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In this thesis, we concentrate on the problem of modelling real document collections, especially sequential document collections. The goal is to discover important hidden topics in the collection automatically by statistical modelling of its content. For the sequential document collections, we want to also capture how the topics change over time. To date, several computational tools such as latent dirichlet allocation (LDA) have been developed for modelling document collections. In this thesis, we develop new topic models for modelling the dynamic characteristics of a sequential document collection such as the news archives. We are, for example, interested in splitting the topics into long-term topics such as 'Eurozone crisis' that are discussed over years, and short-term topics such as 'Winter Olympics in 2014' that are only popular for several weeks. We first review the popular models for detecting the hidden topics and their evolution, and then propose two new approaches to detect these two kinds of topics. To provide real world data for the evaluation of our new approaches, we additionally design a pipeline for constructing sequential document collections through collecting documents from the Web. To investigate the performance of our new approaches from different aspects, we conduct qualitative and quantitative experiments on two different kinds of datasets respectively: news documents collected by the pipeline and 17 years' documents from the Neural Information Processing Systems (NIPS) conferences. The qualitative experiments aim at evaluating the quality of the discovered topics, whereas the quantitative experiments concern about their ability to predict new words from the unseen documents.

Solutions of thermoresponsive polymers exhibit a drastic and discontinuous change in their properties with temperature. A thermoresponsive polymer that is soluble at low temperatures but undergoes reversible phase transition in a solvent with rising temperature resulting in precipitation or cloud formation is said to exhibit Lower Critical Solution Temperature (LCST)-type behaviour. On the other hand, polymers that exhibit Upper Critical Solution Temperature (UCST)-type behaviour are soluble in water at temperatures above UCST and become reversible insoluble when temperature decreases below upper critical solution temperature. This work deals with the synthesis of novel upper critical solution temperature block copolymers and the effect of pH and electrolyte on their cloud point temperatures. The polymers poly(N-acryloylglycinamide) (PNAGA), poly(ethyleneoxide)-b-poly(N-acryloylglycinamide) (PEO-b-PNAGA), poly(N-isopropyl acrylamide)-b-poly(N-acryloylglycinamide) (PNIPAAm-b-PNAGA) and poly(ethyleneoxide)-b-poly(N-acryloylglycinamide)-b-poly(N-isopropyl acrylamide) (PEO-b-PNAGA-b-PNIPAAm) were synthesized by Reversible Addition-Fragmentation chain-Transfer polymerization in dimethyl sulphoxide. PEO-b-PNAGA and PEO-b-PNAGA-b-PNIPAAm exhibited UCST-type behaviour both in pure water (studied by NMR) and 0.1M NaCl solutions (studied by turbidimetry). Poly (ethyleneoxide) (PEO) block played an important role in enhancing the UCST behaviour of PNAGA by improving the polymers solubility. Yet, higher cloud points in 0.1M NaCl were observed than for PNAGA due to the presence of hydrophobic dodecyl end group. Measuring the particle size between 10-50 °C by dynamic light scattering proved that the polymers phase separated on cooling below the UCST. PEO-b-PNAGA-b-PNIPAAm showed multiresponsive behaviour both in pure water and electrolyte solution exhibiting both LCST and UCST. Change in pH had a dramatic effect on the UCST of PNAGA owing to the carboxylic acid end group shifting the cloud points to higher temperatures with increase in pH. The cloud points were lower for the PNAGA block copolymers in pH 4 buffer solutions compared to that of PNAGA itself due to high solubility of poly (ethylene oxide) block in aqueous solutions.

