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  • 251.
    Norgren, Marcus
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Steering Method for Nonholonomic Motion Planning based on Quadratic Programming and Differential Flatness2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this thesis, an optimization based steering methods based on differential flatness and quadratic programming has been investigated. The method has been implemented into an RRT*-planner and tested in simulation.

    Differential flatness is a useful property of certain dynamical systems that allows the states and inputs of the system to be transformed to a differentially flat representation, allowing for feasible trajectory generation by purely geometric methods. In the following thesis, the general 1-trailer system is considered.

    The purpose of the steering method is to conncet two arbitray sampled points with a feasible trajectory, with low computational effort, in order for it to be used in real time. This is done by parameterization of the trajectory using polynomials as basis functions and formulating the problem as a convex quadratic program, minimizing acceleration and jerk, subject to boundary conditions and nonholonomic constraints on velocity, acceleration and curvature.

    The results show that it is possible to formulate and solve nonholonomic motion planning problems using quadratic programming methods. The results also show promise in terms of path quality and computational time, however, some challanges regarding the method, mainly regarding, sampling, feasibility and time allocation, are also reported which must be adressed further.

    The steering method shows promising results in terms of the generated paths and solution time, but more testing and implementation is required for further evaluation.

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  • 252.
    Nungesser, Ernesto
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Diagonal Future of Some Non-diagonal Bianchi A Spacetimes with Matter of Vlasov Type2014In: Progress in Mathematical Relativity, Gravitation and Cosmology: Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimarães, Portugal, September 3-7, 2012, Springer Berlin/Heidelberg, 2014, p. 349-353Conference paper (Refereed)
    Abstract [en]

    We have been able to show that after a possible basis change the future of the non-diagonal Bianchi II and VI0 spacetimes with collisionless matter is asymptotically diagonal assuming small data. More precisely these solutions are asymptotic to the Collins-Stewart solution with dust and the Ellis-MacCallum solution respectively.

  • 253.
    Nydahl, Pelle
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Robust Portfolio Optimization with Correlation Penalties2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Robust portfolio optimization models attempt to address the standard optimization method's high sensitivity to noise in the parameter estimates, by taking an investor's uncertainty about the estimates into account when finding an optimal portfolio. In this thesis, we study robust variations of an extension of the mean-variance problem, where an additional term penalizing the portfolio's correlation with an exogenous return sequence is included in the objective. Using a normalized risk factor model of the asset returns, estimations are done using EMA filtering as well as exponentially weighted linear regression. We show that portfolio performance can significantly improve with respect to a range of metrics, such as Sharpe ratio, expected shortfall and skewness, when using appropriate robust models and hyperparameters. We further show that extending the optimization problem with a correlation penalty can notably reduce portfolio correlation with an arbitrary return sequence, with only a small impact on other performance metrics.

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  • 254.
    Odelius, Lukas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On orthogonalizing weights for the Hermite polynomials2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this paper we study the orthogonal polynomial system on C (z = x + iy) generated by weights of the form w(x, y) = e^{-Q(x, y)} where Q(x, y) is a positive definite quadratic form, we consider the stability of the polynomial system relative to perturbations to the weights and we construct new orthogonalizing weights for the Hermite polynomials.

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  • 255.
    Oliveberg, Max
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Optimal Order Placement Using Markov Models of Limit Order Books2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    We study optimal order placement in a limit order book. By modelling the limit order book dynamics as a Markov chain, we can frame the purchase of a single share as a Markov Decision Process. Within the framework of the model, we can estimate optimal decision policies numerically. The trade rate is varied using a running cost control variable. The optimal policy is found to result in a lower cost of trading as a function of the trade rate compared to a market order only strategy.

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  • 256.
    Olsen, Kristian Stølevik
    et al.
    Nordita SU; Institut für Theoretische Physik II—Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, D-40225, Germany.
    Hansen, Alex
    PoreLab, Department of Physics, Norwegian University of Science and Technology, NO-7491, Trondheim, Norway, NO-7491.
    Flekkøy, Eirik Grude
    PoreLab, The Njord Centre, Department of Physics, University of Oslo, Oslo, NO-0316, Norway; PoreLab, Department of Chemistry, Norwegian University of Science and Technology, Trondheim, NO-7491, Norway.
    Hyper-Ballistic Superdiffusion of Competing Microswimmers2024In: Entropy, E-ISSN 1099-4300, Vol. 26, no 3, article id 274Article in journal (Refereed)
    Abstract [en]

    Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker–Planck equation arises. The solution exhibits hyper-ballistic superdiffusive motion, with a diffusion exponent of four. A microscopic simulation strategy is proposed, which shows excellent agreement with theoretical analysis.

  • 257.
    Olsson, Jimmy
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Westerborn, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Efficient parameter inference in general hidden Markov models using the filter derivatives2016In: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 3984-3988Conference paper (Refereed)
    Abstract [en]

    Estimating online the parameters of general state-space hidden Markov models is a topic of importance in many scientific and engineering disciplines. In this paper we present an online parameter estimation algorithm obtained by casting our recently proposed particle-based, rapid incremental smoother (Paris) into the framework of recursive maximum likelihood estimation for general hidden Markov models. Previous such particle implementations suffer from either quadratic complexity in the number of particles or from the well-known degeneracy of the genealogical particle paths. By using the computational efficient and numerically stable Paris algorithm for estimating the needed prediction filter derivatives we obtain a fast algorithm with a computational complexity that grows only linearly with the number of particles. The efficiency and stability of the proposed algorithm are illustrated in a simulation study.

  • 258.
    Olsson, Magnus
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Role Mining With Hierarchical Clustering and Binary Similarity Measures2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Role engineering, a critical task in role-based access control systems, is the process of identifying a complete set of roles that accurately reflect the structure of an organization. Role mining, a data-driven approach, utilizes data mining techniques on user-permission assignments represented as binary data to automatically derive these roles. However, relying solely on data-driven methods often leads to the generation of a large set of roles lacking interpretability. To address this limitation, this thesis presents a role mining algorithm, whose results can be viewed as an initial step in the role engineering process, in order to streamline the task of defining semantically meaningful roles, where human analysis is an inevitable post-processing step. The algorithm is based on hierarchical clustering analysis, and its main objective is identifying a sufficiently small set of roles that cover as large a proportion of the user-permission assignments as possible. To evaluate the performance of the algorithm, multiple real-world data sets representing diverse access control scenarios are utilized. The evaluation focuses on comparing various binary similarity measures, with the goal of determining the most suitable characteristics of a binary similarity measure to be used for role mining. The evaluation of different binary similarity measures provides insights into their effectiveness in achieving accurate role definitions to be used as a foundation for constructing meaningful roles. Ultimately, this research contributes to the advancement of role mining methodologies, facilitating improved access control systems that align with organizational needs and enhance security and efficiency.

