Quantum Tomography with Phase Space Measurements

This thesis addresses the use of covariant phase space observables in quantum tomography. Necessary and sufficient conditions for the informational completeness of covariant phase space observables are proved, and some state reconstruction formulae are derived. Different measurement schemes for measuring phase space observables are considered. Special emphasis is given to the quantum optical eight-port homodyne detection scheme and, in particular, on the effect of non-unit detector efficiencies on the measured observable. It is shown that the informational completeness of the observable does not depend on the efficiencies. As a related problem, the possibility of reconstructing the position and momentum distributions from the marginal statistics of a phase space observable is considered. It is shown that informational completeness for the phase space observable is neither necessary nor sufficient for this procedure. Two methods for determining the distributions from the marginal statistics are presented. Finally, two alternative methods for determining the state are considered. Some of their shortcomings when compared to the phase space method are discussed.

Mathematical modeling of level of anaesthesia from EEG measurements

Problem of modeling of anaesthesia depth level is studied in this Master Thesis. It applies analysis of EEG signals with nonlinear dynamics theory and further classification of obtained values. The main stages of this study are the following: data preprocessing; calculation of optimal embedding parameters for phase space reconstruction; obtaining reconstructed phase portraits of each EEG signal; formation of the feature set to characterise obtained phase portraits; classification of four different anaesthesia levels basing on previously estimated features. Classification was performed with: Linear and quadratic Discriminant Analysis, k Nearest Neighbours method and online clustering. In addition, this work provides overview of existing approaches to anaesthesia depth monitoring, description of basic concepts of nonlinear dynamics theory used in this Master Thesis and comparative analysis of several different classification methods.

Moment Operators of Observables in Quantum Mechanics, with Applications to Quantization and Homodyne Detection

The questions studied in this thesis are centered around the moment operators of a quantum observable, the latter being represented by a normalized positive operator measure. The moment operators of an observable are physically relevant, in the sense that these operators give, as averages, the moments of the outcome statistics for the measurement of the observable. The main questions under consideration in this work arise from the fact that, unlike a projection valued observable of the von Neumann formulation, a general positive operator measure cannot be characterized by its first moment operator. The possibility of characterizing certain observables by also involving higher moment operators is investigated and utilized in three different cases: a characterization of projection valued measures among all the observables is given, a quantization scheme for unbounded classical variables using translation covariant phase space operator measures is presented, and, finally, a mathematically rigorous description is obtained for the measurements of rotated quadratures and phase space observables via the high amplitude limit in the balanced homodyne and eight-port homodyne detectors, respectively. In addition, the structure of the covariant phase space operator measures, which is essential for the above quantization, is analyzed in detail in the context of a (not necessarily unimodular) locally compact group as the phase space.

Molecular modeling of asymmetric induction in heterogeneously catalyzed hydrogenation of the C=O bond

