Dimensionality reduction approaches have been used to exploit the redundancy in a Cartesian coordinate representation of molecular motion by producing low-dimensional representations of molecular motion. This has been used to help visualize complex energy landscapes, to extend the time scales of simulation, and to improve the efficiency of optimization. Until recently, linear approaches for dim...

In soccer, like in business, results are often the best indicator of a team’s performance in a certain competition but insufficient to a coach to asses his team performance. As a consequence, measurement tools play an important role in this particular field. In this research work, a performance tool for soccer, based only in Cartesian coordinates is presented. Capable of calculating final game ...

Cartesian moments are frequently used global geometrical features in computer vision for object pose estimation and recognition. We derive a closed form expression for 3-D Cartesian moment of order p+q+r of a superellipsoid in its canonical coordinate system. We also show how 3-D Cartesian moment of a globally deformed superellipsoid in general position and orientation can be computed as a line...

In certain territories of the East Kazakhstan region (Ust-Kamenogorsk, Semipalatinsk, Ulba object, Zaisan), a method for calculating seismic potential (maximum possible earthquake magnitude) was tested using geomagnetic data: values Z-component calculated in geocentric solar-magnetospheric coordinate system (GSM). Estimates based on data were compared with seismogenic zones territory region, ob...

While it is possible to numerically evolve the relativistic fluid equations using any chosen coordinate mesh, typically there are distinct computational advantages associated with different types of candidate grids. For example, astrophysical flows that are governed by rotation tend to give rise to advection variables that are naturally conserved when a cylindrical mesh is used. On the other ha...

Robot arms require an "arm controller" to command joint motors to achieve a coordinated motion in an external Cartesian coordinate space. In the same sense, robot vehicles require a "vehicle controller" to command the motors to achieve a coordinated motion specified in terms of an external Cartesian coordinate space. This paper presents the design of a general purpose vehicle controller. The ve...

Canonical quantization entails using Cartesian coordinates, and Cartesian coordinates exist only in flat spaces. This situation can either be questioned or accepted. In this paper we offer a brief and introductory overview of how a flat phase space metric can be incorporated into a covariant, coordinate-free quantization procedure involving a continuous-time (Wiener measure) regularization of t...

Implementations of the Bayes filtering for vision based aircraft tracking suffer fundamental difficulties in the Cartesian coordinate. This is because of the uncertainty of the noise model in the flight dynamic equation when the aircraft state is described in these coordinates. Recently, the Logarithmic Polar Coordinate (LPC) framework has been successfully applied in the bearings-only tracking...