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  • 259.
    Orback, Arvid
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sandström, Robin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A novel approach to model an energy flexibility market using temperature proxies2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The global demand for energy increases. This causes a problem concering the strain put on energy grids and energy production. The problem occurs when the aggregated energy consumption peaks temporarily and is known as peak loads. These peak loads will sometimes exceed the capacity of an isolated grid and thereby put a strain on either the grid or the power suppliers. One way of preventing strained grids is to invest in new infrastructure to expand the grid. If the bottleneck in the system concerns the supply of energy, more power needs to go to the grid. However, one way of counteracting the problem short-term is to have some consumers shift or reduce their load during peak loads. The reduced or shifted load is called the flexible load, and this report proposes a mathematical model for a marketplace where units can sell their flexible load to grid operators or to energy producers for an economic compensation. The model is adapted to the energy production of heating, and depends on a state-space model that simulates the indoor temperature dynamics of units selling their flexible load on the marketplace. The results of this report show that simulating a flexibility market with temperature dynamics enable units to shift or reduce their loads for a monetary compensation. Consequently, the effect of having peak loads on the energy grid is mitigated. The proxy temperature model used shows potential but generates some unrealistic values of the indoor temperature as a consequence of poorly estimated model coefficients.

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  • 260.
    Ossmark, Viktor
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Road Segmentation and Optimal Route Prediction using Deep Neural Networks and Graphs2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Observing the earth from above is a great way of understanding our world better. From space, many complex patterns and relationships on the ground can be identified through high-quality satellite data. The quality and availability of this data in combination with recent advancement in various deep learning techniques allows us to find these patterns more effectively then ever. In this thesis, we will analyze satellite imagery by using deep neural networks in an attempt to find road networks in different cities around the world. Once we have located networks of roads in the cities we will represent them as graphs and deploy the Dijkstra shortest path algorithm to find optimal routes within these networks.

    Having the ability to efficiently use satellite imagery for near real-time road detection and optimal route prediction has many possible applications, especially from a humanitarian and commercial point of view. For example, in the humanitarian realm, the frequency of natural disasters is unfortunately increasing due to climate change and the need for emergency real-time mapping for relief organisations in the case of a severe flood or similar is growing. 

    The state-of-the-art deep neural network models that will be implemented, compared and contrasted for this task are mainly based on the U-net and ResNet architectures. However, before introducing these architectures the reader will be given a comprehensive introduction and theoretical background of deep neural networks to distinctly formulate the mathematical groundwork. The final results demonstrates an overall strong model performance across different metrics and data sets, with the highest obtained IoU-score being approximately 0.7 for the segmentation task. For some models we can also see a high degree of similarity between the predicted optimal paths and the ground truth optimal paths.

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  • 261.
    Pahne, Elsa
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Åkerlund, Louise
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Modelling Credit Spread Risk in the Banking Book (CSRBB)2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Risk measurement tools and strategies have until recently been calibrated for a low-for-long interest rate environment. However, in the current higher interest rate environment, banking supervisory entities have intensified their regulatory pressure on institutions to enhance their assessment and monitoring of interest rate risk and credit spread risk. The European Banking Authority (EBA) has released updated guidelines on the assessment and monitoring of Credit Spread Risk in the Banking Book (CSRBB), which will replace the current guidelines by 31st December 2023. The new guidelines identify the CSRBB as a separate risk category apart from Interest Rate Risk in the Banking Book (IRRBB), and specifies the inclusion of liabilities in therisk calculations. This paper proposes a CSRBB model that conforms to the updated EBA guidelines. The model uses a historical simulation Value at Risk (HSVaR) and Expected Shortfall (ES) approach, and includes a 90-day holding period, as suggested by Finansinspektionen (FI). To assess the effectiveness of the model, it is compared with a standardised model of FI, and subjected to backtesting. Additionally, the paper suggests modifications to the model to obtain more conservative results.

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  • 262.
    Parkash, Mohit
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Halladgi Naghadeh, Diana
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Portfolio Strategies Under Different Inflationary Regimes2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In 2023, the topic of ongoing inflation is being discussed almost daily as it has become inevitable. The global economy is facing significant uncertainty and downward pressure as several leading developed nations adopted expansionary fiscal policies and quantitative easing monetary policies during the pandemic. Those action has lead to an unprecedented level of inflation today. The purpose of this report is to investigate different portfolio strategies and evaluate how various asset classes perform under varying inflationary conditions. Using regression analysis, the study assesses the performance of different assets during high and low inflation regimes. Additionally, two different portfolio strategies are implemented and compared against the 60/40 portfolio strategy, which is considered a benchmark approach among investors.

    The first strategy involves a modified version of the Markowitz optimization method, which determines the optimal weights of the portfolio during high and low inflationary environments. The second strategy entails identifying a signal and then dynamically adjusting the portfolio's weights based on the signal's value. The findings indicate that during high inflation periods, oil, gold, energy, basic materials, and technology sectors exhibit strong performance. Furthermore, the results reveal that the first strategy is more effective than the second strategy and the 60/40 benchmark.

    An interesting topic for further investigation is exploring the impact of short selling on portfolio allocation and strategy, which was not addressed in this report.

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  • 263.
    Parra, Rodrigo
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Lelong numbers on projective varieties2010Licentiate thesis, monograph (Other academic)
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  • 264.
    Peng, Shen
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Lisser, Abdel
    Laboratory of Signals and Systems, CentraleSupelec, Bat Breguet, 3 Rue Joliot Curie, 91190, Gif-sur-Yvette, France.
    Singh, Vikas Vikram
    Department of Mathematics, IIT Delhi, New Delhi, India.
    Gupta, Nalin
    Department of Mathematics, IIT Delhi, New Delhi, India.
    Balachandar, Eshan
    Department of Mathematics, IIT Delhi, New Delhi, India.
    Games with distributionally robust joint chance constraints2021In: Optimization Letters, ISSN 1862-4472, E-ISSN 1862-4480Article in journal (Refereed)
    Abstract [en]

    This paper studies an n-player non-cooperative game where each player has expected-value payoff function and chance-constrained strategy set. We consider the case where the row vectors defining the constraints are independent random vectors whose probability distributions are not completely known and belong to a certain distributional uncertainty set. The chance-constrained strategy sets are defined using a distributionally robust framework. We consider one density based uncertainty set and four two-moments based uncertainty sets. One of the considered uncertainty sets is based on a nonnegative support. Under the standard assumptions on the players’ payoff functions, we show that there exists a Nash equilibrium of a distributionally robust chance-constrained game for each uncertainty set. As an application, we study Cournot competition in electricity market and perform the numerical experiments for the case of two electricity firms.

  • 265.
    Persson, Liam
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Modelling regime shifts for foreign exchange market data using hidden Markov models2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Financial data is often said to follow different market regimes. These regimes, which not possible to observe directly, are assumed to influence the observable returns. In this thesis such regimes are modeled using hidden Markov models. We will investigate whether the five different currency pairs EUR/NOK, USD/NOK, EUR/USD, EUR/SEK, and USD/SEK exhibit market regimes that can be described using hidden Markov modeling. We will find the most optimal number of states and study the mean, variance, and correlations in each market regime.

