In this thesis we consider two research problems, namely, (i) language constructs for modelling stochastic programming (SP) problems and (ii) solution methods for processing instances of different classes of SP problems. We first describe a new design of an SP modelling system which provides greater extensibility and reuse. We implement this enhanced system and develop solver connections. We also investigate in detail the following important classes of SP problems: singlestage SP with risk constraints, two-stage linear and stochastic integer programming problems. We report improvements to solution methods for single-stage problems with second-order stochastic dominance constraints and two-stage SP problems. In both cases we use the level method as a regularisation mechanism. We also develop novel heuristic methods for stochastic integer programming based on variable neighbourhood search. We describe an algorithmic framework for implementing decomposition methods such as the L-shaped method within our SP solver system. Based on this framework we implement a number of established solution algorithms as well as a new regularisation method for stochastic linear programming. We compare the performance of these methods and their scale-up properties on an extensive set of benchmark problems. We also implement several solution methods for stochastic integer programming and report a computational study comparing their performance. The three solution methods, (a) processing of a single-stage problem with second-order stochastic dominance constraints, (b) regularisation by the level method for two-stage SP and (c) method for solving integer SP problems, are novel approaches and each of these makes a contribution to knowledge.

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In an exploratory approach to data analysis, it is often useful to consider the observations as generated from a set of latent generators or 'sources' via a generally unknown mapping. Reconstructing sources from their mixtures is an extremely ill-posed problem in general. However, solutions to such inverse problems can, in many cases, be achieved by incorporating prior knowledge about the problem, captured in the form of constraints. This setting is a natural candidate for the application of the Bayesian method- ology, allowing us to incorporate "soft" constraints in a natural manner. This Thesis proposes the use of sparse statistical decomposition methods for ex- ploratory analysis of datasets. We make use of the fact that many natural signals have a sparse representation in appropriate signal dictionaries. The work described in this Thesis is mainly driven by problems in the analysis of large datasets, such as those from functional magnetic resonance imaging of the brain for the neuro-scientific goal of extracting relevant 'maps' from the data. We first propose Bayesian Iterative Thresholding, a general method for solv- ing blind linear inverse problems under sparsity constraints, and we apply it to the problem of blind source separation. The algorithm is derived by maximiz- ing a variational lower-bound on the likelihood. The algorithm generalizes the recently proposed method of Iterative Thresholding. The probabilistic view en- ables us to automatically estimate various hyperparameters, such as those that control the shape of the prior and the threshold, in a principled manner. We then derive an efficient fully Bayesian sparse matrix factorization model for exploratory analysis and modelling of spatio-temporal data such as fMRI. We view sparse representation as a problem in Bayesian inference, following a ma- chine learning approach, and construct a structured generative latent-variable model employing adaptive sparsity-inducing priors. The construction allows for automatic complexity control and regularization as well as denoising. The performance and utility of the proposed algorithms is demonstrated on a variety of experiments using both simulated and real datasets. Experimental results with benchmark datasets show that the proposed algorithms outper- form state-of-the-art tools for model-free decompositions such as independent component analysis.

Currently the degree sequence problem for 3-hypergraphs is still unsolved efficiently. This paper researches the 3-hypergraphic problem in terms of edge switching and exchanges in the sequence to implement Dewdney’s reduction. It proposes the idea of an irreducible decomposition and makes use of it to find some sufficient conditions for a 3-hypergraphic sequence. In addition, this paper explores a related problem: intersection preserving mappings. / May 2016

Three Essays in Energy and Environmental Economics Author: Mgr. Lukáš Rečka Supervisor: Mgr. Milan Ščasný, Ph.D. Academic Year: 2018/2019 Abstract This thesis consists of three articles that share the main theme - energy and environment. The dissertation aims mainly at the Czech energy system and analyses it development after the Velvet Revolution and its possible future development. The first article applies Logarithmic Mean Divisia Index decomposition to analyses the main driving forces of significant reduction in air quality pollutants during the transition of the Czech economy towards market economy in the 1990s. It continues then to investigate how the driving forces affected the emissions volumes during succeeding the post-transition period up to 2016. The second article reacts on the 2015 governmental decision to lift brown coal mining limits in the North Bohemia coal basin. The paper analyses the impacts of maintaining the ban on mining coal reserves and compares them with three alternative options that would each weaken the environmental protections of the ban. The impacts of each of these alternative governmental propostions are analysed on the Czech energy system, the fuel- and the technology-mix, the costs of generating energy, related emissions and external costs associated with the emissions....

