2,013 research outputs found
Computing trisections of 4-manifolds
Algorithms that decompose a manifold into simple pieces reveal the geometric
and topological structure of the manifold, showing how complicated structures
are constructed from simple building blocks. This note describes a way to
algorithmically construct a trisection, which describes a -dimensional
manifold as a union of three -dimensional handlebodies. The complexity of
the -manifold is captured in a collection of curves on a surface, which
guide the gluing of the handelbodies. The algorithm begins with a description
of a manifold as a union of pentachora, or -dimensional simplices. It
transforms this description into a trisection. This results in the first
explicit complexity bounds for the trisection genus of a -manifold in terms
of the number of pentachora (-simplices) in a triangulation.Comment: 15 pages, 9 figure
Visual perceptual load reduces auditory detection in typically developing individuals but not in individuals with Autism Spectrum Disorders
Objective: Previous studies examining selective attention in individuals with autism spectrum disorder (ASD) have yielded conflicting results, some suggesting superior focused attention (e.g. on visual search tasks), others demonstrating greater distractibility. This pattern could be accounted for by the proposal (derived by applying the Load theory of attention, e.g. Lavie, 2005) that ASD is characterized by an increased perceptual capacity (Remington, Swettenham, Campbell, & Coleman, 2009). Recent studies in the visual domain support this proposal. Here we hypothesize that ASD involves an enhanced perceptual capacity that also operates across sensory modalities, and test this prediction, for the first time using a signal detection paradigm. Method: 17 neurotypical (NT) and 15 ASD adolescents performed a visual search task under varying levels of visual perceptual load while simultaneously detecting presence/absence of an auditory tone embedded in noise. Results: Detection sensitivity (d’) for the auditory stimulus was similarly high for both groups in the low visual perceptual load condition (e.g. 2 items: p = .391, d = 0.31, 95% CI [-.39, 1.00]). However, at a higher level of visual load, auditory d’ reduced for the NT group but not the ASD group leading to a group difference (p = .002, d = 1.2, 95% CI [.44, 1.96]). As predicted, when visual perceptual load was highest, both groups then showed a similarly low auditory d’ (p = .9, d = 0.05, 95% CI [-.65, .74]). Conclusions: These findings demonstrate that increased perceptual capacity in ASD operates across modalities
Degenerations of ideal hyperbolic triangulations
Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The
deformation variety D(T), a subset of which parameterises (incomplete)
hyperbolic structures obtained on M using T, is defined and compactified by
adding certain projective classes of transversely measured singular
codimension-one foliations of M. This leads to a combinatorial and geometric
variant of well-known constructions by Culler, Morgan and Shalen concerning the
character variety of a 3-manifold.Comment: 31 pages, 11 figures; minor changes; to appear in Mathematische
Zeitschrif
Imprints of the QCD Phase Transition on the Spectrum of Gravitational Waves
We have investigated effects of the QCD phase transition on the relic GW
spectrum applying several equations of state for the strongly interacting
matter: Besides the bag model, which describes a first order transition, we use
recent data from lattice calculations featuring a crossover. Finally, we
include a short period of inflation during the transition which allows for a
first order phase transition at finite baryon density. Our results show that
the QCD transition imprints a step into the spectrum of GWs. Within the first
two scenarios, entropy conservation leads to a step-size determined by the
relativistic degrees of freedom before and after the transition. The inflation
of the third scenario much stronger attenuates the high-frequency modes: An
inflationary model being consistent with observation entails suppression of the
spectral energy density by a factor of ~10^(-12).Comment: 11 pages, 13 figure
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