Long-Range Connections in Transportation Networks

Since its recent introduction, the small-world effect has been identified in several important real-world systems. Frequently, it is a consequence of the existence of a few long-range connections, which dominate the original regular structure of the systems and implies each node to become accessible from other nodes after a small number of steps, typically of order $\ell \propto \log N$. However, this effect has been observed in pure-topological networks, where the nodes have no spatial coordinates. In this paper, we present an alalogue of small-world effect observed in real-world transportation networks, where the nodes are embeded in a hree-dimensional space. Using the multidimensional scaling method, we demonstrate how the addition of a few long-range connections can suubstantially reduce the travel time in transportation systems. Also, we investigated the importance of long-range connections when the systems are under an attack process. Our findings are illustrated for two real-world systems, namely the London urban network (streets and underground) and the US highways network enhanced by some of the main US airlines routes

The simplicity of planar networks

Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a non trivial and non local information about the spatial organization of these graphs. We define the simplicity index as the average ratio of these lengths and the simplicity profile characterizes the simplicity at different scales. We measure these metrics on artificial (roads, highways, railways) and natural networks (leaves, slime mould, insect wings) and show that there are fundamental differences in the organization of urban and biological systems, related to their function, navigation or distribution: straight lines are organized hierarchically in biological cases, and have random lengths and locations in urban systems. In the case of time evolving networks, the simplicity is able to reveal important structural changes during their evolution.Comment: 8 pages, 4 figure

On time-varying collaboration networks

The patterns of scientific collaboration have been frequently investigated in terms of complex networks without reference to time evolution. In the present work, we derive collaborative networks (from the arXiv repository) parameterized along time. By defining the concept of affine group, we identify several interesting trends in scientific collaboration, including the fact that the average size of the affine groups grows exponentially, while the number of authors increases as a power law. We were therefore able to identify, through extrapolation, the possible date when a single affine group is expected to emerge. Characteristic collaboration patterns were identified for each researcher, and their analysis revealed that larger affine groups tend to be less stable

Lattice Model of an Ionic Liquid at an Electrified Interface

We study ionic liquids interacting with electrified interfaces. The ionic fluid is modeled as a Coulomb lattice gas. We compare the ionic density profiles calculated using a popular modified Poisson-Boltzmann equation with the explicit Monte Carlo simulations. The modified Poisson-Boltzmann theory fails to capture the structural features of the double layer and is also unable to correctly predict the ionic density at the electrified interface. The lattice Monte Carlo simulations qualitatively capture the coarse-grained structure of the double layer in the continuum. We propose a convolution relation that semiquantitatively relates the ionic density profiles of a continuum ionic liquid and its lattice counterpart near an electrified interface

Reply to 'Comment on "Vortex distribution in a confining potential"

We argue that contrary to recent suggestions, non-extensive statistical mechanics has no relevance for inhomogeneous systems of particles interacting by short-range potentials. We show that these systems are perfectly well described by the usual Boltzmann-Gibbs statistical mechanics

Mapping road network communities for guiding disease surveillance and control strategies

Human mobility is increasing in its volume, speed and reach, leading to the movement and introduction of pathogens through infected travelers. An understanding of how areas are connected, the strength of these connections and how this translates into disease spread is valuable for planning surveillance and designing control and elimination strategies. While analyses have been undertaken to identify and map connectivity in global air, shipping and migration networks, such analyses have yet to be undertaken on the road networks that carry the vast majority of travellers in low and middle income settings. Here we present methods for identifying road connectivity communities, as well as mapping bridge areas between communities and key linkage routes. We apply these to Africa, and show how many highly-connected communities straddle national borders and when integrating malaria prevalence and population data as an example, the communities change, highlighting regions most strongly connected to areas of high burden. The approaches and results presented provide a flexible tool for supporting the design of disease surveillance and control strategies through mapping areas of high connectivity that form coherent units of intervention and key link routes between communities for targeting surveillance.Comment: 11 pages, 5 figures, research pape