In their 2006 paper, Wang and Xu develop a convergence theory for nonconforming finite element methods. Moreover, they explicitly construct consistent FE spaces of minimal polynomial degree for the discretization of the Sobolev spaces $H^m(\mathbb{R}^n)$ for $n\ge m$ on simplicial meshes. Their main results will be presented in this talk.
At first, I will explain the reason why vector computers have the ability to outperform scalar architectures and what prerequisites are needed to make this possible. If these prerequisites are full-filled, one speaks of vectorizing code. In the main part of the talk, I will show code segments of the three possible types of code (non-vectorizing, vectorizing, and code that has to be transformed by the compiler to be vectorized). I will also explain the right way to access main memory on a vector system.
After that, some of the changes that have to be applied to a simple FEM program to obtain vectorizing code are presented.
In this talk, we study probabilistic properties of pattern classifiers in discrete feature space. The principle of Bayesian averaging of recognition performance is used for the analysis. We consider two cases: a) prior probabilities of classes are unknown, and b) prior probabilities of classes are known. The misclassification probability is represented as a random value, for which the characteristic function (expressed via Kummer hypergeometric function) and absolute moments are analytically derived. For the case of unknown priors, an approximate formula for calculation of sufficient learning sample size is obtained. The comparison between the performances for two considered cases is made. As an example, we consider the problem of mutational hotspots classification in genetic sequences.
Basic principles of mass spectroscopy are introduced. Starting with simple problems of spectrum analysis, we present challanging problems which are directly related to the solution of first kind integral equations.
