1,289 research outputs found
Overlap properties of geometric expanders
The {\em overlap number} of a finite -uniform hypergraph is
defined as the largest constant such that no matter how we map
the vertices of into , there is a point covered by at least a
-fraction of the simplices induced by the images of its hyperedges.
In~\cite{Gro2}, motivated by the search for an analogue of the notion of graph
expansion for higher dimensional simplicial complexes, it was asked whether or
not there exists a sequence of arbitrarily large
-uniform hypergraphs with bounded degree, for which . Using both random methods and explicit constructions, we answer this
question positively by constructing infinite families of -uniform
hypergraphs with bounded degree such that their overlap numbers are bounded
from below by a positive constant . We also show that, for every ,
the best value of the constant that can be achieved by such a
construction is asymptotically equal to the limit of the overlap numbers of the
complete -uniform hypergraphs with vertices, as
. For the proof of the latter statement, we establish the
following geometric partitioning result of independent interest. For any
and any , there exists satisfying the
following condition. For any , for any point and
for any finite Borel measure on with respect to which
every hyperplane has measure , there is a partition into measurable parts of equal measure such that all but
at most an -fraction of the -tuples
have the property that either all simplices with
one vertex in each contain or none of these simplices contain
High-resolution satellite-based cloud-coupled estimates of total downwelling surface radiation for hydrologic modelling applications
A relatively simple satellite-based radiation model yielding high-resolution (in space and time) downwelling longwave and shortwave radiative fluxes at the Earth's surface is presented. The primary aim of the approach is to provide a basis for deriving physically consistent forcing fields for distributed hydrologic models using satellite-based remote sensing data. The physically-based downwelling radiation model utilises satellite inputs from both geostationary and polar-orbiting platforms and requires only satellite-based inputs except that of a climatological lookup table derived from a regional climate model. Comparison against ground-based measurements over a 14-month simulation period in the Southern Great Plains of the United States demonstrates the ability to reproduce radiative fluxes at a spatial resolution of 4 km and a temporal resolution of 1 h with good accuracy during all-sky conditions. For hourly fluxes, a mean difference of &minus;2 W m<sup>&minus;2</sup> with a root mean square difference of 21 W m<sup>&minus;2</sup> was found for the longwave fluxes whereas a mean difference of &minus;7 W m<sup>&minus;2</sup> with a root mean square difference of 29 W m<sup>&minus;2</sup> was found for the shortwave fluxes. Additionally, comparison against advanced downwelling longwave and solar insolation products during all-sky conditions showed comparable uncertainty in the longwave estimates and reduced uncertainty in the shortwave estimates. The relatively simple form of the model enables future usage in ensemble-based applications including data assimilation frameworks in order to explicitly account for input uncertainties while providing the potential for conditioning estimates from other readily available products derived from more sophisticated retrieval algorithms
Property (T) and rigidity for actions on Banach spaces
We study property (T) and the fixed point property for actions on and
other Banach spaces. We show that property (T) holds when is replaced by
(and even a subspace/quotient of ), and that in fact it is
independent of . We show that the fixed point property for
follows from property (T) when 1
. For simple Lie groups and their lattices, we prove that the fixed point property for holds for any if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement
Methods of genetic toxicology in the assessment of genomic damage induced by electromagnetic ionizing radiation
Medical or occupational exposure of patients and healthcare personnel to ionizing radiation (IR) can be a cause of genetic disorders. In this article we discuss the efficiency of the following tests used to comprehensively assess the effects of ionizing radiation on the genetic apparatus of a cell: The Ames test, the micronucleus test and the FISH method. We provide examples of their use, outline their advantages and drawbacks, estimate the possibility of designing more advanced test systems and discuss requirements for their implementation
Differential criterion of a bubble collapse in viscous liquids
The present work is devoted to a model of bubble collapse in a Newtonian
viscous liquid caused by an initial bubble wall motion. The obtained bubble
dynamics described by an analytic solution significantly depends on the liquid
and bubble parameters. The theory gives two types of bubble behavior: collapse
and viscous damping. This results in a general collapse condition proposed as
the sufficient differential criterion. The suggested criterion is discussed and
successfully applied to the analysis of the void and gas bubble collapses.Comment: 5 pages, 3 figure
Regular graphs of large girth and arbitrary degree
For every integer d > 9, we construct infinite families {G_n}_n of
d+1-regular graphs which have a large girth > log_d |G_n|, and for d large
enough > 1,33 log_d |G_n|. These are Cayley graphs on PGL_2(q) for a special
set of d+1 generators whose choice is related to the arithmetic of integral
quaternions. These graphs are inspired by the Ramanujan graphs of
Lubotzky-Philips-Sarnak and Margulis, with which they coincide when d is prime.
