extension enables the model to relate information learnt about circuits with that about their associated AVOW diagrams, and use this information as a schema to improve its efficiency at problem solving
Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
We study the low energy effective theory for a non-Fermi liquid state in 2+1
dimensions, where a transverse U(1) gauge field is coupled with a patch of
Fermi surface with N flavors of fermion in the large N limit. In the low energy
limit, quantum corrections are classified according to the genus of the 2d
surface on which Feynman diagrams can be drawn without a crossing in a double
line representation, and all planar diagrams are important in the leading
order. The emerging theory has the similar structure to the four dimensional
SU(N) gauge theory in the large N limit. Because of strong quantum fluctuations
caused by the abundant low energy excitations near the Fermi surface, low
energy fermions remain strongly coupled even in the large N limit. As a result,
there are infinitely many quantum corrections that contribute to the leading
frequency dependence of the Green's function of fermion on the Fermi surface.
On the contrary, the boson self energy is not modified beyond the one-loop
level and the theory is stable in the large N limit. The non-perturbative
nature of the theory also shows up in correlation functions of gauge invariant
operators.Comment: 14 pages, 20 figures; v2) Sec. V on correlation function of gauge
invariant operators added; v3) typos corrected, minor changes (to appear in
PRB
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