Social structures influence a variety of human behaviors including mobility patterns, but the extent to which one individuals movements can predict anothers remains an open question. Further, latent information about an individuals mobility can be pr
esent in the mobility patterns of both social and non-social ties, a distinction that has not yet been addressed. Here we develop a colocation network to distinguish the mobility patterns of an egos social ties from those of non-social colocators, individuals not socially connected to the ego but who nevertheless arrive at a location at the same time as the ego. We apply entropy and predictability measures to analyse and bound the predictive information of an individuals mobility pattern and the flow of that information from their top social ties and from their non-social colocators. While social ties generically provide more information than non-social colocators, we find that significant information is present in the aggregation of non-social colocators: 3-7 colocators can provide as much predictive information as the top social tie, and colocators can replace up to 85% of the predictive information about an ego, compared with social ties that can replace up to 94% of the egos predictability. The presence of predictive information among non-social colocators raises privacy concerns: given the increasing availability of real-time mobility traces from smartphones, individuals sharing data may be providing actionable information not just about their own movements but the movements of others whose data are absent, both known and unknown individuals.
Given the rapid recent trend of urbanization, a better understanding of how urban infrastructure mediates socioeconomic interactions and economic systems is of vital importance. While the accessibility of location-enabled devices as well as large-sca
le datasets of human activities, has fueled significant advances in our understanding, there is little agreement on the linkage between socioeconomic status and its influence on movement patterns, in particular, the role of inequality. Here, we analyze a heavily aggregated and anonymized summary of global mobility and investigate the relationships between socioeconomic status and mobility across a hundred cities in the US and Brazil. We uncover two types of relationships, finding either a clear connection or little-to-no interdependencies. The former tend to be characterized by low levels of public transportation usage, inequitable access to basic amenities and services, and segregated clusters of communities in terms of income, with the latter class showing the opposite trends. Our findings provide useful lessons in designing urban habitats that serve the larger interests of all inhabitants irrespective of their economic status.
Given the rapidly evolving landscape of linguistic prevalence, whereby a majority of the worlds existing languages are dying out in favor of the adoption of a comparatively fewer set of languages, the factors behind this phenomenon has been the subje
ct of vigorous research. The majority of approaches investigate the temporal evolution of two competing languages in the form of differential equations describing their behavior at large scale. In contrast, relatively few consider the spatial dimension of the problem. Furthermore while much attention has focused on the phenomena of language shift---the adoption of majority languages in lieu of minority ones---relatively less light has been shed on linguistic coexistence, where two or more languages persist in a geographically contiguous region. Here, we study the geographical component of language spread on a discrete medium to monitor the dispersal of language species at a microscopic level. Language dynamics is modeled through a reaction-diffusion system that occurs on a heterogeneous network of contacts based on population flows between urban centers. We show that our framework accurately reproduces empirical linguistic trends driven by a combination of the Turing instability, a mechanism for spontaneous pattern-formation applicable to many natural systems, the heterogeneity of the contact network, and the asymmetries in how people perceive the status of a language. We demonstrate the robustness of our formulation on two datasets corresponding to linguistic coexistence in northern Spain and southern Austria.
The recent availability of digital traces from Information and Communications Technologies (ICT) has facilitated the study of both individual- and population-level movement with unprecedented spatiotemporal resolution, enabling us to better understan
d a plethora of socioeconomic processes such as urbanization, transportation, impact on the environment and epidemic spreading to name a few. Using empirical spatiotemporal trends, several mobility models have been proposed to explain the observed regularities in human movement. With the advent of the World Wide Web, a new type of virtual mobility has emerged that has begun to supplant many traditional facets of human activity. Here we conduct a systematic analysis of physical and virtual movement, uncovering both similarities and differences in their statistical patterns. The differences manifest themselves primarily in the temporal regime, as a signature of the spatial and economic constraints inherent in physical movement, features that are predominantly absent in the virtual space. We demonstrate that once one moves to the time-independent space of events, i.e the sequences of visited locations, these differences vanish, and the statistical patterns of physical and virtual mobility are identical. The observed similarity in navigating these markedly different domains point towards a common mechanism governing the movement patterns, a feature we describe through a Metropolis-Hastings type optimization model, where individuals navigate locations through decision-making processes resembling a cost-benefit analysis of the utility of locations. In contrast to existing phenomenological models of mobility, we show that our model can reproduce the commonalities in the empirically observed statistics with minimal input.
