121 research outputs found
Toric symplectic ball packing
We define and solve the toric version of the symplectic ball packing problem,
in the sense of listing all 2n-dimensional symplectic-toric manifolds which
admit a perfect packing by balls embedded in a symplectic and torus equivariant
fashion.
In order to do this we first describe a problem in geometric-combinatorics
which is equivalent to the toric symplectic ball packing problem. Then we solve
this problem using arguments from Convex Geometry and Delzant theory.
Applications to symplectic blowing-up are also presented, and some further
questions are raised in the last section.Comment: 17 pages, 6 figure
Symplectic bifurcation theory for integrable systems
This paper develops a symplectic bifurcation theory for integrable systems in
dimension four. We prove that if an integrable system has no hyperbolic
singularities and its bifurcation diagram has no vertical tangencies, then the
fibers of the induced singular Lagrangian fibration are connected. The image of
this singular Lagrangian fibration is, up to smooth deformations, a planar
region bounded by the graphs of two continuous functions. The bifurcation
diagram consists of the boundary points in this image plus a countable
collection of rank zero singularities, which are contained in the interior of
the image. Because it recently has become clear to the mathematics and
mathematical physics communities that the bifurcation diagram of an integrable
system provides the best framework to study symplectic invariants, this paper
provides a setting for studying quantization questions, and spectral theory of
quantum integrable systems.Comment: 42 pages, 19 figure
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Risk Taking in Hospitalized Patients with Acute and Severe Traumatic Brain Injury
Rehabilitation can improve cognitive deficits observed in patients with traumatic brain injury (TBI). However, despite rehabilitation, the ability of making a choice often remains impaired. Risk taking is a daily activity involving numerous cognitive processes subserved by a complex neural network. In this work we investigated risk taking using the Balloon Analogue Risk Task (BART) in patients with acute TBI and healthy controls. We hypothesized that individuals with TBI will take less risk at the BART as compared to healthy individuals. We also predicted that within the TBI group factors such as the number of days since the injury, severity of the injury, and sites of the lesion will play a role in risk taking as assessed with the BART. Main findings revealed that participants with TBI displayed abnormally cautious risk taking at the BART as compared to healthy subjects. Moreover, healthy individuals showed increased risk taking throughout the task which is in line with previous work. However, individuals with TBI did not show this increased risk taking during the task. We also investigated the influence of three patients’ characteristics on their performance at the BART: Number of days post injury, Severity of the head injury, and Status of the frontal lobe. Results indicate that performance at the BART was influenced by the number of days post injury and the status of the frontal lobe, but not by the severity of the head injury. Reported findings are encouraging for risk taking seems to naturally improve with time postinjury. They support the need of conducting longitudinal prospective studies to ultimately identify impaired and intact cognitive skills that should be trained postinjury
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