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  • 266.
    Persson, Sebastian
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Hansson, Niklas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Stochastic Optimization of Asset Management Project Portfolios: A Risk-Informed Approach2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Asset management within the nuclear industry has become an increasingly relevant topic as safety requirements have tightened and energy security has become more important. Asset management ensures performance and reliability in a nuclear facility by balancing costs, opportunities, and risks to get the most out of assets. Asset management processes can often be modeled as capital budgeting problems, where investments are evaluated based on costs and benefits, which establishes a link to mathematical optimization. This study addresses asset management at the Swedish nuclear power plant, Forsmark, and aims to implement an optimization model to improve the project selection related to maintenance and replacement of assets at the plant. First, the most relevant areas of nuclear asset management are identified through a comprehensive literature review. The most relevant method, identified as a mix between risk-informed asset management and capital budgeting, is then implemented to fit the prerequisites at Forsmark. Several models of different complexity are developed and the resulting stochastic model incorporates uncertainty of input variables by assuming underlying distributions. Finally, a methodology to incorporate a quantitative risk measure in the optimization is suggested through the use of conditional value at risk. Results are generated based on simulated data and illustrate the potential of implementing the method at Forsmark.

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  • 267.
    Pirani, M.
    et al.
    Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada..
    Baldi, S.
    School of Mathematics, Southeast University, Nanjing 210096, China, and also with the Delft Center for System and Control, Delft University of Technology, 2628 CD Delft, The Netherlands.
    Johansson, Karl H.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Impact of Network Topology on the Resilience of Vehicle Platoons2022In: IEEE transactions on intelligent transportation systems (Print), ISSN 1524-9050, E-ISSN 1558-0016, Vol. 23, no 9, p. 15166-15177Article in journal (Refereed)
    Abstract [en]

    This paper presents a comprehensive study on the impact of information flow topologies on the resilience of distributed algorithms that are widely used for estimation and control in vehicle platoons. In the state of the art, the influence of information flow topology on both internal and string stability of vehicle platoons has been well studied. However, understanding the impact of information flow topology on cyber-security tasks, e.g., attack detection, resilient estimation and formation algorithms, is largely open. By means of a general graph theory framework, we study connectivity measures of several platoon topologies and we reveal how these measures affect the ability of distributed algorithms to reject communication disturbances, to detect cyber-attacks, and to be resilient against them. We show that the traditional platoon topologies relying on interaction with the nearest neighbor are very fragile with respect to performance and security criteria. On the other hand, appropriate platoon topologies, namely k-nearest neighbor topologies, are shown to fulfill desired security and performance levels. The framework we study covers undirected and directed topologies, ungrounded and grounded topologies, or topologies on a line and on a ring. We show that there is a trade-off in the network design between the robustness to disturbances and the resilience to adversarial actions. Theoretical results are validated via simulations.

  • 268.
    Plonczak, Antoni
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Explaining Turbulence Predictions from Deep Neural Networks: Finding Important Features with Approximate Shapley Values2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Deep-learning models have been shown to produce accurate predictions in various scientific and engineering applications, such as turbulence modelling, by efficiently learning complex nonlinear relations from data. However, deep networks are often black boxes and it is not clear from the model parameters which inputs are more important to a prediction. As a result, it is difficult to understand whether models are taking into account physically relevant information and little theoretical understanding of the phenomenon modelled by the deep network can be gained. 

    In this work, methods from the field of explainable AI, based on Shapley Value approximation, are applied to compute feature attributions in previously trained fully convolutional deep neural networks for predicting velocity fluctuations in an open channel turbulent flow using wall quantities as inputs. The results show that certain regions in the inputs to the model have a higher importance to a prediction, which is verified by computational experiments that confirm the models are more sensitive to those inputs as compared to randomly selected inputs, if the error in the prediction is considered. These regions correspond to certain strongly distinguishable features (visible structures) in the model inputs. The correlations between the regions with high importance and visible structures in the model inputs are investigated with a linear regression analysis. The results indicate that certain physical characteristics of these structures are highly correlated to the importance of individual input features within these structures.

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  • 269.
    Pramanik, Satyajit
    et al.
    Stockholm Univ, S-10691 Stockholm, Sweden.;Nordita SU.
    Wettlaufer, John S.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, S-10691 Stockholm, Sweden.;Yale Univ, New Haven, CT 06520 USA.;Univ Oxford, Math Inst, Oxford OX2 6GG, England..
    Confinement- induced control of similarity solutions in premelting dynamics and other thin film problems2019In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 79, no 3, p. 938-958Article in journal (Refereed)
    Abstract [en]

    We study the combined effects of nonlocal elasticity and confinement-induced ordering on the dynamics of thermomolecular pressure gradient driven premelted films bound by an elastic membrane. The confinement-induced ordering is modeled using a film thickness dependent viscosity. When there is no confinement-induced ordering, we recover the similarity solution for the evolution of the elastic membrane, which exhibits an in finite sequence of oscillations. However, when the confinement-induced viscosity is comparable to the bulk viscosity, the numerical solutions of the full system reveal the conditions under which the oscillations and similarity solutions vanish. Implications of our results for general thermomechanical dynamics, frost heave observations, and cryogenic cell preservation are discussed. Finally, through its influence on the viscosity, the confinement effect implicitly introduces a new universal length scale into the volume flux. Thus, there are a host of thin film problems, from droplet breakup to wetting/dewetting dynamics, whose properties (similarity solutions, regularization, and compact support) will change under the action of the confinement effect. Therefore, our study suggests revisiting the mathematical structure and experimental implications of a wide range of problems within the framework of the confinement effect.

  • 270.
    Prashant, Prashant
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Development and Assessment of Re-Fleet Assignment Model under Environmental Considerations2020Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The imminent threat of global catastrophe due to climate change gets more real by each passing year. The Aviation trade association, IATA, claims that Aviation accounts for approximately 2% of the Greenhouse Gases (GHG) caused by human activities, and 3.5% of the total Radiative Forcing. With continuous increase in Aviation industry and subsequent drop in fossil fuel prices, these numbers are only expected to up with time. In Addition, these numbers do not include the effects of altitude of emission and many environmentalists believe that the number for some pollutants could be at least 2-3 times larger than IATA estimates. This rising concern engages the Aviation industry to investigate possible methods to alleviate their environmental impact. 

    The first part of this thesis provides a framework to support Airlines in monitoring their current environmental footprint during the process of scheduling. This objective is realised by developing a robust system for estimating the fuel consumed (ergo quantity of major Greenhouse Gases emitted) by a particular fleet type operating a certain leg, which is then employed in a Fleet Assignment (FA) Operation to reduce emissions and increase the Contribution. An emissions estimation model for Turbojet Aeroplane fleets is created for Industrial Optimizers AB’sMP2 software. The emissions estimation model uses historic fuel consumption data provided by ICAO for a given fleet type to estimate the quantity (in kg) of environmental pollutants during the Landing and Takeoff operation (below 3000 ft) and the Cruise, Climb and Descent operation (above 3000 ft). 

    The second part of this thesis concerns with assigning monetary weights to the pollutant estimates to calculate an emission cost. This emission cost is then added to MP2’s Fleet Assignment’s objective function as an additional Operational cost to perform a Contribution maximization optimization subjected to the legality constraints. The effects of these monetary weights levied on the results of Fleet Assignment are studied, and utilizing curve-fitting and mathematical optimization, monetary weights are estimated for the desired reduction in GHG emissions. 

