21,990 research outputs found
Recurrence networks - A novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing structural properties of
time series from complex systems. Starting from the concept of recurrences in
phase space, the recurrence matrix of a time series is interpreted as the
adjacency matrix of an associated complex network which links different points
in time if the evolution of the considered states is very similar. A critical
comparison of these recurrence networks with similar existing techniques is
presented, revealing strong conceptual benefits of the new approach which can
be considered as a unifying framework for transforming time series into complex
networks that also includes other methods as special cases.
It is demonstrated that there are fundamental relationships between the
topological properties of recurrence networks and the statistical properties of
the phase space density of the underlying dynamical system. Hence, the network
description yields new quantitative characteristics of the dynamical complexity
of a time series, which substantially complement existing measures of
recurrence quantification analysis
Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods
Complex network theory provides a powerful framework to statistically
investigate the topology of local and non-local statistical interrelationships,
i.e. teleconnections, in the climate system. Climate networks constructed from
the same global climatological data set using the linear Pearson correlation
coefficient or the nonlinear mutual information as a measure of dynamical
similarity between regions, are compared systematically on local, mesoscopic
and global topological scales. A high degree of similarity is observed on the
local and mesoscopic topological scales for surface air temperature fields
taken from AOGCM and reanalysis data sets. We find larger differences on the
global scale, particularly in the betweenness centrality field. The global
scale view on climate networks obtained using mutual information offers
promising new perspectives for detecting network structures based on nonlinear
physical processes in the climate system.Comment: 24 pages, 10 figure
Complex Network Tools to Understand the Behavior of Criminality in Urban Areas
Complex networks are nowadays employed in several applications. Modeling
urban street networks is one of them, and in particular to analyze criminal
aspects of a city. Several research groups have focused on such application,
but until now, there is a lack of a well-defined methodology for employing
complex networks in a whole crime analysis process, i.e. from data preparation
to a deep analysis of criminal communities. Furthermore, the "toolset"
available for those works is not complete enough, also lacking techniques to
maintain up-to-date, complete crime datasets and proper assessment measures. In
this sense, we propose a threefold methodology for employing complex networks
in the detection of highly criminal areas within a city. Our methodology
comprises three tasks: (i) Mapping of Urban Crimes; (ii) Criminal Community
Identification; and (iii) Crime Analysis. Moreover, it provides a proper set of
assessment measures for analyzing intrinsic criminality of communities,
especially when considering different crime types. We show our methodology by
applying it to a real crime dataset from the city of San Francisco - CA, USA.
The results confirm its effectiveness to identify and analyze high criminality
areas within a city. Hence, our contributions provide a basis for further
developments on complex networks applied to crime analysis.Comment: 7 pages, 2 figures, 14th International Conference on Information
Technology : New Generation
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