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  • 151.
    Hynek, Mariusz
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On various aspects of extended objects2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis concerns classical and quantum aspects of minimal manifolds embedded in flat Minkowski space. In particular, we study the Lie algebra of diffeomorphisms on 2 dimensional compact manifolds as well as discuss singularity formation for relativistic minimal surfaces in co-dimension one. We also present a new approach to the Lorentz anomaly in string theory based on operator product expansion. Finally, we consider the spectrum of a family of Schr\"odinger operators describing quantum minimal surfaces and provide bounds for the eigenvalues for finite $N$ as well as in the limit where N tends to infinity.

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  • 152.
    Hårderup, Peder
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    The Applicability and Scalability of Graph Neural Networks on Combinatorial Optimization2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This master's thesis investigates the application of Graph Neural Networks (GNNs) to address scalability challenges in combinatorial optimization, with a primary focus on the minimum Total Dominating set Problem (TDP) and additionally the related Carrier Scheduling Problem (CSP) in networks of Internet of Things. The research identifies the NP-hard nature of these problems as a fundamental challenge and addresses how to improve predictions on input graphs of sizes much larger than seen during training phase. Further, the thesis explores the instability in such scalability when leveraging GNNs for TDP and CSP. Two primary measures to counter this scalability problem are proposed and tested: incorporating node degree as an additional feature and modifying the attention mechanism in GNNs. Results indicate that these countermeasures show promise in addressing scalability issues in TDP, with node degree inclusion demonstrating overall performance improvements while the modified attention mechanism presents a nuanced outcome with some metrics improved at the cost of others. Application of these methods to CSP yields bleak results, evincing the challenges of scalability in more complex problem domains. The thesis contributes by detecting and addressing scalability challenges in combinatorial optimization using GNNs and provides insights for further research in refining methodologies for real-world applications.

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  • 153.
    in 't Veld, Niels Floris Leonardus
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Comparing two approaches of modelling fish harvesting strategies using optimal control2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Optimal control is a paradigm for solving optimization problems involving dynamical systems, which are to be controlled. It is able to solve fish harvesting problems, in which we want to optimize harvesting out-take by considering fishing as a control function that acts on the state of the dynamical system, which represents the growth of fish species in the environment. Other modelling aspects of optimal control are defining terminal costs and running costs, e.g. maximizing profit. We keep the terminal condition comparable for a different number of species. It is based on the initial population. By using the optimal control Hamiltonian and Pontryagin’s Maximum Principle we can calculate the optimal state trajectories corresponding to suitable optimal controls. The Hamiltonian is dependent on the state equation and the running costs. We present two approaches of modelling the running costs. An approach that is not directly translatable to the fish harvesting problem, but it leads to a smooth Hamiltonian, which greatly simplifies derivation and computation. The other, which is equivalent to maximizing profit, leads to a non-smooth Hamiltonian. This leads to jump-discontinuous derivatives needed for computation. We propose to regularize the derivatives of the Hamiltonian using suitable smooth functions, such that it is equivalent to regularizing the Hamiltonian directly. We give details for implementing both approaches up to systems of n competing species. After which we go into detail on algorithms and programming structure implemented. Finally, in modest numerical experiments, for one and two species, we show the relation between the optimal control and the terminal costs. But more interestingly, that the smooth Hamiltonian models are inadequate and regularized Hamiltonian models are the preferred choice. Intriguingly, the latter approach results in steady state solution, wherethe control acts as a stabilizer.

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  • 154.
    Inde, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Using Semi-Supervised Learning for Email Classification2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this thesis, we investigate the use of self-training, a semi-supervised learning method, to improve binary classification of text documents. This means making use of unlabeled samples, since labeled samples can be expensive to generate. More specifically, we want to classify emails that are retrieved by Skandinaviska Enskilda Banken (SEB). The method is tested on two datasets: the first is IMDB reviews, consisting of both labeled (good or bad) and unlabeled movie reviews; the second is provided by SEB and consists of labeled and unlabeled emails. First, supervised learning was investigated. Three different vectorization methods including two bag-of-words models and one doc2vec model were included. These were tested using five different machine learning classification methods. The comparison of the F1-score showed that doc2vec vectorization and the logistic regression classification method performed well and was used in the self-training investigation. We find that self-training on the IMDB dataset only yielded improvement for low number of labeled samples. For the SEB dataset we find that by using self-training, we can achieve the same F1-score using only around 1000 labeled samples (less than 10% of the labeled dataset), as using supervised methods on the full labeled set. We conclude that self-training can improve classification performance and also be used indirectly to reduce manual labeling efforts.

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  • 155.
    Irell Fridlund, Albin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Heberlein, Johanna
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Dispersion Trading: A Way to Hedge Vega Risk in Index Options2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Since the introduction of derivatives to the financial markets, volatility trading has emerged as a method for investors to make money in every market condition. In parallel with introducing derivatives to the financial markets, hedging methods have emerged and are today essential instruments for the liquidity providers active in the markets. The most commonly used hedging method is delta hedging which cancels out the directional risk in the option. Hedging the vega risk with dispersion trading seems to be both a profitable and accurate hedging method. This thesis examines the effectiveness of dispersion trading for reducing the vega risk in OMXS30 options. This is investigated by backtesting a strategy based on going short OMXS30 index volatility and long volatility on a tracking portfolio with a zero net vega. This investigation aims to determine if the dispersion trading strategy can be a reliable risk management tool. It was found that vega could accurately be hedged using dispersion trading. However, when considering the bid-ask spread, the strategy did not show profitability over the simulated period. Weighting the portfolio more in favour of companies with smaller bid-ask spreads did not show improved profitability.

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  • 156.
    Issa, Alan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A Framework to Model Bond Liquidity2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The liquidity of financial assets can be studied in various different ways. In this thesis, liquidity is defined as the cost and time required to liquidate a position. While the liquidity of highly traded financial instruments like stocks is typically determined by analyzing the order book, the lack of an order book for over-the-counter bond trading presents challenges for estimating bond liquidity. The objective of this thesis is to develop a framework for estimating the cost and time required to liquidate a bond position. To achieve this, we propose a theoretical order book model based on the order book of more actively traded instruments, and estimate the model parameters using bond transaction data.

    The volume available to trade in the theoretical order book was modelled as gamma distributed stochastic process. The distribution of the liquidation cost could thereafter be derived where the parameters were estimated using the maximum likelihood estimation. The liquidation time, or liquidity horizon, was then determined through the solution of an optimization problem.

    The proposed framework for estimating bond liquidity produced promising results. The estimated parameters of the gamma distributed stochastic process accurately captured the behavior of bond trading volumes, allowing for a reliable estimation of the distribution of liquidation costs. Additionally, the optimization problem used to determine the liquidity horizon produced reasonable estimates.

