198,962 research outputs found
A framework for evaluating complex networks measurements
A good deal of current research in complex networks involves the
characterization and/or classification of the topological properties of given
structures, which has motivated several respective measurements. This letter
proposes a framework for evaluating the quality of complex network measurements
in terms of their effective resolution, degree of degeneracy and
discriminability. The potential of the suggested approach is illustrated with
respect to comparing the characterization of several model and real-world
networks by using concentric and symmetry measurements. The results indicate a
markedly superior performance for the latter type of mapping
Complex Network Approach to the Statistical Features of the Sunspot Series
Complex network approaches have been recently developed as an alternative
framework to study the statistical features of time-series data. We perform a
visibility-graph analysis on both the daily and monthly sunspot series. Based
on the data, we propose two ways to construct the network: one is from the
original observable measurements and the other is from a
negative-inverse-transformed series. The degree distribution of the derived
networks for the strong maxima has clear non-Gaussian properties, while the
degree distribution for minima is bimodal. The long-term variation of the
cycles is reflected by hubs in the network which span relatively large time
intervals. Based on standard network structural measures, we propose to
characterize the long-term correlations by waiting times between two subsequent
events. The persistence range of the solar cycles has been identified over
15\,--\,1000 days by a power-law regime with scaling exponent
of the occurrence time of the two subsequent and successive strong minima. In
contrast, a persistent trend is not present in the maximal numbers, although
maxima do have significant deviations from an exponential form. Our results
suggest some new insights for evaluating existing models. The power-law regime
suggested by the waiting times does indicate that there are some level of
predictable patterns in the minima.Comment: 18 pages, 11 figures. Solar Physics, 201
Bayesian interpolation
Although Bayesian analysis has been in use since Laplace, the Bayesian method of model-comparison has only recently been developed in depth. In this paper, the Bayesian approach to regularization and model-comparison is demonstrated by studying the inference problem of interpolating noisy data. The concepts and methods described are quite general and can be applied to many other data modeling problems. Regularizing constants are set by examining their posterior probability distribution. Alternative regularizers (priors) and alternative basis sets are objectively compared by evaluating the evidence for them. āOccam's razorā is automatically embodied by this process. The way in which Bayes infers the values of regularizing constants and noise levels has an elegant interpretation in terms of the effective number of parameters determined by the data set. This framework is due to Gull and Skilling
On Risk Evaluation and Control of Distributed Multi-Agent Systems
In this paper, we deal with risk evaluation and risk-averse optimization of
complex distributed systems with general risk functionals. We postulate a novel
set of axioms for the functionals evaluating the total risk of the system. We
derive a dual representation for the systemic risk measures and propose a way
to construct non-trivial families of measures by using either a collection of
linear scalarizations or non-linear risk aggregation. The new framework
facilitates risk-averse sequential decision-making by distributed methods. The
proposed approach is compared theoretically and numerically to some of the
systemic risk measurements in the existing literature.
We formulate a two-stage decision problem with monotropic structure and
systemic measure of risk. The structure is typical for distributed systems
arising in energy networks, robotics, and other practical situations. A
distributed decomposition method for solving the two-stage problem is proposed
and it is applied to a problem arising in communication networks. We have used
this problem to compare the methods of systemic risk evaluation. We show that
the proposed risk aggregation leads to less conservative risk evaluation and
results in a substantially better solution of the problem at hand as compared
to an aggregation of the risk of individual agents and other methods
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