571 research outputs found
Twenty-two-year cycle of the upper limiting rigidity of Daly waves
The method of calculating energy losses along regular particle trajectories is applied to obtain the predicted cosmic ray anisotropies from 200 to 500 GV. The tilt angle of the interplanetary neutral sheet varies to simulate a 22-year cycle magnetic cycle. The calculated values of solar diurnal and semidiurnal, and sidereal diurnal intensity waves are compared with observations
How Damage Diversification Can Reduce Systemic Risk
We consider the problem of risk diversification in complex networks. Nodes
represent e.g. financial actors, whereas weighted links represent e.g.
financial obligations (credits/debts). Each node has a risk to fail because of
losses resulting from defaulting neighbors, which may lead to large failure
cascades. Classical risk diversification strategies usually neglect network
effects and therefore suggest that risk can be reduced if possible losses
(i.e., exposures) are split among many neighbors (exposure diversification,
ED). But from a complex networks perspective diversification implies higher
connectivity of the system as a whole which can also lead to increasing failure
risk of a node. To cope with this, we propose a different strategy (damage
diversification, DD), i.e. the diversification of losses that are imposed on
neighboring nodes as opposed to losses incurred by the node itself. Here, we
quantify the potential of DD to reduce systemic risk in comparison to ED. For
this, we develop a branching process approximation that we generalize to
weighted networks with (almost) arbitrary degree and weight distributions. This
allows us to identify systemically relevant nodes in a network even if their
directed weights differ strongly. On the macro level, we provide an analytical
expression for the average cascade size, to quantify systemic risk.
Furthermore, on the meso level we calculate failure probabilities of nodes
conditional on their system relevance
Shear viscosity of a crosslinked polymer melt
We investigate the static shear viscosity on the sol side of the
vulcanization transition within a minimal mesoscopic model for the
Rouse-dynamics of a randomly crosslinked melt of phantom polymers. We derive an
exact relation between the viscosity and the resistances measured in a
corresponding random resistor network. This enables us to calculate the
viscosity exactly for an ensemble of crosslinks without correlations. The
viscosity diverges logarithmically as the critical point is approached. For a
more realistic ensemble of crosslinks amenable to the scaling description of
percolation, we prove the scaling relation between the critical
exponent of the viscosity, the thermal exponent associated with the
gel fraction and the crossover exponent of a random resistor network.Comment: 8 pages, uses Europhysics Letters style; Revisions: results extende
Scale-free download network for publications
The scale-free power-law behavior of the statistics of the download frequency
of publications has been, for the first time, reported. The data of the
download frequency of publications are taken from a well-constructed web page
in the field of economic physics (http://www.unifr.ch/econophysics/). The
Zipf-law analysis and the Tsallis entropy method were used to fit the download
frequency. It was found that the power-law exponent of rank-ordered frequency
distribution is which is consistent with the
power-law exponent for the cumulated frequency
distributions. Preferential attachment model of Barabasi and Albert network has
been used to explain the download network.Comment: 3 pages, 2 figure
Search in weighted complex networks
We study trade-offs presented by local search algorithms in complex networks
which are heterogeneous in edge weights and node degree. We show that search
based on a network measure, local betweenness centrality (LBC), utilizes the
heterogeneity of both node degrees and edge weights to perform the best in
scale-free weighted networks. The search based on LBC is universal and performs
well in a large class of complex networks.Comment: 14 pages, 5 figures, 4 tables, minor changes, added a referenc
Spectral Theory of Sparse Non-Hermitian Random Matrices
Sparse non-Hermitian random matrices arise in the study of disordered
physical systems with asymmetric local interactions, and have applications
ranging from neural networks to ecosystem dynamics. The spectral
characteristics of these matrices provide crucial information on system
stability and susceptibility, however, their study is greatly complicated by
the twin challenges of a lack of symmetry and a sparse interaction structure.
In this review we provide a concise and systematic introduction to the main
tools and results in this field. We show how the spectra of sparse
non-Hermitian matrices can be computed via an analogy with infinite dimensional
operators obeying certain recursion relations. With reference to three
illustrative examples --- adjacency matrices of regular oriented graphs,
adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency
matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the
use of these methods to obtain both analytic and numerical results for the
spectrum, the spectral distribution, the location of outlier eigenvalues, and
the statistical properties of eigenvectors.Comment: 60 pages, 10 figure
What are the Best Hierarchical Descriptors for Complex Networks?
This work reviews several hierarchical measurements of the topology of
complex networks and then applies feature selection concepts and methods in
order to quantify the relative importance of each measurement with respect to
the discrimination between four representative theoretical network models,
namely Erd\"{o}s-R\'enyi, Barab\'asi-Albert, Watts-Strogatz as well as a
geographical type of network. The obtained results confirmed that the four
models can be well-separated by using a combination of measurements. In
addition, the relative contribution of each considered feature for the overall
discrimination of the models was quantified in terms of the respective weights
in the canonical projection into two dimensions, with the traditional
clustering coefficient, hierarchical clustering coefficient and neighborhood
clustering coefficient resulting particularly effective. Interestingly, the
average shortest path length and hierarchical node degrees contributed little
for the separation of the four network models.Comment: 9 pages, 4 figure
Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure
We study the tailoring of structured random graph ensembles to real networks,
with the objective of generating precise and practical mathematical tools for
quantifying and comparing network topologies macroscopically, beyond the level
of degree statistics. Our family of ensembles can produce graphs with any
prescribed degree distribution and any degree-degree correlation function, its
control parameters can be calculated fully analytically, and as a result we can
calculate (asymptotically) formulae for entropies and complexities, and for
information-theoretic distances between networks, expressed directly and
explicitly in terms of their measured degree distribution and degree
correlations.Comment: 25 pages, 3 figure
Binary Models for Marginal Independence
Log-linear models are a classical tool for the analysis of contingency
tables. In particular, the subclass of graphical log-linear models provides a
general framework for modelling conditional independences. However, with the
exception of special structures, marginal independence hypotheses cannot be
accommodated by these traditional models. Focusing on binary variables, we
present a model class that provides a framework for modelling marginal
independences in contingency tables. The approach taken is graphical and draws
on analogies to multivariate Gaussian models for marginal independence. For the
graphical model representation we use bi-directed graphs, which are in the
tradition of path diagrams. We show how the models can be parameterized in a
simple fashion, and how maximum likelihood estimation can be performed using a
version of the Iterated Conditional Fitting algorithm. Finally we consider
combining these models with symmetry restrictions
Sample-size dependence of the ground-state energy in a one-dimensional localization problem
We study the sample-size dependence of the ground-state energy in a
one-dimensional localization problem, based on a supersymmetric quantum
mechanical Hamiltonian with random Gaussian potential. We determine, in the
form of bounds, the precise form of this dependence and show that the
disorder-average ground-state energy decreases with an increase of the size
of the sample as a stretched-exponential function, , where the
characteristic exponent depends merely on the nature of correlations in the
random potential. In the particular case where the potential is distributed as
a Gaussian white noise we prove that . We also predict the value of
in the general case of Gaussian random potentials with correlations.Comment: 30 pages and 4 figures (not included). The figures are available upon
reques
- …