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  • 157.
    Issa, Tomas
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Navia, Nicolas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Enhancing Portfolio Modelling: Integrating Transaction Costs and Capital Injections2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This master's thesis addresses the often overlooked aspect of transaction costs, capital injections, and withdrawals in fund management theory. The research collaboration with Havsfonden, a newly launched quantitative ESG investment fund, aims to enhance their understanding of transaction costs and capital injections while improving their investment model. The thesis includes a comprehensive literature review, the development of a portfolio model that integrates transaction costs and capital injections, and the numerical implementation and testing of the model using MATLAB. Three distinct models focusing on transaction costs, including linear, fixed, and a combination of both, were created. Additionally, three models were developed to examine capital injections, with one based on past performance and the others considering a constant inflow of capital. The findings indicate that our models provide reasonable implementation and effectively capture the nature of capital injections and transaction costs.

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  • 158.
    Jacobsson, Anton
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Learning.
    Lundqvist, Johan
    KTH, School of Industrial Engineering and Management (ITM), Learning.
    Matematiklärares syn på muntlig matematikför elever med matematiksvårigheter: En innehållsanalytisk studie om stödjande faktorer2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Mathematics has a unique subject language that students need to master in writing as well as verbally. Shortcomings in the oral mathematical communication capacity contribute to the fact that students with mathematical difficulties do not receive an approved grade in mathematics for grade 9. These students need help and support from their environment in order not to risk being disapproved. This study has been conducted with the purpose of portraying and analyzing mathematics teachers' views on supportive factors for students with mathematical difficulties focusing on oral mathematical communication skills. As a method, a content analytical research approach with inductive thematic methodology has been used and the study is based on five semi structured interviews. Mathematics teachers' views have been judged to be possible to be depicted and analyzed by the following six themes:

    1. The balance between oral and written communication

    2. The oral mathematical communications skills components

    3. Activities based on the students' needs

    4. Supporting learning environment for the student

    5. The student's participation in mathematical discussions

    6. Cooperation with the parents

    Teachers agree that students with mathematical difficulties need adaptations of content and knowledge objectives for oral mathematical ability. However, there is no unanimity in the teacher's view of adequate goals and content, but this is considered being the result of a variety of factors such as the student's knowledge, teacher's interpretation of the curriculum, the written focus in mathematics, the lack of adequate situations to assess oral capacity, stress and time shortages and the less good availability of special educators. Students with mathematical difficulties also need support in the context they are in. This believes teachers can be managed by either blending the context of differences in student knowledge or ensuring that students with mathematical difficulties interact with friends who they feel safe interacting with. Teachers also try to support the students with control, control and order, which can be explained by the fact that these students experience through their teens. The teacher makes a subjective assessment of the students' need for governance, and this then paves the way for the students to participate and influence in different ways. Teachers also have different expectations of student performance in a participation, where some teachers believe that the students are performing, with which some people are content with a participation. Teachers thus have different focus on these students ‐ either knowledge or value goals. The last theme concerns teachers' views on cooperation with the parents. Some teachers are interpreted believing that this contact contributes positively whereas others have not been interpreted having the same beliefs.

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  • 159.
    Jaeckel, William
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Versteegh, Nicolai
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A Dual-Lens Approach to Loss Given Default Estimation: Traditional Methods and Variable Analysis2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This report seeks to thoroughly examine different approaches to estimating Loss Given Default through a comparison of traditional estimation methods, as well as a deeper variable analysis on micro, small, and medium-sized companies using primarily regression decision trees. The comparative study concluded that estimating loss given default depends heavily on business-specific factors and data variety. While regression models offer interpretability and machine learning techniques offer superior prediction, model selection should balance complexity, computational demands, implementation ease, and overall performance. From the variable analysis, loan size and guarantor property ownership emerged as key drivers for a lower Loss Given Default.

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  • 160.
    Jakobsson, Eric
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Åhlgren, Thor
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Applying Peaks-Over-Threshold for Increasing the Speed of Convergence of a Monte Carlo Simulation2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis investigates applying the semiparametric method Peaks-Over-Threshold on data generated from a Monte Carlo simulation when estimating the financial risk measures Value-at-Risk and Expected Shortfall. The goal is to achieve a faster convergence than a Monte Carlo simulation when assessing extreme events that symbolise the worst outcomes of a financial portfolio. Achieving a faster convergence will enable a reduction of iterations in the Monte Carlo simulation, thus enabling a more efficient way of estimating risk measures for the portfolio manager. 

    The financial portfolio consists of US life insurance policies offered on the secondary market, gathered by our partner RessCapital. The method is evaluated on three different portfolios with different defining characteristics. 

    In Part I an analysis of selecting an optimal threshold is made. The accuracy and precision of Peaks-Over-Threshold is compared to the Monte Carlo simulation with 10,000 iterations, using a simulation of 100,000 iterations as the reference value. Depending on the risk measure and the percentile of interest, different optimal thresholds are selected. 

    Part II presents the result with the optimal thresholds from Part I. One can conclude that Peaks-Over-Threshold performed significantly better than a Monte Carlo simulation for Value-at-Risk with 10,000 iterations. The results for Expected Shortfall did not achieve a clear improvement in terms of precision, but it did show improvement in terms of accuracy. 

    Value-at-Risk and Expected Shortfall at the 99.5th percentile achieved a greater error reduction than at the 99th. The result therefore aligned well with theory, as the more "rare" event considered, the better the Peaks-Over-Threshold method performed. 

    In conclusion, the method of applying Peaks-Over-Threshold can be proven useful when looking to reduce the number of iterations since it do increase the convergence of a Monte Carlo simulation. The result is however dependent on the rarity of the event of interest, and the level of precision/accuracy required.

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  • 161.
    Jalaei, Soroosh
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Sustainability Filtration and Optimization: A Stepwise Integration Approach2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis explores the integration of sustainability into Modern Portfolio Theory (MPT) optimization by introducing stepwise filtration and optimization. This study acknowledges the growing importance of sustainability in investment strategies and modifies the traditional MPT framework to include environmental, social, and governance (ESG) factors. A systematic filtration process is conducted where each asset undergoes a step-by-step filtration based on different ESG criteria. For each filtration step, portfolio optimization is performed to find the most efficient portfolios under the filtered criteria. The effect of each filtration on portfolio risk and return profile provides insights into the trade-offs between financial performance and sustainability impacts. The findings indicate that investors considering the ethical aspects of ESG can achieve these goals without significantly affecting the portfolio risk and return. However, investors incorporating all aspects of ESG will experience a higher drop in the efficient frontier. Moreover, while investigating an additional index, including more companies, investors can attain a better portfolio profile while incorporating all aspects of ESG.

