The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools and procedures to analyse the statistical properties of networks defined by arbitrary degree distributions and other constraints. Doing so reveals the highly ...

We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit spaces. For time-frequency molecules we recover some boundedness results on modulation spaces, for time-scale molecules we obtain the boundedness on homogeno...

earthquakes are a particular concern because of the serious hazard they present. the existence of seismicity patterns such as the foreshock and aftershock clusters, doughnut pattern, seismic quiescence etc show that the earthquake occurrence in the active tectonic regions is not random and clustering phenomena are obvious characteristics of these events in space and time. fractal analysis, as a...

Demand response Allows the management of customer consumption of electricity in response to supply conditions. Distributed generation Electric energy that is distributed to the grid from many decentralized locations, such as from wind farms and solar panel installations. Distribution grid The part of the grid dedicated to delivering electric energy directly to residential, commercial, and indus...

This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation c x ∂t u − Δu 0 in a bounded smooth domain in R from partial on part of the boundary dynamic boundary measurements. In this paper, we prove that the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subset Γ of the boundary determines explicitly the co...

This paper addresses the local grid map-building problem. Sensor readings are interpreted using a feedforward neural network, and a Bayesian rule is used to update the occupancy probabilities of the grid cells. A comparison of three neural network configurations is made in the map building of indoor environments, using the sonar sensors of the Nomad 200 simulator. The architecture with best res...