Fluctuation scaling in complex systems: Taylor's law and beyond1

Eisler, Zoltán; Bartos, I.; Kertész, János

doi:10.1080/00018730801893043

Cited by 289 publications

(381 citation statements)

References 92 publications

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“…However, the central finding on the existence of two different regimes remains unaffected. The interpretation of FS exponents in terms of correlations assumes that the underlying stochastic process is stationary (32). However, the fact that n i (t) increases over time demonstrates that the system cannot be stationary.…”

Section: Resultsmentioning

confidence: 99%

“…FS has been applied successfully to a number of complex systems whose interacting elements participate in some dynamic process. Examples of application domains range from fluctuations in population sizes in ecology to fluctuations in stock-trading activity in financial markets (30)(31)(32). Here we outline how FS can be used in the current problem, and refer the reader to SI Text for details.…”

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confidence: 99%

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Spontaneous emergence of social influence in online systems

Onnela

Reed‐Tsochas

2010

Proc. Natl. Acad. Sci. U.S.A.

236

212

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Social influence drives both offline and online human behavior. It pervades cultural markets, and manifests itself in the adoption of scientific and technical innovations as well as the spread of social practices. Prior empirical work on the diffusion of innovations in spatial regions or social networks has largely focused on the spread of one particular technology among a subset of all potential adopters. Here we choose an online context that allows us to study social influence processes by tracking the popularity of a complete set of applications installed by the user population of a social networking site, thus capturing the behavior of all individuals who can influence each other in this context. By extending standard fluctuation scaling methods, we analyze the collective behavior induced by 100 million application installations, and show that two distinct regimes of behavior emerge in the system. Once applications cross a particular threshold of popularity, social influence processes induce highly correlated adoption behavior among the users, which propels some of the applications to extraordinary levels of popularity. Below this threshold, the collective effect of social influence appears to vanish almost entirely, in a manner that has not been observed in the offline world. Our results demonstrate that even when external signals are absent, social influence can spontaneously assume an on-off nature in a digital environment. It remains to be seen whether a similar outcome could be observed in the offline world if equivalent experimental conditions could be replicated.collective behavior | social networks | fluctuation scaling S ocial influence captures the ways in which people affect each others' beliefs, feelings, and behaviors. It has traditionally been within the domain of social psychology with a particular focus on microlevel processes among individuals (1), but it also plays a prominent role across the social sciences, for example in the study of contagion in sociology (2), herding behavior in economics (3), speculative bubbles in financial markets (4), voting behavior (5), and interpersonal health (6). Social influence plays an especially important role in cultural markets (7), for products such as books and music, and generally pervades any arena of life where the attitudes and tastes of individuals are influenced by others.It is often useful to distinguish between local and global sources of influence, which typically are identified with an individual's interpersonal environment and the mass media, respectively (8). The overall social influence arises from a mixture of local and global influences, which themselves emerge from different signals. The fact that these two processes operate at very different scales poses considerable challenges for the empirical study of social influence. For the purposes of our study, we define (i) local signal as information on the behavior of individuals who are friends or acquaintances of ego, the person whose behavior is being analyzed, and (ii) global signal as i...

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Spontaneous emergence of social influence in online systems

Onnela

Reed‐Tsochas

2010

Proc. Natl. Acad. Sci. U.S.A.

236

212

View full text Add to dashboard Cite

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“…At the same time this average behavior results from an interesting regime of broad fluctuations obeying a form of Taylor scaling. 58 The numerical experiments concerning the translocation of the globule through a repulsive plane with a hole are perhaps the most interesting both within the context of the present investigation, and in the perspective of future applications. Besides providing a strong support to the postulated form of the topological free energy correction, our results indicate how far reaching can be the influence of n c in determining behaviors such as entropic forces driven by topology.…”

Section: Discussionmentioning

confidence: 99%

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

2014

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The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter depending on the knot kind is an amplitude such that relative probabilities of knots do not vary with the temperature T , in the limit of long chains. We arrive at this conclusion by simulating interacting self-avoiding rings at low T on the cubic lattice, both with unrestricted topology and with setups where the globule is divided by a slip link in two loops (preserving their topology) which compete for the chain length, either in contact or separated by a wall as for translocation through a membrane pore. These findings suggest that in macromolecular environments there may be entropic forces with a purely topological origin, whence portions of polymers holding complex knots should tend to expand at the expense of significantly shrinking other topologically simpler portions. 1

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“…Furthermore, the length of the tail of the τ * R distributions grows with the edge weight for the original sequence, which is in contrast to the uniformly random times sequence for which the variance is smaller for higher weights. To better quantify the difference in relay times within the group of edges with equal weight in Figure 4 (d) we show a scatter plot where each point corresponds to the variance and the average of τ R for an edge group (similar to fluctuation scaling [29]). For the uniformly random times we can use Eq.…”

Section: Spreading Speed On Single Linksmentioning

confidence: 99%

Multiscale analysis of spreading in a large communication network

et al. 2012

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Abstract. In temporal networks, both the topology of the underlying network and the timings of interaction events can be crucial in determining how some dynamic process mediated by the network unfolds. We have explored the limiting case of the speed of spreading in the SI model, set up such that an event between an infectious and susceptible individual always transmits the infection. The speed of this process sets an upper bound for the speed of any dynamic process that is mediated through the interaction events of the network. With the help of temporal networks derived from large-scale time-stamped data on mobile phone calls, we extend earlier results that point out the slowing-down effects of burstiness and temporal inhomogeneities. In such networks, links are not permanently active, but dynamic processes are mediated by recurrent events taking place on the links at specific points in time. We perform a multi-scale analysis and pinpoint the importance of the timings of event sequences on individual links, their correlations with neighboring sequences, and the temporal pathways taken by the networkscale spreading process. This is achieved by studying empirically and analytically different characteristic relay times of links, relevant to the respective scales, and a set of temporal reference models that allow for removing selected time-domain correlations one by one.

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Fluctuation scaling in complex systems: Taylor's law and beyond1

Cited by 289 publications

References 92 publications

Spontaneous emergence of social influence in online systems

Spontaneous emergence of social influence in online systems

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

Multiscale analysis of spreading in a large communication network

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