    Finally, a recursive algorithm based on Newton-Raphson method is designed and tested for calculating pollutant weights for untested schedules.

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  • 271.
    Prelipcean, Adrian Corneliu
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Gidofalvi, Gyözö
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Susilo, Yusak Octavius
    KTH, School of Architecture and the Built Environment (ABE), Transport Science, System Analysis and Economics.
    Measures of transport mode segmentation of trajectories2016In: International Journal of Geographical Information Science, ISSN 1365-8816, E-ISSN 1365-8824, Vol. 30, no 9, p. 1763-1784Article in journal (Refereed)
    Abstract [en]

    Rooted in the philosophy of point- and segment-based approaches for transportation mode segmentation of trajectories, the measures that researchers have adopted to evaluate the quality of the results (1) are incomparable across approaches, hence slowing the progress in the field and (2) do not provide insight about the quality of the continuous transportation mode segmentation. To address these problems, this paper proposes new error measures that can be applied to measure how well a continuous transportation mode segmentation model performs. The error measures introduced are based on aligning multiple inferred continuous intervals to ground truth intervals, and measure the cardinality of the alignment and the spatial and temporal discrepancy between the corresponding aligned segments. The utility of this new way of computing errors is shown by evaluating the segmentation of three generic transportation mode segmentation approaches (implicit, explicit–holistic, and explicit–consensus-based transport mode segmentation), which can be implemented in a thick client architecture. Empirical evaluations on a large real-word data set reveal the superiority of explicit–consensus-based transport mode segmentation, which can be attributed to the explicit modeling of segments and transitions, which allows for a meaningful decomposition of the complex learning task.

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  • 272.
    Prudhomme, Maxime
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Modeling Organic Installs in a Free-to-Play Game2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The Free-To-Play industry relies on getting a huge inflow of new players that might result in future gross bookings. Consequently, getting organic new players is crucial to ensure its health, especially as they have no direct associated acquisition cost. In addition, forecasting helps business planning as future gross bookings result from those news installs. This thesis investigates methods such as Linear Regression, Ridge, Lasso regularization, time-series analysis, and Prophet to forecast the inflow of organic installs and try to understand the factors impacting it. Using the data from 3 games for two platforms and 15 countries, it investigates the differences in behavior observed over the segments. This thesis first focuses on a specific segment by modeling the inflow of organic installs for the game number 17 on iOS in the United States of America. On this segment, the best model is the Lasso model using, among others, a Prophet model as a variable. However, the generalization to all segments is difficult. On average, exponential decay over time is the best way to forecast the future inflow of organic as it presents the more consistent performances over all segments.

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  • 273.
    Ratusznik, Wojciech
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Modern Credit Value Adjustment2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Counterparty risk calculations have gained importance after the latest financial crisis. The bankruptcy of Lehman Brothers showed that even large financial institutiones face a risk of default. Hence, it is important to measure the risk of default for all the contracts written between financial institutions. Credit Value Adjustment, CVA, is an industry standard method for such calculations. Nevertheless, the implementation of this method is contract dependent and the necessary computer simulations can be very intensive. Monte Carlo simulations have for a long time been known as a precise but slow technique to evaluate the cash flows for contracts of all kinds. Measuring the exposure of a contract written on structured products might require half a day of calculations if the implementation is written without significant optimization. Several ideas have been presented by researchers and applied in the industry, the idea explored and implemented in this thesis was based on using Artificial Neural Networks in Python. This procedure require a decomposition of the Expected Exposure calculation within the CVA and generating a large data set using a standard Monte Carlo simulation. Three network architectures have been tested and the final performance was compared with using standard techniques for the very same calculation. The performance gain was significant, a portfolio of 100 counterparties with 10 contracts each would take 20 minutes of calculations in total when using the best performing architecture whereas a parallel C++ implementation of the standard method would require 2.6 days.

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  • 274.
    Reddy, G. M. M.
    et al.
    Univ Sao Paulo Sao Carlos, Dept Appl Math & Stat, Inst Math & Comp Sci, POB 668, BR-13560970 Sao Paulo, Brazil..
    Vynnycky, Michael
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Cuminato, J. A.
    Univ Sao Paulo Sao Carlos, Dept Appl Math & Stat, Inst Math & Comp Sci, POB 668, BR-13560970 Sao Paulo, Brazil..
    An efficient adaptive boundary algorithm to reconstruct Neumann boundary data in the MFS for the inverse Stefan problem2019In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 349, p. 21-40Article in journal (Refereed)
    Abstract [en]

    In this exposition, a simple practical adaptive algorithm is developed for efficient and accurate reconstruction of Neumann boundary data in the inverse Stefan problem, which is a highly nontrivial task. Primarily, this algorithm detects the satisfactory location of the source points from the boundary in reconstructing the boundary data in the inverse Stefan problem efficiently. To deal with the ill-conditioning of the matrix generated by the MFS, we use Tikhonov regularization and the algorithm is designed in such a way that the optimal regularization parameter is detected automatically without any use of traditional methods like the discrepancy principle, the L-curve criterion or the generalized cross-validation (GCV) technique. Furthermore, this algorithm can be thought of as an alternative to the concept of Beck's future temperatures for obtaining stable and accurate fluxes, but without it being necessary to specify data on any future time interval. A MATLAB code for the algorithm is discussed in more-than-usual detail. We have studied the effects of accuracy and measurement error (random noise) on both optimal location and number of source points. The effectiveness of the proposed algorithm is shown through several test problems, and numerical experiments indicate promising results.

  • 275.
    Renström, Niklas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Maximizing Recommendation System Accuracy In E-Commerce for Clothing And Accessories for Children2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The industry of electronic commerce (e-commerce) constitutes a great part of the yearly retail consumption in Sweden. Looking at recent years, it has been seen that a rapidly growing sector within the mentioned field is the clothing industry for clothes and accessories for children and newborns. To get an overview of the items and help customers to find what they are looking for, many web stores have a system called a Recommendation System. The mechanics behind this service can look rather different depending on the method used. However, their unified goal is to provide a list of recommended items of interest to the customer. 

    A branch within this field is the Session Based Recommendation System (SBRS). These are models which are designed to work with the trace of products, called a session, that a user currently has visited on the web store. Based on that information they then formulate an output of recommended items. The SBRS models have been especially popularized since the majority of customers browse in an anonymous behavior, which means that they due to time efficiency often neglect the possibility of creating or logging into any personal web store account. This however limits the accessible information that a system can make use of to shape its item list. 

    It can be seen that the number of articles exploring SBRS within the fashion branch of clothing and accessories for children is very limited. This thesis is made to fill that gap. After a thorough literature study, three models were found to be of certain interest, the Short-Term Attention/Memory Priority (STAMP) model, Long Short-Term Memory (LSTM) model, and Gated Recurrent Unit (GRU) model. Further, the LSTM model is included as it is the collaborative company, BabyShop Group AB's current used method. 

    The results of this thesis show that the GRU model is a promising method, managing to predict the next item for a customer more consistently than any other of the evaluated models. Furthermore, it can also be seen that what embeddings the models use to represent the products plays a significant role in the learning and evaluation of the used data set. 

