Vulnerability of weighted networks

In real networks complex topological features are often associated with a diversity of interactions as measured by the weights of the links. Moreover, spatial constraints may as well play an important role, resulting in a complex interplay between topology, weight, and geography. In order to study the vulnerability of such networks to intentional attacks, these attributes must be therefore considered along with the topological quantities. In order to tackle this issue, we consider the case of the world-wide airport network, which is a weighted heterogeneous network whose evolution and structure are influenced by traffic and geographical constraints. We first characterize relevant topological and weighted centrality measures and then use these quantities as selection criteria for the removal of vertices. We consider different attack strategies and different measures of the damage achieved in the network. The analysis of weighted properties shows that centrality driven attacks are capable to shatter the network's communication or transport properties even at very low level of damage in the connectivity pattern. The inclusion of weight and traffic therefore provides evidence for the extreme vulnerability of complex networks to any targeted strategy and need to be considered as key features in the finding and development of defensive strategies

The Swiss Board Directors Network in 2009

We study the networks formed by the directors of the most important Swiss boards and the boards themselves for the year 2009. The networks are obtained by projection from the original bipartite graph. We highlight a number of important statistical features of those networks such as degree distribution, weight distribution, and several centrality measures as well as their interrelationships. While similar statistics were already known for other board systems, and are comparable here, we have extended the study with a careful investigation of director and board centrality, a k-core analysis, and a simulation of the speed of information propagation and its relationships with the topological aspects of the network such as clustering and link weight and betweenness. The overall picture that emerges is one in which the topological structure of the Swiss board and director networks has evolved in such a way that special actors and links between actors play a fundamental role in the flow of information among distant parts of the network. This is shown in particular by the centrality measures and by the simulation of a simple epidemic process on the directors network.Comment: Submitted to The European Physical Journal

On embeddings of CAT(0) cube complexes into products of trees

We prove that the contact graph of a 2-dimensional CAT(0) cube complex ${\bf X}$ of maximum degree $\Delta$ can be coloured with at most $\epsilon(\Delta)=M\Delta^{26}$ colours, for a fixed constant $M$. This implies that ${\bf X}$ (and the associated median graph) isometrically embeds in the Cartesian product of at most $\epsilon(\Delta)$ trees, and that the event structure whose domain is ${\bf X}$ admits a nice labeling with $\epsilon(\Delta)$ labels. On the other hand, we present an example of a 5-dimensional CAT(0) cube complex with uniformly bounded degrees of 0-cubes which cannot be embedded into a Cartesian product of a finite number of trees. This answers in the negative a question raised independently by F. Haglund, G. Niblo, M. Sageev, and the first author of this paper.Comment: Some small corrections; main change is a correction of the computation of the bounds in Theorem 1. Some figures repaire

Relationships between Arctic sea ice drift and strength modelled by NEMO-LIM3.6

Sea ice cover and thickness have substantially decreased in the Arctic Ocean since the beginning of the satellite era. As a result, sea ice strength has been reduced, allowing more deformation and fracturing and leading to increased sea ice drift speed. We use the version 3.6 of the global ocean–sea ice NEMO-LIM model (Nucleus for European Modelling of the Ocean coupled to the Louvain-la-Neuve sea Ice Model), satellite, buoy and submarine observations, as well as reanalysis data over the period from 1979 to 2013 to study these relationships. Overall, the model agrees well with observations in terms of sea ice extent, concentration and thickness. The seasonal cycle of sea ice drift speed is reasonably well reproduced by the model. NEMO-LIM3.6 is able to capture the relationships between the seasonal cycles of sea ice drift speed, concentration and thickness, with higher drift speed for both lower concentration and lower thickness, in agreement with observations. Model experiments are carried out to test the sensitivity of Arctic sea ice drift speed, thickness and concentration to changes in sea ice strength parameter P*. These show that higher values of P* generally lead to lower sea ice deformation and lower sea ice thickness, and that no single value of P* is the best option for reproducing the observed drift speed and thickness. The methodology proposed in this analysis provides a benchmark for a further model intercomparison related to the relationships between sea ice drift speed and strength, which is especially relevant in the context of the upcoming Coupled Model Intercomparison Project 6 (CMIP6).David Docquier and Antoine Barthélemy work on the PRIMAVERA project (PRocess-based climate sIMulation: AdVances in high-resolution modelling and European climate Risk Assessment), which is funded by the European Commission’s Horizon 2020 programme, grant agreement no. 641727. François Massonnet is funded by the Belgian Fonds National de la Recherche Scientifique (FNRS) and was funded by the Ministerio de Economía, Industria y Competitividad (MINECO). Neil F. Tandon is supported by the Canadian Sea Ice and Snow Evolution (CanSISE) Network. Olivier Lecomte is a research assistant within the Belgian FNRS. The present research benefited from computational resources made available on the Tier-1 supercomputer of the Fédération Wallonie-Bruxelles, infrastructure funded by the Walloon Region under the grant agreement no. 1117545. Computational resources have also been provided by the Consortium des Équipements de Calcul Intensif (CÉCI), funded by the Fonds de la Recherche Scientifique de Belgique (F.R.S.-FNRS) under grant no. 2.5020.11. We would like to thank Hugues Goosse, Martin Vancoppenolle, Jonathan Raulier and Véronique Dansereau for their very helpful comments regarding this study. We also acknowledge Pierre-Yves Barriat for his help in using computing resources at UCL and Damien François for his advice in improving Python scripts. Finally, we thank the editor Dirk Notz and the two anonymous reviewers for helping to improve the original paper.Peer ReviewedPostprint (published version

World citation and collaboration networks: uncovering the role of geography in science

Modern information and communication technologies, especially the Internet, have diminished the role of spatial distances and territorial boundaries on the access and transmissibility of information. This has enabled scientists for closer collaboration and internationalization. Nevertheless, geography remains an important factor affecting the dynamics of science. Here we present a systematic analysis of citation and collaboration networks between cities and countries, by assigning papers to the geographic locations of their authors' affiliations. The citation flows as well as the collaboration strengths between cities decrease with the distance between them and follow gravity laws. In addition, the total research impact of a country grows linearly with the amount of national funding for research & development. However, the average impact reveals a peculiar threshold effect: the scientific output of a country may reach an impact larger than the world average only if the country invests more than about 100,000 USD per researcher annually.Comment: Published version. 9 pages, 5 figures + Appendix, The world citation and collaboration networks at both city and country level are available at http://becs.aalto.fi/~rajkp/datasets.htm

Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients

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

Solvable Metric Growing Networks

Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen to be embedded in a metric arrangement, where the geographic distance between vertices plays a crucial role. The present work proposes a model for growing network that takes into account the geographic distance between vertices: the probability that they are connected is higher if they are located nearer than farther. In this framework, the mean degree of vertices, degree distribution and shortest path length between two randomly chosen vertices are analysed

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