    A central ambition of this study has been enlighten investors regarding the different aspects of ESG and the trade-offs of integrating sustainability into investment practices. Thus, this study seeks to refine the investor decision-making process and encourage investors to make more informed sustainable decisions.

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  • 162.
    Jama, Fuaad
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Deep reinforcement learning approach to portfolio management2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis evaluates the use of a Deep Reinforcement Learning (DRL) approach to portfolio management on the Swedish stock market. The idea is to construct a portfolio that is adjusted daily using the DRL algorithm Proximal policy optimization (PPO) with a multi perceptron neural network. The input to the neural network was historical data in the form of open, high, and low price data. The portfolio is evaluated by its performance against the OMX Stockholm 30 index (OMXS30). Furthermore, three different approaches for optimization are going to be studied, in that three different reward functions are going to be used. These functions are Sharp ratio, cumulative reward (Daily return) and Value at risk reward (which is a daily return with a value at risk penalty). The historival data that is going to be used is from the period 2010-01-01 to 2015-12-31 and the DRL approach is then tested on two different time periods which represents different marked conditions, 2016-01-01 to 2018-12-31 and 2019-01-01 to 2021-12-31. The results show that in the first test period all three methods (corresponding to the three different reward functions) outperform the OMXS30 benchmark in returns and sharp ratio, while in the second test period none of the methods outperform the OMXS30 index.

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  • 163.
    Jansson, Daniel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Niklasson, Nils
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Dimensioning of Charging Infrastructure Using Model-Based Systems Engineering2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis work is performed in collaboration with Syntell AB and a client company interested in assistance with charging infrastructure dimensioning. The aim of this thesis is to develop an executable, generalizable model that can aid decision making regarding charging infrastructure. Furthermore, this is done within a Model-Based Systems Engineering (MBSE) context, which enables representation of the system as a model. 

    As the data and model concerning the client company is classified, it is not presented in this report. Instead, to further enhance the aim of developing a generalizable model, a test case is produced for this project work. This case consists of passenger electric vehicles and chargers in a metropolitan setting, where data is gathered from public sources. 

    The results show that the model is executable and flexible to fit any type of electric vehicle and different specifications of chargers. Using an MBSE approach enables the project owner to customize the model development for the specific use case. Additionally, defining a system in focus establishes what the system uptime is, enabling calculations of availability. The results for this specific use case are interpreted to show how the model can be used to aid the dimensioning of charging infrastructure using the model output. To further verify the model representation of the system, the model can be run in live-mode, where vehicles and chargers can be added while the model is running to instantly examine the system dynamics. 

    Concluding, the method for utilizing the model to evaluate systems availability is described. The model output, as well as the thorough description of the model, can be used to increase the knowledge within MBSE for executable modeling.

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  • 164.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Stabilitetsundersökning vid lösning av Maxwells ekvationer med finita differensmetoder1992Independent thesis Advanced level (professional degree), 12 credits / 18 HE creditsStudent thesis
  • 165. Jiangping, Hu
    et al.
    Xiaoming, Hu
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Tielong, Shen
    Cooperative shift estimation of target trajectory using clustered sensors2014In: Journal of Systems Science and Complexity, ISSN 1009-6124, E-ISSN 1559-7067, Vol. 27, no 3, p. 413-429Article in journal (Refereed)
    Abstract [en]

    In this paper, a mathematical model for target tracking using nonlinear scalar range sensors is formulated first. A time-shift sensor scheduling strategy is addressed on the basis of a k-barrier coverage protocol and all the sensors are divided into two classes of clusters, active cluster, and submissive cluster, for energy-saving. Then two types of time-shift nonlinear filters are proposed for both active and submissive clusters to estimate the trajectory of the moving target with disturbed dynamics. The stochastic stability of the two filters is analyzed. Finally, some numerical simulations are given to demonstrate the effectiveness of the new filters with a comparison of EKF.

  • 166. Jinhuan, Wang
    et al.
    Zhixin, Liu
    Xiaoming, Hu
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Consensus control design for multi-agent systems using relative output feedback2014In: Journal of Systems Science and Complexity, ISSN 1009-6124, E-ISSN 1559-7067, Vol. 27, no 2, p. 237-251Article in journal (Refereed)
    Abstract [en]

    This paper studies the consensus problem of multi-agent systems in which all agents are modeled by a general linear system. The authors consider the case where only the relative output feedback between the neighboring agents can be measured. To solve the consensus problem, the authors first construct a static relative output feedback control under some mild constraints on the system model. Then the authors use an observer based approach to design a dynamic relative output feedback control. If the adjacent graph of the system is undirected and connected or directed with a spanning tree, with the proposed control laws, the consensus can be achieved. The authors note that with the observer based approach, some information exchange between the agents is needed unless the associated adjacent graph is completely connected.

  • 167.
    Johnson, Marcus
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Forslund, Herman
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    AI Based Methods for Matrix Multiplication in High Resolution Simulations of Radio Access Networks2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The increasing demand for mobile data has placed significant strain on radio access networks (RANs), leading to a continuous need for increased network capacity. In keeping with that, a significant advancement in modern RANs is the ability to utilize several receivers and transmitters, to allow for beamforming. One way to increase the capacity of the network is therefore to optimize the resource allocation by preprocessing the transmitted signals, which involves several costly matrix multiplications (MMs). The aim of the project was to investigate the potential of accelerating Ericsson's RAN simulations by using AI based approximate matrix multiplication (AMM) algorithms. The main focus was on the multiply additionless (MADDNESS) algorithm, a product quantization technique that has achieved speedups of up to 100 times compared to exact MM, and 10 times faster than previous AMM methods. A complex matrix handling version of MADDNESS was implemented in Java and Python respectively, and its speed and accuracy were evaluated against Ericsson's current MM implementation. The proposed implementation did not beat the benchmark with respect to speed, instead resulting in a 4-10 times slowdown in runtime. However, this may largely be due to the fact that the used languages do not allow for complete control over memory resource allocation. As such, the implementations at hand do not incorporate all the crucial features of the algorithm. Particularly, the handicapped version does not fully leverage the vectorization potential, which is one of the key contributors to the speed of the algorithm. Consequently, further improvements are necessary before employing the techniques in an end-to-end implementation.

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  • 168.
    Jonsäll, Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Mattsson, Emma
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Data Driven Modeling for Aerodynamic Coefficients2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Accurately modeling aerodynamic forces and moments are crucial for understanding thebehavior of an aircraft when performing various maneuvers at different flight conditions.However, this task is challenging due to complex nonlinear dependencies on manydifferent parameters. Currently, Computational Fluid Dynamics (CFD), wind tunnel,and flight tests are the most common methods used to gather information about thecoefficients, which are both costly and time–consuming. Consequently, great efforts aremade to find alternative methods such as machine learning.