    Moreover, a benchmark model included in this thesis also shows the importance of filtering the data set of sessions. It can be seen that a majority of customers visit already-seen products, logged happenings most likely due to refreshing web pages or similar actions. This causes the session data set to be characterized by repeated items. For future work, it would therefore indeed be interesting to see how this data set can be filtered in a different way. To see how that affects the outcome of the used metrics in this thesis.

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  • 276.
    Ribberheim, Olle
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Carbon Intensity Estimation of Publicly Traded Companies2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The purpose of this master thesis is to develop a model to estimate the carbon intensity, i.e the carbon emission relative to economic activity, of publicly traded companies which do not report their carbon emissions. By using statistical and machine learning models, the core of this thesis is to develop and compare different methods and models with regard to accuracy, robustness, and explanatory value when estimating carbon intensity. Both discrete variables, such as the region and sector the company is operating in, and continuous variables, such as revenue and capital expenditures, are used in the estimation. Six methods were compared, two statistically derived and four machine learning methods. The thesis consists of three parts: data preparation, model implementation, and model comparison. The comparison indicates that boosted decision tree is both the most accurate and robust model. Lastly, the strengths and weaknesses of the methodology is discussed, as well as the suitability and legitimacy of the boosted decision tree when estimating carbon intensity.

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  • 277.
    Ringh, Axel
    et al.
    Chalmers Univ Technol, Dept Math Sci, S-41296 Gothenburg, Sweden.;Univ Gothenburg, Dept Math Sci, S-41296 Gothenburg, Sweden..
    Haasler, Isabel
    Ecole Polytechn Fed Lausanne, Signal Proc Lab, LTS 4, CH-1015 Lausanne, Switzerland..
    Chen, Yongxin
    Georgia Inst Technol, Sch Aerosp Engn, Atlanta, GA 30332 USA..
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Mean Field Type Control With Species Dependent Dynamics via Structured Tensor Optimization2023In: IEEE Control Systems Letters, E-ISSN 2475-1456, Vol. 7, p. 2898-2903Article in journal (Refereed)
    Abstract [en]

    In this letter we consider mean field type control problems with multiple species that have different dynamics. We formulate the discretized problem using a new type of entropy-regularized multimarginal optimal transport problems where the cost is a decomposable structured tensor. A novel algorithm for solving such problems is derived, using this structure and leveraging recent results in entropy-regularized optimal transport. The algorithm is then demonstrated on a numerical example in robot coordination problem for search and rescue, where three different types of robots are used to cover a given area at minimal cost.

  • 278.
    Ringh, Axel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. Shanghai Jiao Tong Univ, Dept Automat, Shanghai, Peoples R China; Shanghai Jiao Tong Univ, Sch Math, Shanghai, Peoples R China.
    Lower bounds on the maximum delay margin by analytic interpolation2018In: 2018 IEEE 57th Annual Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 5463-5469, article id 8618930Conference paper (Refereed)
    Abstract [en]

    We study the delay margin problem in the context of recent works by T. Qi, J. Zhu, and J. Chen, where a sufficient condition for the maximal delay margin is formulated in terms of an interpolation problem obtained after introducing a rational approximation. Instead we omit the approximation step and solve the same problem directly using techniques from function theory and analytic interpolation. Furthermore, we introduce a constant shift in the domain of the interpolation problem. In this way we are able to improve on their lower bound for the maximum delay margin.

  • 279.
    Ringström, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    The Cauchy problem in general relativity2009 (ed. 1)Book (Refereed)
  • 280.
    Risberg, Jonatan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Basil-GAN2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Developments in computer vision has sought to design deep neural networks which trained on a large set of images are able to generate high quality artificial images which share semantic qualities with the original image set. A pivotal shift was made with the introduction of the generative adversarial network (GAN) by Goodfellow et al.. Building on the work by Goodfellow more advanced models using the same idea have shown great improvements in terms of both image quality and data diversity. GAN models generate images by feeding samples from a vector space into a generative neural network. The structure of these so called latent vector samples show to correspond to semantic similarities of their corresponding generated images. In this thesis the DCGAN model is trained on a novel data set consisting of image sequences of the growth process of basil plants from germination to harvest. We evaluate the trained model by comparing the DCGAN performance on benchmark data sets such as MNIST and CIFAR10 and conclude that the model trained on the basil plant data set achieved similar results compared to the MNIST data set and better results in comparison to the CIFAR10 data set. To argue for the potential of using more advanced GAN models we compare the results from the DCGAN model with the contemporary StyleGAN2 model. We also investigate the latent vector space produced by the DCGAN model and confirm that in accordance with previous research, namely that the DCGAN model is able to generate a latent space with data specific semantic structures. For the DCGAN model trained on the data set of basil plants, the latent space is able to distinguish between images of early stage basil plants from late stage plants in the growth phase. Furthermore, utilizing the sequential semantics of the basil plant data set, an attempt at generating an artificial growth sequence is made using linear interpolation. Finally we present an unsuccessful attempt at visualising the latent space produced by the DCGAN model using a rudimentary approach at inverting the generator network function.

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  • 281.
    Rodrigues, Ana
    et al.
    CMUP and Departamento de Matemática Pura, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal .
    Dias, Ana Paula S.
    CMUP and Departamento de Matemática Pura, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal .
    Hopf bifurcation with SN-symmetry2009In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 22, no 3, p. 627-666Article in journal (Refereed)
    Abstract [en]

    We study Hopf bifurcation with SN-symmetry for the standard absolutely irreducible action of SN obtained from the action of SN by permutation of N coordinates. Stewart (1996 Symmetry methods in collisionless many-body problems, J. Nonlinear Sci. 6 543–63) obtains a classification theorem for the C-axial subgroups of SN × S1. We use this classification to prove the existence of branches of periodic solutions with C-axial symmetry in systems of ordinary differential equations with SN-symmetry posed on a direct sum of two such SN-absolutely irreducible representations, as a result of a Hopf bifurcation occurring as a real parameter is varied. We determine the (generic) conditions on the coefficients of the fifth order SN × S1-equivariant vector field that describe the stability and criticality of those solution branches. We finish this paper with an application to the cases N = 4 and N = 5.

  • 282.
    Rodrigues, Ana
    et al.
    CMUP and Dep. de Matemática Pura, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal.
    Dias, Ana Paula S.
    Centro de Matemática da Universidade do Porto (CMUP) and Dep. de Matemática Pur, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal.
    Matthews, Paul C.
    School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom.
    Generating functions for Hopf bifurcation with Sn-symmetry2009In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 25, no 3, p. 823-842Article in journal (Refereed)
    Abstract [en]

    Hopf bifurcation in the presence of the symmetric group (acting naturally by permutation of coordinates) is a problem with relevance to coupled oscillatory systems. To study this bifurcation it is important to construct the Taylor expansion of the equivariant vector field in normal form. We derive generating functions for the numbers of linearly independent invariants and equivariants of any degree, and obtain recurrence relations for these functions. This enables us to determine the number of invariants and equivariants for all , and show that this number is independent of for sufficiently large . We also explicitly construct the equivariants of degree three and degree five, which are valid for arbitrary .

