Representation theory, which encodes the elements of a group as linear operators on a vector space, has far-reaching implications in physics. Fundamental results in quantum physics emerge directly from the representations describing physical symmetries. We first examine the connections between specific representations and the principles of quantum mechanics. Then, we shift our focus to the braid group, which describes the algebraic structure of braids. We apply representations of the braid group to physical systems in order to investigate quasiparticles known as anyons. Finally, we obtain governing equations of anyonic systems to highlight the differences between braiding statistics and conventional Bose-Einstein/Fermi-Dirac statistics.

Materials at extreme conditions exhibit properties that differ substantially from ambient conditions. High pressure and high temperature expose anharmonic, non-linear behavior, and can provoke phase transitions among other effects. Experimental setups to study that sort of effects are typically costly and experiments themselves are laborious. It is common to apply theoretical techniques in order to provide a road-map for experimental research. In this thesis I cover computational algorithms based on first-principles calculations for high-temperature and high-pressure conditions. The two thoroughly described algorithms are: 1) the free energy studies using temperature-dependent effective potential method (TDEP), and 2) a higher-order elastic constants calculation procedure. The algorithms are described in an easy to follow manner with motivation for every step covered. The Free energy calculation algorithm is demonstrated with applications to hexagonal close-packed Iron at the conditions close to the inner Earth Core’s. The algorithm of elastic constants calculation is demonstrated with application to Molybdenum, Tantalum, and Niobium. Other projects included in the thesis are the study of effects of van der Waals corrections on the graphite and diamond equations of state. / Material vid extrema förhållanden uppvisar egenskaper som skiljer sig avsevärt från omgivningsförhållanden. Högt tryck och hög temperatur exponera anharmonicity, icke-linjärt beteende, och kan framkalla fasövergångar bland andra effekter. Experimentella uppställningar för att studera denna typ av effekter är vanligtvis dyra och experiment själva är mödosam. Det är vanligt att tillämpa teoretiska metoder för att ge en färdplan för experimentell forskning. I denna avhandling täcker jag beräkningsalgoritmer baserat på första principer beräkningar för hög temperatur och högt tryck. De två grundligt beskrivna algoritmer är: 1) den fria energin studier med temperaturberoende effektiv potentiell metod (TDEP), och 2) en högre ordning elastiska konstantberäkningsproceduren. Algoritmerna beskrivs i en lätt att följa sätt med motivation för varje steg som omfattas. Den fria energiberäkningsalgoritm visas med program till hexagonal tätpackad järn på villkoren nära jordens inre kärna. Algoritmen av elastiska konstanter beräkning demonstreras med tillämpning till molybden, tantal, och niob. Andra projekt som ingår i avhandlingen är effekterna av van der Waals-korrigeringar på tillståndsekvation och elastiska konstanter i grafit och diamant.

The aim of the study is to provide knowledge about how children explore, understand and reason about the physical phenomenon of friction. This study have been based on the younger children’s exploring. The method of the study has been observation in order to get as close to the environment that’s being investigated and to bring attention to the younger children’s actions. A nonparticipating observation was also used for the observer to influence the children as little as possible. The observations that have been made have taken place over two days and have been video recorded to ensure documentation of children's reasoning, body language and actions. The result shows how the children focused on overcoming the friction to get an object to slide instead of getting stuck. The participants’ interaction also emerged in the result as central to driving the exploration further. The conclusions drawn after the study is that the result can be linked to the preschool’s curriculum, which addresses the fact that the children should be given the opportunity to explore, discuss and develop understanding of physical phenomena. The study has also highlighted that hills can be used as a tool for teaching and exploring the phenomenon of friction.

We introduce slow-roll inflation in string theory on both a conceptual level and a detailed one. In order to do this we first briefly review important concepts of inflation and string theory. We then reconstruct models of string inflation in the so-called Racetrack scenario for two different cases where the difference being the number of Kähler moduli used as inflaton. Furthermore, we briefly relate our results to the more recent discussion on whether AdS/dS solutions actually exist in string theory. In this instance our results seem to indicate that uplifting is a crucial component to obtain AdS/dS solutions.

