Co-evolution of density and topology in a simple model of city formation

We study the influence that population density and the road network have on each others' growth and evolution. We use a simple model of formation and evolution of city roads which reproduces the most important empirical features of street networks in cities. Within this framework, we explicitely introduce the topology of the road network and analyze how it evolves and interact with the evolution of population density. We show that accessibility issues -pushing individuals to get closer to high centrality nodes- lead to high density regions and the appearance of densely populated centers. In particular, this model reproduces the empirical fact that the density profile decreases exponentially from a core district. In this simplified model, the size of the core district depends on the relative importance of transportation and rent costs.Comment: 13 pages, 13 figure

Statistical Analysis of the Road Network of India

In this paper we study the Indian Highway Network as a complex network where the junction points are considered as nodes, and the links are formed by an existing connection. We explore the topological properties and community structure of the network. We observe that the Indian Highway Network displays small world properties and is assortative in nature. We also identify the most important road-junctions (or cities) in the highway network based on the betweenness centrality of the node. This could help in identifying the potential congestion points in the network. Our study is of practical importance and could provide a novel approach to reduce congestion and improve the performance of the highway networ

On the equivalence between hierarchical segmentations and ultrametric watersheds

We study hierarchical segmentation in the framework of edge-weighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical segmentations. We end this paper by showing how to use the proposed framework in practice in the example of constrained connectivity; in particular it allows to compute such a hierarchy following a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.Comment: 19 pages, double-colum

Optimal Traffic Networks

Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a combination of topological and metric quantities. It is characterized by a strongly heterogeneous traffic, non-trivial correlations between distance and traffic and a broadly distributed centrality. A clear spatial hierarchical organization, with local hubs distributing traffic in smaller regions, emerges as a result of the optimization. Varying the parameters of the cost function, different classes of trees are recovered, including in particular the minimum spanning tree and the shortest path tree. These results suggest that a variational approach represents an alternative and possibly very meaningful path to the study of the structure of complex weighted networks.Comment: 4 pages, 4 figures, final revised versio

Two-dimensional SIR epidemics with long range infection

We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law $p({\bf x})\sim |{\bf x}|^{-\sigma-2}$ for the probability that a site can infect another site a distance vector ${\bf x}$ apart. As in I we present detailed results for the critical case, for the supercritical case with $\sigma = 2$, and for the supercritical case with $0< \sigma < 2$. For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M. Biskup. For $\sigma=2$ we find generic power laws with $\sigma-$dependent exponents in the supercritical phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead of diverging exponentially with the distance from the critical point, the correlation length increases with an inverse power, as in an ordinary critical point. Finally we study the dependence of the critical exponents on $\sigma$ in the regime $0<\sigma <2$, and compare with field theoretic predictions. In particular we discuss in detail whether the critical behavior for $\sigma$ slightly less than 2 is in the short range universality class, as conjectured recently by F. Linder {\it et al.}. As in I we also consider a modified version of the model where only some of the contacts are long range, the others being between nearest neighbors. If the number of the latter reaches the percolation threshold, the critical behavior is changed but the supercritical behavior stays qualitatively the same.Comment: 14 pages, including 29 figure

Gravity model in the Korean highway

We investigate the traffic flows of the Korean highway system, which contains both public and private transportation information. We find that the traffic flow T(ij) between city i and j forms a gravity model, the metaphor of physical gravity as described in Newton's law of gravity, P(i)P(j)/r(ij)^2, where P(i) represents the population of city i and r(ij) the distance between cities i and j. It is also shown that the highway network has a heavy tail even though the road network is a rather uniform and homogeneous one. Compared to the highway network, air and public ground transportation establish inhomogeneous systems and have power-law behaviors.Comment: 13 page

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

Random planar graphs and the London street network

In this paper we analyse the street network of London both in its primary and dual representation. To understand its properties, we consider three idealised models based on a grid, a static random planar graph and a growing random planar graph. Comparing the models and the street network, we find that the streets of London form a self-organising system whose growth is characterised by a strict interaction between the metrical and informational space. In particular, a principle of least effort appears to create a balance between the physical and the mental effort required to navigate the city

The effects of spatial constraints on the evolution of weighted complex networks

Motivated by the empirical analysis of the air transportation system, we define a network model that includes geographical attributes along with topological and weight (traffic) properties. The introduction of geographical attributes is made by constraining the network in real space. Interestingly, the inclusion of geometrical features induces non-trivial correlations between the weights, the connectivity pattern and the actual spatial distances of vertices. The model also recovers the emergence of anomalous fluctuations in the betweenness-degree correlation function as first observed by Guimer\`a and Amaral [Eur. Phys. J. B {\bf 38}, 381 (2004)]. The presented results suggest that the interplay between weight dynamics and spatial constraints is a key ingredient in order to understand the formation of real-world weighted networks

From spin liquid to magnetic ordering in the anisotropic kagome Y-Kapellasite Y3Cu9(OH)19Cl8: a single crystal study

Y3Cu9(OH)19Cl8 realizes an original anisotropic kagome model hosting a rich magnetic phase diagram [M. Hering et al, npj Computational Materials 8, 1 (2022)]. We present an improved synthesis of large phase-pure single crystals via an external gradient method. These crystals were investigated in details by susceptibility, specific heat, thermal expansion, neutron scattering and local muSR and NMR techniques. At variance with polycristalline samples, the study of single crystals gives evidence for subtle structural instabilities at 33K and 13K which preserve the global symmetry of the system and thus the magnetic model. At 2.1K the compound shows a magnetic transition to a coplanar (1/3,1/3) long range order as predicted theoretically. However our analysis of the spin wave excitations yields magnetic interactions which locate the compound closer to the phase boundary to a classical jammed spin liquid phase. Enhanced quantum fluctuations at this boundary may be responsible for the strongly reduced ordered moment of the Cu2+, estimated to be 0.075muB from muSR