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High-performance photon detectors are essential for fiber communication, which is the foundation of the modern internet. Emerging quantum information technologies, such as quantum key distribution, impose new requirements on the photon detectors used. Superconducting single-photon detectors (SSPDs) exhibit high efficiencies, low dark count rates and fast recovery times, which makes them commonly used for quantum applications. The ability to resolve photon numbers in a wave packet is useful in applications like imaging, characterization of light sources, and in optical quantum computation. Ordinary single-photon detectors like SSPDs are not photon-number resolving (PNR), and are only capable of determining if light is present or not. However, photon-number resolution may be achieved by combining multiple single-photon detectors in an array and split the input over them. In this thesis, we introduce and model PNR detectors based on multiplexing single-photon detectors. Using these models, we investigate the requirements on the single-photon detectors when they are used in a multiplexed scheme and we investigate how a PNR detector may be used in imaging applications. We experimentally realize a temporally multiplexed PNR detector based on SSPDs and show that it is capable of accurately determining the mean photon number for a series of wave packets. We also model a SSPD using the generalized time-dependent Ginzburg-Landau model to investigate how the geometry of the SSPD affects the performance of the detector. We show that the geometric reduction of the critical current in turnarounds is less pronounced than previously reported, which relaxes design restrictions., Högpresterande detektorer är nödvändiga för fiberbaserad kommunikation, vilket är en av grundpelarna i det moderna internet. Ny kvantinformationsteknik såsom kvantkryptering ställer nya krav på detektorerna som används. Supraledande enkelfotondetektorer (SSPD) har hög verkningsgrad, lågt antal falska detektioner och snabb återhämtningstid, vilket har gjort dem till ett populärt val för kvantmekaniska tillämpningar. Möjligheten att mäta antalet fotoner i vågpaket är användbart i tillämpningar såsom att upplösa bilder, karaktärisering av ljuskällor och i optiska kvantberäkningar. Vanliga enkelfotondetektorer så som SSPDs saknar förmågan att mäta antalet fotoner och har bara möjlighet att bestämma om det finns ljus eller inte. Det går dock att bygga fotonräknande detektorer genom att dela upp ljuset över flera enkelfotondetektorer. I denna avhandling så introducerar vi och modellerar fotonräknande detektorer som är baserade på flera enkelfotondetektorer. Genom att använda dessa modeller så undersöker vi kraven som ställs på enkelfotondetektorerna och undersöker hur dessa fotonräknande detektorer kan användas för att upplösa bilder. Vi demonstrerar även en fotonräknande detektor genom att använda SSPDs och visar att denna detektor är kapabel av att bestämma medelantalet fotoner givet en serie av vågpaket. Vi modellerar också SSPDs genom att använda en generaliserad form av den tidsberoende Ginzburg-Landau modellen för att undersöka hur detektorns geometri påverkar dess egenskaper. Vi drar slutsatsen att den geometriska reduktionen av den kritiska strömmen är mindre än vad som tidigare har rapporterats, vilket tillåter en friare design av geometrin.

This thesis describes how a solution can be built to detect human flu-like symptoms. Flu-like symptoms are important to detect to prevent Covid-19 [6]. As people are returning to work there is a need for a simple way of detecting flu-like symptoms to prevent the spread of Covid-19. Other than a solution, this thesis concluded how human flu-like symptoms can be detected, with cameras specifically. This is to know what symptoms are most likely to work for a prototype. The technique of cameras and thermal cameras made this project possible as well as the technique of a single-board computer. The technique of cloud-based services is also an important part of this project. This project has resulted in a novel prototype using a single-board computer, cameras, and various cloud-based services to detect and inform a person if he or she has a human flu-like symptom.

