The mathematical modelling of the reaction and diffusion mechanism of lipophilic toxic compounds in the mammalian cell is a challenging task because of its considerable complexity and variation in the architecture of the cell. The heterogeneity of the cell regarding the enzyme distribution participating in the bio-transformation, makes the modelling even more difficult. In order to reduce the complexity of the model, and to make it less computationally expensive and numerically treatable, Homogenization techniques have been used. The resulting complex system of Partial Differential Equations (PDEs), generated from the model in 2-dimensional axi-symmetric setting is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. The model can be extended to more complex reaction systems and also to 3-dimensional space. For the reduction of complexity and computational cost, we have implemented a model of mixed PDEs and Ordinary Differential Equations (ODEs). We call this model as Non-Standard Compartment Model. Then the model is further reduced to a system of ODEs only, which is a Standard Compartment Model. The numerical results of the PDE Model have been qualitatively verified by using the Compartment Modeling approach. The quantitative analysis of the results of the Compartment Model shows that it cannot fully capture the features of metabolic system considered in general. Hence we need a more sophisticated model using PDEs for our homogenized cell model. / Computational Modelling of the Mammalian Cell and Membrane Protein Enzymology

The shopping industry is rapidly changing as the technology is advancing. This is especially true for the online industry where consumers are nowadays able to to shop much of what the need over the internet. In order to make the shopping experience as smooth as possible, different companies develops their sites and checkouts to be as friction-less as possible. In this thesis, the shipping module of Klarnas checkout was analyzed and different models were created to get an understanding of how the likelihood of a customer finalizing a purchase (conversion rate) could be improved. The shipping module consists of a number of shipping methods along with shipping carriers. Currently, there is no logic to sort the different shipping method/carriers other than a static ordering for all customers. The order of the shipping methods and carriers are what were investigated in the thesis. Hence, the core problem is to understand how the opportunity loss could be minimized by a different ordering of the shipping methods, where the opportunity loss are derived by the reduction in conversion rate between the control group (current setup) and a new model. To achieve this, a dataset was prepared and features were engineered in such a way that the same training and test datasets could be used in all algorithms. The features were engineered using a point-in-time concept so that no target leakage would be present. The target that was used was a plain concatenation of shipping method plus the shipping carrier. Finally, three different methods tackling this multiclass classification problem were investigated, namely Logistic Regression, Extreme Gradient Boosting and Artificial Neural Network. The aim of these algorithms is to create a learner that has been trained on a given dataset and that is able to predict the combination of shipping method plus carrier given a certain set of features. By the end of the investigation, it was concluded that using a model to predict the most relevant shipping method (plus carrier) for the customer made a positive difference on the conversion rate and in turn, the increase in sales. The overall accuracy of the Logistic Regression was 65.09%, 71.61% for the Extreme Gradient Boosting and 70.88% for the Artificial Neural Network. Once the models were trained, they were used in a back-simulation (that would be a proxy for an A/B-test) on a validation set to see the effect on the conversion rate. Here, the results showed that the conversion rate was 84.85% for the Logistic Regression model, 84.95% for the Extreme Gradient Boosting and 85.02% for the Artificial Neural Network. The control group which was a random sample of the current logic had a conversion rate of 84.21%. Thus, implementing the Artificial Neural Network would increase Klarnas sales by about 6.5 SEK per session. / Detaljhandelsindustrin förändras i en snabb takt i samband med att teknologin utvecklas. Detta är speciellt fallet för näthandeln där konsumenter numer har möjligheten att handla i stort sett allt de behöver över internet. För att göra köpupplevelsen så smidig som möjlig utvecklar olika bolag deras hemsidor och online kassor så att de innehåller så lite friktion som möjligt. I denna avhandling utreddes Klarnas leveransmodul som är en den av Klarnas onlinekassa (Checkout). Här utvecklades flera modeller och analyserades för att få en förståelse för hur sannolikheten att kunden slutför ett köp (konverterinsgrad) kunde ökas. Leveransmodulen består av ett flertalet leveransmetoder tillsammans med en leverantör. I dagsläget finns det ingen logik för att sortera dessa metoder annat än en statisk sortering för alla kunder. Ordningen på leveransmetoderna och leverantörerna är alltså vad som utreddes. Kärnproblemet i denna avhandling är alltså att förstå hur den potentiella förlusten av att ha en suboptimal sortering, där den potentiella förlusten härleds av minskningen av konverteringsgraden mellan den nuvarande lösningen och en ny modell. För att uppnå detta förbereddes ett dataset och variabler skapades på sådant vis att både tränings och test datan kunde användas för samtliga algoritmer. Variablerna skapades med en Point-in-time koncept så att ingen ogiltig information skulle komma med. Målvariabeln, eller den beroende variabeln, var en enkel ihopslagning av leveransmetoden plus leverantörens namn. Sedan användes tre algoritmer för att tackla detta multiklass klassifikationsproblem, nämligen Logistisk Regression, Extreme Gradient Boosting samt ett Artificiellt Neuralt Nätverk. Målet med dessa algoritmer är att skapa en modell som tränats på ett givet dataset och som kan förutspå kombinationen av leveransmetod plus leverantör givet ett bestämt set av värden på variablerna. I slutet av utredningen drogs slutsatsen att en modell, som kunde förutspå den mest relevanta leveransmetoden (plus leverantör) för kunden, hade en positiv inverkan på konverteringsgraden och i sin tur ökningen i försäljning. Noggrannheten för den Logistiska Regressionen var 65.09%, för Extreme Gradient Boosting var den 71 69% och för det Artificiella Neurala Nätverket var den 70.88%. Efter att modellerna tränats användes de i en simulering (som skulle representera ett A/B-test) på ett valideringsset för att förstå effekten på konverteringsgraden. Här visade resultaten att konverteringsgraden var 84.55% för Logistiska Regressionen, 84.95% för Extreme Gradient Boosting samt 85.02% för det Artificiella Neurala Nätverket. Kontrollgruppen som bestod av slumpmässigt valda rader från den nuvarande logiken hade en konvertingsgrad på 84.21%. Detta innebar alltså att om det Artificiella Neurala Nätverket hade implementerats, så hade det ökat Klarnas försäljning med ca 6.5 SEK per session.

