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Asymmetrical flow field-flow fractionation (AF4) is a separation and characterization technique for macromolecules and particles, which has been gaining popularity in a multitude of scientific and industrial applications. AF4 is considered a challenging experimental technique to optimize and relatively few tools exist for this purpose. One of the main aims of the work was to provide practitioners of AF4 techniques with software tools, which bridge the gap between domain knowledge and AF4 theory for a more fluid experimental design workflow. This is made possible by a feature of AF4, which makes it stand out from related separation methods by enabling theory-driven prediction of sample behavior over the course of the experiment. In the first part of the computer experiments carried out, an algorithm based on probability theory was developed for predicting the ideal separation of samples based on readily obtainable sample properties. Among the obtained results is a predicted fractogram, which is the end product of an AF4 experiment run. The ability to predict separation of samples finds use in AF4 method development as well as other applications relevant to experimental work. The algorithmic models were constructed to describe real life systems for which experimental data was available and against which performance could be tested. The real world systems modeled included two AF4 instrument channels with different geometries and both natural and synthetic polymer samples. Prediction by the algorithm was compared to previously published experimental data from other authors, after configuring the algorithm to the corresponding experimental setups. The results suggest that the algorithm can relatively closely approximate predictions made by the underlying ideal AF4 theory. For a disperse polymer sample in a separation program for which no simple theoretical result was available, the algorithm's predictions gave promising results for approximating the shape of fractogram curve. In the second part of the computer experiments, a theory based model was fitted to experimental data and performing statistical inference was explored as a technique. Bayesian data analysis was used therein to complete a routine task in AF4 operation and subsequent data processing. The data analysis provided an estimate congruent with theory and external estimates given for the same data by other researchers. Looking forward, possible enhancements to the presented models and their applicability more widely to AF4 work as well as possible developments of computational models in the field are discussed.

Time series analysis has been a popular research topic in the last few decades. In this thesis, we develop time series models to investigate short time series of count data. We first begin with Poisson autoregressive model and extend it to capture day effects explicitly. Then we propose hierarchical Poisson tensor factorization model as an alternative to the traditional count time series models. Furthermore, we suggest acontext-based model as an improvement over hierarchical Poisson tensor factorization model. We implement the models in an open-source probabilistic programming framework Edward. This tool enables us to express the models in form of executable program code and allows us to rapidly prototype models without the need of derivation of model specificupdaterules. We also explore strategies for selecting the best model out of alternatives. We study the proposed models on a dataset containing media consumption data. Our experimental findings demonstrate that the hierarchical Poisson tensor factorization model significantly outperforms the Poisson autoregressive models in predicting event counts. We also visualize the key results of our exploratory data analysis.

DNA sequencing has seen a rapid decrease in price during the last decade. As a result, routine sequencing of bacterial colonies in both clinical and environmental sources is becoming increasingly available. However, accurate identification of the bacterial strains colonizing a sample remains difficult especially in the presence of multiple organisms. Traditional methods based on culturing the bacteria are laborous and ineffective, while methods based on sequencing data have trouble differentiating between closely related variants of the species. Accurate identification of the species or strains contained in a sample would be desirable both in metagenomic studies and in improving the quality of hospital care. The aim of this thesis was to develop a computational method for accurate bacterial strain identification. Based on recent advancements in sequencing read alignment and application of Bayesian inference to bacterial strain identification, the thesis introduces a pipeline capable of rapid and accurate strain identification from high-throughput sequencing data. By representing the within-species variation with multiple reference genomes that have been clustered, the pipeline is able to accurately determine the cluster proportions in a sample from pseudoalignment of reads to the reference genomes. The proportions are estimated using a variational Bayesian method. Accuracy of the method is evaluated on both real and synthetic data containing reads originating from Staphylococcus aureus, Staphylococcus epidermidis, Klebsiella pneumoniae, Campylobacter jejuni and Campylobacter coli. In all cases the cluster proportions are accurately identified and performance is significantly better than that of existing methods.

The crystal structure of magnetite (Fe3O4) involves Fe2+ ions in sites with octahedral (Oh) symmetry and Fe2+ and Fe3+ ions in sites with tetrahedral (Td) symmetry. Magnetite exhibits several interesting physical phenomena, such as the Verwey transition, in which the roles of the different Fe sites are an active subject of research. In the X-ray standing wave (XSW) technique, incoming and diffracted X-ray beams interfere inside a crystal, creating a standing wave with the periodicity of the diffracting atomic lattice. The phase of the wave, i.e. whether the nodes are located on the lattice planes or between them, can be adjusted by finely tuning the diffraction angle. Changing the phase in this way makes it possible to selectively vary the contributions of different atoms and absorption types (dipole versus quadrupole) to the measured total absorption spectrum. Iron K-edge absorption spectra in magnetite were studied in the presence of an XSW in an experiment conducted at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. This thesis presents an analysis of the data gathered during the experiment, with the goal of decomposing the experimentally measured pre-edge peak into its constituent components. The methods used in the analysis include principal component analysis and fitting predicted absorption peaks calculated with the Quanty software to the experimental data. The results show the dipole and quadrupole contributions of the tetrahedral sites responding to changes in the phase of the XSW in opposite ways in a manner consistent with theoretical predictions.

