Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools

We consider the problem of computing a spherical crossing-free geodesic drawing of a planar graph: this problem, as well as the closely related spherical parameterization problem, has attracted a lot of attention in the last two decades both in theory and in practice, motivated by a number of applications ranging from texture mapping to mesh remeshing and morphing. Our main concern is to design and implement a linear time algorithm for the computation of spherical drawings provided with theoretical guarantees. While not being aesthetically pleasing, our method is extremely fast and can be used as initial placer for spherical iterative methods and spring embedders. We provide experimental comparison with initial placers based on planar Tutte parameterization. Finally we explore the use of spherical drawings as initial layouts for (Euclidean) spring embedders: experimental evidence shows that this greatly helps to untangle the layout and to reach better local minima

Independence of the transient fluctuation theorem to thermostatting details

The dependence of fluctuation theorem on the precise mathematical details of thermostatting mechanism for an infinite class of fictious time reversible deterministic thermostats was analyzed. Theoretical and numerical analysis were carried out for a class of time reversible deterministic thermostats that fix various moments of the momentum distribution. In this large thermostat the transient fluctuation theorem (TFT) was found dependent of the precise moment that the thermostat fixes. The study shows that in a non-equilibrium system in contact with a thermostat and having large degrees of freedom, the transient fluctuation relation is insensitive to the details of thermostatting mechanisms

Noise Can Reduce Disorder in Chaotic Dynamics

We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or natural measure) is generally highly inhomogeneous over the set, either diminishing or enhancing the contribution of these orbits into system dynamics. We show analytically and numerically a weak noise to reduce this inhomogeneity and, additionally to obvious perturbing impact, make a regularizing influence on the chaotic dynamics. This universal effect is rooted into the nature of deterministic chaos.Comment: 11 pages, 5 figure

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Method and apparatus for controlling vehicle attitude display

A vehicle attitude display such as a Primary Flight Display presents pitch and bank information by displaying a vehicle avatar as fixed, with respect to a moving artificial horizon whilst displaying a movable symbol at a position along the vehicle avatar that is proportional to the symmetry of the vehicle. Parts of the display are dynamically emphasised or de-emphasised to support rapid assimilation of key data. Display format may be dynamically adjusted depending on vehicle use conditions. Display is intended for use both in-vehicle, and remotely

Fast spherical drawing of triangulations: an experimental study of graph drawing tools

International audienceWe consider the problem of computing a spherical crossing-free geodesic drawing of a planar graph: this problem, as well as the closely related spherical parameterization problem, has attracted a lot of attention in the last two decades both in theory and in practice, motivated by a number of applications ranging from texture mapping to mesh remeshing and morphing. Our main concern is to design and implement a linear time algorithm for the computation of spherical drawings provided with theoretical guarantees. While not being aesthetically pleasing, our method is extremely fast and can be used as initial placer for spherical iterative methods and spring embedders. We provide experimental comparison with initial placers based on planar Tutte parameterization. Finally we explore the use of spherical drawings as initial layouts for (Euclidean) spring embedders: experimental evidence shows that this greatly helps to untangle the layout and to reach better local minima