  • 283.
    Rodrigues, Ana
    et al.
    Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216, USA and CMUP, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal .
    Llibre, Jaume
    Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Spain .
    On the periodic orbits of Hamiltonian systems2010In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, no 4Article in journal (Refereed)
    Abstract [en]

    We show how to apply to Hamiltonian differential systems recent results for studying the periodic orbits of a differential system using the averaging theory. We have chosen two classical integrable Hamiltonian systems, one with the Hooke potential and the other with the Kepler potential, and we study the periodic orbits which bifurcate from the periodic orbits of these integrable systems, first perturbing the Hooke Hamiltonian with a nonautonomous potential, and second perturbing the Kepler problem with an autonomous potential.

  • 284.
    Rodrigues, Ana
    et al.
    Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216 – and – CMUP, Rua do Campo Alegre 687, 4169-007 Porto, Portugal .
    Misiurewicz, Michal
    Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216.
    Non-generic cusps2011In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 363, no 07, p. 3553-3553Article in journal (Refereed)
    Abstract [en]

    We find the order of contact of the boundaries of the cusp for two-parameter families of vector fields on the real line or diffeomorphisms of the real line, for cusp bifurcations of codimensions 1 and 2. Moreover, we create a machinery that can be used for the same problem in higher codimensions and perhaps for other, similar problems.

  • 285.
    Rollier, Michiel
    et al.
    Univ Ghent, Dept Data Anal & Math Modelling, KERMIT, Coupure Links 653, B-9000 Ghent, Belgium..
    Miranda, Gisele
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST). Univ Ghent, Dept Data Anal & Math Modelling, KERMIT, Coupure Links 653, B-9000 Ghent, Belgium.; Sciensano, Dept Epidemiol & Publ Hlth, B-1050 Brussels, Belgium..
    Vergeynst, Jenna
    Univ Ghent, Dept Data Anal & Math Modelling, KERMIT, Coupure Links 653, B-9000 Ghent, Belgium.;Univ Ghent, Dept Data Anal & Math Modelling, BIOMATH, Coupure Links 653, B-9000 Ghent, Belgium..
    Meys, Joris
    Univ Ghent, Dept Data Anal & Math Modelling, KERMIT, Coupure Links 653, B-9000 Ghent, Belgium..
    Alleman, Tijs W.
    Univ Ghent, Dept Data Anal & Math Modelling, BIOMATH, Coupure Links 653, B-9000 Ghent, Belgium..
    Baetens, Jan M.
    Univ Ghent, Dept Data Anal & Math Modelling, KERMIT, Coupure Links 653, B-9000 Ghent, Belgium..
    Mobility and the spatial spread of sars-cov-2 in Belgium2023In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 360, article id 108957Article in journal (Refereed)
    Abstract [en]

    We analyse and mutually compare time series of covid-19-related data and mobility data across Belgium's 43 arrondissements (NUTS 3). In this way, we reach three conclusions. First, we could detect a decrease in mobility during high-incidence stages of the pandemic. This is expressed as a sizeable change in the average amount of time spent outside one's home arrondissement, investigated over five distinct periods, and in more detail using an inter-arrondissement "connectivity index"(CI). Second, we analyse spatio-temporal covid-19-related hospitalisation time series, after smoothing them using a generalise additive mixed model (GAMM). We confirm that some arrondissements are ahead of others and morphologically dissimilar to others, in terms of epidemiological progression. The tools used to quantify this are time-lagged cross-correlation (TLCC) and dynamic time warping (DTW), respectively. Third, we demonstrate that an arrondissement's CI with one of the three identified first-outbreak arrondissements is correlated to a substantial local excess mortality some five to six weeks after the first outbreak. More generally, we couple results leading to the first and second conclusion, in order to demonstrate an overall correlation between CI values on the one hand, and TLCC and DTW values on the other. We conclude that there is a strong correlation between physical movement of people and viral spread in the early stage of the sars-cov-2 epidemic in Belgium, though its strength weakens as the virus spreads.

  • 286.
    Rudert, Emelie
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Development of a Novel Social Media Sentiment Risk Model for Financial Assets2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis aims to investigate the potential effects on Value at Risk (VaR) measurements when including social media sentiments from Reddit and Twitter. The investigated stock companies are Apple, Alphabet and Tesla. Furthermore, the VaR measurements will be computed through volatility forecasts and assumptions about the return distributions. The volatility will be forecasted by two different models and each model will both include and exclude social media sentiments, so there will be four different volatility forecasts for each stock. Moreover, the volatility models will be the Heterogeneous autoregression (HAR) model and the Heterogeneous autoregression Neural Network (HAR-NN) model. The assumptions of return distributions are a log-logistic distribution and a log-normal distribution. In addition to this, the VaR measurements are computed and evaluated through number of breaches for each of the volatility forecasts and for both assumptions of a return distribution. The result shows that there is an improvement in forecasting volatility for Apple and Alphabet, as well as fewer VaR breaches for both assumptions of log-return distributions. However, the results for Tesla showed that the volatility forecasts were better when excluding social media sentiment. A possible reason for this might be due to Twitter posts made by influential people, like Elon Musk that would have a larger effect on the volatility than the average sentiment score over that day. Another possible explanation to this might be due to multicollinearity. Overall, the results showed that the assumption of a log-logistic distribution was more suitable over a log- normal return distribution for all three stocks.

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  • 287. Russo, J. G.
    et al.
    Zarembo, Konstantin
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Wilson Loops in Antisymmetric Representations from Localization in Supersymmetric Gauge Theories2018In: Reviews in Mathematical Physics, ISSN 0129-055X, Vol. 30, no 7, article id 1840014Article in journal (Refereed)
    Abstract [en]

    Large-N phase transitions occurring in massive = 2 theories can be probed by Wilson loops in large antisymmetric representations. The logarithm of the Wilson loop is effectively described by the free energy of a Fermi distribution and exhibits second-order phase transitions (discontinuities in the second derivatives) as the size of representation varies. We illustrate the general features of antisymmetric Wilson loops on a number of examples where the phase transitions are known to occur: N= 2 SQCD with various mass arrangements and N= 2∗ theory. As a byproduct, we solve planar N= 2 SQCD with three independent mass parameters. This model has two effective mass scales and undergoes two phase transitions. In memory of Ludvig Dmitrievich Faddeev.

  • 288.
    Ryblad, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    AI for an Imperfect-Information Wargame with Self-Play Reinforcement Learning2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The task of training AIs for imperfect-information games has long been difficult. However, recently the algorithm ReBeL, a general framework for self-play reinforcement learning, has been shown to excel at heads-up no-limit Texas hold 'em, among other imperfect-information games. In this report the ability to adapt ReBeL to a downscaled version of the strategy wargame \say{Game of the Generals} is explored. It is shown that an implementation of ReBeL that uses no domain-specific knowledge is able to beat all benchmark bots, which indicates that ReBeL can be a useful framework when training AIs for imperfect-information wargames.