When d is not equal to the power of an odd prime, this improves the previous
construction of Imrich in 1984 where he obtained infinite families {I_n}_n of
d+1-regular graphs, realized as Cayley graphs on SL_2(q), and which are
displaying a girth > 0,48 log_d |I_n|. And when d is equal to a power of 2,
this improves a construction by Morgenstern in 1994 where certain families
{M_n}_n of 2^k+1-regular graphs were shown to have a girth > 2/3 log_d |M_n|.Comment: (15 pages) Accepted at Combinatorica. Title changed following
referee's suggestion. Revised version after reviewing proces
Sonoluminescing air bubbles rectify argon
The dynamics of single bubble sonoluminescence (SBSL) strongly depends on the
percentage of inert gas within the bubble. We propose a theory for this
dependence, based on a combination of principles from sonochemistry and
hydrodynamic stability. The nitrogen and oxygen dissociation and subsequent
reaction to water soluble gases implies that strongly forced air bubbles
eventually consist of pure argon. Thus it is the partial argon (or any other
inert gas) pressure which is relevant for stability. The theory provides
quantitative explanations for many aspects of SBSL.Comment: 4 page
Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations
To treat the spectral statistics of quantum maps and flows that are fully
chaotic classically, we use the rigorous Riemann-Siegel lookalike available for
the spectral determinant of unitary time evolution operators . Concentrating
on dynamics without time reversal invariance we get the exact two-point
correlator of the spectral density for finite dimension of the matrix
representative of , as phenomenologically given by random matrix theory. In
the limit the correlator of the Gaussian unitary ensemble is
recovered. Previously conjectured cancellations of contributions of
pseudo-orbits with periods beyond half the Heisenberg time are shown to be
implied by the Riemann-Siegel lookalike
On the distortion of twin building lattices
We show that twin building lattices are undistorted in their ambient group;
equivalently, the orbit map of the lattice to the product of the associated
twin buildings is a quasi-isometric embedding. As a consequence, we provide an
estimate of the quasi-flat rank of these lattices, which implies that there are
infinitely many quasi-isometry classes of finitely presented simple groups. In
an appendix, we describe how non-distortion of lattices is related to the
integrability of the structural cocycle
Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that
We report on some recent developments in the search for optimal network
topologies. First we review some basic concepts on spectral graph theory,
including adjacency and Laplacian matrices, and paying special attention to the
topological implications of having large spectral gaps. We also introduce
related concepts as ``expanders'', Ramanujan, and Cage graphs. Afterwards, we
discuss two different dynamical feautures of networks: synchronizability and
flow of random walkers and so that they are optimized if the corresponding
Laplacian matrix have a large spectral gap. From this, we show, by developing a
numerical optimization algorithm that maximum synchronizability and fast random
walk spreading are obtained for a particular type of extremely homogeneous
regular networks, with long loops and poor modular structure, that we call
entangled networks. These turn out to be related to Ramanujan and Cage graphs.
We argue also that these graphs are very good finite-size approximations to
Bethe lattices, and provide almost or almost optimal solutions to many other
problems as, for instance, searchability in the presence of congestion or
performance of neural networks. Finally, we study how these results are
modified when studying dynamical processes controlled by a normalized (weighted
and directed) dynamics; much more heterogeneous graphs are optimal in this
case. Finally, a critical discussion of the limitations and possible extensions
of this work is presented.Comment: 17 pages. 11 figures. Small corrections and a new reference. Accepted
for pub. in JSTA
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