1,163 research outputs found
L^p boundedness of the wave operator for the one dimensional Schroedinger operator
Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we
consider the associated wave operators W_+, W_- defined as the strong L^2
limits as s-> \pm\infty of the operators e^{isH} e^{-isH_0} We prove that the
wave operators are bounded operators on L^p for all 1<p<\infty, provided
(1+|x|)^2 V(x) is integrable, or else (1+|x|)V(x) is integrable and 0 is not a
resonance. For p=\infty we obtain an estimate in terms of the Hilbert
transform. Some applications to dispersive estimates for equations with
variable rough coefficients are given.Comment: 26 page
Exact bounds for distributed graph colouring
We prove exact bounds on the time complexity of distributed graph colouring.
If we are given a directed path that is properly coloured with colours, by
prior work it is known that we can find a proper 3-colouring in communication rounds. We close the gap between upper and
lower bounds: we show that for infinitely many the time complexity is
precisely communication rounds.Comment: 16 pages, 3 figure
Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem
This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics
Curved Tails in Polymerization-Based Bacterial Motility
The curved actin ``comet-tail'' of the bacterium Listeria monocytogenes is a
visually striking signature of actin polymerization-based motility. Similar
actin tails are associated with Shigella flexneri, spotted-fever Rickettsiae,
the Vaccinia virus, and vesicles and microspheres in related in vitro systems.
We show that the torque required to produce the curvature in the tail can arise
from randomly placed actin filaments pushing the bacterium or particle. We find
that the curvature magnitude determines the number of actively pushing
filaments, independent of viscosity and of the molecular details of force
generation. The variation of the curvature with time can be used to infer the
dynamics of actin filaments at the bacterial surface.Comment: 8 pages, 2 figures, Latex2
The Role of Resilience in Rebuilding Lives of Injured Veterans
The aim of this commentary is to discuss potential clinical implications of introducing resilience
building interventions into care for veterans who are living with a war wound. Some war veterans
are expected to live with a wound upon discharge from an active military role and also to fit into
civilian life. These lifestyle adjustments can tax the person’s coping abilities and in that context may
hinder successful adaptation. The experience of living with a wound or wounds, either acute or
chronic, is connected to losses, including loss of mobility, loss of financial capacity (unable to work
during some of the wound healing period) and losses attached to changed social roles. Psychological
stress is also a common experience for veterans returning to civilian life. Psychological stress is
associated with impaired healing or dysregulation of a biomarker associated with wound healing.
Modern health practice is centred on symptom reduction and working with pathology however,
working with people’s adaptive behaviours such as resilience has not been a consideration. Using
the resilience model as a conceptual framework healthcare professionals can engage with veterans
towards resilience within the context of their personal experience of ill health. Using this
contemporary framework for considering these aspects of care has the potential to facilitate
resistance to stressors associated with being injured potentially averting quality of life impairments
Molecular-orbital theory for the stopping power of atoms in the low velocity regime:the case of helium in alkali metals
A free-parameter linear-combination-of-atomic-orbitals approach is presented
for analyzing the stopping power of slow ions moving in a metal. The method is
applied to the case of He moving in alkali metals. Mean stopping powers for He
present a good agreement with local-density-approximation calculations. Our
results show important variations in the stopping power of channeled atoms with
respect to their mean values.Comment: LATEX, 3 PostScript Figures attached. Total size 0.54
Leptogenesis and neutrino parameters
We calculate the baryonic asymmetry of the universe in the
baryogenesis-via-leptogenesis framework, assuming first a quark-lepton symmetry
and then a charged-neutral lepton symmetry. We match the results with the
experimentally favoured range. In the first case all the oscillation solutions
to the solar neutrino problem, except the large mixing matter solution, can
lead to the allowed range, but with fine tuning of the parameters. In the
second case the general result is quite similar. Some related theoretical hints
are discussed.Comment: RevTex, 21 pages with 8 figure
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