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  • 289.
    Sacchi, Giorgio
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Computationally Efficient Explainable AI: Bayesian Optimization for Computing Multiple Counterfactual Explanantions2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In recent years, advanced machine learning (ML) models have revolutionized industries ranging from the healthcare sector to retail and E-commerce. However, these models have become increasingly complex, making it difficult for even domain experts to understand and retrace the model's decision-making process. To address this challenge, several frameworks for explainable AI have been proposed and developed. This thesis focuses on counterfactual explanations (CFEs), which provide actionable insights by informing users how to modify inputs to achieve desired outputs. However, computing CFEs for a general black-box ML model is computationally expensive since it hinges on solving a challenging optimization problem.

    To efficiently solve this optimization problem, we propose using Bayesian optimization (BO), and introduce the novel algorithm Separated Bayesian Optimization (SBO). SBO exploits the formulation of the counterfactual function as a composite function. Additionally, we propose warm-starting SBO, which addresses the computational challenges associated with computing multiple CFEs. By decoupling the generation of a surrogate model for the black-box model and the computation of specific CFEs, warm-starting SBO allows us to reuse previous data and computations, resulting in computational discounts and improved efficiency for large-scale applications.

    Through numerical experiments, we demonstrate that BO is a viable optimization scheme for computing CFEs for black-box ML models. BO achieves computational efficiency while maintaining good accuracy. SBO improves upon this by requiring fewer evaluations while achieving accuracies comparable to the best conventional optimizer tested. Both BO and SBO exhibit improved capabilities in handling various classes of ML decision models compared to the tested baseline optimizers. Finally, Warm-starting SBO significantly enhances the performance of SBO, reducing function evaluations and errors when computing multiple sequential CFEs. The results indicate a strong potential for large-scale industry applications.

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  • 290.
    Sandqvist, Tor
    KTH, School of Architecture and the Built Environment (ABE), Philosophy and History, Philosophy.
    Reflections on the Empirical Applicability of Mathematics2018In: Technology and Mathematics, Springer Nature , 2018, p. 325-343Chapter in book (Refereed)
    Abstract [en]

    This paper addresses the not infrequently voiced view that the immense usefulness of mathematics in the physical sciences constitutes a deep philosophical mystery, with potentially far-reaching implications concerning the relationship between the inquiring mind and the material world. It grants the broadly Humean point that the very possibility of inductive projection from past to future, by whatever intellectual means, must be considered a remarkable and perhaps inexplicable fact, but calls into question the idea that the utility of mathematics in this regard is especially baffling. While the aims pursued in pure mathematics may differ radically from those of engineers and scientists, in their development of concepts and theories mathematicians are nevertheless beholden to the same fundamental standards of simplicity and similarity that must govern any reasonable inductive projection; and this fact, it is suggested, may go a considerable way towards explaining why many mathematical constructs lend themselves to empirical application.

  • 291.
    Satayeva, Malika
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Probability, Mathematical Physics and Statistics.
    MultiModal Neural Network for Healthcare Applications2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    BACKGROUND. Multimodal Machine Learning is a powerful paradigm that capitalizes on the complementary predictive capabilities of different data modalities, such as text, image, time series. This approach allows for an extremely diverse feature space, which proves useful for combining different real-world tasks into a single model. Current architectures in the field of multimodal learning often integrate feature representations in parallel, a practice that not only limits their interpretability but also creates a reliance on the availability of specific modalities. Interpretability and robustness to missing inputs are particularly important in clinical decision support systems. To address these issues, the iGH Research Group at EPFL proposed a modular sequential input fusion called Modular Decision Support Network (MoDN). MoDN was tested on unimodal tabular inputs for multitask outputs and was shown to be superior to its monolithic parallel counterparts, while handling any number and combination of inputs and providing continuous real-time predictive feedback. AIM. We aim to extend MoDN to MultiModN with multimodal inputs and compare the benefits and limitations of sequential fusion with a state-of-the-art parallel fusion (P-Fusion) baseline.METHODS & FINDINGS. We align our experimental setup with a previously published P-Fusion baseline, focusing on two binary diagnostic predictive tasks (presence of pleural effusion and edema) in a popular multimodal clinical benchmark dataset (MIMIC).We perform four experiments: 1) comparing MultiModN to P-Fusion, 2) extending the architecture to multiple tasks, 3) exploring MultiModN's inherent interpretability in several metrics, and 4) testing its ability to be resistant to biased missingness by simulating missing not at random (MNAR) data during training and flipping the bias at inference. We show that MultiModN's sequential architecture does not compromise performance compared with the P-Fusion baseline, despite the added advantages of being multitask, composable and inherently interpretable. The final experiment shows that MultiModN resists catastrophic failure from MNAR data, which is particularly prevalent in clinical settings.

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  • 292.
    Schmekel, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Predicting Coherent Turbulent Structures with Artificial Neural Networks2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Turbulent flow is widespread in many applications, such as airplanes or cars. Such flow is characterized by being highly chaotic and impossible to predict far into the future. In turbulent flow, there exist regions that have different properties compared to neighboring flow; these regions are called coherent turbulent structures. These structures are connected to Reynolds stress which is essential for modeling turbulent flow. Machine learning techniques have recently had very impressive results for modeling turbulence. In this thesis, we investigate their capabilities of modeling coherent structures. We use data from a highly accurate simulation to create two different artifical neural networks. These networks are tuned by hand, trained, and then we evaluate their performance. We investigate the loss of the networks and the statistical properties of their predictions and compare them to the simulated data.

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  • 293.
    Sellerstam, Otto
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Pricing in the Heston Model and Its Rough Variation2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis presents the theoretical material needed to price European call options in the classical and rough version of the Heston model, as well as how to do this in practice from a computational perspective. The theoretical material includes an introduction to measure theory, which is then used to build the foundations of probability theory and stochastic calculus, together with more novel topics such as fractional calculus and a short exposition of the fractional Brownian motion. Moreover, parameter estimation for the respective models and computational methods to calculate options prices are also discussed.

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  • 294. Shao, Wen-Ze
    et al.
    Ge, Qi
    Gan, Zong-Liang
    Deng, Hai-Song
    Li, Haibo
    KTH, School of Computer Science and Communication (CSC), Media Technology and Interaction Design, MID.
    A Generalized Robust Minimization Framework for Low-Rank Matrix Recovery2014In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, p. 656074-Article in journal (Refereed)
    Abstract [en]

    This paper considers the problem of recovering low-rank matrices which are heavily corrupted by outliers or large errors. To improve the robustness of existing recovery methods, the problem is solved by formulating it as a generalized nonsmooth nonconvex minimization functional via exploiting the Schatten p-norm (0 < p <= 1) and L-q(0 <q <= 1) seminorm. Two numerical algorithms are provided based on the augmented Lagrange multiplier (ALM) and accelerated proximal gradient (APG) methods as well as efficient root-finder strategies. Experimental results demonstrate that the proposed generalized approach is more inclusive and effective compared with state-of-the-art methods, either convex or nonconvex.