All organs, including the brain, need a pathway to remove neurotoxic extracellular proteins. In the brain this is called the glymphatic system. The glymphatic system works by exchanging proteins from interstitial fluids to cerebrospinal fluids. The extracellular proteins are then removed through the cerebrospinal fluid drains. The glymphatic system is believed to be driven by arterial pulsatility, cerebrospinal fluid production and respiration. Cerebrospinal fluids enters the brain alongside arteries. In this project, we investigate if a simulated pulsatile flow in a common carotid artery can drive cerebrospinal fluid flow running along the artery, using computational simulations of a linearly elastic and fluid-structure multiphysical model in COMSOL. Our simulations show that a heartbeat pulse increases the arterial radius of the common carotid artery by 6 %. Experimental data, assessed using 4D magnetic resonance imaging of a living human, show an increase of 13 %. Moreover, our results indicate that arterial displacement itself is not able to drive cerebrospinal fluid flow. Instead, it seems to create a back and forth flow that possibly could help with the protein exchange between the cerebrospinal and interstitial fluids. Overall, the results indicate that the COMSOL Multiphysics linearly elastic model is not ideal for approximations of soft non-linearly elastic solids, such as soft polydimethylsiloxane and artery walls work for stiffer materials. The long term aim is to simulate a part of the glymphatic system and the present work is a starting point to reach this goal. As the simulations in this work are simplified there are more things to test in the future. For example, using the same geometries a non-linear elastic model could be tested. The pulsatile waveform or the geometry could be made more complex. Furthermore the model could be scaled down to represent a penetrating artery in the brain instead of the common carotid artery.

We consider diagonal-norm classical summation-by-parts (SBP) operators us-ing the simultaneous approximation term (SAT) method of imposing boundaryconditions. We derive a formula for the inverse of these SBP-SAT discretizationmatrices. This formula is then used to show that it is possible to construct a secondorder accurate SBP-SAT operator using only seven grid points.

This thesis aims to study how flat dielectric lenses can be designed. The usage of flat lenses is steadily increasing as they are smaller and less bulky than traditional convex lenses. Instead of a lens with a curved surface the permittivity in the lens is varied to achieve the same effect. Two different computational methods were investigated when approaching this problem: physical and geometrical optics. In physical optics the incoming radio waves are treated as waves in contrast to geometrical optics where it is considered as rays. Both methods are used as approximations of Maxwell's equations. The variation of permittivity in the lens was formulated as an optimisation problem where the lens' focusing abilities were maximised. The optimisation was implemented with an interior point method. Both arbitrary permittivity distributions as well as predetermined distributions were examined in this work. All optimised lens models were then simulated in a full wave commercial simulation software to verify and compare the two. The simulations showed that both approaches gave promising results as they focused the electromagnetic wave in a satisfying way. However the physical optics approach was more prominent as the focused radio waves had a much higher magnitude than the approach based on geometrical optics. The conclusion was therefore that physical optics is the preferred approach.