Nukleiinihapot ovat luonnollisia yksi- tai kaksisäikeisiä polymeerejä, jotka koostuvat deoksiribo- tai ribonukleosideistä linkitettynä toisiinsa fosfodiesterisidoksella. Kun tällaisia ketjuja valmistetaan kemiallisin menetelmin fosfaattiryhmä olisi aktivoitava tietyllä tavalla ja funktionaaliset ryhmät, jotka eivät osallistu reaktioon, olisi suojattava väliaikaisesti tai pysyvästi. Kiinnostus nukleiinihappokemiaan johtuu synteettisten oligomeerien ja niiden analogien kasvavasta tarpeesta välttämättöminä tutkimusvälineinä molekyylibiologiassa ja lääketieteessä. Tutkielman kirjallisessa osassa esitettiin erilaisia menetelmiä lyhyiden oligonukleotidien kemialliselle synteesille. Fosfodiesterisidosten muodostuminen tapahtuu yleensä joko fosfotriesterin tai fosfiitti-triesterin välituotteiden avulla. P(III)-välituotteiden suuremman reaktiivisuuden vuoksi fosfiitti-triesterimenetelmä ja erityisesti fosforamidiittimenetelmä ovat herättäneet huomiota. Oligonukleotidisynteesin lähtöaineiksi on ehdotettu useita erilaisia nukleosidi-fosforamidiitteja, kun on etsitty tasapainoa stabiilisuuden ja reaktiivisuuden välillä. Tämän vuoksi H-fosfonaattimenetelmää, jossa yhdistetään sekä fosfotriesteri- että fosfiitti-triesterimenetelmien edut ja lisäksi fosfodiesterimenetelmän edut (esim. fosforikeskuksen suojaavan ryhmän puute), voidaan käyttää vaihtoehtona fosforamidiittimenetelmälle erityisesti RNA:n sekä hapoille labiilien oligonukleotidianalogien synteesissä. Kaikilla menetelmillä on kuitenkin hyvät puolet sekä huonot puolet, joten ei olisi vielä olemassa yleisesti sovellettavaa ja tehokasta synteesimenetelmää, vaan ne sopivat eri tapauksiin. Esimerkiksi suuren mittakaavan synteesin tapauksessa tulee ottaa huomioon reaktioaika, reagenssi, puhdistusmenetelmä ja muut resurssit. Lisäksi lähestymistavat ovat yleensä joko erittäin työläitä etenkin lopputuotteen puhdistuksessa tai monivaiheisia sekvenssejä, joiden kokonaistuotto on alhainen. Kokeellisessa osassa valmistettiin kolmenlaisina Brønsted happokatalyytteinä pentakarboksisyklopentadieenit (PCCP). Tutkittiin mahdollisuutta käyttää PCCP-johdonnaisia regioselektiiviseen nukleosidin 5’-hydroksyyliryhmän suojaamiseen asetaaliryhmällä. Menetelmällä onnistuttiin valmistamaan tyydyttävä määrä 5’-O-asetaalisuojattua tymidiiniä. Menetelmä vaikuttaa lupaavalta pienellä jatkokehityksellä.

Vlasiator is a new massively parallel hybrid-Vlasov simulation code being developed at the Finnish Meteorological Institute with the purpose of building new global magnetospheric model going beyond magnetohydrodynamics (MHD). It solves Vlasov's equation for the ion distribution function in the full six-dimensional phase space and describes the electrons as a massless charge neutralising fluid using the MHD equations, thus including ion kinetic effects. The Vlasov equation solver is based on a second-order, three-dimensional finite volume wave-propagation algorithm, making use of Strang splitting to separate translation in space from acceleration in velocity space. The electromagnetic fields are obtained through a second-order, finite volume upwind constrained transport method which conserves the divergence of the magnetic by construction. This work presents the numerical and physical validation tests developed and/or run by the author for Vlasiator, without however covering the technical aspects pertaining to implementation or parallelisation. The numerical quality of the solvers is being assessed for their isotropy, their conservation of div B = 0 and their order of accuracy in space and time. The physical validation tests include an assessment of the diffusive properties of the Vlasov solver, a brief discussion of results obtained from the Riemann problem displaying kinetic effects in the shock solution and finally dispersion plots for quasiperpendicular and quasiparallel wave modes are presented and discussed. The conclusions are that Vlasiator performs well and in line with the expected characteristics of the methods implemented, provided the resolution is good enough. In space, ion kinetic scales should be resolved for kinetic effects going beyond an MHD description to emerge. In velocity space the resolution should yield a smooth discretisation of the ion distribution function, otherwise spurious non-physical artefacts can crop up in the results. The higher-order correction terms included in the solvers ensure good orders of accuracy even for discontinuous solutions, the conservation of div B = 0 is provided up to floating-point accuracy and dispersion plots match remarkably well analytic solutions.