    This thesis focus on finding machine learning models that can model the static and thedynamic aerodynamics coefficients for lift, drag, and pitching moment. Seven machinelearning models for static estimation were trained on data from CFD simulations.The main focus was on dynamic aerodynamics since these are more difficult toestimate. Here two machine learning models were implemented, Long Short–TermMemory (LSTM) and Gaussian Process Regression (GPR), as well as the ordinaryleast squares. These models were trained on data generated from simulated flighttrajectories of longitudinal movements.

    The results of the study showed that it was possible to model the static coefficients withlimited data and still get high accuracy. There was no machine learning model thatperformed best for all three coefficients or with respect to the size of the training data.The Support vector regression was the best for the drag coefficients, while there wasno clear best model for the lift and moment. For the dynamic coefficients, the ordinaryleast squares performed better than expected and even better than LSTM and GPR forsome flight trajectories. The Gaussian process regression produced better results whenestimating a known trajectory, while the LSTM was better when predicting values ofa flight trajectory not used to train the models.

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  • 169.
    Julin, Lovisa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Analysing Blood Cell Differentiation via Optimal Transport2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Cell differentiation is the process of a cell developing from one cell type to another. It is of interest to analyse the differentiation from stem cells to different types of mature cells, and discover what genes are involved in regulating the differentiation to specific cells, for instance to get insights to what is causing certain diseases and find potential treatments. 

    In this project, two mathematical models are developed for analysing blood cell differentiation (haematopoiesis) with methods based on optimal transportation. Optimal transportation is about moving one mass distribution to another at minimal cost. Modelling a sample of cells as point masses placed in a space based on the cells' gene expressions, accessed by single-cell RNA sequencing, optimal transportation is used to find transitions between cells that costs the least in terms of changes in gene expression. With this, cell-to-cell trajectories, from haematopoietic stem cells to mature blood cells, are obtained.

    With the first model, cells are divided into groups based on their maturity, which is determined by using diffusion pseudotime, and optimal transportation is preformed between groups. The resulting trajectories suggest that haematopoietic stem cells possibly can develop into the same mature cell type in different ways, and that the cell fate for some cell types is decided late on in development. In future work, the gene regulation along the obtained trajectories can be analysed. The second model is developed to be more general than the first, and not be dependent on a group division before preforming optimal transportation.

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  • 170.
    Jyrkäs, Tim
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A Convex Optimisation Approach to Portfolio Allocation2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The mean variance framework (MV) developed by Markowitz in his groundbreaking paper offers a quantitative and rational approach to portfolio selection. It is well known to market practitioners however that the MV optimal portfolios tend to perform subpar. One of the issues of the MV portfolios is that they require the inverse of a large covariance matrix, which is often ill-conditioned. In this thesis, we develop a new approach to circumvent these issues. We propose an optimisation approach akin to least squares linear regression and compare the performance with an establish method, covariance shrinkage. When tested on a set of 30 futures contracts, we find that the models yield promising results albeit somewhat lower than that of the benchmark.

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  • 171.
    Jónsdóttir, Sigurlaug Rún
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Real-time Optimal Braking for Marine Vessels with Rotating Thrusters2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Collision avoidance is an essential component of autonomous shipping. As ships begin to advance towards autonomy, developing an advisory system is one of the first steps. An advisory system with a strong collision avoidance component can help the crew act more quickly and accurately in dangerous situations. One way to avoid colission is to make the vessel stop as fast as possible. In this work, two scenarios are studied, firstly, stopping along a predefined path, and secondly, stopping within a safe area defined by surrounding obstacles. The first scenario was further worked with to formulate a real-time solution.

    Movements of a vessel, described in three degrees of freedom with continuous dynamics, were simulated using mathematical models of the forces acting on the ship. Nonlinear optimal control problems were formulated for each scenario and solved numerically using discretization and a direct multiple shooting method. The results for the first problem showed that the vessel could stop without much deviation from the path. Paths with different curvatures were tested, and it was shown that a slightly longer distance was traveled when the curvature of the path was greater. The results for the second problem showed that the vessel stays within the safe area and chooses a relatively straight path as the optimal way of stoping. This results in a shorter distance traveled compared to the solution of the first problem.

    Two different real-time approaches were formulated, firstly a receding-horizon approach and secondly a lookup-based approach. Both approaches were solved with real-time feasibility, where the receding-horizon approach gave a better solution while lookup-based approach had a shorter computational time.

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  • 172.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A sector condition for local robustness of limit cycles2006In: 2006 American Control Conference, Vols 1-12, 2006, Vol. 1-12, p. 5014-5019Conference paper (Refereed)
    Abstract [en]

    Robustness of periodic oscillations in autonomous feedback systems are considered for systems with separable nonlinearities. Local quadratic separation of the nonlinear dynamics from the linear part of the dynamics is used to characterize a set of systems that exhibit periodic oscillation in a bounded frequency and amplitude range. The main analysis condition can be formulated as a feasibility problem for linear matrix inequalities.

  • 173.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Primal and dual criteria for robust stability applied to large scale systems2012In: Distributed Decision Making and Control, Springer, 2012, Vol. 417, p. 3-25Chapter in book (Refereed)
    Abstract [en]

    Primal and dual formulations of stability criteria based on multipliers will be discussed. The foundation for multiplier-based stability analysis is the use of a convex cone of multipliers to characterize the uncertainty in a system. The primal and dual stability criteria are formulated as convex feasibility tests involving the nominal dynamics and multipliers from the cone and the polar cone, respectively. The motivation for introducing the dual is that it provides additional insight into the stability criterion and that it is sometimes easier to use than the primal. The case considered in this chapter is that of uncertainty as it represents the interconnection of a complex network. The multipliers are used to describe characteristic properties of the network such as the spectral location or the structure of the underlying graph.

  • 174.
    Jönsson, Ulf T.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, C. -Y
    Verification of consensus in networks of heterogeneous LTI agents2010In: Proceedings of SICE Annual Conference 2010, 2010, p. 2570-2575Conference paper (Refereed)
    Abstract [en]

    A framework for robust stability of large scale systems consisting of linear time-invariant systems interconnected over a network will be surveyed and applied to solve heterogeneous consensus problems. The purpose of distributed consensus algorithms is to reach an agreement regarding a certain quantity of interest that depends on the state of all systems. In most of consensus literature, dynamics of all agents in the network are assumed to be the same and of low dimensions. This simplifies the analysis and, for the most elementary networks, stability and the rate of convergence can be determined from the eigenvalues of the interconnection matrix. Here we discuss analogous results for the case where the individual dynamics are heterogeneous and possibly of infinite dimensions. Our criterion for consensus resembles the classical Nyquist criterion. An interesting aspect of this criterion is that in some instances a three-dimensional plot is required in order to make analysis accurate.

