2 Discrete vector fields. 4 2.1 W-contractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Algebraic discrete vector fields. . . . . . . . . . . . . . . . . . . . . 6 2.3 V-paths and admissible vector fields. . . . . . . . . . . . . . . . . . 7 2.4 Reductions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4.1 Definition. . . . . . . . . . . . . . . . . ...

It is shown that the encoding/decoding problem for any asynchronous -user discrete memoryless multiple-access channel can be reduced to corresponding problems for at most 2 1 single-user discrete memoryless channels. This result, which extends a similar result for Gaussian channels, reduces the seemingly hard task of finding good multiple-access codes to the much better understood task of findi...

Gaussian processes are a powerful, non-parametric tool that can be be used in supervised learning, namely in regression but also in classification problems. The main advantages of this method are the ability of GPs to provide uncertainty estimates and to learn the noise and smoothness parameters from training data. The aim of this short tutorial is to provide the basic theoretical aspects of Ga...

The stochastic processes of almost exclusive interest in modeling channel noise are the Gaussian processes. Gaussian processes are stochastic processes for which the random variables N(t1), N(t2), . . . , N(tk) are jointly Gaussian for all t1, . . . , tk and all k > 0. Today we start by giving a more complete discussion of jointly Gaussian random variables. We restrict our attention to zero mea...

This paper presents a novel technique by which non-Gaussian vibrations are synthesized by generating a sequence of random Gaussian processes of varying root-mean-square (rms) levels and durations. The technique makes use of previous research by the authors which shows that non-Gaussian vibrations from wheeled vehicles comprise of a sequence of Gaussian segments. Synthesis is achieved by creatin...

Bounds for non-commutative versions of two classical strong mixing coefficients for q-Gaussian processes are found in terms of the angle between the underlying Hilbert spaces. As a consequence, we construct a ψ-mixing qGaussian stationary sequence with growth conditions on variances of partial sums. If classical processes with analogous properties were to exist, they would provide a counter-exa...

Stretching process of sheet metals in both cases of axisymmetric and non-axisymmetric is analyzed. A rigid-plastic, normal anisotrop material is assumed and large strain formulation is applied. Triangular elements are used and stiffness equations of elements are obtained from virtual work principle. These nonlinear equations are linearized by Newton-Raphsons method and are solved by Gaussian el...