214 research outputs found
Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?
We study the Laplacian operator of an uncorrelated random network and, as an
application, consider hopping processes (diffusion, random walks, signal
propagation, etc.) on networks. We develop a strict approach to these problems.
We derive an exact closed set of integral equations, which provide the averages
of the Laplacian operator's resolvent. This enables us to describe the
propagation of a signal and random walks on the network. We show that the
determining parameter in this problem is the minimum degree of vertices
in the network and that the high-degree part of the degree distribution is not
that essential. The position of the lower edge of the Laplacian spectrum
appears to be the same as in the regular Bethe lattice with the
coordination number . Namely, if , and
if . In both these cases the density of eigenvalues
as , but the limiting behaviors near
are very different. In terms of a distance from a starting vertex,
the hopping propagator is a steady moving Gaussian, broadening with time. This
picture qualitatively coincides with that for a regular Bethe lattice. Our
analytical results include the spectral density near
and the long-time asymptotics of the autocorrelator and the
propagator.Comment: 25 pages, 4 figure
Development of Taenia pisiformis in golden hamster (Mesocricetus auratus)
The life cycle of Taenia pisiformis includes canines as definitive hosts and rabbits as intermediate hosts. Golden hamster (Mesocricetus auratus) is a rodent that has been successfully used as experimental model of Taenia solium taeniosis. In the present study we describe the course of T. pisiformis infection in experimentally infected golden hamsters. Ten females, treated with methyl-prednisolone acetate were infected with three T. pisiformis cysticerci each one excised from one rabbit. Proglottids released in faeces and adults recovered during necropsy showed that all animals were infected. Eggs obtained from the hamsters' tapeworms, were assessed for viability using trypan blue or propidium iodide stains. Afterwards, some rabbits were inoculated with eggs, necropsy was performed after seven weeks and viable cysticerci were obtained. Our results demonstrate that the experimental model of adult Taenia pisiformis in golden hamster can replace the use of canines in order to study this parasite and to provide eggs and adult tapeworms to be used in different types of experiments
Synchronization in small-world systems
We quantify the dynamical implications of the small-world phenomenon. We
consider the generic synchronization of oscillator networks of arbitrary
topology, and link the linear stability of the synchronous state to an
algebraic condition of the Laplacian of the graph. We show numerically that the
addition of random shortcuts produces improved network synchronizability.
Further, we use a perturbation analysis to place the synchronization threshold
in relation to the boundaries of the small-world region. Our results also show
that small-worlds synchronize as efficiently as random graphs and hypercubes,
and more so than standard constructive graphs
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
Network synchronization: Optimal and Pessimal Scale-Free Topologies
By employing a recently introduced optimization algorithm we explicitely
design optimally synchronizable (unweighted) networks for any given scale-free
degree distribution. We explore how the optimization process affects
degree-degree correlations and observe a generic tendency towards
disassortativity. Still, we show that there is not a one-to-one correspondence
between synchronizability and disassortativity. On the other hand, we study the
nature of optimally un-synchronizable networks, that is, networks whose
topology minimizes the range of stability of the synchronous state. The
resulting ``pessimal networks'' turn out to have a highly assortative
string-like structure. We also derive a rigorous lower bound for the Laplacian
eigenvalue ratio controlling synchronizability, which helps understanding the
impact of degree correlations on network synchronizability.Comment: 11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex
Networks 2007
Bose-Einstein Condensation on inhomogeneous complex networks
The thermodynamic properties of non interacting bosons on a complex network
can be strongly affected by topological inhomogeneities. The latter give rise
to anomalies in the density of states that can induce Bose-Einstein
condensation in low dimensional systems also in absence of external confining
potentials. The anomalies consist in energy regions composed of an infinite
number of states with vanishing weight in the thermodynamic limit. We present a
rigorous result providing the general conditions for the occurrence of
Bose-Einstein condensation on complex networks in presence of anomalous
spectral regions in the density of states. We present results on spectral
properties for a wide class of graphs where the theorem applies. We study in
detail an explicit geometrical realization, the comb lattice, which embodies
all the relevant features of this effect and which can be experimentally
implemented as an array of Josephson Junctions.Comment: 11 pages, 9 figure
Natural preconditioning and iterative methods for saddle point systems
The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the sequential quadratic programming approach to nonlinear optimization. This survey concerns iterative solution methods for these problems and, in particular, shows how the problem formulation leads to natural preconditioners which guarantee a fast rate of convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness---in terms of rapidity of convergence---is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends
Proton Drip-Line Calculations and the Rp-process
One-proton and two-proton separation energies are calculated for proton-rich
nuclei in the region . The method is based on Skyrme Hartree-Fock
calculations of Coulomb displacement energies of mirror nuclei in combination
with the experimental masses of the neutron-rich nuclei. The implications for
the proton drip line and the astrophysical rp-process are discussed. This is
done within the framework of a detailed analysis of the sensitivity of rp
process calculations in type I X-ray burst models on nuclear masses. We find
that the remaining mass uncertainties, in particular for some nuclei with
, still lead to large uncertainties in calculations of X-ray burst light
curves. Further experimental or theoretical improvements of nuclear mass data
are necessary before observed X-ray burst light curves can be used to obtain
quantitative constraints on ignition conditions and neutron star properties. We
identify a list of nuclei for which improved mass data would be most important.Comment: 20 pages, 9 figures, 2 table
Generalized uncertainty inequalities
In this paper, Heisenberg-Pauli-Weyl-type uncertainty inequalities are
obtained for a pair of positive-self adjoint operators on a Hilbert space,
whose spectral projectors satisfy a ``balance condition'' involving certain
operator norms. This result is then applied to obtain uncertainty inequalities
on Riemannian manifolds, Riemannian symmetric spaces of non-compact type,
homogeneous graphs and unimodular Lie groups with sublaplacians.Comment: 19 page
Spectral Graph Analysis for Process Monitoring
Process monitoring is a fundamental task to support operator decisions under ab- normal situations. Most process monitoring approaches, such as Principal Components Analysis and Locality Preserving Projections, are based on dimensionality reduction. In this paper Spectral Graph Analysis Monitoring (SGAM) is introduced. SGAM is a new process monitoring technique that does not require dimensionality reduction techniques. The approach it is based on the spectral graph analysis theory. Firstly, a weighted graph representation of process measurements is developed. Secondly, the process behavior is parameterized by means of graph spectral features, in particular the graph algebraic connectivity and the graph spectral energy. The developed methodology has been illustrated in autocorrelated and non-linear synthetic cases, and applied to the well known Tennessee Eastman process benchmark with promising results.Fil: Musulin, Estanislao. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Rosario. Centro Internacional Franco Argentino de Ciencias de la InformaciĂłn y Sistemas; Argentin
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