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Register a new userHidden scaling patterns and universality in written communication
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The temporal statistics exhibited by written correspondence appear to be media dependent, with features which have so far proven difficult to characterize. We explain the origin of these difficulties by disentangling the role of spontaneous activity from decision-based prioritizing processes in human dynamics, clocking all waiting times through each agents `proper time measured by activity. This unveils the same fundamental patterns in written communication across all media (letters, email, sms), with response times displaying truncated power-law behavior and average exponents near -3/2. When standard time is used, the response time probabilities are theoretically predicted to exhibit a bi-modal character, which is empirically borne out by our new years-long data on email. These novel perspectives on the temporal dynamics of human correspondence should aid in the analysis of interaction phenomena in general, including resource management, optimal pricing and routing, information sharing, emergency handling.
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Understanding the patterns of mobility of individuals is crucial for a number of reasons, from city planning to disaster management. There are two common ways of quantifying the amount of travel between locations: by direct observations that often involve privacy issues, e.g., tracking mobile phone locations, or by estimations from models. Typically, such models build on accurate knowledge of the population size at each location. However, when this information is not readily available, their applicability is rather limited. As mobile phones are ubiquitous, our aim is to investigate if mobility patterns can be inferred from aggregated mobile phone call data alone. Using data released by Orange for Ivory Coast, we show that human mobility is well predicted by a simple model based on the frequency of mobile phone calls between two locations and their geographical distance. We argue that the strength of the model comes from directly incorporating the social dimension of mobility. Furthermore, as only aggregated call data is required, the model helps to avoid potential privacy problems.
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Models of social mobility inspired by the Newtons law of gravity have been used for several decades to describe migrations of people, goods, and information. Despite an eminent reference and widespread use, these models lack the background theory, being often viewed as a collection of empirical recipes which rely on adjustable parameters. Here we propose a tractable and fundamental mechanism of social mobility, which explains distance scaling of migration flows and predicts the value of the scaling exponent. The mechanism reveals two key aspects framing social flows, which have direct analogy in physics: symmetry and dissipation. In particular, we identify the conditions for the social gravity scaling, when the power law exponent equals 2, and explain deviations from this behaviour, including saturation transitions. The resulting flow distribution is determined by the spatial structure of the underlying social network, rather than by distance explicitly. The theory is verified for residential migration in suburb networks of major Australian cities with diverse structure, population and size. The mechanism is directly translatable to other social contexts, such as flows of goods or information, and provides a universal understanding of how dynamic patterns of social mobility emerge from structural network properties.
Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are within those systems known to exhibit a discontinuous dynamical transition with a two step relaxation. We consider a general scaling approach, within mean field theory, for such systems by considering the behavior of the density correlator <q(t)> and the dynamical susceptibility <q^2(t)> -<q(t)>^2. Focusing on the Fredrickson and Andersen (FA) facilitated spin model on the Bethe lattice, we extend a cluster approach that was previously developed for continuous glass transitions by Arenzon et al (Phys. Rev. E 90, 020301(R) (2014)) to describe the decay to the plateau, and consider a damage spreading mechanism to describe the departure from the plateau. We predict scaling laws, which relate dynamical exponents to the static exponents of mean field bootstrap percolation. The dynamical behavior and the scaling laws for both density correlator and dynamical susceptibility coincide with those predicted by MCT. These results explain the origin of scaling laws and the universal behavior associated with the glass transition in mean field, which is characterized by the divergence of the static length of the bootstrap percolation model with an upper critical dimension d_c=8.
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