Consider the following mechanism for the random evolution of a distribution of mass on the integer lattice Z. At unit rate, independently for each site, the mass at the site is split into two parts by choosing a random proportion distributed according to some specified probability measure on [0,1] and dividing the mass in that proportion. One part then moves to each of the two adjacent sites. T...

BINoculars is a tool for data reduction and analysis of large sets of surface diffraction data that have been acquired with a two-dimensional X-ray detector. The intensity of each pixel of a two-dimensional detector is projected onto a three-dimensional grid in reciprocal-lattice coordinates using a binning algorithm. This allows for fast acquisition and processing of high-resolution data sets ...

A novel scheme to achieve three-dimensional (3D) target location in bistatic radar systems is evaluated. The proposed scheme develops the additional information of the bistatic radar, that is the transmit angles, to estimate the 3D coordinates of the targets by using multiple-input multiple-output techniques with a uniform circular array on transmit and a uniform linear array on receive. The tr...

The Serret-Andoyer transformation is a classical method for reducing the free rigid body dynamics, expressed in Eulerian coordinates, to a 2-dimensional Hamiltonian flow. First, we show that this transformation is the computation, in 3-1-3 Eulerian coordinates, of the symplectic (Marsden-Weinstein) reduction associated with the lifted left-action of SO(3) on T ∗SO(3)—a generalization and extens...

High dimensional data modeling is difficult mainly because the so-called "curse of dimensionality". We propose a technique called "Gaussianization" for high dimensional density estimation, which alleviates the curse of dimensionality by exploiting the independence structures in the data. Gaussianization is motivated from recent developments in the statistics literature: projection pursuit, inde...

This thesis is about the application of Neural Networks in the sensing of an object position relative to a reference point. An object is rotated a certain angle in space and a Neural Network was then used to estimate its orientation. Previous methods had always been to transform 3-dimensional data into 2-dimensional data before presenting it to the network. In this thesis 3-dimensional data is ...

In 1940 Paul Erdős introduced the ‘rational Hilbert space’, which consists of all vectors in the real Hilbert space 2 that have only rational coordinates. He showed that this space has topological dimension one, yet it is totally disconnected and homeomorphic to its square. In this note we generalize the construction of this peculiar space and we consider all subspaces E of the Banach spaces p ...

We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of formalism quantum mechanical harmonic oscillator problem in phase-space that canonical-type NC 2-D space, and noting square length latter case is analogous to Hamiltonian former case, we arrive at conclusion area are quantized such an if expressed entirely terms length. ext...

The main objective of this paper is to study the Euclidean displacement of a 5-DOF parallel mechanism performing three translation and two independent rotations with identical limb structures-recently revealed by performing the type synthesis-in a higher dimensional projective space, rather than relying on classical recipes, such as Cartesian coordinates and Euler angles. In this paper, Study's...

This report reproduces and brieey discusses an algorithm proposed by Butz 2] for calculating a mapping between one-dimensional values and n-dimensional values regarded as being the coordinates of points lying on Hilbert Curves. It suggests some practical improvements to the algorithm and presents an algorithm for calculating the inverse of the mapping, from n-dimensional values to one-dimension...