16,538 research outputs found
Universal features of correlated bursty behaviour
Inhomogeneous temporal processes, like those appearing in human
communications, neuron spike trains, and seismic signals, consist of
high-activity bursty intervals alternating with long low-activity periods. In
recent studies such bursty behavior has been characterized by a fat-tailed
inter-event time distribution, while temporal correlations were measured by the
autocorrelation function. However, these characteristic functions are not
capable to fully characterize temporally correlated heterogenous behavior. Here
we show that the distribution of the number of events in a bursty period serves
as a good indicator of the dependencies, leading to the universal observation
of power-law distribution in a broad class of phenomena. We find that the
correlations in these quite different systems can be commonly interpreted by
memory effects and described by a simple phenomenological model, which displays
temporal behavior qualitatively similar to that in real systems
Temporal Networks
A great variety of systems in nature, society and technology -- from the web
of sexual contacts to the Internet, from the nervous system to power grids --
can be modeled as graphs of vertices coupled by edges. The network structure,
describing how the graph is wired, helps us understand, predict and optimize
the behavior of dynamical systems. In many cases, however, the edges are not
continuously active. As an example, in networks of communication via email,
text messages, or phone calls, edges represent sequences of instantaneous or
practically instantaneous contacts. In some cases, edges are active for
non-negligible periods of time: e.g., the proximity patterns of inpatients at
hospitals can be represented by a graph where an edge between two individuals
is on throughout the time they are at the same ward. Like network topology, the
temporal structure of edge activations can affect dynamics of systems
interacting through the network, from disease contagion on the network of
patients to information diffusion over an e-mail network. In this review, we
present the emergent field of temporal networks, and discuss methods for
analyzing topological and temporal structure and models for elucidating their
relation to the behavior of dynamical systems. In the light of traditional
network theory, one can see this framework as moving the information of when
things happen from the dynamical system on the network, to the network itself.
Since fundamental properties, such as the transitivity of edges, do not
necessarily hold in temporal networks, many of these methods need to be quite
different from those for static networks
Temporal Features as Measures of Tie Strength in Mobile Phone Networks
The use of auto-recorded communication data, such as mobile phone call logs, has reshaped our capacity to model and understand of social systems. In such studies, the strength of a tie between two people has been of great value from both theoretical and sociological perspectives, yet it is not easy to quantify. Tie strengths are commonly measured in terms of communication intensity (number or duration of calls, etc) as a form of convenience rather than a justified choice, yet these intensity-based measures do not uncover the myriad of ways in which such intensity takes place, hindering information about the strength of ties. Here, we conceive tie strength as a latent variable we want to predict based on features of the time sequences of interactions. We assume that tie strength is expressed as the structural overlap in social networks, in a manner inspired by Granovetter's hypothesis, where strong ties are embedded in community structures, while weak ties serve as inter-community bridges. With this assumption, we use temporal and static features to predict overlap in lieu of the latent tie strength. We analyze a mobile phone dataset of ~6.5 million people for a period of 4 months, and measure overlap based on an extended network of ~77 million users, to ensure minimal sampling errors. We observe a strong relationship between local topology and tie-level behaviour, with some temporal features outperforming communication intensity in overlap prediction. Indeed, the number of bursty cascades, differences in daily behaviour and temporal stability play large roles in our models. We find that communication intensity is one of many characterizations of tie strength for which the Granovetter effect is observable
Techniques for the Fast Simulation of Models of Highly dependable Systems
With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system
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
- …