There are many clinical situations where magnetic resonance imaging (MRI) is preferable over other imaging modalities, while the major disadvantage is the relatively long scan time. Due to limited resources, this means that not all patients can be offered an MRI scan, even though it could provide crucial information. It can even be deemed unsafe for a critically ill patient to undergo the examination. In MRI, there is a trade-off between resolution, signal-to-noise ratio (SNR) and the time spent gathering data. When time is of utmost importance, we seek other methods to increase the resolution while preserving SNR and imaging time. In this work, I have studied one of the most promising methods for this task. Namely, constructing super-resolution algorithms to learn the mapping from a low resolution image to a high resolution image using convolutional neural networks. More specifically, I constructed networks capable of transferring high frequency (HF) content, responsible for details in an image, from one kind of image to another. In this context, contrast or weight is used to describe what kind of image we look at. This work only explores the possibility of transferring HF content from T1-weighted images, which can be obtained quite quickly, to T2-weighted images, which would take much longer for similar quality. By doing so, the hope is to contribute to increased efficacy of MRI, and reduce the problems associated with the long scan times. At first, a relatively simple network was implemented to show that transferring HF content between contrasts is possible, as a proof of concept. Next, a much more complex network was proposed, to successfully increase the resolution of MR images better than the commonly used bicubic interpolation method. This is a conclusion drawn from a test where 12 participants were asked to rate the two methods (p=0.0016) Both visual comparisons and quality measures, such as PSNR and SSIM, indicate that the proposed network outperforms a similar network that only utilizes images of one contrast. This suggests that HF content was successfully transferred between images of different contrasts, which improves the reconstruction process. Thus, it could be argued that the proposed multi-contrast model could decrease scan time even further than what its single-contrast counterpart would. Hence, this way of performing multi-contrast super-resolution has the potential to increase the efficacy of MRI.

Bacteria can quickly spread throughout the human body, making certain diseases hard or impossible to cure. In order to understand how the bacteria can initiate and develop into an infection, microfluidic chambers in a lab environment are used as a template of how bacteria reacts to different types of flows. However, accurately tracking the movement of bacteria is a difficult task, where small objects has to be captured with a high resolution and digitally analysed with computationally heavy methods. Popular imaging methods utilise digital holographic microscopy, where three-dimensional movement is captured in two-dimensional images by numerical reconstruction of the diffraction of light. Since numerical reconstructions become computationally heavy when a good accuracy is required, this master's thesis work focus on evaluating the possibility of using convolutional neural networks to quickly and accurately determine the spatial properties of bacteria. By thorough testing and analysis of state of the art and old networks a new network design is presented, designed to eliminate as many imaging issues as possible. We found that there are certain network design choices that help with reducing the overall error of the system, and with a well chosen training set with sensible augmentations, some networks were able to reach a 60% classification accuracy when determining the vertical rotation of the bacteria. Unfortunately, due to the lack of experimental data where the ground-truth is known, not much experimental testing could be performed. However, a few tests showed that images of high quality could be classified within the expected range of vertical rotation. / Bakterier kan snabbt sprida sig genom människokroppen, vilket försvårar starkt möjligheterna att kurera vissa sjukdomar. För att få en inblick i hur bakterier kan initiera och utvecklas till en infektion används som mall laborativa uppställningar med vätskekanaler i mikroskala när man söker förstå hur bakterier reagerar på olika typer av flöden. Att spåra dessa rörelser med god säkerhet är dock en utmaning, då man experimentellt söker fånga små skalor med hög upplösning, som sedan ska analyseras med datorintensiva metoder. Populära avbildningsmetoder använder sig utav digital holografisk mikroskopi, där tredimensionella rörelser kan fångas med hjälp av tvådimensionella bilder genom att numeriskt återskapa ljusets brytningsmönster mot objekten. Eftersom dessa metoder blir beräkningstunga när god säkerhet krävs så utforskar detta examensarbete möjligheterna att utnyttja faltningsnätverk för att snabbt och säkert bestämma vertikalrotationen hos bakterier avbildade med holografi. Genom nogranna tester av moderna samt äldre nätverk så presenteras en ny nätverksdesign, utvecklad i mål med att eliminera så många avbildningsproblem som möjligt. Vi fann att vissa designval vid nätverksutvecklingen kan hjälpa med att reducera klassificeringsfelen givet vårt system, och med en väl utvald träningsmängd med lämpliga justeringar så lyckades vi nå en klassificeringssäkerhet på över 60% med vissa nätverk. På grund av bristande experimentellt data där de riktiga värdena är kända så har ingen utförlig experimentell analys utförts, men några tester på experimentella bilder i god kvalité har visats ge resultat som tyder på en korrekt analys inom den förväntade vertikalrotationen.

