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

Structure comparison of binary and weighted niche-overlap graphs

In ecological networks, niche-overlap graphs are considered as complex systems. They represent the competition between two predators that share common resources. The purpose of this paper is to investigate the structural properties of these graphs considered as weighted networks and compare their measures with the ones calculated for the binary networks. To conduct this study, we select four classical network measures : the degree of nodes, the clustering coefficient, the assortativity, and the betweenness centrality. These measures were used to analyse different type of networks such as social networks, biological networks, world wide web, etc. Interestingly, we identify significant differences between the structure of the binary and the weighted niche-overlap graphs. This study indicates that weight information reveals different features that may provide other implications on the dynamics of these networks

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

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

Filtering and Tracking with Trinion-Valued Adaptive Algorithms

A new model for three-dimensional processes based on the trinion algebra is introduced for the first time. Compared with the pure quaternion model, the trinion model is more compact and computationally more efficient, while having similar or comparable performance in terms of adaptive linear filtering. Moreover, the trinion model can effectively represent the general relationship of state evolution in Kalman filtering, where the pure quaternion model fails. Simulations on real-world wind recordings and synthetic data sets are provided to demonstrate the potentials of this new modeling method

Single or Multiple Consensus for Linear Orders

International audienc

Modeling positive and negative pieces of evidence in uncertainty

International audienceIn Dempster-Shafer theory, belief degrees on any subset A ⊆ Ω of states of nature are computed through a basic belief massm(A), that quantifies the strength of the statement: “the agent has some reason to believe that the true world is in A”. We may be interested into representing some negative belief, as for example: “the agent has some reason not to believe that the true world is in A”. However, as remarked by Smets, this is not allowed in the theory of Dempster-Shafer. Attempts to model this situation have been proposed by Smets, and by Dubois, Prade and Smets in the framework of possibility theory. These solutions however, do not seem to be able to handle all the facets of the problem, and have the drawback to come up with an interval or a pair of values. In this paper, we propose an alternative solution consisting in assigning a single number to a pair of events