This thesis considers a novel problem of obtaining global channel state information (CSI) at every node in an ad-hoc wireless network. A class of protocols for dissemination and estimation are developed which attempt to minimize the staleness of the estimates throughout the network. This thesis also provides an optimal protocol for CSI dissemination in networks with complete graph topology and a near optimal protocol in networks having incomplete graph topology. In networks with complete graph topology, the protocol for CSI dissemination is shown to have a resemblance to finding Eulerian tours in complete graphs. For networks having incomplete graph topology, a lower bound on maximum staleness is given and a near optimal algorithm based on finding minimum connected dominating sets and proper scheduling is described in this thesis.

This thesis considers a novel problem of obtaining global channel state information (CSI) at every node in an ad-hoc wireless network. A class of protocols for dissemination and estimation are developed which attempt to minimize the staleness of the estimates throughout the network. This thesis also provides an optimal protocol for CSI dissemination in networks with complete graph topology and a near optimal protocol in networks having incomplete graph topology. In networks with complete graph topology, the protocol for CSI dissemination is shown to have a resemblance to finding Eulerian tours in complete graphs. For networks having incomplete graph topology, a lower bound on maximum staleness is given and a near optimal algorithm based on finding minimum connected dominating sets and proper scheduling is described in this thesis.

In forest ecosystems, substantial part of carbon enters soil in the form of plant litter. The decomposition of litter and soil organic matter represents an important process affecting nutrient cycling and carbon balance in soils. Fungi are considered the primary decomposers in terrestrial ecosystems due to the production of wide range of extracellular enzymes that allow them to attack the lignocellulose matrix in litter. Even if fungi represent key players in organic matter decomposition, the information about the structure and diversity of their communities is still limited and the roles of individual fungal taxa in forest soils remain unclear. This Ph.D. thesis focused on the characterization of fungal communities in forest soils and their potential to decompose plant litter. The method for in-depth analysis of complex microbial communities from environmental samples was established and used. In addition, single eukaryotic functional gene was analysed in soil for the first time at a depth that allowed reliable estimation of diversity. It was demonstrated that microbial community composition differs among horizons of forest soil profile. Despite similar diversity, significant differences in microbial community composition were observed between the DNA and RNA. Several microbial groups highly...

Dead plant biomass is a key pool of carbon in terrestrial ecosystems. Its decomposition in soil environments is thus an essential process of the carbon cycle. Fungi are considered to be the primary decomposers in soil ecosystems because of their physiological adaptations and enzymatic apparatus composed from highly effective oxidative and hydrolytic enzymes. Many recent works show that in addition to fungi, bacteria may also play a significant role in lignocellulose decomposition and among bacteria, the members of the phylum Actinobacteria are often regarded to significantly contribute to cellulose and lignocellulose decomposition. This thesis is focused on the evaluation of the role that fungi and Actinobacteria play in dead plant biomass degradation. First, it explored mechanisms involved in degradation, in particular the enzymatic breakdown of major lignocellulose components as cellulose, hemicelluloses and lignin. Enzymatic apparatus of the saprotrophic fungus Fomes fomentarius was explored both in vitro as well as in vivo. Several Actinobacteria were isolated from soil and comparative experiments, investigating production of hydrolytic enzymes, were carried out to track the transformation of polysaccharides and lignin by these strains. To explain the roles of lignocellulose decomposers in...

Vegetation of post-mining sites determines soil microbial community structure and soil processes Mgr. Michaela Urbanová Abstract The aim of this thesis, which consists of four published articles, was to investigate the effect of vegetation on soil microbial communities and processes in de novo developing soil substrate on the brown-coal spoil heaps in the surrounding of city Sokolov. Spoil material - soil clayey substrate, which had been gradually mined from the opencast brown coal mine, stratified onto spoil heaps and reclaimed by assisted afforestation with selected tree species or left for spontaneous plant succession, changes its biotic and abiotic characteristic in the course of time and particularly under the influence of plants. Changes of spoil substrate characteristics are related to the growth of plant roots and particularly also to the production of plant biomass, which is decomposed gradually and takes part of soil, where participates to soil organic matter. The process of plant dead materials decomposition and transformation is the function of the activity of soil organisms and among them notably soil microorganisms. Moreover, the presence of many of them is closely related to the presence of vegetation, whose symbionts or pathogens are. The exact mechanisms of the plant-microbes interactions...