86,930 research outputs found
Evaluating the Comprehension of Euler Diagrams
We describe an empirical investigation into layout criteria that can help with the comprehension of Euler diagrams. Euler diagrams are used to represent set inclusion in applications such as teaching set theory, database querying, software engineering, filing system organisation and bio-informatics. Research in automatically laying out Euler diagrams for use with these applications is at an early stage, and our work attempts to aid this research by informing layout designers about the importance of various Euler diagram aesthetic criteria. The three criteria under investigation were: contour jaggedness, zone area inequality and edge closeness. Subjects were asked to interpret diagrams with different combinations of levels for each of the criteria. Results for this investigation indicate that, within the parameters of the study, all three criteria are important for understanding Euler diagrams and we have a preliminary indication of the ordering of their importance
Exact Multi-Restricted Schur Polynomial Correlators
We derive a product rule satisfied by restricted Schur polynomials. We focus
mostly on the case that the restricted Schur polynomial is built using two
matrices, although our analysis easily extends to more than two matrices. This
product rule allows us to compute exact multi-point correlation functions of
restricted Schur polynomials, in the free field theory limit. As an example of
the use of our formulas, we compute two point functions of certain single trace
operators built using two matrices and three point functions of certain
restricted Schur polynomials, exactly, in the free field theory limit. Our
results suggest that gravitons become strongly coupled at sufficiently high
energy, while the restricted Schur polynomials for totally antisymmetric
representations remain weakly interacting at these energies. This is in perfect
accord with the half-BPS (single matrix) results of hep-th/0512312. Finally, by
studying the interaction of two restricted Schur polynomials we suggest a
physical interpretation for the labels of the restricted Schur polynomial: the
composite operator is constructed from the half BPS
``partons'' and .Comment: 42 page
Bulk quartic vertices from boundary four-point correlators
We present arguments which suggest that the bulk higher-spin gravity duals of
weakly-coupled conformal field theories obey some refined notion of locality.
In particular, we discuss the Mellin amplitude programme in this context. We
focus on the vector model and minimal higher-spin gravity as a
paradigmatic example of such holographic dual pairs. We restrict ourselves to
three- and four-point functions of scalar primary operators, but the
qualitative conclusions are expected to hold for the generic case.Comment: 13 pages. Contribution to the proceedings of the "International
Workshop on Higher Spin Gauge Theories" (4-6 November 2015, Singapore
Clafer: Lightweight Modeling of Structure, Behaviour, and Variability
Embedded software is growing fast in size and complexity, leading to intimate
mixture of complex architectures and complex control. Consequently, software
specification requires modeling both structures and behaviour of systems.
Unfortunately, existing languages do not integrate these aspects well, usually
prioritizing one of them. It is common to develop a separate language for each
of these facets. In this paper, we contribute Clafer: a small language that
attempts to tackle this challenge. It combines rich structural modeling with
state of the art behavioural formalisms. We are not aware of any other modeling
language that seamlessly combines these facets common to system and software
modeling. We show how Clafer, in a single unified syntax and semantics, allows
capturing feature models (variability), component models, discrete control
models (automata) and variability encompassing all these aspects. The language
is built on top of first order logic with quantifiers over basic entities (for
modeling structures) combined with linear temporal logic (for modeling
behaviour). On top of this semantic foundation we build a simple but expressive
syntax, enriched with carefully selected syntactic expansions that cover
hierarchical modeling, associations, automata, scenarios, and Dwyer's property
patterns. We evaluate Clafer using a power window case study, and comparing it
against other notations that substantially overlap with its scope (SysML, AADL,
Temporal OCL and Live Sequence Charts), discussing benefits and perils of using
a single notation for the purpose
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