37 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
Linking the trans-Planckian and the information loss problems in black hole physics
The trans-Planckian and information loss problems are usually discussed in
the literature as separate issues concerning the nature of Hawking radiation.
Here we instead argue that they are intimately linked, and can be understood as
"two sides of the same coin" once it is accepted that general relativity is an
effective field theory.Comment: 10 pages, 2 figures. Replaced with the version to be published in
General Relativity and Gravitatio
Shaping the top asymmetry
We study different profiles of the distribution of the top forward-backward
asymmetry, depending on the invariant mass of the t tbar pair. We show that
they can be reproduced by one or more light colour octets, while keeping
moderate departures of the t tbar cross section and invariant mass
distributions with respect to the Standard Model predictions at Tevatron and
LHC.Comment: LaTeX 14 pages. Final version to appear in PLB, with an enlarged
discussion about dijet constraint
Model-independent measurement of the top quark polarisation
We introduce a new asymmetry in the decay t -> W b -> l nu b, which is shown
to be directly proportional to the polarisation of the top quark along a chosen
axis, times a sum of W helicity fractions. The latter have already been
precisely measured at the Tevatron and the Large Hadron Collider. Therefore,
this new asymmetry can be used to obtain a model-independent measurement of the
polarisation of top quarks produced in any process at hadron or lepton
colliders.Comment: LaTeX 12 pages. Discussion expanded with a new plot, references
added. Final version to appear in PL
Asymptotic Lower Bounds for a class of Schroedinger Equations
We shall study the following initial value problem: \begin{equation}{\bf
i}\partial_t u - \Delta u + V(x) u=0, \hbox{} (t, x) \in {\mathbf R} \times
{\mathbf R}^n, \end{equation} where is a real short--range
potential, whose radial derivative satisfies some supplementary assumptions.
More precisely we shall present a family of identities satisfied by the
solutions to the previous Cauchy problem. As a by--product of these identities
we deduce some uniqueness results and a lower bound for the so called local
smoothing which becomes an identity in a precise asymptotic sense.Comment: 24 pages. to appear on Comm. Math. Phy
Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes
When network and graph theory are used in the study of complex systems, a
typically finite set of nodes of the network under consideration is frequently
either explicitly or implicitly considered representative of a much larger
finite or infinite region or set of objects of interest. The selection
procedure, e.g., formation of a subset or some kind of discretization or
aggregation, typically results in individual nodes of the studied network
representing quite differently sized parts of the domain of interest. This
heterogeneity may induce substantial bias and artifacts in derived network
statistics. To avoid this bias, we propose an axiomatic scheme based on the
idea of node splitting invariance to derive consistently weighted variants of
various commonly used statistical network measures. The practical relevance and
applicability of our approach is demonstrated for a number of example networks
from different fields of research, and is shown to be of fundamental importance
in particular in the study of spatially embedded functional networks derived
from time series as studied in, e.g., neuroscience and climatology.Comment: 21 pages, 13 figure
Hopf algebras and Markov chains: Two examples and a theory
The operation of squaring (coproduct followed by product) in a combinatorial
Hopf algebra is shown to induce a Markov chain in natural bases. Chains
constructed in this way include widely studied methods of card shuffling, a
natural "rock-breaking" process, and Markov chains on simplicial complexes.
Many of these chains can be explictly diagonalized using the primitive elements
of the algebra and the combinatorics of the free Lie algebra. For card
shuffling, this gives an explicit description of the eigenvectors. For
rock-breaking, an explicit description of the quasi-stationary distribution and
sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes
will only appear on the version on Amy Pang's website, the arXiv version will
not be updated.
Transitions of cardio-metabolic risk factors in the Americas between 1980 and 2014
Describing the prevalence and trends of cardiometabolic risk factors that are associated with non-communicable diseases (NCDs) is crucial for monitoring progress, planning prevention, and providing evidence to support policy efforts. We aimed to analyse the transition in body-mass index (BMI), obesity, blood pressure, raised blood pressure, and diabetes in the Americas, between 1980 and 2014
A complementary study approach unravels novel players in the pathoetiology of Hirschsprung disease
Hirschsprung disease (HSCR, OMIM 142623) involves congenital intestinal obstruction
caused by dysfunction of neural crest cells and their progeny during enteric nervous system
(ENS) development. HSCR is a multifactorial disorder; pathogenetic variants accounting for
disease phenotype are identified only in a minority of cases, and the identification of novel
disease-relevant genes remains challenging. In order to identify and to validate a potential
disease-causing relevance of novel HSCR candidate genes, we established a complementary study approach, combining whole exome sequencing (WES) with transcriptome analysis of murine embryonic ENS-related tissues, literature and databas
A century of trends in adult human height
Being taller is associated with enhanced longevity, and higher education and earnings. We reanalysed 1472 population-based studies, with measurement of height on more than 18.6 million participants to estimate mean height for people born between 1896 and 1996 in 200 countries. The largest gain in adult height over the past century has occurred in South Korean women and Iranian men, who became 20.2 cm (95% credible interval 17.5-22.7) and 16.5 cm (13.3-19.7) taller, respectively. In contrast, there was little change in adult height in some sub-Saharan African countries and in South Asia over the century of analysis. The tallest people over these 100 years are men born in the Netherlands in the last quarter of 20th century, whose average heights surpassed 182.5 cm, and the shortest were women born in Guatemala in 1896 (140.3 cm; 135.8-144.8). The height differential between the tallest and shortest populations was 19-20 cm a century ago, and has remained the same for women and increased for men a century later despite substantial changes in the ranking of countries