  • 175.
    Karlsson, Jessika
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Bayesian Structural Time Series in Marketing Mix Modelling2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Marketing Mix Modelling has been used since the 1950s, leveraging statistical inference to attribute media investments to sales. Typically, regression models have been used to model the relationship between the two. However, the media landscape evolves at an increasingly rapid pace, driving the need for more refined models which are able to accurately capture these changes. One class of such models are Bayesian structural time series, which are the focal point in this thesis. This class of models retains the relationship between media investments and sales, while also allowing for model parameters to vary over time. The effectiveness of these models is evaluated with respect to prediction accuracy and certainty, both in and out-of-sample. A total of four different models of varying degrees of complexity were investigated. It was concluded that the in-sample performance was similar across models, yet when it came to out-of-sample performance models with time-varying performance outperformed their static counterparts, with respect to uncertainty. Furthermore, the functional form of the intercept influenced the uncertainty of the forecasts on extended time horizons.

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  • 176.
    Karlsson Lille, William
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Saphir, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Value at Risk Estimation with Neural Networks: A Recurrent Mixture Density Approach2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In response to financial crises and opaque practices, governmental entities and financial regulatory bodies have implemented several pieces of legislature and directives meant to protect investors and increase transparency. Such regulations often impose strict liquidity requirements and robust estimations of the risk borne by a financial firm at any given time. Value at Risk (VaR) measures how much an investment can stand to lose with a certain probability over a specified period of time and is ubiquitous in its use by institutional investors and banks alike. In practice, VaR estimations are often computed from simulations of historical data or parameterized distributions. 

    Inspired by the recent success of Arimond et al. (2020) in using a neural network for VaR estimation, we apply a combination of recurrent neural networks and a mixture density output layer for generating mixture density distributions of future portfolio returns from which VaR estimations are made. As in Arimond et al., we suppose the existence of two regimes stylized as bull and bear markets and employ Monte Carlo simulation to generate predictions of future returns. Rather than use a swappable architecture for the parameters in the mixture density distribution, we here let all parameters be generated endogenously in the neural network. The model's success is then validated through Christoffersen tests and by comparing it to the benchmark VaR estimation models, i.e., the mean-variance approach and historical simulation. 

    We conclude that recurrent mixture density networks show limited promise for the task of predicting effective VaR estimates if used as is, due to the model consistently overestimating the true portfolio loss. However, for practical use, encouraging results were achieved when manually shifting the predictions based on an average of the overestimation observed in the validation set. Several theories are presented as to why overestimation occurs, while no definitive conclusion could be drawn. As neural networks serve as black box models, their use for conforming to regulatory requirements is thus deemed questionable, likewise the assumption that financial data carries an inherent pattern with potential to be accurately approximated. Still, reactivity in the VaR estimations by the neural network is significantly more pronounced than in the benchmark models, motivating continued experimentation with machine learning methods for risk management purposes. Future research is encouraged to identify the source of overestimation and explore different machine learning techniques to attain more accurate VaR predictions.

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  • 177.
    Kastengren, Marcus
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Offline Reinforcement Learning for Remote Electrical Tilt Optimization: An application of Conservative Q-Learning2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In telecom networks adjusting the tilt of antennas in an optimal manner, the so called remote electrical tilt (RET) optimization, is a method to ensure quality of service (QoS) for network users. Tilt adjustments made during operations in real-world networks are usually executed through a suboptimal policy, and a significant amount of data is collected during the execution of such policy. The policy collecting the data is known as the behavior policy and can be used to learn improved tilt update policies in an offline manner. In this thesis the RET optimization problem is formulated in a offline Reinforcement Learning (RL) setting, where the objective is to learn an optimal policy from batches of data collected by the logging policy. Offline RL is a challenging problem where traditional RL algorithms can fail to learn policies that will perform well when evaluated online.In this thesis Conservative Q-learning (CQL) is applied to tackle the challenges of offline RL, with the purpose of learning improved policies for tilt adjustment from data in a simulated environment. Experiments are made with different types of function approximators to model the Q-function. Specifically, an Artificial Neural Network (ANN) and a linear model are employed in the experiments. With linear function approximation, two novel algorithms which combine the properties of CQL and the classic Least Squares Policy Iteration (LSPI) algorithm are proposed. They are also used for learning RET adjustment policies. In online evaluation in the simulator one of the proposed algorithms with simple linear function approximation achieves similar results to CQL with the more complex artificial neural network function approximator. These versions of CQL outperform both the behavior policy and the naive Deep Q-Networks (DQN) method.

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  • 178.
    Kazi, Mehnaz
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Stanojlovic, Natalija
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Deep Learning Approach for Time- to-Event Modeling of Credit Risk2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis explores how survival analysis models performs for default risk prediction of small-to-medium sized enterprises (SME) and investigates when survival analysis models are preferable to use. This is examined by comparing the performance of three deep learning models in a survival analysis setting, a traditional survival analysis model Cox Proportional Hazards, and a traditional credit risk model logistic regression. The performance is evaluated by three metrics; concordance index, integrated Brier score and ROC-AUC. The models are trained on financial data from Swedish SME holding profit and loss statement and balance sheet results. The dataset is divided into two feature sets: a smaller and a larger, additionally the features are binned. 

    The results show that DeepHit and Logistic Hazard performed the best with the three metrics in mind. In terms of the AUC score all three deep learning survival models generally outperform the logistic regression model. The Cox Proportional Hazards (Cox PH) showed worse performance than the logistic regression model on the non-binned feature sets while having more comparable results in the case where the data was binned. In terms of the concordance index and integrated Brier score the Cox Proportional Hazards model consistently performed the worst out of all survival models. The largest significant performance gain for the concordance index and AUC score was however seen by the Cox PH model when binning was applied to the larger feature set. The concordance index went from 0.65 to 0.75 and the test AUC went from 76.56% to 83.91% for the larger set to larger dataset with binned features.

    The main conclusions is that the neural networks models did outperform the traditional models slightly and that binning had a great impact on all models, but in particular for the Cox PH model.

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  • 179.
    Keller, Lea
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Comparative Analysis of Biological Networks by Control Theoretic Methods2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This project deals with two Goodwin models of circadian rythms and three reduced models in understanding the Belousov-Zhabotinski models of chemical reaction. They are examined and compared by applying dynamical systems theory and control theoretical tools. More precisely, stability analysis of equilibria and the Hopf bifurcations. Moreover, we investigate the issues such as positivity and boundeness of the trajectories. Some are carried out by mathematical analysis and some are carried out by numerical simulations performed by Matlab. In particular, we provide a complete parameter description on stability of the Goodwin model in terms of the Hill number, which seems non-addressed in the literature.