Modifiering av metallytor med starkt adsorberade kirala organiska molekyler är eventuellt den mest relevanta teknik man vet i dag för att skapa kirala ytor. Den kan utnyttjas i katalytisk produktion av enantiomeriskt rena kirala föreningar som behövs t.ex. som läkemedel och aromkemikalier. Trots många fördelar av asymmetrisk heterogen katalys jämfört med andra sätt för att få kirala föreningar, har den ändå inte blivit ett allmänt verktyg för storskaliga tillämpningar. Detta beror t.ex. på brist på djupare kunskaper i katalytiska reaktionsmekanismer och ursprunget för asymmetrisk induktion. I denna studie användes molekylmodelleringstekniker för att studera asymmetriska, heterogena katalytiska system, speciellt hydrering av prokirala karbonylföreningar till motsvarande kirala alkoholer på cinchona-alkaloidmodifierade Pt-katalysatorer. 1-Fenyl-1,2-propandion (PPD) och några andra föreningar, som innehåller en prokiral C=O-grupp, användes som reaktanter. Konformationer av reaktanter och cinchona-alkaloider (som kallas modifierare) samt vätebundna 1:1-komplex mellan dem studerades i gas- och lösningsfas med metoder som baserar sig på vågfunktionsteori och täthetsfunktionalteori (DFT). För beräkningen av protonaffiniteter användes också högst noggranna kombinationsmetoder såsom G2(MP2). Den relativa populationen av modifierarnas konformationer varierade som funktion av modifieraren, dess protonering och lösningsmedlet. Flera reaktant–modifierareinteraktionsgeometrier beaktades. Slutsatserna på riktning av stereoselektivitet baserade sig på den relativa termodynamiska stabiliteten av de diastereomeriska reaktant–modifierare-komplexen samt energierna hos π- och π*-orbitalerna i den reaktiva karbonylgruppen. Adsorption och reaktioner på Pt(111)-ytan betraktades med DFT. Regioselektivitet i hydreringen av PPD och 2,3-hexandion kunde förklaras med molekyl–yta-interaktioner. Storleken och formen av klustret använt för att beskriva Pt-ytan inverkade inte bara på adsorptionsenergierna utan också på de relativa stabiliteterna av olika adsorptionsstrukturer av en molekyl. Populationerna av modifierarnas konformationer i gas- och lösningsfas korrelerade inte med populationerna på Pt-ytan eller med enantioselektiviteten i hydreringen av PPD på Pt–cinchona-katalysatorer. Vissa modifierares konformationer och reaktant–modifierare-interaktionsgeometrier var stabila bara på metallytan. Teoretiskt beräknade potentialenergiprofiler för hydrering av kirala α-hydroxiketoner på Pt implicerade preferens för parvis additionsmekanism för väte och selektiviteter i harmoni med experimenten. De uppnådda resultaten ökar uppfattningen om kirala heterogena katalytiska system och kunde därför utnyttjas i utvecklingen av nya, mera aktiva och selektiva kirala katalysatorer.

Extreme Observables and Optimal Measurements in Quantum Theory

Optimization of quantum measurement processes has a pivotal role in carrying out better, more accurate or less disrupting, measurements and experiments on a quantum system. Especially, convex optimization, i.e., identifying the extreme points of the convex sets and subsets of quantum measuring devices plays an important part in quantum optimization since the typical figures of merit for measuring processes are affine functionals. In this thesis, we discuss results determining the extreme quantum devices and their relevance, e.g., in quantum-compatibility-related questions. Especially, we see that a compatible device pair where one device is extreme can be joined into a single apparatus essentially in a unique way. Moreover, we show that the question whether a pair of quantum observables can be measured jointly can often be formulated in a weaker form when some of the observables involved are extreme. Another major line of research treated in this thesis deals with convex analysis of special restricted quantum device sets, covariance structures or, in particular, generalized imprimitivity systems. Some results on the structure ofcovariant observables and instruments are listed as well as results identifying the extreme points of covariance structures in quantum theory. As a special case study, not published anywhere before, we study the structure of Euclidean-covariant localization observables for spin-0-particles. We also discuss the general form of Weyl-covariant phase-space instruments. Finally, certain optimality measures originating from convex geometry are introduced for quantum devices, namely, boundariness measuring how ‘close’ to the algebraic boundary of the device set a quantum apparatus is and the robustness of incompatibility quantifying the level of incompatibility for a quantum device pair by measuring the highest amount of noise the pair tolerates without becoming compatible. Boundariness is further associated to minimum-error discrimination of quantum devices, and robustness of incompatibility is shown to behave monotonically under certain compatibility-non-decreasing operations. Moreover, the value of robustness of incompatibility is given for a few special device pairs.