Functional Data Analysis (FDA) is a field that has been growing rapidly over the last few decades, with much ongoing research and many recent publications. The focus for Functional Data Analysis is the study of so called functional data, that is data that is assumed to have been generated from a true, underlying function, where we can only observe a sequence of measurements. We propose a method that can identify a suitable placement of knots purely based on the data, without any predefined basis functions. For functional data specifically, some recent research has been published where the authors introduce tree based methods for knot placement. In this thesis we continue that research and investigate the method further by fully following the regression tree paradigm with evaluation of different methods to avoid over-fitting. Throughout this thesis we will call this method Knot Optimization with Recursive Partitioning (KORP). We have evaluated our method on both simulated data sets and on the MNIST handwriting data set and compared both with uniform placement of knots and a genetic algorithm for identifying optimal placement of knots. Our conclusion from the study of the proposed method, is that the method works very well, both for simple data sets and for functional data. It generally performs better than both Uniform placement and Genetic Algorithms.

We derive a computationally efficient expression of the photon-counting distribution for a uniformly illuminated array of single-photon detectors. The expression takes the number of single detectors, their quantum efficiency, and their dark count rate into account. Using this distribution we compute the error of the array detector by comparing the output to that of an ideal detector. We conclude from the error analysis that the quantum efficiency must be very high in order for the detector to resolve a handful of photons with high probability. Furthermore, we conclude that in the worst-case scenario the required array size scales quadratically with the number of photons that should be resolved. We also simulate a temporal array and investigate how large the error is for different parameters, and we compute the optimal size of the array that yields the smallest error., QC 20200206

In the Machine Learning field, more and more of the data collection is commercialised, even with monetary rewards to people and organisations for providing input data for models. Even if data collection is not associated with direct costs for the researcher, there are many cases where there are indirect, or circumstancial, costs associated with it. An established concept in game theory is "Shapley Values", which has had a lot of success in the field of statistics and machine learning over the last number of years, for example as a technique for variable importance estimations. Now, researchers have proposed using Shapley Values also to quantify the worth, or value, of an observation in a model (Data Shapley Values). However, little effort has earlier been spent to properly evaluate these in an Ordinary Least Squares setting, especially since there is already a very established way of quantifying an observations influence (Cook's Distance), which should be reasonably well aligned. Hence, this thesis sets out to explore the use of Data Shapley in Linear Regression models, with the purpose to research if this is a valuable concept for a researcher using OLS models. This thesis will try to approach the topic by answering the following specific questions: * What is a suitable set of parameters for estimating Data Shapley-values for linear regression models? * How well does Data Shapley values and Cooks Distance values agree on the valuation of an observation? * Is it possible to use Data Shapley values to detect outliers also in linear regression models? Data Shapley is studied in some detail with the use of four different datasets and models, and Data Shapley values that are estimated using three different metrics and four different configurations of the estimation algorithm. Results are compared with Cook's Distance for evaluation. The main conclusion from this research is that Data Shapley is a serious contender to Cook's Distance in capturing the worth of an observat

In dieser Arbeit wird die Problematik des Schotterflugs unter Hochgeschwindigkeitszügen untersucht. Zum einen durch die Messung der Unterbodenströmung eines 1:50 Zugmodells in einem Wasserschleppkanal durch Anwendung des optischen Messverfahrens Particle Image Velocimetry und zum anderen durch vereinfachte Impulsberechnungen des Bewegungsverlaufs eines Schottersteins. Für jeweils drei verschiedene Zugmodell- und Bodenkonfigurationen wurde die horizontale und vertikale Geschwindigkeitskomponente in der Symmetrieebene zwischen dem festen Boden und dem Modellunterboden gemessen. Die durch die Geschwindigkeitsfelder induzierten aerodynamischen Lasten wurden für einen vereinfachten, freistehenden und virtuellen Schotterstein im Gleisbett berechnet, um die Auslösung und die Bewegung über dem Gleisbett und die daran anschließende Flugbahn zu simulieren., In this thesis the issue of ballast flight for high-speed trains is closely examined using (a) two-component high-speed particle image velocimetry of the undercarriage flow beneath 1:50 high-speed train models in a water-towing tank and (b) simplified momentum calculations regarding the path of motion of a dislodged trackbed ballast particle. The horizontal and vertical velocity components in the vertical plane extending between the trackbed and the train undercarriage in the trackbed line of symmetry were measured for three different train and three different ground configurations. The measured undercarriage flow fields were applied to an exposed, simplified and virtual ballast particle in the trackbed to simulate its dislodgement, its transport over the trackbed and its flight path.

