Energy equation for turbulent flow in a rotating system was derived in terms of second order correlation tensors, where the correlation tensors were functions of space coordinates, distance between two points and time. To reveal the relationship of turbulent energy between two points, one point was taken as origin of the coordinate system. Due to rotation, the Coriolis force played an important...

Network coordinates (NC) system is an efficient mechanism for Internet distance prediction with scalable measurements. The intrinsical cause for the unsatisfactory accuracy of the simulation-based NC algorithms has been identified. Then Pharos, a fully decentralised and hierarchical scheme, is proposed to solve this problem. Pharos leverages multiple coordinate sets at different distance scales...

A coordinate system is described which provides a natural means for representing hexagonally-organized pixels. The coordinate system has the unusual property that its basis vectors are not orthogonal. Vector-space properties and operations are described in this coordinate system, and shown to be straightforward computations. Some image processing algorithms, including calculations of image grad...

In modern multivariate statistical analysis, affine invariance or equivariance for statistical procedures are properties of paramount interest and importance. A statistical procedure lacking such a property can sometimes acquire it if carried out not on the original data but rather on suitably transformed data, in some cases accompanied by a retransformation back to the original coordinate syst...

A standard approach to tracking is to use the Extended Kalman Filter (EKF) applied to a non-linear state-space model. We will compare two conceivable choices of state variables for modeling civil aircrafts. One where Cartesian velocities are used and one where absolute velocity and heading angle are used. In both choices, Cartesian coordinates are used for position and angular velocity for turn...

2. Hamiltonian Dynamics ................... 6 -2.1 Equations of Motion .................. 6 2.2 Symmetry, Integrals, and Cyclic Coordinates ....... 7 2.3 Motion Near a Known Periodic Solution ......... 8 2.4 Change of Independent Variable ............. 9 2.5 The Motion of a Particle in an Accelerator ........ 10 2.6 Floquet’s Theorem .................. 13 2.7 Higher-Order Terms ...................

Path integration is a navigation strategy widely observed in nature where an animal maintains a running estimate, called the home vector, of its location during an excursion. Evidence suggests it is both ancient and ubiquitous in nature, and has been studied for over a century. In that time, canonical and neural network models have flourished, based on a wide range of assumptions, justification...

This paper addresses the issue of the security of Internet Coordinate Systems, by proposing a general method for malicious behavior detection during coordinate computations. We first show that the dynamics of a node, in a coordinate system without abnormal or malicious behavior, can be modeled by a Linear State Space model and tracked by a Kalman filter. Then we show, that the obtained model ca...

Determination of the sub-chondral bone density, or more precisely the internal density spot, can be used to evaluate the capability of a knee to sustain normal kinematics. To use this technique as a mean of knee kinematics control, the position of the internal density spot must be determined in a reproducible way. This paper presents a definition of an intrinsic polar coordinate system, allowin...