In this thesis, we demonstrate the use of machine learning in numerically solving both linear and non-linear parabolic partial differential equations. By using deep learning, rather than more traditional, established numerical methods (for example, Monte Carlo sampling) to calculate numeric solutions to such problems, we can tackle even very high dimensional problems, potentially overcoming the curse of dimensionality. This happens when the computational complexity of a problem grows exponentially with the number of dimensions. In Chapter 1, we describe the derivation of the computational problem needed to apply the deep learning method in the case of the linear Kolmogorov PDE. We start with an introduction to a few core concepts in Stochastic Analysis, particularly Stochastic Differential Equations, and define the Kolmogorov Backward Equation. We describe how the Feynman-Kac theorem means that the solution to the linear Kolmogorov PDE is a conditional expectation, and therefore how we can turn the numerical approximation of solving such a PDE into a minimisation. Chapter 2 discusses the key ideas behind the terminology deep learning; specifically, what a neural network is and how we can apply this to solve the minimisation problem from Chapter 1. We describe the key features of a neural network, the training process, and how parameters can be learned through a gradient descent based optimisation. We summarise the numerical method in Algorithm 1. In Chapter 3, we implement a neural network and train it to solve a 100-dimensional linear Black-Scholes PDE with underlying geometric Brownian motion, and similarly with correlated Brownian motion. We also illustrate an example with a non-linear auxiliary Itô process: the Stochastic Lorenz Equation. We additionally compute a solution to the geometric Brownian motion problem in 1 dimensions, and compare the accuracy of the solution found by the neural network and that found by two other numerical methods: Monte Carlo sampling and finite differences, as well as the solution found using the implicit formula for the solution. For 2-dimensions, the solution of the geometric Brownian motion problem is compared against a solution obtained by Monte Carlo sampling, which shows that the neural network approximation falls within the 99\% confidence interval of the Monte Carlo estimate. We also investigate the impact of the frequency of re-sampling training data and the batch size on the rate of convergence of the neural network. Chapter 4 describes the derivation of the equivalent minimisation problem for solving a Kolmogorov PDE with non-linear coefficients, where we discretise the PDE in time, and derive an approximate Feynman-Kac representation on each time step. Chapter 5 demonstrates the method on an example of a non-linear Black-Scholes PDE and a Hamilton-Jacobi-Bellman equation. The numerical examples are based on the code by Beck et al. in their papers "Solving the Kolmogorov PDE by means of deep learning" and "Deep splitting method for parabolic PDEs", and are written in the Julia programming language, with use of the Flux library for Machine Learning in Julia. The code used to implement the method can be found at https://github.com/julia-sand/pde_approx

This study discusses the methods, algorithms and implementation techniques involved in the computational solution of unconstrained minimization problem : min x ∈ Rn f : Rn −! R Where Rn denotes the n-dimensional Euclidean space. The main goal in this study was to implement an easy-to-use software package running in personal computers for unconstrained minimization of multidimensional functions. This software package includes C language implementations of six minimization methods (listed below), an user-interface for entering each minimization problem, and an interface to a general software system called MathematicaTM which is used for plotting the problem function and the minimization route. The following minimization methods are discussed here : - Parabolic interpolation in one-dimension - Downhill simplex method in multidimensions - Direction set method in multidimensions - Variable metric method in multidimensions - Conjugate gradients method in multidimensions - Modified steepest descent method in multidimensions The first part of this study discusses the theoretical background of the minimization algorithms to be implemented in the software package. The second part introduces the overall design of the minimization software and in greater detail describes the individual software modules, which, as a whole, implement the software package. The third part introduces the techniques for testing the minimization algorithms, describes the set of test problems, and discusses the test results.