Fluid flow and dispersion predictions in porous media by utilizing advanced numerical methods

Diplomityön tavoitteena oli tarkastella numeerisen virtauslaskennan avulla virtaukseen liittyviä ilmiöitä ja kaasun dispersiota. Diplomityön sisältö on jaettu viiteen osaan; johdantoon, teoriaan, katsaukseen virtauksen mallinnukseen huokoisessa materiaalissa liittyviin tutkimusselvityksiin, numeeriseen mallinnukseen sekä tulosten esittämiseen ja johtopäätöksiin. Diplomityön alussa kiinnitettiin huomiota erilaisiin kokeellisiin, numeerisiin ja teoreettisiin mallinnusmenetelmiin, joilla voidaan mallintaa virtausta huokoisessa materiaalissa. Kirjallisuusosassa tehtiin katsaus aikaisemmin julkaistuihin puoliempiirisiin ja empiirisiin tutkimusselvityksiin, jotka liittyvät huokoisen materiaalin aiheuttamaan painehäviöön. Numeerisessa virtauslaskenta osassa rakennettiin ja esitettiin huokoista materiaalia kuvaavat numeeriset mallit käyttäen kaupallista FLUENT -ohjelmistoa. Työn lopussa arvioitiin teorian, numeerisen virtauslaskennan ja kokeellisten tutkimusselvitysten tuloksia. Kolmiulotteisen huokoisen materiaalinnumeerisessa mallinnuksesta saadut tulokset vaikuttivat lupaavilta. Näiden tulosten perusteella tehtiin suosituksia ajatellen tulevaa virtauksen mallinnusta huokoisessa materiaalissa. Osa tässä diplomityössä esitetyistä tuloksista tullaan esittämään 55. Kanadan Kemiantekniikan konferenssissa Torontossa 1619 Lokakuussa 2005. ASME :n kansainvälisessä tekniikan alan julkaisussa. Työ on hyväksytty esitettäväksi esitettäväksi laskennallisen virtausmekaniikan (CFD) aihealueessa 'Peruskäsitteet'. Lisäksi työn yksityiskohtaiset tulokset tullaan lähettämään myös CES:n julkaisuun.

Elicitation of Customer Requirements with Group Methods in Software Engineering

Vaatimusmäärittely on tärkeä vaihe ohjelmistotuotannossa, koska virheelliset ja puutteelliset asiakasvaatimukset vaikuttavat huomattavasti asiakkaan tyytymättömyyteen ohjelmistotuotteessa. Ohjelmistoinsinöörit käyttävät useita erilaisia menetelmiä ja tekniikoita asiakasvaatimusten kartoittamiseen. Erilaisia tekniikoita asiakasvaatimusten keräämiseen on olemassa valtava määrä.Diplomityön tavoitteena oli parantaa asiakasvaatimusten keräämisprosessia ohjelmistoprojekteissa. Asiakasvaatimusten kartoittamiseen käytettävien tekniikoiden arvioinnin perusteella kehitettiin parannettu asiakasvaatimusten keräämisprosessi. Kehitetyn prosessin testaamiseksi ja parantamiseksi järjestettiin ryhmätyöistuntoja liittyen todellisiin ohjelmistokehitysprojekteihin. Tuloksena vaatimusten kerääminen eri sidosryhmiltä nopeutui ja tehostui. Prosessi auttoi muodostamaan yleisen kuvan kehitettävästä ohjelmistosta, prosessin avulla löydettiin paljon ideoita ja prosessi tehosti ideoiden analysointia ja priorisointia. Prosessin suurin kehityskohde oli fasilitaattorin ja osallistujien valmistautumisessa ryhmätyöistuntoihin etukäteen.

