In this note we consider the ansatz for Multiple Schramm-Loewner Evolutions (SLEs) proposed by Bauer, Bernard and Kytölä from a more probabilistic point of view. Here we show their ansatz is a consequence of conformal invariance, reparameterisation invariance and a notion of absolute continuity. In so doing we demonstrate that it is only consistent to grow multiple SLEs if their κ parameters ar...

Silhouettes play a crucial role in visualization, graphics and vision. This work focuses on the global behaviors of silhouettes, especially their topological evolutions, such as their splitting, merging, appearing and disappearing. The dynamics of silhouettes are governed by the topology, the curvature of the surface, and the viewpoint. Some theoretical results are established: the integration ...

In this paper, we attempt to replicate an experiment by Marocco and Nolfi in which a grounded communication system was evolved in robot swarms. We hoped to develop bidirectional communication without any hard-coding by testing neural networks on a navigation task in which effective communication was essential to achieving the best score. In order to build a communication system, controllers wou...

The description of large temporal graphs requires effective methods giving an appropriate mesoscopic partition. Many approaches exist today to detect “communities”, ie groups of nodes that are densely connected (Fortunato, 2010), in static graphs. However, many networks are intrinsically dynamical, and need a dynamic mesoscale description, as interpreting them as static networks would cause...

Regional and metropolitan networks are undergoing rapid transformations, propelled by shifting bandwidth and market paradigms. These evolutions have revealed some serious limitations with legacy SONET/SDH infrastructures and opened up many new avenues for the application of new, maturing optical technologies. This chapter presents a critical look at some of the major evolutions and challenges s...

We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schrödinger evolutions. As a consequence we obtain some uniqueness results that generalize (a weak form of) Hardy’s version of the uncertainty principle. We also obtain corresponding results for heat evolutions.