Particle Induced X-ray Emission (PIXE) was originally introduced as an ion-beam analytical technique in Lund in the 1970s and has since then been part of the available techniques in many laboratories around the world. The external beam PIXE set-up is used in probing the annual tree rings. The goal is to see the effects of volcanic eruption activities from the perspectives of tree plants here in Finland. In the theory part, I tried to include the description of how volcanoes are formed and created with a bit of volcanic activity history, the growth metabolism mechanism in tree plants and characteristics x-ray productions. The two tree sample used for this experiment were gotten from two different regions of Finland. The first tree is a Pine tree from Parikkala(a small place near Savolinna) in the south-eastern part of Finland and the second tree is a Spruce tree from Pielavesi (place near Kuopio) in the central part of Finland. These samples were carefully prepared for ionisation. The collected spectra data were analysed in a software called PyMCA. PyMCA has been developed by the Software Group of the European Synchrotron Radiation Facility (ESRF). PyMCA is a ready to use and in many aspects state-of-the-art, set of applications implementing most of the needs of X-ray fluorescence data analysis. PyMCA is use to interpret X-ray fluorescence spectra from a diverse array of samples

In condition-based maintenance data is collected from a machine to provide advice on frequency and location of developing faults. Statistical inference is needed to transform the data into information on the health of the machine. The ultimate goal is to minimise the machine down-time due to unexpected breakage. Predictive maintenance attempts to forecast the condition of the machine components from the observed data, and to maintain the machine just before it breaks down. The research question this thesis aims to solve is how to diagnose and predict component health based on data collected from the machine. Based on the literature, hidden Markov model is selected for further study. There is usually uncertainty relating to the parameters and structure of the model due to the complicated causal relationships in the modelling problem. Therefore the thesis concentrates in finding a suitable inference algorithm which is able to learn the model from data. Six different frequentist and Bayesian algorithms are tested with a synthetic example. A hypothesis is put forward that a hybrid genetic variational Bayesian algorithm could be used to find the best performing hidden Markov model of component health. As expected, the hybrid variational algorithm performs better than the other examined algorithms, especially when there is uncertainty relating to the model structure. However, since there typically is an imbalance between the data depicting faults and the data depicting the normal behaviour, the simulated test case shows that even the best performing variational algorithm has difficulties in identifying the correct model. This results in increased uncertainty in the health predictions. The thesis confirms that the hidden Markov model has many good qualities for modelling component health based on remote monitoring data. Due to the versatility of the model, it can be modified to account for the many details of component degradation behaviour in different machines.

In this thesis, we aim to introduce the reader to profinite groups. Profinite groups are defined by two characteristics: firstly, they have a topology defined on them (notably, they are compact). Secondly, they are constructed from some collection of finite groups, each equipped with a discrete topology and forming what is known as an inverse system. The profinite group emerges as an inverse limit of its constituent groups. This definition is, at this point, necessarily quite abstract. Thus, before we can really understand profinite groups we must examine two areas: first, we will study topological groups. This will give us the means to deal with groups as topological spaces. Topological groups have some characteristics that differentiate them from general topological spaces: in particular, a topological group is always a homogeneous space. Secondly, we will explore inverse systems and inverse limits, which will take us into category theory. While we could explain these concepts without categories, this thesis takes the view that category theory gives us a useful “50000-feet view” by giving these ideas a wider mathematical context. In the second chapter, we will go through preliminary information concerning group theory, general topology and category theory that will be needed later. We will begin with some basic concepts from group theory and point-set topology. These sections will mostly contain information that is familiar from the introductory university courses. The chapter will then continue by introducing some basic concepts of category theory, including inverse systems and inverse limits. For these, we will give an application by showing how the Cantor set is homeomorphic to an inverse limit of a collection of finite sets. In the third chapter, we will examine topological groups and prove some of their properties. In the fourth chapter, we will introduce an example of profinite groups: Zp, the additive group of p-adic integers. This will be expanded into a ring and then into the field Qp. We will discuss the uses of Zp and Qp and show how to derive them as an inverse limit of finite, compact groups.