ADVANCED NUMERICAL METHODS FOR SIMULATING MICROBUBBLE IN AN AERATED MIXING TANK

Fluid mixing in mechanically agitated tanks is one of the major unit operations in many industries. Bubbly flows have been of interest among researchers in physics, medicine, chemistry and technology over the centuries. The aim of this thesis is to use advanced numerical methods for simulating microbubble in an aerated mixing tank. Main components of the mixing tank are a cylindrical vessel, a rotating Rushton turbine and the air nozzle. The objective of Computational Fluid Dynamics (CFD) is to predict fluid flow, heat transfer, mass transfer and chemical reactions. The CFD simulations of a turbulent bubbly flow are carried out in a cylindrical mixing tank using large eddy simulation (LES) and volume of fluid (VOF) method. The Rushton turbine induced flow is modeled by using a sliding mesh method. Numerical results are used to describe the bubbly flows in highly complex liquid flow. Some of the experimental works related to turbulent bubbly flow in a mixing tank are briefly reported. Numerical simulations are needed to complete and interpret the results of the experimental work. Information given by numerical simulations has a major role in designing and scaling-up mixing tanks. The results of this work have been reported in the following scientific articles: ·Honkanen M., Koohestany A., Hatunen T., Saarenrinne P., Zamankhan P., Large eddy simulations and PIV experiments of a two-phase air-water mixer, in Proceedings of ASME Fluids Engineering Summer Conference (2005). ·Honkanen M., Koohestany A., Hatunen T., Saarenrinne P., Zamankhan P., Dynamical States of Bubbling in an Aerated Stirring Tank, submitted to J. Computational Physics.

Methods of Design and Testing of Real Time Systems

Teollusuussovelluksissa vaaditaan nykyisin yhä useammin reaaliaikaista tiedon käsittelyä. Luotettavuus on yksi tärkeimmistä reaaliaikaiseen tiedonkäsittelyyn kykenevän järjestelmän ominaisuuksista. Sen saavuttamiseksi on sekä laitteisto, että ohjelmisto testattava. Tämän työn päätavoitteena on laitteiston testaaminen ja laitteiston testattavuus, koska luotettava laitteistoalusta on perusta tulevaisuuden reaaliaikajärjestelmille. Diplomityössä esitetään digitaaliseen signaalinkäsittelyyn soveltuvan prosessorikortin suunnittelu. Prosessorikortti on tarkoitettu sähkökoneiden ennakoivaa kunnonvalvontaa varten. Uusimmat DFT (Desing for Testability) menetelmät esitellään ja niitä sovelletaan prosessorikortin sunnittelussa yhdessä vanhempien menetelmien kanssa. Kokemukset ja huomiot menetelmien soveltuvuudesta raportoidaan työn lopussa. Työn tavoitteena on kehittää osakomponentti web -pohjaiseen valvontajärjestelmään, jota on kehitetty Sähkötekniikan osastolla Lappeenrannan teknillisellä korkeakoululla.

Adaptive MCMC methods with applications in environmental and geophysical models

This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.

Streptavidin - A Versatile Binding Protein for Solid-Phase Immunoassays

Streptavidin, a tetrameric protein secreted by Streptomyces avidinii, binds tightly to a small growth factor biotin. One of the numerous applications of this high-affinity system comprises the streptavidin-coated surfaces of bioanalytical assays which serve as universal binders for straightforward immobilization of any biotinylated molecule. Proteins can be immobilized with a lower risk of denaturation using streptavidin-biotin technology in contrast to direct passive adsorption. The purpose of this study was to characterize the properties and effects of streptavidin-coated binding surfaces on the performance of solid-phase immunoassays and to investigate the contributions of surface modifications. Various characterization tools and methods established in the study enabled the convenient monitoring and binding capacity determination of streptavidin-coated surfaces. The schematic modeling of the monolayer surface and the quantification of adsorbed streptavidin disclosed the possibilities and the limits of passive adsorption. The defined yield of 250 ng/cm² represented approximately 65 % coverage compared with a modelled complete monolayer, which is consistent with theoretical surface models. Modifications such as polymerization and chemical activation of streptavidin resulted in a close to 10-fold increase in the biotin-binding densities of the surface compared with the regular streptavidin coating. In addition, the stability of the surface against leaching was improved by chemical modification. The increased binding densities and capacities enabled wider high-end dynamic ranges in the solid-phase immunoassays, especially when using the fragments of the capture antibodies instead of intact antibodies for the binding of the antigen. The binding capacity of the streptavidin surface was not, by definition, predictive of the low-end performance of the immunoassays nor the assay sensitivity. Other features such as non-specific binding, variation and leaching turned out to be more relevant. The immunoassays that use a direct surface readout measurement of time-resolved fluorescence from a washed surface are dependent on the density of the labeled antibodies in a defined area on the surface. The binding surface was condensed into a spot by coating streptavidin in liquid droplets into special microtiter wells holding a small circular indentation at the bottom. The condensed binding area enabled a denser packing of the labeled antibodies on the surface. This resulted in a 5 - 6-fold increase in the signal-to-background ratios and an equivalent improvement in the detection limits of the solid-phase immunoassays. This work proved that the properties of the streptavidin-coated surfaces can be modified and that the defined properties of the streptavidin-based immunocapture surfaces contribute to the performance of heterogeneous immunoassays.