Starting from our recent chemical master equation derivation of the model of an autocatalytic reaction-diffusion chemical system with reactions $U+2V {stackrel {lambda_0}{rightarrow}}~ 3 V;$ and $V {stackrel {mu}{rightarrow}}~P$, $U {stackrel { u}{ri
ghtarrow}}~ Q$, we determine the effects of intrinsic noise on the momentum-space behavior of its kinetic parameters and chemical concentrations. We demonstrate that the intrinsic noise induces $n rightarrow n$ molecular interaction processes with $n geq 4$, where $n$ is the number of molecules participating of type $U$ or $V$. The momentum dependences of the reaction rates are driven by the fact that the autocatalytic reaction (inelastic scattering) is renormalized through the existence of an arbitrary number of intermediate elastic scatterings, which can also be interpreted as the creation and subsequent decay of a three body composite state $sigma = phi_u phi_v^2$, where $phi_i$ corresponds to the fields representing the densities of $U$ and $V$. Finally, we discuss the difference between representing $sigma$ as a composite or an elementary particle (molecule) with its own kinetic parameters. In one dimension we find that while they show markedly different behavior in the short spatio-temporal scale, high momentum (UV) limit, they are formally equivalent in the large spatio-temporal scale, low momentum (IR) regime. On the other hand in two dimensions and greater, due to the effects of fluctuations, there is no way to experimentally distinguish between a fundamental and composite $sigma$. Thus in this regime $sigma$ behave as an entity unto itself suggesting that it can be effectively treated as an independent chemical species.
We give a first principles derivation of the stochastic partial differential equations that describe the chemical reactions of the Gray-Scott model (GS): $U+2V {stackrel {lambda}{rightarrow}} 3 V;$ and $V {stackrel {mu}{rightarrow}} P$, $U {stackrel
{ u}{rightarrow}} Q$, with a constant feed rate for $U$. We find that the conservation of probability ensured by the chemical master equation leads to a modification of the usual differential equations for the GS model which now involves two composite fields and also intrinsic noise terms. One of the composites is $psi_1 = phi_v^2$, where $ < phi_v >_{eta} = v$ is the concentration of the species $V$ and the averaging is over the internal noise $eta_{u,v,psi_1}$. The second composite field is the product of three fields $ chi = lambda phi_u phi_v^2$ and requires a noise source to ensure probability conservation. A third composite $psi_2 = phi_{u} phi_{v}$ can be also be identified from the noise-induced reactions. The Hamiltonian that governs the time evolution of the many-body wave function, associated with the master equation, has a broken U(1) symmetry related to particle number conservation. By expanding around the (broken symmetry) zero energy solution of the Hamiltonian (by performing a Doi shift) one obtains from our path integral formulation the usual reaction diffusion equation, at the classical level. The Langevin equations that are derived from the chemical master equation have multiplicative noise sources for the density fields $phi_u, phi_v, chi$ that induce higher order processes such as $n rightarrow n$ scattering for $n > 3$. The amplitude of the noise acting on $ phi_v$ is itself stochastic in nature.
In the last few years we have witnessed the emergence, primarily in on-line communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is the folks
onomy, a tripartite structure of users, resources, and tags -- labels collaboratively applied by the users to the resources in order to impart meaningful structure on an otherwise undifferentiated database. Here we propose a mathematical model of such tripartite structures which represents them as random hypergraphs. We show that it is possible to calculate many properties of this model exactly in the limit of large network size and we compare the results against observations of a real folksonomy, that of the on-line photography web site Flickr. We show that in some cases the model matches the properties of the observed network well, while in others there are significant differences, which we find to be attributable to the practice of multiple tagging, i.e., the application by a single user of many tags to one resource, or one tag to many resources.
There has been a considerable amount of interest in recent years on the robustness of networks to failures. Many previous studies have concentrated on the effects of node and edge removals on the connectivity structure of a static network; the networ
ks are considered to be static in the sense that no compensatory measures are allowed for recovery of the original structure. Real world networks such as the world wide web, however, are not static and experience a considerable amount of turnover, where nodes and edges are both added and deleted. Considering degree-based node removals, we examine the possibility of preserving networks from these types of disruptions. We recover the original degree distribution by allowing the network to react to the attack by introducing new nodes and attaching their edges via specially tailored schemes. We focus particularly on the case of non-uniform failures, a subject that has received little attention in the context of evolving networks. Using a combination of analytical techniques and numerical simulations, we demonstrate how to preserve the exact degree distribution of the studied networks from various forms of attack.
