Inf-semilattice approach to self-dual morphology

Today, the theoretical framework of mathematical morphology is phrased in terms of complete lattices and operators defined on them. That means in particular that the choice of the underlying partial ordering is of eminent importance, as it determines the class of morphological operators that one ends up with. The duality principle for partially ordered sets, which says that the opposite of a partial ordering is also a partial ordering, gives rise to the fact that all morphological operators occur in pairs, e.g., dilation and erosion, opening and closing, etc. This phenomenon often prohibits the construction of tools that treat foreground and background of signals in exactly the same way. In this paper we discuss an alternative framework for morphological image processing that gives rise to image operators which are intrinsically self-dual. As one might expect, this alternative framework is entirely based upon the definition of a new self-dual partial ordering

Unraveling Coordination Problems

Strategic uncertainty complicates policy design in coordination games. To rein in strategic uncertainty, the planner in this paper connects the problem of policy design to that of equilibrium selection using a global games approach. We characterize the subsidy scheme that induces coordination on a given outcome of the game as its unique equilibrium. Optimal subsidies are symmetric for identical players, continuous functions of model parameters, and do not make the targeted strategies strictly dominant for any of the players; these properties differ starkly from canonical results in the literature. Uncertainty about payoffs impels policy moderation as aggressive intervention might itself induce coordination failure. JEL codes: D81, D82, D83, D86, H20. Keywords: mechanism design, global games, contracting with externalities, unique implementation

Nanosecond repetitively pulsed discharges in N2-O2 mixtures: Inception cloud and streamer emergence

We evaluate the nanosecond temporal evolution of tens of thousands of positive discharges in a 16 cm point-plane gap in high purity nitrogen 6.0 and in N2–O2 gas mixtures with oxygen contents of 100 ppm, 0.2%, 2% and 20%, for pressures between 66.7 and 200 mbar. The voltage pulses have amplitudes of 20 to 40 kV with rise times of 20 or 60 ns and repetition frequencies of 0.1 to 10 Hz. The discharges first rapidly form a growing cloud around the tip, then they expand much more slowly like a shell and finally after a stagnation stage they can break up into rapid streamers. The radius of cloud and shell in artificial air is about 10% below the theoretically predicted value and scales with pressure p as theoretically expected, while the observed scaling of time scales with p raises questions. We find characteristic dependences on the oxygen content. No cloud and shell stage can be seen in nitrogen 6.0, and streamers emerge immediately. The radius of cloud and shell increases with oxygen concentration. On the other hand, the stagnation time after the shell phase is maximal for the intermediate oxygen concentration of 0.1% and the number of streamers formed is minimal; here the cloud and shell phase seem to be particularly stable against destabilization into streamers

Image decompositions and transformations as peaks and wells

10 pages to be submitted to ISMM2011International audienceAn image may be decomposed as a difference between an image of peaks and an image of wells. Applying a morphological operator to these two components before reconstructing a final image produces interesting filters for grey tone or binary images. This decomposition depends upon the point of view from where the image is considered

Hierarchical characterization of complex networks

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work discusses on how the concepts of hierarchical node degree and hierarchical clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, can be used in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.Comment: 19 pages, 23 figure

Multivariate risks and depth-trimmed regions

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this abstract axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from the multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship.Comment: 26 pages. Substantially revised version with a number of new results adde