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Probability theory provides a uniquely valid set of rules for plausible reasoning. This enables us to apply this mathematical formalism of probability, also known as Bayesian, with greater flexibility to problems of scientific inference. In this thesis, we are concerned with applying this method to the analysis of visibility data from radio interferometers. Any radio interferometry observation can be described using the Radio Interferometry Measurement Equation (RIME). Throughout the thesis, we use the RIME to model the visibilities in performing the probabilistic analysis. We first develop the theory for employing the RIME in performing Bayesian analysis of interferometric data. We then apply this to the problem of super-resolution with radio interferometers by performing model selection successfully between different source structures, all smaller in scale than the size of the point spread function (PSF) of the interferometer, on Westerbork Synthesis Radio Telescope (WSRT) simulations at a frequency of 1.4 GHz. We also quantify the change in the scale of the sources that can be resolved by WSRT at this frequency, with changing signal-to-noise (SNR) of the data, using simulations. Following this, we apply this method to a 5 GHz European VLBI Network (EVN) observation of the flaring blazar CGRaBS J0809+5341, to ascertain the presence of a jet emanating from its core, taking into account the imperfections in the station gain calibration performed on the data, especially on the longest baselines, prior to our analysis. We find that the extended source model is preferred over the point source model with an odds ratio of 109 : 1. Using the flux-density and shape parameter estimates of this model, we also derive the brightness temperature of the blazar (10¹¹-10¹² K), which confirms the presence of a relativistically boosted jet with an intrinsic brightness temperature lower than the apparent brightness temperature, consistent with the literature. We also develop a Bayesian criterion for super-resolution in the presence of baseline-dependent noise and calibration errors and find that these errors play an important role in determining how close one can get to the theoretical super-resolution limit. We then proceed to include fringe-fitting, the process of solving for the time and frequency dependent phase variations introduced by the interstellar medium and the Earth's atmosphere, in our probabilistic approach. Fringe-fitting is one of the first corrections made to Very Long Baseline Interferometry (VLBI) observations, and, by extending our method to include simultaneous fringefitting and source structure estimation, we will be able to perform end-to-end VLBI analysis using our method. To this end, we estimate source amplitude and fringe-fitting phase terms (phase offsets and delays) on 43 GHz Very Long Baseline Array and 230 GHz Event Horizon Telescope (EHT) simulations of point sources. We then perform model selection on a 5 μas extended Gaussian source (one-fourth the size of the PSF) on a synthetic 230 GHz EHT observation. Finally we incorporate turbulent time-varying phase offsets and delays in our model selection and show that the delays can be estimated to within 10-16 per cent error (often better than contemporary software packages) while simultaneously estimating the extended source structure.

X-ray crystallography is extensively deployed to determine the structure of proteins, both unbound and bound to different molecules. Crystallography has the power to visually reveal the binding of small molecules, assisting in their development in structure-based lead design. Currently, however, the methods used to detect binding, and the subjectivity of inexperienced modellers, are a weak-point in the field. Existing methods for ligand identification are fundamentally flawed when identifying partially-occupied states in crystallographic datasets; the ambiguity of conventional electron density maps, which present a superposition of multiple states, prevents robust ligand identification. In this thesis, I present novel methods to clearly identify bound ligands and other changed states in the case where multiple crystallographic datasets are available, such as in crystallographic fragment screening experiments. By applying statistical methods to signal identification, more crystallographic binders are detected than by state-of-the-art conventional approaches. Standard modelling practice is further challenged regarding the modelling of multiple chemical states in crystallography. The pervading modelling approach is to model only the bound state of the protein; I show that modelling an ensemble of bound and unbound states leads to better models. I conclude with a discussion of possible future applications of multi-datasets methods in X-ray crystallography, including the robust identification of conformational heterogeneity in protein structures.