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  • 180.
    Kerry, Ruth
    et al.
    Department of Geography, Brigham Young University, Proro, UT and CRSSA, Rutgers University,New Brunswick, NJ.
    Goovaerts, Pierre
    Biomedware Inc., Ann Arbor, MI,.
    Haining, Robert P.
    Department of Geography, University ofCambridge, Cambridge, UK,.
    Ceccato, Vania
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment.
    Applying Geostatistical Analysis to Crime Data: Car-Related Thefts in the Baltic States2010In: Geographical Analysis, ISSN 0016-7363, E-ISSN 1538-4632, Vol. 42, no 1, p. 53-77Article in journal (Refereed)
    Abstract [en]

    Geostatistical methods have rarely been applied to area-level offense data. This article demonstrates their potential for improving the interpretation and understanding of crime patterns using previously analyzed data about car-related thefts for Estonia, Latvia, and Lithuania in 2000. The variogram is used to inform about the scales of variation in offense, social, and economic data. Area-to-area and area-to-point Poisson kriging are used to filter the noise caused by the small number problem. The latter is also used to produce continuous maps of the estimated crime risk (expected number of crimes per 10,000 habitants), thereby reducing the visual bias of large spatial units. In seeking to detect the most likely crime clusters, the uncertainty attached to crime risk estimates is handled through a local cluster analysis using stochastic simulation. Factorial kriging analysis is used to estimate the local- and regional-scale spatial components of the crime risk and explanatory variables. Then regression modeling is used to determine which factors are associated with the risk of car-related theft at different scales.

  • 181. Khesin, B.
    et al.
    Lenells, Jonatan
    Baylor University, United States .
    Misiołek, G.
    Preston, S. C.
    Curvatures of Sobolev metrics on diffeomorphism groups2013In: Pure and Applied Mathematics Quarterly, ISSN 1558-8599, E-ISSN 1558-8602, Vol. 9, no 2, p. 291-332Article in journal (Refereed)
    Abstract [en]

    Many conservative partial differential equations correspond to geodesic equations on groups of diffeomorphisms. Stability of their solutions can be studied by examining sectional curvature of these groups: negative curvature in all sections implies exponential growth of perturbations and hence suggests instability, while positive curvature suggests stability. In the first part of the paper we survey what we currently know about the curvature-stability relation in this context and provide detailed calculations for several equations of continuum mechanics associated to Sobolev H0 and H1 energies. In the second part we prove that in most cases (with some notable exceptions) the sectional curvature assumes both signs.

  • 182.
    Khong, Sei Zhen
    et al.
    Univ Melbourne, Dept Elect & Elect Engn, Melbourne, Vic 3010, Australia..
    Cantoni, Michael
    Univ Melbourne, Dept Elect & Elect Engn, Melbourne, Vic 3010, Australia..
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Robust stability properties of the nu-gap metric for time-varying systems2011In: 2011 50TH IEEE CONFERENCE ON DECISION AND CONTROL AND EUROPEAN CONTROL CONFERENCE (CDC-ECC), IEEE , 2011, p. 2028-2033Conference paper (Refereed)
    Abstract [en]

    The stability of uncertain feedback interconnections of causal time-varying linear systems is studied in terms of a recently established generalisation of the nu-gap metric. In particular, a number of robustness results from the well-known linear time-invariant theory are extended. The time-varying generalisations include: sufficient conditions for robust stability; a bound on robust performance; and two-sided bounds on the induced norm of the variation in a closed-loop mapping as an open-loop component of the feedback interconnection is perturbed. Underlying assumptions are verified for causal systems that exhibit linear periodically time-varying behaviour. This includes a class of sampled-data systems as a special case. Within the periodic context considered, it can be shown that a robust stability condition is also necessary.

  • 183.
    Kindbom, Hannes
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Reineck, Viktor
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Insights on Creating a Growth Machine Using Attribution Modelling2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Given access to detailed tracking data, the problem of attribution modelling has recently gained attention in both academia and the industry. Being able to determine the influence of each marketing channel in driving conversions can help advertisers to allocate their marketing budgets accordingly and ultimately increase their customer base and achieve a higher Return On Investment (ROI). However, Last-Touch Attribution (LTA), the current industry standard to approach the problem, has been criticized for oversimplification. 

    In this degree project, two data-driven attribution models are therefore compared to the LTA model on real data from an insurance company, with the objective to optimize for customer base growth and ROI. Raw attributions for each channel are obtained after training the models to predict conversion or non-conversion. By using a linear function to obtain a Customer Lifetime Value (CLV) estimate, the attributions are then adjusted to the ROI of each channel and finally validated through an attribution based budget allocation and historical marketing data replay.

    The experimental results demonstrate that all models reach approximately 82% accuracy on balanced data, just below the calculated theoretical maximum. While current research consistently argues for more complex data-driven Multi-Touch Attribution (MTA) models, this project provides a nuance to this field of research in showing that the LTA model may, in fact, be suitable in some cases. A new approach to develop specialized models based on correlations between conversion and contextual variables, then shows that attribution models for mobile users specifically yield higher accuracy. The sum of such unnormalized attributions function as indicators for the conversion strength of contextual variables and can further assist decision making.

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  • 184.
    Klabbers, Rob
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Roslagstullsbacken 23, Stockholm, 106 91, Sweden.
    Lamers, Jules
    School of Mathematics and Statistics, University of Melbourne, Melbourne, 3010, VIC, Australia.
    How Coordinate Bethe Ansatz Works for Inozemtsev Model2022In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 390, no 2, p. 827-905Article in journal (Refereed)
    Abstract [en]

    Three decades ago, Inozemtsev discovered an isotropic long-range spin chain with elliptic pair potential that interpolates between the Heisenberg and Haldane–Shastry spin chains while admitting an exact solution throughout, based on a connection with the elliptic quantum Calogero–Sutherland model. Though Inozemtsev’s spin chain is widely believed to be quantum integrable, the underlying algebraic reason for its exact solvability is not yet well understood. As a step in this direction we refine Inozemtsev’s ‘extended coordinate Bethe ansatz’ and clarify various aspects of the model’s exact spectrum and its limits. We identify quasimomenta in terms of which the M-particle energy is close to being (functionally) additive, as one would expect from the limiting models. This moreover makes it possible to rewrite the energy and Bethe-ansatz equations on the elliptic curve, turning the spectral problem into a rational problem as might be expected for an isotropic spin chain. We treat the M= 2 particle sector and its limits in detail. We identify an S-matrix that is independent of positions despite the more complicated form of the extended coordinate Bethe ansatz. We show that the Bethe-ansatz equations reduce to those of Heisenberg in one limit and give rise to the ‘motifs’ of Haldane–Shastry in the other limit. We show that, as the interpolation parameter changes, the ‘scattering states’ from Heisenberg become Yangian highest-weight states for Haldane–Shastry, while bound states become (sl2-highest weight versions of) affine descendants of the magnons from M= 1. We are able to treat this at the level of the wave function and quasimomenta. For bound states we find an equation that, for given Bethe integers, relates the ‘critical’ values of the spin-chain length and the interpolation parameter for which the two complex quasimomenta collide; it reduces to the known equation for the ‘critical length’ in the limit of the Heisenberg spin chain. We also elaborate on Inozemtsev’s proof of the completeness for M= 2 by passing to the elliptic curve. Our review of the two-particle sectors of the Heisenberg and Haldane–Shastry spin chains may be of independent interest.