The SABR model has for a long time been an invaluable tool for capturing the volatility smile and to price nancial derivatives not quoted in the market. However, the current negative rate environment in the EUR market has led to numerous challenges for nancial institutions. One of the most problematic issues is that the SABR model used for volatility interpolation and extrapolation fails when rates are negative. A related issue is that SABR based techniques for transformation of cap volatilities between dierent tenors, do not work anymore. This thesis describes how to use an extension of the SABR model, known as the shifted SABR, to solve these issues. Using three dierent methods, the shifted SABR model is calibrated to EUR cap volatilities based on 6 month EURIBOR. However, market standard is to quote a mixture of 3 month and 6 month cap volatilities, thus the volatilities have to be transformed to a common tenor before calibration. To this end we have developed a technique for volatility transformation in a multi curve framework when rates are negative. The concept is derived by applying It^o's formula on an arbitrage relation between shifted forward rates. The results show that two of the methods for calibrating the shifted SABR model have a good t to liquid contracts. However, the methods vary in performance capturing far OTM caps. Our developed volatility transformation technique also works well, and the sensitivity to the potentially unknown correlation between forward rates is low. The implications are that the extension of the SABR model to the shifted SABR model works ne, both in terms of pricing of caps and volatility transformation in a multi curve framework. Although, it comes to the cost of some additional complexity of extending formulas and arbitrage relations, that used to hold in a positive rate environment., Popular Science Summary Negative Rates when dealing with Caps Negative rates have become a more common view on the leading markets. This creates problems for nancial institutions, as some of their existing models break down. We have analyzed three methods, used for calibration to caps, and developed a new technique that deals with some of the problems related to negative rates. In June 2014 the European Central Bank (ECB) did something extremely unusual seen from a historical perspective: they applied negative deposit rates. For nancial institutions and investors this was an entirely new situation. Historically, negative rates have been regarded as impossible. The economic intuition behind this is that negative rates actual means you have to pay for lending money. The motivation for negative interest rates diers depending on the national bank. The main reason in the Eurozone and Sweden is to ght the growing threat of de ation. Policymakers want to make it less attractive to save money. As such lowering the interest rate on savings should potentially make it more attractive to invest the money instead. Financial institutions use statistical models in dierent areas such as pricing and risk validation. An example is the SABR model which for a long time has been an invaluable tool for capturing the volatility smile and to price cap contracts not quoted in the market. However, the current negative rate environment in the European market has led to numerous challenges for nancial institutions. One of the most problematic issues is that the SABR model used for volatility interpolation and extrapolation fails when rates are negative. A related issue is that SABR based techniques for transformation of cap volatilities, do not work anymore. Our work1 focuses on the pricing of cap contracts available on the European market. Caps are contracts based on a set of simpler contracts known as caplets. Each caplet provides the holder an insurance guaranteeing that the rate connected

This thesis is about BIM (Building Information Model/Modelling) and answer from The Railroad Industries point of view the questions asked in the report. There are different perceptions in the industry about what BIM means and what it is. This thesis will try to clarify the meaning of the concept BIM. Further on the thesis examines to which extent and how BIM is used in the railroad industry where the purpose has been to follow up Trafikverkets investment on implementing BIM. To do this Trafikverkets strategies and regulations has been studied. Beyond that focus has been on processes in the building industry where the purpose has been if there is knowledge that can be applied on the railroad industry. Finally the thesis treats in short terms signalling design and BIM. To many people BIM is a new way of working but it has been around for a while. Already in the end of the 1970’s some industries started using 3D-modelling. It is important to point out that BIM is not a computer program but it is a way of working with 3D-modelling and how to handle the information in those models. The thesis is based on a literature study where most of the literature is coming from the building industry because they are ahead in the development of using BIM. Beyond the literature study interviews has been performed with people in the railroad industry that is working or has been working with BIM. The analysis discusses the questions asked in the thesis in a broad perspective based on the gathered information. The answers to the questions are found in the result.