This work explores the lateral spreading of hot, thick, Paleoproterozoic crust via a series of 2D thermomechanical numerical models based on two geometrical a priori models of the thickened crust: plateau and plateau margin. High Paleoproterozoic radiogenic heat production is assumed. The material viscosity is temperature-dependent following the Arrhenius law. The experiments use two sets of rheological parameters for the crust: dry (granite/felsic granulite/mafic granulite) and wet (granite/diorite/mafic granulite). The results of the modeling are compared to seismic reflection sections and surface geological observations from the Paleoproterozoic Svecofennian orogen. Numerical modelling is performed with Ellipsis, a particle-in-cell finite element code suitable for 2D thermo-mechanical modelling of lithospheric deformation. It uses Lagrangian particles for tracking material interfaces and histories, which allow recording of material P-T-t paths. Plateau-models are based on a 480 km long section of 65 km-thick three-layer plateau crust. In the plateau margin-models, a transition from 65 km thick plateau to 40 km thick foreland is imposed in the middle of the model. The models are extended symmetrically from both ends with slow (1.9 mm/a) and fast (19 mm/a) velocities. Gravitational collapse is simulated with an additional set of fixed boundary plateau margin models. The models are studying the effect of free moving boundaries on the crustal structure and the conditions for mid-crustal flow. Strong mid-crustal channel flow is seen in plateau margin models with dry rheology and slow extension or with fixed boundaries. With fast extension or wet rheology channel flow grows weaker/diminishes. In models with slow extension or fixed boundaries, partial melting controls the style of deformation in the middle crust. Vertical movement of the partially molten material destroys lateral flow structures in plateau regions. According to P-T-t paths, the model materials do not experience high enough temperatures to match HT-LP metamorphic conditions typical for Svecofennian orogenic rocks. Metamorphic conditions in the dry rheology models have counterparts in the LT-LP (>650 °C at ≤600 MPa) amphibolite facies rocks of the Pielavesi area. Plateau margin models with dry rheology and slow extension or fixed boundaries developed mid-crustal channel flow, thinning of middle crust, exhumation of mid-crustal domes and smooth Moho, all of which are found in crustal scale reflection sections. Results of this work suggest plateau margin architecture prior to extension that took place at slow velocities or through purely gravitational collapse, although peak temperature of Svecofennian HT-LP metamorphism was not attained.

Topological defects are some of the more common phenomena of many extensions of the standard model of particle physics. In some sense, defects are a consequence of an unresolvable misalignment between different regions of the system, much like cracks in ice or kinks in an antiquated telephone cord. In our context, they present themselves as localised inhomogeneities of the fundamental fields, emerging at the boundaries of the misaligned regions at the cost of, potentially massive, trapped energy. Should the cosmological variety exist in nature, they are hypothesised to emerge from some currently unknown cosmological phase transition, leaving their characteristic mark on the evolution of the nascent universe. As of date, so called cosmic strings are perhaps the most promising type of cosmic defect, at least with respect to their observational prospects. Cosmic strings, as the name suggest, are linelike topological defects; exceedingly thin, yet highly energetic. Given the advent of gravitational wave astronomy, a substantial amount of research is devoted to detailed and expensive real-time computer simulations of various cosmic string models in hopes of extracting their effects on the gravitational wave background. In this thesis we discuss the Abelian-Higgs model, a toy model of a gauge theory of a complex scalar field and a real vector field. Through a choice of a symmetry-breaking scalar potential, this model permits line defects, so called local strings. We discuss some generalities of classical field theory as well as those of the interesting mathematical theory of topological defects. We apply these to our model and present the necessary numerical methods for writing our own cosmic string simulation. We use the newly written simulation to reproduce a number of contemporary results on the scaling properties of the string networks and present some preliminary results from a less investigated region of the model parameter space, attempting to compare the effects of different types of string-string interactions. Furthermore, preliminary results are presented on the thermodynamic evolution of the system and the effects a common computational trick, comoving string width, are discussed with respect to the evolution of the equation of state.

