Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented.Comment: 36 pages, 18 figure

Voronoi Drawings of Trees

This paper investigates the following problem: Given a tree T, can we find a set of points in the plane such that the Voronoi diagram of this set of points is a drawing of T? We study trees that can be drawn as Voronoi diagrams both in the Euclidean and in the Manhattan metric. Characterizations of drawable trees are given and different drawing algorithms that take into account additional geometric constraints are presented

Exploring the effects of colouring graph diagrams on people of various backgrounds

Colour is one of the primary aesthetic elements of a visualization. It is often used successfully to encode information such as the importance of a particular part of the diagram or the relationship between two parts. Even so, there are few investigations into the human reading of colour coding on diagrams from the scientific community. In this paper we report on an experiment with graph diagrams comparing a black and white composition with two other colour treatments. We drew our subjects from engineering, art, visual design, physical education, tourism, psychology and social science disciplines. We found that colouring the nodes of interest reduced the time taken to find the shortest path between the two nodes for all subjects. Engineers, tourism and social scientists proved significantly faster with artist/designers just below the overall average speed. From this study, we contribute that adding particular colour treatments to diagrams increases legibility. In addition, preliminary work investigating colour treatments and schemes indicates potential for future gains. © 2014 Springer-Verlag

Interpretability in Fuzzy Systems Optimization: A Topological Approach

International audienceWhen dealing with complex problems, it is often the case that fuzzy systems must undergo an optimization process. During this process, the preservation of interpretability is a major concern. Here we present a new mathematical framework to analyze the notion of interpretability of a fuzzy partition, and a generic algorithm to preserve it. This approach is rather flexible and it helps to highly automatize the optimization process. Some tools come from the field of algebraic topology