Asymmetric beams can create significant bias in estimates of the power spectra from cosmic microwave background (CMB) experiments. With the temperature power spectrum many orders of magnitude stronger than the B-mode power spectrum any systematic error that couples the two must be carefully controlled and/or removed. In this thesis, I derive unbiased estimators for the CMB temperature and polarisation power spectra taking into account general beams and scan strategies. I test my correction algorithm on simulations of two temperature-only experiments and demonstrate that it is unbiased. I also develop a map-making algorithm that removes beam asymmetry bias at the map level. I demonstrate its implementation using simulations. I present two new map-making algorithms that create polarisation maps clean of temperature-to-polarisation leakage systematics due to differential gain and pointing between a detector pair. Where a half wave plate is used, I show that the spin-2 systematic due to differential ellipticity can also be removed using my algorithms. The first algorithm is designed to work with scan strategies that have a good range of crossing angles for each map pixel and the second for scan strategies that have a limited range of crossing angles. I demonstrate both algorithms by using simulations of time ordered data with realistic scan strategies and instrumental noise. I investigate the role that a scan strategy can have in mitigating certain common systematics by averaging systematic errors down with many crossing angles. I present approximate analytic forms for the error on the recovered B-mode power spectrum that would result from these systematic errors. I use these analytic predictions to search the parameter space of common satellite scan strategies to identify the features of a scan strategy that have most impact in mitigating systematic effects.

<p dir="ltr">Topological Data Analysis (TDA) with its roots embedded in the field of algebraic topology has successfully found its applications in computational biology, drug discovery, machine learning and in many diverse areas of science. One of its cornerstones, persistent homology, captures topological features latent in the data. Recent progress in TDA allows us to integrate these finer topological features into traditional machine learning and deep learning pipelines. However, the utilization of topological methods within a conventional deep learning framework remains relatively uncharted. This thesis presents four scenarios where computational topology tools are employed to advance machine learning.</p><p dir="ltr">The first one involves integrating persistent homology to explore high-dimensional cytometry data. The second one incorporates Extended persistence in a supervised graph classification framework and demonstrates leveraging TDA in cases where data naturally aligns with higher-order elements by extending graph neural networks to higher-order networks, applied specifically in non-manifold mesh classification. The third and fourth scenarios delve into enhancing graph neural networks through multiparameter persistence.</p>

In this thesis, I use the new generation of radio interferometer along with X-ray observations to investigate the dynamics and energetics of radio-loud active galaxies which are key to understanding AGN feedback and the evolution of galaxies as a whole. I present new JVLA observations of powerful radio source and use innovative techniques to undertake a detailed analysis of JVLA observations of powerful radio galaxies. I compare two of the most widely used models of spectral ageing, the Kardashev-Pacholczyk and Jaffe-Perola models and also results of the more complex, but potentially more realistic, Tribble model. I find that the Tribble model provides both a good fit to observations as well as providing a physically realistic description of the source. I present the first high-resolution spectral maps of the sources and find that the best-fitting injection indices across all models take higher values than has previously been assumed. I present characteristic hot spot advance speeds and compare them to those derived from dynamical ages, confirming that the previously known discrepancy in speed remains present in older radio sources even when ages are determined at high spectral and spatial resolutions. I show that some previously common assumptions made in determining spectral ages with narrow-band radio telescopes may not always hold. I present results from a study of the powerful radio galaxy 3C223 at low frequencies with LOFAR to determine its spectrum on spatially small scales and tightly constrain the injection index, which I find to be consistent with the high values found at GHz frequencies. Applying this new knowledge of the low energy electron population, I perform synchrotron / inverse-Compton model fitting and find that the total energy content of the radio galaxy lobes increases by a factor greater than 2 compared to previous studies. Using this result to provide revised estimates of the internal pressure, I find the northern lobe to be in pressure balance with the external medium and the southern lobe to be overpressured. I go on to present the first large sample investigation of the properties of jets in Fanaroff and Riley type I radio galaxies (FR-I) at X-ray energies based on data from the Chandra archive. I explore relations between the properties of the jets and the properties of host galaxies in which they reside. I find previously unknown correlations to exist, relating photon index, volume emissivity, jet volume and luminosity, and find that the previously held assumption of a relationship between luminosities at radio and X-ray wavelengths is linear in nature when bona fide FR-I radio galaxies are considered. In addition, I attempt to constrain properties which may play a key role in determination of the diffuse emission process. I test a simple model in which large-scale magnetic field variations are primarily responsible for determining jet properties; however, we find that this model is inconsistent with our best estimates of the relative magnetic field strengths in my sample.

