107 research outputs found
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Wellformedness Properties in Euler Diagrams: An Eye Tracking Study for Visualisation Evaluation
In the field of information visualisation, Euler diagrams are an important tool used in various application areas such as engineering, medicine and social analysis. To effectively use Euler diagrams, some of the wellformedness properties needs to be avoided, as they are considered to reduce user comprehension. From the previous empirical studies, we know some properties are swappable but there is no clear justification which property would be the best to use. In this paper, we considered two main wellformedness properties (duplicated curve labels and disconnected zones) to test which among the two affect user comprehension the most, based on the task performance (accuracy and response time), preference and eye movements of the users. Twelve participants performed three different types of tasks with nine diagrams of each property (so, in total eighteen diagrams) and the results showed that duplicated curve labels property slows down and trigger extra eye movements, causing delays for the tasks. Though there is no significant difference in the accuracy but the insights obtained from the response time, preference and eye movements will be useful for software developers on the optimal way to visualise Euler diagrams in real world application areas
The impact of topological and graphical choices on the perception of Euler diagrams
This paper establishes the impact of topological and graphical properties on the comprehension of Euler diagrams. To-date, various studies have examined the impact of individual properties of Euler diagrams, such as curve shape and orientation. This has allowed us to establish guides for using these properties such as âdraw Euler diagrams with circlesâ and âdraw Euler diagrams without regard to orientationâ. However, until the work described here, questions still remain, for example âdo these guides, when combined, make a significant difference to real-world Euler diagrams?â, and if so, âshould they be used by those visualising set data with Euler diagrams?â To answer these questions an empirical study was conducted to compare Euler diagrams that have been drawn by others for their real-world data, against versions that adhere to all of the guides in combination. The study establishes that both the accuracy and the speed with which information is derived from Euler diagrams is significantly improved when Euler diagrams adhere, where possible, to all the guides. The improvement is considerable when using the guided diagrams, with on average, the error rate being more than halved from 21.4% to 10.3%, and a 9 s improvement in the average time taken, from 34.2s to 24.9s. As Euler diagrams are regularly used to visualise information in a multitude of areas, ranging from crime control to social network analysis, our results indicate that applying the guides to these diagrams will improve the ability of users to accurately and quickly extract information
Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams
In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations and their cardinalities. The data sets are represented by closed curves and the data set relationships are depicted by the overlaps between these curves. Both the sets and their intersections are easily visible as the closed curves are preattentively processed and form common regions that have a strong perceptual grouping effect. Besides set relations such as intersection, containment and disjointness, the cardinality of the sets and their intersections can also be depicted in the same diagram (referred to as area-proportional) through the size of the curves and their overlaps. Size is a preattentive feature and so similarities, differences and trends are easily identified. Thus, such diagrams facilitate data analysis and reasoning about the sets. However, drawing these diagrams manually is difficult, often impossible, and current automatic drawing methods do not always produce appropriate diagrams.
This dissertation presents novel automatic drawing methods for different types of Euler diagrams and a user study of how such diagrams can help probabilistic judgement. The main drawing algorithms are: eulerForce, which uses a force-directed approach to lay out Euler diagrams; eulerAPE, which draws area-proportional Venn diagrams with ellipses. The user study evaluated the effectiveness of area- proportional Euler diagrams, glyph representations, Euler diagrams with glyphs and text+visualization formats for Bayesian reasoning, and a method eulerGlyphs was devised to automatically and accurately draw the assessed visualizations for any Bayesian problem. Additionally, analytic algorithms that instantaneously compute the overlapping areas of three general intersecting ellipses are provided, together with an evaluation of the effectiveness of ellipses in drawing accurate area-proportional Venn diagrams for 3-set data and the characteristics of the data that can be depicted accurately with ellipses
A cognitive exploration of the ânon-visualâ nature of geometric proofs
Why are Geometric Proofs (Usually) âNon-Visualâ? We asked this question as
a way to explore the similarities and differences between diagrams and text (visual
thinking versus language thinking). Traditional text-based proofs are considered
(by many to be) more rigorous than diagrams alone. In this paper we focus on
human perceptual-cognitive characteristics that may encourage textual modes for
proofs because of the ergonomic affordances of text relative to diagrams. We suggest
that visual-spatial perception of physical objects, where an object is perceived
with greater acuity through foveal vision rather than peripheral vision, is similar
to attention navigating a conceptual visual-spatial structure. We suggest that attention
has foveal-like and peripheral-like characteristics and that textual modes
appeal to what we refer to here as foveal-focal attention, an extension of prior
work in focused attention
Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons
We study d=2+1 non-commutative U(1) YMCS, concentrating on the one-loop
corrections to the propagator and to the dispersion relations. Unlike its
commutative counterpart, this model presents divergences and hence an IR/UV
mechanism, which we regularize by adding a Majorana gaugino of mass m_f, that
provides (softly broken) supersymmetry. The perturbative vacuum becomes stable
for a wide range of coupling and mass values, and tachyonic modes are generated
only in two regions of the parameters space. One such region corresponds to
removing the supersymmetric regulator (m_f >> m_g), restoring the well-known
IR/UV mixing phenomenon. The other one (for m_f ~ m_g/2 and large \theta) is
novel and peculiar of this model. The two tachyonic regions turn out to be very
different in nature. We conclude with some remarks on the theory's off-shell
unitarity.Comment: 42 pages, 11 figures, uses Axodraw. Bibliography revise
The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification
We present a smorgasbord of results on the stabiliser ZX-calculus for odd
prime-dimensional qudits (i.e. qupits). We derive a simplified rule set that
closely resembles the original rules of qubit ZX-calculus. Using these rules,
we demonstrate analogues of the spider-removing local complementation and
pivoting rules. This allows for efficient reduction of diagrams to the affine
with phases normal form. We also demonstrate a reduction to a unique form,
providing an alternative and simpler proof of completeness. Furthermore, we
introduce a different reduction to the graph state with local Cliffords normal
form, which leads to a novel layered decomposition for qupit Clifford
unitaries. Additionally, we propose a new approach to handle scalars formally,
closely reflecting their practical usage. Finally, we have implemented many of
these findings in DiZX, a new open-source Python library for qudit
ZX-diagrammatic reasoning.Comment: 44 pages, lots of figures, accepted to QPL 202
Categorification and applications in topology and representation theory
International audienc
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