<p>Many kernel matrices from differential equations or data science applications possess low or approximately low off-diagonal rank for certain key matrix subblocks; such matrices are referred to as rank-structured. Operations on rank-structured matrices like factorization and linear system solution can be greatly accelerated by converting them into hierarchical matrix forms, such as the hiearchically semiseparable (HSS) matrix form. The dominant cost of this conversion process, called HSS construction, is the low-rank approximation of certain matrix blocks. Low-rank approximation is also a required step in many other contexts throughout numerical linear algebra. In this work, a proxy point low-rank approximation method is detailed for general analytic kernel matrices, in both one and several dimensions. A new accuracy analysis for this approximation is also provided, as well as numerical evidence of its accuracy. The extension of this method to kernels in several dimensions is novel, and its new accuracy analysis makes it a convenient choice to use over existing proxy point methods. Finally, a new HSS construction algorithm using this method for certain Cauchy and Toeplitz matrices is given, which is asymptotically faster than existing methods. Numerical evidence for the accuracy and efficacy of the new construction algorithm is also provided.</p>

The ambition of this project is to contribute to the development of optimisation techniques for underground mining. This resulted in a mathematical model to optimise a type of underground transportation system called the ramp. The ramp is a tunnel from the underground mining areas which trucks use to transport material up to the surface. We consider the case where the ramp only fits one truck at a time and it therefore needs passing bays where trucks can meet. We were inspired by an article which optimised the positions of the passing bays and the schedule for the trucks, during a certain time period. We extended that work by proposing a new mathematical model that can handle a more general and complex mine. The result from optimally solving the model gives the positioning of the passing bays and a schedule which completes a number of trips down and up the ramp as quickly as possible. The model can be used both for long-term and short-term planning. The long-term planning regards the positions of the passing bays. The model can therefore be used before the passing bays are constructed to gain insights about where to place them. The short-term planning is about finding an optimal trip schedule given the placement of the passing bays. The model can therefore also be used to provide a haulage schedule for an upcoming time period.

The simulation program GTperform is used to estimate the machine settings from performance measurements for the gas turbine model STG-800 at Siemens Industrial Turbomachinery in Finspång, Sweden. By evaluating different settings within the program, the engineers try to estimate the one that generatesthe performance measurement. This procedure is done manually at Siemens and is very time-consuming. This project aims to establish an algorithm that automatically establishes the correct machine setting from the performance measurements. Two algorithms were implemented in Python: Simulated Annealing and Gradient Descent. The algorithms analyzed two possible objective functions, and objective were tested on three gas turbines located at different locations. The first estimated the machine setting that generated the best fit to the performance measurements, while the second established the most likely solution for the machine setting from probability distributions. Multiple simulations have been run for the two algorithms and objective functions to evaluate the performances. Both algorithms successfully established satisfactory results for the second objective function. The Simulated Annealing, in particular, established solutions with a lower spread compared to Gradient Descent. The algorithms give a possibility to automatically establish the machine settings for the simulation program, reducing the work for the engineers.

The calibration between a camera and an industrial robot is a well-established area of research. Nevertheless, traditional setups concentrate on the case in which the camera is either attached to the robot or static. With the advent of Augmented Reality (AR) capable devices, such as headsets, glasses, phones, or tablets, the device's camera is now free to roam the scene in an unconstrained manner.In order to unlock a new set of applications, the AR device needs to be aware of the precise location of the robot. Unfortunately, this new embodiment of robot to moving camera calibration has comparatively received much less attention. In this thesis, we will explore the aforementioned setup motivated by a real use case at ABB robotics. After exploring the mathematical preliminaries, we will analyze the problem from two different mathematical formalisms and implement the solution in a resource-constrained device, leading to a new patent pending approach.

Low frequency acoustic room behaviour can be approximated using numerical methods. Traditionally, music studio control rooms are built with complex geometries, making their eigenmodes difficult to predict mathematically. Hence, a summation-by-parts method with simultaneous-approximation-terms is derived to approximate the time dependent acoustic wave equation in three dimensions. The derived model is limited to rectangular prismatic rooms but planned to be expanded to handle complex geometries in the future. Semi-reflecting boundary conditions are used, corresponding to tabulated reflection and absorption properties of real. walls. Two speakers are modeled as omnidirectional point sources placed on a boundary, to mimic common studio setups. Through tests and examination of eigenvalues of the matrices in the method, conditions for stability and reflection coefficients are derived. Simulations of sound pressure distribution produced by the model correlate well to room mode theory, suggesting the model to be accurate in the application of predicting low frequency acoustic room behaviour. However, the convergence rate of the model turns out to be lower than expected when point sources are introduced. Future steps towards applying the model to real music studio control rooms include modeling the walls as changes in density and wave speed rather than boundaries of the domain. This would potentially allow more complex geometries to be modeled within a larger, rectangular domain.