This doctoral thesis is focused on value based management. The basic principle of value based management states that the main object in an organization is value enhancement. Within an organization the concept of value based management connects activities and people participating in business processes to maintain that the resources the owners put into the business are evaluated. The essential task of value based management is to find and identify factors which contribute increasing performance and creating the value of a company, known as value drivers. The purpose of this thesis is to identify the factors which by significant amount affect the value of the mechanical engineering enterprises in the Czech Republic. In the first part of the thesis an analysis of current academic knowledge in area of value drivers is made. The base of the analysis is created by foreign resources because there is only limited amount of information in domestic literature. Besides the determination of value approach and its benefits attention is mainly paid to organizing results from value generators area. Findings of secondary resources analysis are used for own research problem. The second part of the thesis includes determination of the main objects and the research problem as well as formulation of the research questions and tested hypotheses. The third part is focused on describing methods which were used in the thesis. In the thesis was applied logical (induction – deduction, analysis – synthesis, generalization – concretaization) and empirical methods (comparsion method, quantitative research methods). Primary data was collected by using a questionnaire. Obtained data was analyzed using logarithmic decomposition of the return on equity, Boosted Trees and descriptive statistics (for example measures of location, measures of variability) and more statistical methods for analysis of statistical hypothesis (Kolmogorov-Smirnov test, Lilliefors test for normality, F-test, Student’s t-test, Chi-squared test, Fisher’s exact test, Spearman’s rank correlation coefficient). In the fourth part of the thesis the branch of manufacturing industry is characterized and the identification of performance factors is accomplished applying logarithmic decomposition of the return on equity. The other subjects of research were companies in a branch called “Manufacturing of machines and devices”. The fifth part of the thesis includes summary of findings of the prime research and its discussion. Primary data was obtained by a questionnaire survey and completed with accounting information of respondents. The findings of the research show that main determinants affecting the value of engineering companies in the Czech Republic are return on assets, profit margin, consumption, sales profitability, personnel costs and value added. The qualitative value drivers are good reputation, human resources (employees) and its characteristics, business and flexibility, performance and productivity, assets, competency responsible staff, attentiveness to requirement of customers, innovation and quality.

Degradation of water resources has become one of the most pressing global concerns currently facing mankind. Constructed Wetlands (CWs) represent a concept to combat deterioration of water resources by acting as buffers between wastewater and receiving water bodies. Still, constructing wetlands for the sole purpose of wastewater treatment is a challenging task. To contribute to this research area, the fundamental question raised in this doctorate thesis was: how do factors such as vegetation and residing water movements (hydraulics) influence wastewater treatment in CWs? Also, effects of different data analysis methods for results of CW hydraulics and wastewater treatment were investigated. Research was focused on  phosphorus (P), ammonium-nitrogen (NH4+-N) and solids (TSS) in wastewater and o n P in macrophyte biomass. Studies were performed in pilot-scale free water surface (FWS) CW systems in Kenya (Chemelil) and Sweden (Halmstad) and as computer simulations. Results from the Chemelil CWs demonstrated that meeting effluent concentration standards simultaneously for all water quality parameters in one CW was difficult. Vegetation harvest, and thus nutrient uptake by young growing macrophytes, was important for maintaining low effluents of NH4+-N and P, especially during dry seasons. On the other hand, mature and dense vegetation