Integrating Hamiltonian systems defined on the Lie groups SO(4) and SO(1,3)

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E³, the spheres S³ and the hyperboloids H³ with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions is illustrated.

A new solution of the rendering equation with stratified Monte Carlo approach

This paper is turned to the advanced Monte Carlo methods for realistic image creation. It offers a new stratified approach for solving the rendering equation. We consider the numerical solution of the rendering equation by separation of integration domain. The hemispherical integration domain is symmetrically separated into 16 parts. First 9 sub-domains are equal size of orthogonal spherical triangles. They are symmetric each to other and grouped with a common vertex around the normal vector to the surface. The hemispherical integration domain is completed with more 8 sub-domains of equal size spherical quadrangles, also symmetric each to other. All sub-domains have fixed vertices and computable parameters. The bijections of unit square into an orthogonal spherical triangle and into a spherical quadrangle are derived and used to generate sampling points. Then, the symmetric sampling scheme is applied to generate the sampling points distributed over the hemispherical integration domain. The necessary transformations are made and the stratified Monte Carlo estimator is presented. The rate of convergence is obtained and one can see that the algorithm is of super-convergent type.

Quasi Monte Carlo approach with uniform separation for solving of the rendering equation, ICNAAM 2007

This paper is directed to the advanced parallel Quasi Monte Carlo (QMC) methods for realistic image synthesis. We propose and consider a new QMC approach for solving the rendering equation with uniform separation. First, we apply the symmetry property for uniform separation of the hemispherical integration domain into 24 equal sub-domains of solid angles, subtended by orthogonal spherical triangles with fixed vertices and computable parameters. Uniform separation allows to apply parallel sampling scheme for numerical integration. Finally, we apply the stratified QMC integration method for solving the rendering equation. The superiority our QMC approach is proved.

Hybrid fault detection and isolation in an heater bank of an HVAC system

In this work a hybrid technique that includes probabilistic and optimization based methods is presented. The method is applied, both in simulation and by means of real-time experiments, to the heating unit of a Heating, Ventilation Air Conditioning (HVAC) system. It is shown that the addition of the probabilistic approach improves the fault diagnosis accuracy.

Distributed space-time block coding for 3 and 4 relay nodes: Imperfect synchronisation and a solution

Most research on distributed space time block coding (STBC) has so far focused on the case of 2 relay nodes and assumed that the relay nodes are perfectly synchronised at the symbol level. By applying STBC to 3-or 4-relay node systems, this paper shows that imperfect synchronisation causes significant performance degradation to the conventional detector. To this end, we propose a new STBC detection solution based on the principle of parallel interference cancellation (PIC). The PIC detector is moderate in computational complexity but is very effective in suppressing the impact of imperfect synchronisation.

Integrated optics for nulling interferometry in the thermal infrared: progress and recent achievements

The search for Earth-like exoplanets, orbiting in the habitable zone of stars other than our Sun and showing biological activity, is one of the most exciting and challenging quests of the present time. Nulling interferometry from space, in the thermal infrared, appears as a promising candidate technique for the task of directly observing extra-solar planets. It has been studied for about 10 years by ESA and NASA in the framework of the Darwin and TPF-I missions respectively. Nevertheless, nulling interferometry in the thermal infrared remains a technological challenge at several levels. Among them, the development of the "modal filter" function is mandatory for the filtering of the wavefronts in adequacy with the objective of rejecting the central star flux to an efficiency of about 105. Modal filtering takes benefit of the capability of single-mode waveguides to transmit a single amplitude function, to eliminate virtually any perturbation of the interfering wavefronts, thus making very high rejection ratios possible. The modal filter may either be based on single-mode Integrated Optics (IO) and/or Fiber Optics. In this paper, we focus on IO, and more specifically on the progress of the on-going "Integrated Optics" activity of the European Space Agency.