Multiple changes have occurred in the landscape of the cities and brought new challenges to the use of land in the urban areas. Urban areas have become more compact, population has grown and whereas the amount of public spaces have decreased. Many public spaces have turned into quasi-public or even private spaces. Urban planners and decision-makers must take into account the needs of even more different actors than before. When the number of public spaces has decreased, some of the groups using it, have become more easily excluded from it. A battle of the right to be and use the public spaces are fought between different groups. Adolescents are one of these groups that often tend to be excluded, even though public spaces are significant for their free-time. They also lack places where to be or meet each other. In addition, knowledge about the meanings and qualities of the places where adolescents spend time is scarce. This master's thesis is a case study of Vuosaari suburb in the Eastern Helsinki. The aim is to explore the public and quasi-public spaces where the local adolescents spend their time. Furthermore, qualities and meanings as well as adolescents needs in those spaces are studied. The data used in this study was collected through interviews and place mapping. In place mapping adolescents could mark the places where they hang out on the map and describe them in written form. The study is based on the idea of subjective construction of space and place perception, which are also affected by cultural and environmental factors. Adolescent's perception of public and quasi-public spaces is explored through theory of affordances. Affordance implies to the possible threats and possibilities that one might find from the surrounding environment. The public and quasi-public spaces that are used by adolescents in Vuosaari are moreover classified into loose spaces, spaces of doing and tight spaces. Loose spaces are free from the adult control whereas in the tight spaces and spaces of doing adolescents are under adult surveillance. Tight spaces are aimed to certain kind of doing and it is not possible to differ from the activities designated beforehand. In the spaces of doing it is possible to perform different activities more freely. However, challenging the norms of those spaces leads to sanctions. The study found that adolescents use different kind of public and quasi-public spaces. How they use and value them is dependent on their needs and preferences. The findings suggest that socializing and activities play a major role for adolescents in the public and quasi-public spaces. Also accessibility and closeness of home are important factors for adolescents when choosing the hangout places. Ambiguity characterizes the spaces adolescents prefer. They are sometimes used to expose oneself in front of others, but on the other hand adolescents seek places where they can avoid adult control. Therefore, especially loose spaces, that offer possibility to avoid adult control, proved to be important for adolescents. Additionally, social and functional affordances were valued as well as spaces where those affordances could be found. Adolescents should not however be bundled into one category, since they have different needs in public and quasi-public spaces. Their needs are dependent on factors such as gender and personal preferences. Hence, urban planners and decision-makers ought to offer as diverse public and quasi-public spaces as possible. Furthermore, adolescent's use of public and quasi-public spaces should be accepted.

As a consequence of industrialization, metal concentrations in nature are big enough to have harmful effects on humans, animals and the environment. On that grounds, EU legislates maximum metal concentrations in several matrices. More sensitive and more selective analytical techniques are required in making sure these norms are being followed. To assess the biological activity and toxicity, along with the total metal concentration, the knowledge on the oxidation state of the metal and speciation is to be signified. In the literature part of the thesis the most used sample pretreatment and analysis techniques in metal determination in the years 2007–2017 are covered. Atomic absorption spectrometry and inductively coupled plasma based techniques are compared in determination of total metal concentration. Liquid chromatography and capillary electrophoresis coupled with mass spectrometry detection are presented as techniques used in speciation analysis. Also, sample pretreatment techniques are presented – especially solid-phase extraction – as well as parameters influencing extraction efficiency and selectivity. New sorbent materials, their synthesis and characterization, and applications are discussed in the last section of the literature part. A few studies regarding metal speciation analysis are also presented. Some future aspects of solid-phase extraction are evaluated in the end of literature part. In the experimental part of the thesis, metals were determined with inductively coupled mass spectrometer (ICP-MS) from boric acid containing waters in Loviisa Nuclear Power Plant. Determination of metals relates directly to the safe operation of the plant. However, the large concentration of boric acid in the process water samples prevents their analysis with ICP-MS. In the experimental part, boric acid concentration was diluted with two sample pretreatment methods: esterification or on-line aerosol dilution. Aerosol dilution was a better approach in process water analysis than esterification. Thus, three analytical methods using aerosol dilution in different boric acid and metal concentrations were optimized. Validation of two of these methods are presented in the end of the experimental part.