growing for at least 4 months secured meeting TSS standards. Phosphorus in above-ground green biomass accounted for almost 1/3 of the total P mass removal, demonstrating high potential for P removal through macrophyte harvest in CWs. Also, results suggested that harvest should be species-specific to achieve high P removal by macrophytes and overall acceptable wastewater treatment in CWs. Still, different methods to estimate evapotranspiration (ET) from the Chemelil CWs showed that water balance calculations greatly impacted estimations of wastewater treatment results. Hydraulic tracer studies performed in the Chemelil and Halmstad CWs showed that mature and dense emergent vegetation in CWs could reduce effective treatment volumes (e-values), which emphasized the importance of regulating this type of vegetation. Also, it was shown that hydraulic tracer studies with lithium chloride performed in CWs with dense emergent vegetation had problems with low tracer recoveries. This problem could be reduced by promoting the distribution of incoming tracer solution into the CW using a barrier near the CW inlet pipe. Computer simulation results showed that the choice of tracer data analysis method greatly influenced quantifications of CW hydraulics and pollutant removal. The e-value could be 50% higher and the pollutant removal 13% higher depending upon used method. Moreover, unrealistic evalues (above 100%) in published literature could to some extent be explained by tracer data analysis method. Hence, to obtain more reliable hydraulic data and wastewater treatment results from CWs, more attention should be paid to the choice of tracer data analysis method. / Konstruerade våtmarker representerar ett koncept för möjligheten att nå en hållbar vattenresurshantering genom att agera som ”filter” mellan föroreningskälla och viktiga vattenresurser såsom sjöar och hav. Mycket kunskap saknas däremot om hur man konstruerar våtmarker med en optimal och pålitlig vattenreningskapacitet. Den här avhandlingen undersöker därför hur vegetation och vattnets väg genom våtmarken (hydrauliken) påverkar avloppsvattenrening i våtmarker. Dessutom undersöktes hur valet av dataanalysmetod av insamlad data påverkar resultaten. Studier genomfördes i Kenya och Sverige i experimentvåtmarker (ca. 40-60 m2) och inkluderadedatainsamling av vattenkvalité, hydraulik (spårämnesexperiment) samt biomassa och fosfor i biomassan av två olika våtmarksväxter. Dessutom genomfördes datorsimuleringar. Resultaten från Kenya visade att växtskörd och efterföljande näringsupptag av nyskördade växter var viktig för att uppnå låga utgående koncentrationer av fosfor och ammonium i en tropisk våtmark, speciellt under torrsäsongen. Däremot var en välutvecklad och tät vegetation viktig för reningen av partiklar. Fosfor i grön växtbiomassa representerade cirka 1/3 av våtmarkernas totala fosforrening, vilket påvisade potentialen i att genom skörd ta bort fosfor från avloppsvatten m.h.a. konstruerade våtmarker. Resultaten pekade också på att skörden bör vara art-specifik för att uppnå en hög fosforrening och generellt bra vattenreningsresultat. Dock visade olika beräkningsmetoder att vattenbalansen i en tropisk våtmark markant kan påverka vattenreningsresultaten. Resultaten från spårämnesexperimenten demonstrerade att den effektiva våtmarksvolymen för vattenrening blev mindre vid hög täthet av övervattensväxter. Detta pekade på att regelbunden växtskörd var viktig för att uppnå god vattenrening i våtmarker. Experiment med spårämnet litium visade att man kan få felaktiga resultat p.g.a. att en del spårämne fasthålls på botten i våtmarken om denna har mycket övervattensväxter. Därför bör spridningen av spårämnet i sådana våtmarker underlättas m.h.a. en spridningsbarriär nära inloppsröret. Simuleringar visade också att valet av dataanalysmetod av spårämnesdata starkt kan påverka resultaten och därmed också vår tolkning av en våtmarks hydraulik och reningskapacitet. Den effektiva volymen kunde vara 50% högre och reningseffekten 13% högre beroende på vilken metod som användes. Likaså kan valet av dataanalysmetod ha bidragit till överskattade och orealistiska effektiva volymer (över 100%) i artiklar publicerade de senaste 25 åren. Genom att fokusera mer på valet av dataanalysmetod och t.ex. jämföra resultaten från två olika metoder kan man minimera risken för bristfälliga resultat och därmed felaktiga slutsatser om en våtmarks vattenreningskapacitet.