  • 185.
    Klai, Amin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Examining Inclusion of a Sustainability Criterion in Portfolio Optimization - Could an Investor Benefit from it?2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In today's society sustainability has become an important subject and has an impact on various sectors. Corporations include sustainability in their corporate strategy, which further affects the field of corporate finance. This has lead to a new insight among investors to include a sustainability criterion in their investment processes. This research has investigated how Investor AB could optimize their portfolio by including sustainability criterion (ESG) and how different portfolio setups will differ from each other. 

    The research has been conducted utilizing Markowitz portfolio optimization described by Markowitz theory. The application of the theory has been extended with a third criterion of a weighted ESG score rating where the optimal solutions were found using the notion of Pareto optimality and quadratic programming. Different cases have been created to find how more sustainable portfolios can differ from each other.

    The research shows that portfolios consisting of companies with higher ESG rating do not significantly decrease the expected return but can suffer from higher standard deviation, which indicates that it is driven by assets with higher ESG score rating.

    The obtained results show that the portfolios obtained including the third criterion will not always obtain a value of Jensen's Alpha above zero (0) and are therefore not optimal strategies to outperform the benchmark index, SIX Return Index. A portfolio that consists of non-sustainable and sustainable assets has performed better than other portfolios that under- or overperform from the perspective of sustainability. 

    The conclusion is that an investor must sacrifice a higher weighted ESG score rating of its portfolio to obtain a higher expected return and less risk. An investor that aims for higher return, must exclude the sustainability criterion.

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  • 186.
    Kohn, Kathlén
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Deuker, Ernst Ulrich
    Der Komplex der nicht-chromatischen Skalen2017In: Mitteilungen der DMV, ISSN 0942-5977, Vol. 25, p. 17-25Article in journal (Refereed)
    Abstract [en]

    We consider the space of all musical scales with the ambition to systematize it.To do this, we pursue the idea to view certain scales as basic constituents and to“mix” all remaining scales from these. The German version of this article appearedinMitteilungen der DMV, volume 25, issue 1

  • 187.
    Koivumäki, Jussi T.
    et al.
    Faculty of Medicine and Health Technology, and Centre of Excellence in Body-on-Chip Research, Tampere University, Tampere, Finland.
    Hoffman, Johan
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Maleckar, Mary M.
    Computational Physiology Department, Simula Research Laboratory, Oslo, Norway.
    Einevoll, Gaute T.
    Centre for Integrative Neuroplasticity, University of Oslo, Oslo, Norway; Department of Physics, University of Oslo, Oslo, Norway; Department of Physics, Norwegian University of Life Sciences, Ås, Norway.
    Sundnes, Joakim
    Computational Physiology Department, Simula Research Laboratory, Oslo, Norway.
    Computational cardiac physiology for new modelers: Origins, foundations, and future2022In: Acta Physiologica, ISSN 1748-1708, E-ISSN 1748-1716, Vol. 236, no 2, article id e13865Article, review/survey (Refereed)
    Abstract [en]

    Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

  • 188.
    Korac Dalenmark, Maximilian
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Modelling Credit Spread Risk with a Focus on Systematic and Idiosyncratic Risk2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis presents an application of Principal Component Analysis (PCA) and Hierarchical PCA to credit spreads. The aim is to identify the underlying factors that drive the behavior of credit spreads as well as the left over idiosyncratic risk, which is crucial for risk management and pricing of credit derivatives. The study employs a dataset from the Swedish market of credit spreads for different maturities and ratings, split into Covered Bonds and Corporate Bonds, and performs PCA to extract the dominant factors that explain the variation in the data of the former set. The results show that most of the systemic movements in Swedish covered bonds can be extracted using a mean which coincides with the first principal component. The report further explores the idiosyncratic risk of the credit spreads to further the knowledge regarding the dynamics of credit spreads and improving risk management in credit portfolios, specifically in regards to new regulation in the form of the Fundemental Review of the Trading Book (FRTB). The thesis also explores a more general model on corporate bonds using HPCA and K-means clustering. Due to data issues it is less explored but there are useful findings, specifically regarding the feasibility of using clustering in combination with HPCA.

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  • 189.
    Krantz, Oscar
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Climate Risk in Financial Markets2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    We investigate various methods for generating a market-based proxy for climate related transition risk in financial markets, and use these to determine the sensitivities of various investments towards climate change policies. We find that assets tied to the energy and materials sector have consistently high sensitivity towards market factors which are likely to decline in response to climate regulations, and as such consequently face mark-to-market losses conditional on systemic climate events. For beta estimation we use both traditional linear regression and the dynamic conditional beta model developed by Engle, based on multivariate GARCH volatility models. We find suggestive evidence that our stylised climate factors, based on stranded assets, responds negatively to news of policies related to a move towards renewable energies.

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  • 190.
    Kurlberg, Par
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Lagarias, Jeffrey C.
    Pomerance, Carl
    On Sets of Integers Which Are Both Sum-Free and Product-Free2013In: Integers: Electronic Journal of Combinatorial Number Theory, E-ISSN 1553-1732Article in journal (Refereed)
    Abstract [en]

    We consider sets of positive integers containing no sum of two elements in the set and also no product of two elements. We show that the upper density of such a set is strictly smaller than 1/2 and that this is best possible. Further, we also find the maximal order for the density of such sets that are also periodic modulo some positive integer.

  • 191.
    Kurlberg, Pär
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Level Repulsion for Arithmetic Toral Point Scatterers in Dimension 32022In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 23, no 12, p. 4449-4462Article in journal (Refereed)
    Abstract [en]

    We show that arithmetic toral point scatterers in dimension three (“Šeba billiards on R3/ Z3”) exhibit strong level repulsion between the set of “new” eigenvalues. More precisely, let Λ : = { λ1< λ2< … } denote the unfolded set of new eigenvalues. Then, given any γ> 0 , |{i≤N:λi+1-λi≤ϵ}|N=Oγ(ϵ4-γ)as N→ ∞ (and ϵ> 0 small.) To the best of our knowledge, this is the first mathematically rigorous demonstration of a level repulsion phenomena for the quantization of a deterministic system.