Statistical Methods for Conservation and Alignment Quality in Proteins

Construction of multiple sequence alignments is a fundamental task in Bioinformatics. Multiple sequence alignments are used as a prerequisite in many Bioinformatics methods, and subsequently the quality of such methods can be critically dependent on the quality of the alignment. However, automatic construction of a multiple sequence alignment for a set of remotely related sequences does not always provide biologically relevant alignments.Therefore, there is a need for an objective approach for evaluating the quality of automatically aligned sequences. The profile hidden Markov model is a powerful approach in comparative genomics. In the profile hidden Markov model, the symbol probabilities are estimated at each conserved alignment position. This can increase the dimension of parameter space and cause an overfitting problem. These two research problems are both related to conservation. We have developed statistical measures for quantifying the conservation of multiple sequence alignments. Two types of methods are considered, those identifying conserved residues in an alignment position, and those calculating positional conservation scores. The positional conservation score was exploited in a statistical prediction model for assessing the quality of multiple sequence alignments. The residue conservation score was used as part of the emission probability estimation method proposed for profile hidden Markov models. The results of the predicted alignment quality score highly correlated with the correct alignment quality scores, indicating that our method is reliable for assessing the quality of any multiple sequence alignment. The comparison of the emission probability estimation method with the maximum likelihood method showed that the number of estimated parameters in the model was dramatically decreased, while the same level of accuracy was maintained. To conclude, we have shown that conservation can be successfully used in the statistical model for alignment quality assessment and in the estimation of emission probabilities in the profile hidden Markov models.

Active sulphide mine tailings impoundments as sources of contaminated drainage: controlling factors, methods of characterisation and geochemical constraints for mitigation