Data centers provide a demanding and complex environment for networking as there is a need to provide fairness, throughput, and responsiveness while balancing great volumes of data and different types of flows. Programmable scheduling aims to make networking more flexible by providing capabilities for testing, modifying, and running a greater number of scheduling algorithms on switches than currently is possible. This is done by having a hardware design on top of which scheduling algorithms can be run as software. Over the years, multiple different abstractions for the switch scheduler have been suggested, with the aim of being capable of running at line rate. This thesis is a literature review of different programmable scheduler designs, focusing on Push-In First-Out, Push-In Extract-Out, Strict Priority Push-In First-Out, and Admission-In First-Out designs. This work provides an overview of the designs and their hardware implementations, observing their strengths and weaknesses regarding the data center environment. These designs are compared to one another with a focus on trade-offs between metrics like speed, expressiveness, and scalability, with a discussion on how these trade-offs ensure that there is currently no design that is above the others in all aspects.

Denna avhandling ställer frågor kring vad det innebär för den långa matematiken i gymnasiet när programmering tillkommer enligt läroplanen. Först granskas den tidigare forskningen kring programmering och matematik i gymnasiet och till vilka slutsatser man kommit i dessa. Att programmering kan vara till nytta för studeranden i yrkeslivet är givet, men huruvida programmering skall höra till matematiken är en av huvudfrågorna i avhandlingen. Eftersom det inte finns mycket forskning kring programmering i matematik i Finland har här även används forskning gjort i andra länder. Samma sak gäller för den aktuella åldersgruppen, därför har även forskning med studeranden i ungefär samma ålder använts. Inget undervisningsmaterial ännu finns för programmeringen i gymnasiet. Därför finns här också förslag till uppgiftstyper som kunde användas i undervisningen. Dessa exempel får fritt modifieras och användas som hjälp vid planering av undervisningen. En annan användning av denna avhandling kunde vara att låta den vara som grund för kommande planering av programmering i gymnasiet angående så väl i vilka ämnen programmering hanteras och hur denna undervisning

Progressiivisen web-sovelluksen (Progressive Web Application, PWA) tarkoitus on hämärtää tai jopa poistaa raja sovelluskaupasta ladattavan sovelluksen ja normaalin verkkosivuston välillä. PWA-sovellus on kuin mikä tahansa normaali verkkosivusto, mutta se täyttää lisäksi seuraavat mittapuut: Sovellus skaalautuu mille tahansa laitteelle. Sovellus tarjotaan salatun yhteyden yli. Sovellus on mahdollista asentaa puhelimen kotinäytölle pikakuvakkeeksi, jolloin sovellus avautuu ilman selaimesta tuttuja navigointityökaluja ja lisäksi sovelluksen voi myös avata ilman verkkoyhteyttä. Tässä työssä käydään läpi PWA-sovelluksen rakennustekniikoita ja määritellään milloin sovelluson PWA-sovellus. Työssä mitataan PWA-sovelluksen nopeutta Service Workerin välimuistitallennusominaisuuksien ollessa käytössä ja ilman. PWA-sovelluksen luomista ja käyttöönottoa tarkastellaan olemassa olevassa yksityisessä asiakasprojektissa. Projektin tarkastelussa kiinnitetään huomiota PWA-sovelluksen tuomiin etuihin ja kipupisteisiin. Tuloksen arvioimiseksi otetaan Google Chromen Lighthouse -työkalua käyttäen mittaukset sovelluksen progressiivisuudesta ja nopeudesta. Lisäksi sovellusta vasten ajetaan Puppeteer-kirjastoa hyödyntäen latausnopeuden laskeva testi useita kertoja sekä tarkastellaan PWA-sovelluksen Service Workerin välimuistin hyödyllisyyttä suorituskyvyn ja latausajan kannalta. Jotta Service Workerin välimuistin käytöstä voidaan tehdä johtopäätökset, nopeuden muutosta tarkastellaan progressiivisten ominaisuuksien ollessa käytössä ja niiden ollessa pois päältä. Lisäksi tarkastellaan Googlen tapaustutkimuksen kautta Service Workerin vaikutuksia sovelluksen nopeuteen. Testitulokset osoittavat että Service Workerin välimuistin hyödyntäminen on nopeampaa kaikissa tapauksissa. Service Workerin välimuisti on nopeampi kuin selaimen oma välimuisti. Service Worker voi myös olla pysähtynyt ja odotustilassa käyttäjän selaimessa. Silti Service Workerin aktivoiminen ja välimuistin käyttäminen on nopeampaa kuin selaimen välimuistista tai suoraan verkosta lataaminen.