  • 192.
    Kurlberg, Pär
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Klurman, Oleksiy
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A note on multiplicative automatic sequences, II2020In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 52, no 1, p. 185-188Article in journal (Refereed)
    Abstract [en]

    We prove that any q'>𝑞q‐automatic multiplicative function𝑓:ℕ→ℂ either essentially coincides with a Dirichlet character, or vanishes on all sufficiently large primes. This confirms a strong form of a conjecture of Bell, Bruin and Coons [Trans. Amer. Math. Soc. 364 (2012) 933–959].

  • 193.
    Kurlberg, Pär
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Rosenzweig, Lior
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Superscars for arithmetic toral point scatterers2016In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 349, no 1, p. 329-360Article in journal (Refereed)
    Abstract [en]

    We investigate eigenfunctions of the Laplacian perturbed by a delta potential on the standard tori in dimensions . Despite quantum ergodicity holding for the set of "new" eigenfunctions we show that superscars occur-there is phase space localization along families of closed orbits, in the sense that some semiclassical measures contain a finite number of Lagrangian components of the form , for uniformly bounded from below. In particular, for both and , eigenfunctions fail to equidistribute in phase space along an infinite subsequence of new eigenvalues. For , we also show that some semiclassical measures have both strongly localized momentum marginals and non-uniform quantum limits (i.e., the position marginals are non-uniform). For , superscarred eigenstates are quite rare, but for we show that the phenomenon is quite common-with denoting the counting function for the new eigenvalues below x, there are eigenvalues with the property that any semiclassical limit along these eigenvalues exhibits superscarring.

  • 194.
    Kurlberg, Pär
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ueberschär, Henrik
    Superscars in the Seba billiard2017In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, To appear in J. Eur. Math. Soc. (JEMS)Article in journal (Refereed)
  • 195.
    Kurlberg, Pär
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Zickert, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Formal uniqueness in Ewald sphere corrected single particle analysisManuscript (preprint) (Other academic)
  • 196.
    Kuroiwa, Yohei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A positive partial realization of time series2009In: 17th European Signal Processing Conference (EUSIPCO 2009), 2009, p. 413-416Conference paper (Refereed)
    Abstract [en]

    For a given partial covariance sequence (C 0,C 1,⋯,C n) and for each MA part of the ARMA modeling filter of degree n, an AR part of the ARMA modeling filter of degree n for the solution to the rational covariance extension problem is obtained by solving a nonlinear equation, which is homotopic to a nonlinear equation determining the maximum entropy AR filter.

  • 197.
    Köhler, William
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A Bayesian Approach to Predicting Default, Prepayment and Order Return in Unsecured Consumer Loans2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This paper presents an approach to model the risks associated with defaults, prepayments, and order returns in the context of unsecured consumer credits, specifically in buy-now-pay-later (BNPL) loans. The paper presents a Bayesian competing risk proportional hazard model to model the time to default, prepayment, and order return in BNPL loans. Model parameters are estimated using Markov chain Monte Carlo (MCMC) sampling techniques and Bayesian inference is developed using a unique dataset containing monthly performance data of fixed-duration interest-bearing consumer loans.

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    fulltext
  • 198.
    Köpp, Wiebke
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Friederici, Anke
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Atzori, Marco
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Weinkauf, Tino
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Notes on Percolation Analysis of Sampled Scalar Fields2021In: Topological Methods in Data Analysis and Visualization VI: Theory, Applications, and Software / [ed] Ingrid Hotz, Talha Bin Masood, Filip Sadlo, Julien Tierny, Springer Nature , 2021, p. 39-54Conference paper (Refereed)
    Abstract [en]

    Percolation analysis is used to explore the connectivity of randomly connected infinite graphs. In the finite case, a closely related percolation function captures the relative volume of the largest connected component in a scalar field’s superlevel set. While prior work has shown that random scalar fields with little spatial correlation yield a sharp transition in this function, little is known about its behavior on real data. In this work, we explore how different characteristics of a scalar field—such as its histogram or degree of structure—influence the shape of the percolation function. We estimate the critical value and transition width of the percolation function, and propose a corresponding normalization scheme that relates these values to known results on infinite graphs. In our experiments, we find that percolation analysis can be used to analyze the degree of structure in Gaussian random fields. On a simulated turbulent duct flow data set we observe that the critical values are stable and consistent across time. Our normalization scheme indeed aids comparison between data sets and relation to infinite graphs.

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    koeppfriederici21
  • 199. Lahtinen, V.
    et al.
    Månsson, Teresia
    KTH.
    Ardonne, E.
    Quantum criticality in many-body parafermion chains2021In: SciPost Physics Core, ISSN 2666-9366, Vol. 4, no 2, article id 014Article in journal (Refereed)
    Abstract [en]

    We construct local generalizations of 3-state Potts models with exotic critical points. We analytically show that these are described by non-diagonal modular invariant partition functions of products of Z3 parafermion or u(1)6 conformal field theories (CFTs). These correspond either to non-trivial permutation invariants or block diagonal invariants, that one can understand in terms of anyon condensation. In terms of lattice parafermion operators, the constructed models correspond to parafermion chains with many-body terms. Our construction is based on how the partition function of a CFT depends on symmetry sectors and boundary conditions. This enables to write the partition function corresponding to one modular invariant as a linear combination of another over different sectors and boundary conditions, which translates to a general recipe how to write down a microscopic model, tuned to criticality. We show that the scheme can also be extended to construct critical generalizations of k-state clock type models. 

  • 200.
    Landberg, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Market Surveillance Using Empirical Quantile Model and Machine Learning2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In recent years, financial trading has become more available. This has led to more market participants and more trades taking place each day. The increased activity also implies an increasing number of abusive trades. To detect the abusive trades, market surveillance systems are developed and used. In this thesis, two different methods were tested to detect these abusive trades on high-dimensional data. One was based on empirical quantiles, and the other was based on an unsupervised machine learning technique called isolation forest. The empirical quantile method uses empirical quantiles on dimensionally reduced data to determine if a datapoint is an outlier or not. Principal Component Analysis (PCA) is used to reduce the dimensionality of the data and handle the correlation between features.Isolation forest is a machine learning method that detects outliers by sorting each datapoint in a tree structure. If a datapoint is close to the root, it is more likely to be an outlier. Isolation forest have been proven to detect outliers in high-dimensional datasets successfully, but have not been tested before for market surveillance. The performance of both the quantile method and isolation forest was tested by using recall and run-time. 

    The conclusion was that the empirical quantile method did not detect outliers accurately when all dimensions of the data were used. The method most likely suffered from the curse of dimensionality and could not handle high dimensional data. However, the performance increased when the dimensionality was reduced. Isolation forest performed better than the empirical quantile method and detected 99% of all outliers by classifying 226 datapoints as outliers out of a dataset with 184 true outliers and 1882 datapoints.

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    fulltext
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