Low quality mine drainage from tailings facilities persists as one of the most significant global environmental concerns related to sulphide mining. Due to the large variation in geological and environmental conditions at mine sites, universal approaches to the management of mine drainage are not always applicable. Instead, site-specific knowledge of the geochemical behaviour of waste materials is required for the design and closure of the facilities. In this thesis, tailings-derived water contamination and factors causing the pollution were investigated in two coeval active sulphide mine sites in Finland: the Hitura Ni mine and the Luikonlahti Cu-Zn-Co-Ni mine and talc processing plant. A hydrogeochemical study was performed to characterise the tailingsderived water pollution at Hitura. Geochemical changes in the Hitura tailings were evaluated with a detailed mineralogical and geochemical investigation (solid-phase speciation, acid mine drainage potential, pore water chemistry) and using a spatial assessment to identify the mechanisms of water contamination. A similar spatial investigation, applying selective extractions, was carried out in the Luikonlahti tailings area for comparative purposes (Hitura low-sulphide tailings vs. Luikonlahti sulphide-rich tailings). At both sites, hydrogeochemistry of tailings seepage waters was further characterised to examine the net results of the processes observed within the impoundments and to identify constraints for water treatment. At Luikonlahti, annual and seasonal variation in effluent quality was evaluated based on a four-year monitoring period. Observations pertinent to future assessment and mine drainage prevention from existing and future tailings facilities were presented based on the results. A combination of hydrogeochemical approaches provided a means to delineate the tailings-derived neutral mine drainage at Hitura. Tailings effluents with elevated Ni, SO₄ ^2- and Fe content had dispersed to the surrounding aquifer through a levelled-out esker and underneath the seepage collection ditches. In future mines, this could be avoided with additional basal liners in tailings impoundments where the permeability of the underlying Quaternary deposits is inadequate, and with sufficiently deep ditches. Based on the studies, extensive sulphide oxidation with subsequent metal release may already initiate during active tailings disposal. The intensity and onset of oxidation depended on e.g. the Fe sulphide content of the tailings, water saturation level, and time of exposure of fresh sulphide grains. Continuous disposal decreased sulphide weathering in the surface of low-sulphide tailings, but oxidation initiated if they were left uncovered after disposal ceased. In the sulphide-rich tailings, delayed burial of the unsaturated tailings had resulted in thick oxidized layers, despite the continuous operation. Sulphide weathering and contaminant release occurred also in the border zones. Based on the results, the prevention of sulphide oxidation should already be considered in the planning of tailings disposal, taking into account the border zones. Moreover, even lowsulphide tailings should be covered without delay after active disposal ceases. The quality of tailings effluents showed wide variation within a single impoundment and between the two different types of tailings facilities assessed. The affecting factors included source materials, the intensity of weathering of tailings and embankment materials along the seepage flow path, inputs from the process waters, the water retention time in tailings, and climatic seasonality. In addition, modifications to the tailings impoundment may markedly change the effluent quality. The wide variation in the tailings effluent quality poses challenges for treatment design. The final decision on water management requires quantification of the spatial and seasonal fluctuation at the site, taking into account changes resulting from the eventual closure of the impoundment. Overall, comprehensive hydrogeochemical mapping was deemed essential in the identification of critical contaminants and their sources at mine sites. Mineralogical analysis, selective extractions, and pore water analysis were a good combination of methods for studying the weathering of tailings and in evaluating metal mobility from the facilities. Selective extractions with visual observations and pH measurements of tailings solids were, nevertheless, adequate in describing the spatial distribution of sulphide oxidation in tailings impoundments. Seepage water chemistry provided additional data on geochemical processes in tailings and was necessary for defining constraints for water treatment.

ContinuousMultimodal Global Optimization with Differential Evolution-Based Methods

Metaheuristic methods have become increasingly popular approaches in solving global optimization problems. From a practical viewpoint, it is often desirable to perform multimodal optimization which, enables the search of more than one optimal solution to the task at hand. Population-based metaheuristic methods offer a natural basis for multimodal optimization. The topic has received increasing interest especially in the evolutionary computation community. Several niching approaches have been suggested to allow multimodal optimization using evolutionary algorithms. Most global optimization approaches, including metaheuristics, contain global and local search phases. The requirement to locate several optima sets additional requirements for the design of algorithms to be effective in both respects in the context of multimodal optimization. In this thesis, several different multimodal optimization algorithms are studied in regard to how their implementation in the global and local search phases affect their performance in different problems. The study concentrates especially on variations of the Differential Evolution algorithm and their capabilities in multimodal optimization. To separate the global and local search search phases, three multimodal optimization algorithms are proposed, two of which hybridize the Differential Evolution with a local search method. As the theoretical background behind the operation of metaheuristics is not generally thoroughly understood, the research relies heavily on experimental studies in finding out the properties of different approaches. To achieve reliable experimental information, the experimental environment must be carefully chosen to contain appropriate and adequately varying problems. The available selection of multimodal test problems is, however, rather limited, and no general framework exists. As a part of this thesis, such a framework for generating tunable test functions for evaluating different methods of multimodal optimization experimentally is provided and used for testing the algorithms. The results demonstrate that an efficient local phase is essential for creating efficient multimodal optimization algorithms. Adding a suitable global phase has the potential to boost the performance significantly, but the weak local phase may invalidate the advantages gained from the global phase.