  • 295.
    Shao, Yuqi
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Data-driven Discovery of Real-time Road Compaction Parameters2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Road compaction is the last and important stage in road construction. Both under-compaction and over-compaction are inappropriate and may lead to road failures. Intelligent compactors has enabled data gathering and edge computing functionalities, which introduces possibilities in data-driven compaction control. Compaction physical processes are complex and are material-dependent. In the road construction industry, material physical models, together with boundary conditions, can be used for modeling effects of compacting the underlying subgrade materials and the pavement (the most widely used is asphalt) itself on site, which can be computed using Finite Element (FE) methods. However, parametrizations of these physical models require large efforts, creating difficulties in using these models to optimize real-time compaction. Our research has, for the first time, bridged the gap between data-driven compaction control and physics by introducing the parameter identification pipeline. Two use cases are investigated, corresponding to offline learning and online learning of parameters. In offline learning, a sequence of actions is learned to maximally reduce parameters uncertainties without observing responses; in online learning, the decisions of actions are made and parameters are derived while sequential observations come in. The parameter identification pipeline developed in this thesis involves compaction simulation using a simple physical model, surrogate model development using Artificial Neural Network (ANN), and online/offline optimization procedure with Approximate Bayesian Computation (ABC). The developed procedure can successfully identify the parameters with low uncertainty for the case that the selected experiments supply enough information to theoretically identify the parameters. For the case of that parameters cannot be theoretically identified by certain experiments, the identified parameters have larger uncertainties.

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  • 296. Siegel, M.
    et al.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    A local target specific quadrature by expansion method for evaluation of layer potentials in 3D2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 364, p. 365-392Article in journal (Refereed)
    Abstract [en]

    Accurate evaluation of layer potentials is crucial when boundary integral equation methods are used to solve partial differential equations. Quadrature by expansion (QBX) is a recently introduced method that can offer high accuracy for singular and nearly singular integrals, using truncated expansions to locally represent the potential. The QBX method is typically based on a spherical harmonics expansion which when truncated at order p has O(p2) terms. This expansion can equivalently be written with p terms, however paying the price that the expansion coefficients will depend on the evaluation/target point. Based on this observation, we develop a target specific QBX method, and apply it to Laplace's equation on multiply-connected domains. The method is local in that the QBX expansions only involve information from a neighborhood of the target point. An analysis of the truncation error in the QBX expansions is presented, practical parameter choices are discussed and the method is validated and tested on various problems.

  • 297.
    Siemieniuk, Karolina
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    B-spline Parametrized Approximation and Variation of Vehicle Trajectories For Autonomous Vehicles Simulation2021Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    A big focus of the Automotive Industry’s work is now on the development ofAutonomous Vehicles (AVs). In order to be able to release them on the market,they need to be tested and validated in a safe and efficient way. That is whycompanies working on the development of AVs use simulation to test the workthey are completing. Before putting an Autonomous Vehicle on any road, itwould be ideal to make sure, it will be able to navigate through the given roadsafely and react to everything that has ever happened on this road. What ismore, for the Autonomous Vehicle to be safely on the roads, it should also beable to react to uncommon situations, not seen exactly in the data it was trainedon before. In this thesis, the focus is on trajectories and their variations. Theaim of this work is to develop a framework, which would allow, having discretedata of traffic participants from chosen locations, to model the trajectories ofthose vehicles and the variations of those trajectories. This is to help withthe testing of Autonomous Vehicles in a simulation environment. The data,which is used to develop this method are from an intersection in Denmark,however, it is believed the method can be applied to data from anywhere,as long as it contains information about x and y coordinates of the vehiclesand the corresponding times of the vehicles being at those positions. In thiswork, only trajectories of cars are considered, but again other vehicles can betaken into account in the future. First, vehicle trajectories from given data aremodelled with the use of B-splines. The routine is set up as a constrainedoptimization problem with seven different constraints developed for a car.The constraints are highly nonlinear and therefore a constrained nonlinearoptimization problem is solved. The chosen method for this is the interior-pointmethod. After obtaining the approximation of the trajectory in the Bsplineform, a variation of it is achieved through the change of the speed of thevehicle and its initial position. A projection of the required velocity change onthe derivative of B-spline basis space is calculated and then a new variation ofthe original approximated trajectory in B-spline form is obtained. The methodwas implemented in Matlab and successfully used to approximate and varytrajectories from a dataset from an intersection in Denmark, Aalborg.

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  • 298.
    Sinander, Pierre
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Ahmed, Asik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Clustering of Unevenly Spaced Mixed Data Time Series2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis explores the feasibility of clustering mixed data and unevenly spaced time series for customer segmentation. The proposed method implements the Gower dissimilarity as the local distance function in dynamic time warping to calculate dissimilarities between mixed data time series. The time series are then clustered with k−medoids and the clusters are evaluated with the silhouette score and t−SNE. The study further investigates the use of a time warping regularisation parameter. It is derived that implementing time as a feature has the same effect as penalising time warping, andtherefore time is implemented as a feature where the feature weight is equivalent to a regularisation parameter.

    The results show that the proposed method successfully identifies clusters in customer transaction data provided by Nordea. Furthermore, the results show a decrease in the silhouette score with an increase in the regularisation parameter, suggesting that the time at which a transaction occurred might not be of relevance to the given dataset. However, due to the method’s high computational complexity, it is limited to relatively small datasets and therefore a need exists for a more scalable and efficient clustering technique.

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  • 299.
    Siridol-Kjellberg, Robert
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Hidden Markov Models for Intrusion Detection Under Background Activity2023Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Detecting a malicious hacker intruding on a network system can be difficult. This challenge is made even more complex by the network activity generated by normal users and by the fact that it is impossible to know the hacker’s exact actions. Instead, the defender of the network system has to infer the hacker’s actions by statistics collected by the intrusion detection system, IDS. This thesis investigates the performance of hidden Markov models, HMM, to detect an intrusion automatically under different background activities generated by normal users. Furthermore, background subtraction techniques with inspiration from computer vision are investigated to see if normal users’ activity can be filtered out to improve the performance of the HMMs.The results suggest that the performance of HMMs are not sensitive to the type of background activity but rather to the number of normal users present. Furthermore, background subtraction enhances the performance of HMMs slightly. However, further investigations into how background subtraction performs when there are many normal users must be done before any definitive conclusions.

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  • 300.
    Sjögreen, Björn
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Yee, H. C.
    Performance of High Order Filter Methods for a Richtmyer-Meshkov Instability2009In: Computational Fluid Dynamics 2006 - Proceedings of the Fourth International Conference on Computational Fluid Dynamics, ICCFD 2006, Springer Berlin/Heidelberg, 2009, p. 771-776Conference paper (Refereed)
    Abstract [en]

    Sixth-order compact and non-compact filter schemes that were designed for multiscale Navier-Stokes, and ideal and non-ideal magnetohydrodynam-ics (MHD) systems are employed to simulate a 2-D Rightmyer-Meshkov instability (RMI). The suppression of this RMI in the presence of a magnetic field was investigated by Samtaney (2003) and Wheatley et al. (2005). Numerical results illustrated here exhibit behavior similar to the work of Samtaney. Due to the different amounts and different types of numerical dissipations contained in each scheme, the structures and the growth of eddies for this chaotic-like inviscid gas dynamics RMI case are highly grid size and scheme dependent, even with many levels of refinement.

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