Many complexity measures are defined as the size of a minimal representation in a specific model class. One such complexity measure, which is important because it is widely applied, is statistical complexity. It is defined for discrete-time, stationary stochastic processes within a theory called computational mechanics. Here, a mathematically rigorous, more general version of this theory is presented, and abstract properties of statistical complexity as a function on the space of processes are investigated. In particular, weak-* lower semi-continuity and concavity are shown, and it is argued that these properties should be shared by all sensible complexity measures. Furthermore, a formula for the ergodic decomposition is obtained. The same results are also proven for two other complexity measures that are defined by different model classes, namely process dimension and generative complexity. These two quantities, and also the information theoretic complexity measure called excess entropy, are related to statistical complexity, and this relation is discussed here. It is also shown that computational mechanics can be reformulated in terms of Frank Knight''s prediction process, which is of both conceptual and technical interest. In particular, it allows for a unified treatment of different processes and facilitates topological considerations. Continuity of the Markov transition kernel of a discrete version of the prediction process is obtained as a new result.

The diploma thesis called Optimization of processes in a distribution company is focused on a firm, fictionally named ABC Ltd which, however, represents a real distribution company, a holding company to be precise, whose parent company is based in the Czech Republic and its subsidiaries are located in Italy, China and Australia. The overall number of staff of the whole concern is sixteen, so it falls into the category of small companies. The main purpose of this paper is to analyze the company's processes. The greatest benefit of the thesis is saving the company's expenses based on optimization of the company's processes. In the introduction to the paper all the goals and benefits are stated. The next chapter reveals a brief description of skills that are vital for working on the practical part of the paper and meeting all the goals that have been set at the beginning. The introduction to the practical part deals with introducing the company ABC Ltd. The main topic of this part is the analysis of the present state of the firm's enterprise architecture. One of these architectures, the process one, describes the company's processes which are divided into the main and the supporting ones. In the main processes the potential for improvements is identified. The conclusion brings evaluation of the limits which follow from the revealed potential and suggestions for supporting the limits in the form of project solution.