Uncovering the spatial structure of mobility networks

The extraction of a clear and simple footprint of the structure of large, weighted and directed networks is a general problem that has many applications. An important example is given by origin-destination matrices which contain the complete information on commuting flows, but are difficult to analyze and compare. We propose here a versatile method which extracts a coarse-grained signature of mobility networks, under the form of a $2\times 2$ matrix that separates the flows into four categories. We apply this method to origin-destination matrices extracted from mobile phone data recorded in thirty-one Spanish cities. We show that these cities essentially differ by their proportion of two types of flows: integrated (between residential and employment hotspots) and random flows, whose importance increases with city size. Finally the method allows to determine categories of networks, and in the mobility case to classify cities according to their commuting structure.Comment: 10 pages, 5 figures +Supplementary informatio

Spatial effect on stochastic dynamics of bistable evolutionary games

We consider the lifetimes of metastable states in bistable evolutionary games (coordination games), and examine how they are affected by spatial structure. A semiclassical approximation based on a path integral method is applied to stochastic evolutionary game dynamics with and without spatial structure, and the lifetimes of the metastable states are evaluated. It is shown that the population dependence of the lifetimes is qualitatively different in these two models. Our result indicates that spatial structure can accelerate the transitions between metastable states

The Spatial Structure of An Accretion Disk

Based on the microlensing variability of the two-image gravitational lens HE1104-1805 observed between 0.4 and 8 microns, we have measured the size and wavelength-dependent structure of the quasar accretion disk. Modeled as a power law in temperature, T proportional to R^-beta, we measure a B-band (0.13 microns in the rest frame) half-light radius of R_{1/2,B} = 6.7 (+6.2 -3.2) x 10^15 cm (68% CL) and a logarithmic slope of beta=0.61 (+0.21 -0.17) for our standard model with a logarithmic prior on the disk size. Both the scale and the slope are consistent with simple thin disk models where beta=3/4 and R_{1/2,B} = 5.9 x 10^15 cm for a Shakura-Sunyaev disk radiating at the Eddington limit with 10% efficiency. The observed fluxes favor a slightly shallower slope, beta=0.55 (+0.03 -0.02), and a significantly smaller size for beta=3/4.Comment: 5 pages, 4 figures, submitted to Ap

Spatially embedded random networks

Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy

We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies. We show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension. We compare and contrast entropy-convergence with mutual-information and structure-factor techniques for quantifying and detecting spatial structure.Comment: 11 pages, 5 figures, http://www.santafe.edu/projects/CompMech/papers/2dnnn.htm

The Jewish 'ghetto': formation and spatial structure

Research into patterns of immigrant settlement has consistently indicated that certain areas of cities are prone to settlement by immigrant groups. This paper proposes that immigrant settlement of such areas may have a particular spacial pattern. Taking the case of the settlement of Leeds, England by Jewish immigrants in the latter six decades of the nineteenth century, we describe the formation of the immigrant Jewish settlement in the area called Leylands.The paper shows first, that Leylands was spacially segregated in comparison with the city overall; and second, that the pattern of settlement was one of intensification of particular streets through time, whereby initially the main, relatively integrated streets were settled, with occupancy moving as time went on to more segregated streets.Analysis of social class defined by occupation suggests that the whole population of Leylands was much poorer than that of Leeds overall. This paper suggests that since the poverty difference was present and possibly more pronounced for the majority, non-Jewish population, that the socio-economic form of the area settlement in Leeds was more likely to have been related to its spacial sgregation than to the social and economic segregation of the immigrant group. It is suggested that the particular characteristics special to certain immigrant groups allowed the Jews of Leylands to overcome their spacial segregation by employing strong social networks on the one hand and through economic mutual help on the other

Spatial structure of Cooper pairs in nuclei

We discuss the spatial structure of the Cooper pair in dilute neutron matter and neutron-rich nuclei by means of the BCS theory and the Skyrme-Hartree-Fock-Bogioliubov model, respectively. The neutron pairing in dilute neutron matter is close to the region of the BCS-BEC crossover in a wide density range, giving rise to spatially compact Cooper pair whose size is smaller than the average interaparticle distance. This behavior extends to moderate low density ($\sim 10^{-1}$ of the saturation density) where the Cooper pair size becomes smallerst ($\sim 5$ fm). The Cooper pair in finite nuclei also exhibits the spatial correlation favoring the coupling of neutrons at small relative distances r \lesim 3 fm with large probability. Neutron-rich nuclei having small neutron separation energy may provide us opportunity to probe the spatial correlation since the neutron pairing and the spatial correlation persists also in an area of low-density neutron distribution extending from the surface to far outside the nucleus.Comment: 13 pages, 5 figures, chapter in "Fifty Years of Nuclear BCS", eds. R.A. Broglia and V.Zelevinsk

Potential and Spatial Structure of Population

The goal of this work is to suggest a mechanism explaining different spatial patterns of residential locations. The basic idea is counterbalance of centripetal and centrifugal forces. This paper complements the previous author's works in this area. This article addresses the following questions: a) agglomeration potential, b) optimal city size, c) equilibrium agricultural density, d) influence of agglomeration on land rent. Both relative location and size distribution of cities and residential patterns in agricultural areas represent interesting objects of study. There exist two main forces, centripetal (agglomeration) and centrifugal (congestion) that shape urban areas. The origin of agglomeration forces is in scale economies, while congestion forces represent a cumulative negative externality from such agglomeration. Following the stylized facts about different production technologies, it is assumed that agricultural technology creates dispersion force (through intensive land use), while industrial technology creates agglomeration force. It is possible to find the optimal city size assuming some scale economies in production counterbalanced by commuting costs. Location heterogeneity is balanced across residents via location rent to bring identical utility. There might be two possibilities: finite optimal size (for low scale economies) and infinitely large city (for high scale economies). The rural community of farmers is also considered. Here the average distance to neighbor (as a proxy to market access) is balanced with the benefits from land ownership. The optimal rural population density is the point maximizing this potential. Finally, the spatial equilibrium is constructed. It consists of discrete cities of optimal size attracting certain fraction of the population and the continuous farmland between them. The concept of potential for agro-industrial cluster is also introduced. It is assumed that rural resident has an access to scale economies in production of a city via commuting, and also has land slot for agricultural activity. There exists equilibrium land rent giving agents identical utility.