Semi-supervised learning (SSL) is a class of supervised learning tasks and techniques that also exploits the unlabeled data for training. SSL significantly reduces labeling related costs and is able to handle large data sets. The primary objective is the extraction of robust inference rules. Decision support systems (DSSs) who utilize SSL have significant advantages. Only a small amount of labe...

A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and themethod of successor function, we obtain the systemwith impulsive effects that has an order o...

The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C∗-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting. First, we show that if G is an amenable groupoid acting on an upper-semicontinuous C∗-bundle A with nuclear section algebra A, then the associated g...

Context. The M dwarf Gliese 581 has recently been found to harbour two super Earths in addition to an already known close-in Neptune-mass planet. Interestingly, these two planets are considered as potentially habitable, and recent theoretical works give further credit to this hypothesis, in particular for the outermost planet (Gl 581 d). Aims. In this paper, we address the issue of the dynamica...

Abstract. We give a new characterization of relative entropy, also known as the Kullback–Leibler divergence. We use a number of interesting categories related to probability theory. In particular, we consider a category FinStat where an object is a finite set equipped with a probability distribution, while a morphism is a measure-preserving function f : X → Y together with a stochastic right in...

The comparison of the long-time behaviour of dynamical systems and their numerical approximations is not straightforward since in general such methods only converge on bounded time intervals. However, one can still compare their asymptotic behaviour using the global attractor, and this is now standard in the deterministic autonomous case. For random dynamical systems there is an additional prob...