13,885 research outputs found
On a conjecture of A. Magnus concerning the asymptotic behavior of the recurrence coefficients of the generalized Jacobi polynomials
In 1995 Magnus posed a conjecture about the asymptotics of the recurrence
coefficients of orthogonal polynomials with respect to the weights on [-1,1] of
the form
with
and . We show rigorously that
Magnus' conjecture is correct even in a more general situation, when the weight
above has an extra factor, which is analytic in a neighborhood of [-1,1] and
positive on the interval. The proof is based on the steepest descendent method
of Deift and Zhou applied to the non-commutative Riemann-Hilbert problem
characterizing the orthogonal polynomials. A feature of this situation is that
the local analysis at has to be carried out in terms of confluent
hypergeometric functions.Comment: 29 pages, 4 figure
Stability mapping of bipartite tight-binding graphs with losses and gain: symmetry and beyond
We consider bipartite tight-binding graphs composed by nodes split into
two sets of equal size: one set containing nodes with on-site loss, the other
set having nodes with on-site gain. The nodes are connected randomly with
probability . We give a rationale for the relevance of such "throttle/brake"
coupled systems (physically open systems) to grasp the stability issues of
complex networks in areas such as biochemistry, neurons or economy, for which
their modelling in terms of non-hermitian Hamiltonians is still in infancy.
Specifically, we measure the connectivity between the two sets with the
parameter , which is the ratio of current adjacent pairs over the total
number of possible adjacent pairs between the sets. For general
undirected-graph setups, the non-hermitian Hamiltonian of
this model presents pseudo-Hermiticity, where is the loss/gain
strength. However, we show that for a given graph setup
becomes symmetric. In both scenarios (pseudo-Hermiticity and symmetric), depending on the parameter combination, the spectra of
can be real even when it is non-hermitian. Thus, we
numerically characterize the average fractions of real and imaginary
eigenvalues of as a function of the parameter set
. We demonstrate, for both setups, that there is a well
defined sector of the plane (which grows with ) where the
spectrum of is predominantly real.Comment: 10 pages, 9 figure
Position guidelines and evidence base concerning determinants of childhood obesity with a European perspective
Childhood obesity is one of the most pressing global public health issues, with rates increasing fastest in countries at low levels of income. Obesity occurring during childhood is likely to persist throughout the life course, and it is a cause of increased disease risk from the early years of life. This supplement is the result of collaborations involving a large and multidisciplinary group of researchers that were established in the context of the ongoing European Horizon 2020 project Science and Technology in childhood Obesity Policy (STOP). The aim, as in the entire STOP project, is to generate evidence that can support better policies to tackle the problem of childhood obesity in Europe and elsewhere. Quality of life and health well-being concerning children needs to consider personalized, population, and planetary facets to tackle childhood obesity at early stages of life, for in-deep phenotyping, integrating personalized medicine and precision public health interventions at global levels. This supplement contributes to this aim. © 2021 The Authors. Obesity Reviews published by John Wiley & Sons Ltd on behalf of World Obesity Federation
Spectral and localization properties of random bipartite graphs
Bipartite graphs are often found to represent the connectivity between the
components of many systems such as ecosystems. A bipartite graph is a set of
nodes that is decomposed into two disjoint subsets, having and
vertices each, such that there are no adjacent vertices within the same set.
The connectivity between both sets, which is the relevant quantity in terms of
connections, can be quantified by a parameter that equals the
ratio of existent adjacent pairs over the total number of possible adjacent
pairs. Here, we study the spectral and localization properties of such random
bipartite graphs. Specifically, within a Random Matrix Theory (RMT) approach,
we identify a scaling parameter that fixes the
localization properties of the eigenvectors of the adjacency matrices of random
bipartite graphs. We also show that, when ) the
eigenvectors are localized (extended), whereas the
localization--to--delocalization transition occurs in the interval
. Finally, given the potential applications of our findings, we
round off the study by demonstrating that for fixed , the spectral
properties of our graph model are also universal.Comment: 17 pages, 10 figure
Lower Cretaceous (Hauterivian-Albian) ammonite biostratigraphy in the Maestrat Basin (E Spain)
Peer reviewedPublisher PD
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