The treatment plan for radiation therapy with protons is based on images from a computed tomography (CT) scanner. This is problematic since the photons in the x-ray beam from the CT scanner and the protons are affected differently by the tissue in the patient, which introduce an uncertainty in the track length of the protons. The hypothesis of this study is that a new generation of CT scanners (DECT), with the capacity to simultaneously scan the patient with two photon spectra of different mean energy, will improve the tissue characterisation and which in turn reduce the uncertainty in the track length of the protons. In this study, the accuracy and precision of a DECT-based method from the literature is compared to the conventional calibration method used today at the University clinics in Sweden to relate the attenuation of the photon beam to the slowing down of the protons. The methods are tested on CT images of a phantom, a plastic body containing tissue equivalent plastic inserts of known elemental composition. The results turned out to be inconclusive as there were large uncertainties in the measurements. The method has potential, as has been shown in the literature, but there are many questions that need to be answered before the method is ready to be implemented at the clinic. / En proton som färdas genom människokroppen deponerar endast en liten del av sin energi längs vägen innan den plötsligt deponerar allt i slutet på dess bana. Hur lång dess bana är beror på protonens ursprungliga energi och den atomära sammansättningen hos vävnaden den passerar igenom. Om sammansättningen är känd går det genom att justera den initiala energin bestämma banlängden. Denna egenskap gör protonen väldigt attraktiv för strålterpi, då det innbär möjligheten att behandla med hög precision samt bespara frisk vävnad onödig dos. Strålterapi med protoner planeras idag med bilder från en skiktröntgen (CT) som underlag. Ett problem med det är att röntgenstrålarna från CT-skannern påverkas annorlunda än protonerna av vävnaden, vilket introducerar en osäkerhet i protonernas banlängd. Hypotesen i denna studie är att en ny generation av CT-scanner (DECT), med möjlighet att simultant skanna patienten med två fotonspektran av olika medelenergi, på ett bättre sätt ska kunna bestämma den atomära sammansättningen för vävnaden och därmed reducera osäkerheten i protonernas banlängd. Noggrannhet och precision för en DECT-baserad metod från litteraturen jämförs med den SECT-baserade kalibreringsmetoden, som idag används på Universitetssjukhusen i Sverige för att relatera fotonstrålens dämpning i vävnaden till protonernas inbromsning. Metoderna testas på CT bilder av ett fantom, en plastkropp innehållandes olika cylindrar av vävnadsekvivalent plast med känd atomär sammansättning. Resultatet av den här studien är inte starkt nog för att bevisa hypotesen för studien. Det insamlade bildmaterialet innehåller höga brusnivåer jämfört med de som rapporteras i literaturen. Brusnivåer är så höga att det mesta av resultatet inte kan anses som statistiskt signifikant. Det är dessutom svårt att göra en direkt jämförelse av prestanda med befintlig teori för vävnadskaraktärisering, då bildmaterialet från de CT skanners som jämfördes är av olika typer. De resultat som publicerats i litteraturen visar att den DECT-baserade metoden har potential, men den här studien gör tydligt att det fortfarande finns frågor som måste besvaras innan metoden är redo att implementeras kliniskt.

This project started early in the summer of 2016 when it became evident there was a need for an effective and efficient signal analysis toolkit for the Littoral Acoustic Demonstration Center Gulf Ecological Monitoring and Modeling (LADC-GEMM) Research Consortium. LADC-GEMM collected underwater acoustic data in the northern Gulf of Mexico during the summer of 2015 using Environmental Acoustic Recording Systems (EARS) buoys. Much of the visualization of data was handled through short scripts and executed through terminal commands, each time requiring the data to be loaded into memory and parameters to be fed through arguments. The vision was to develop a graphical user interface (GUI) that would increase the productivity of manual signal analysis. It has been expanded to make several calculations autonomously for cataloging and meta data storage of whale clicks. Over the last year and a half, a working prototype has been developed with MathWorks matrix laboratory (MATLAB), an integrated development environment (IDE). The prototype is now very modular and can accept new tools relatively quickly when development is completed. The program has been named Banshee, as the mythical creatures are known to “wail”. This paper outlines the functionality of the GUI, explains the benefits of frequency analysis, the physical models that facilitate these analytics, and the mathematics performed to achieve these models.

Four dimensional imaging has become part of the standard of care for diagnosing and treating non-small cell lung cancer. In radiotherapy applications 4D fan-beam computed tomography (4D-CT) and 4D cone-beam computed tomography (4D-CBCT) are two advanced imaging modalities that afford clinical practitioners knowledge of the underlying kinematics and structural dynamics of diseased tissues and provide insight into the effects of regular organ motion and the nature of tissue deformation over time. While these imaging techniques can facilitate the use of more targeted radiotherapies, issues surrounding image quality and accuracy currently limit the utility of these images clinically. The purpose of this project is to develop methods that retrospectively compensate for anatomical motion in 4D-CBCT and correct motion artifacts present in 4D-CT to improve the image quality of reconstructed volume and assist in localizing respiration-influenced, diseased tissue and mobile structures of interest. In the first half of the project, a series of motion compensation (MoCo) workflow methods incorporating groupwise deformable image registration and projection-warped reconstruction were developed for use with 4D-CBCT imaging. In the latter half of the project, novel motion artifact observation and artifact- weighted groupwise registration-based image correction algorithms were designed and tested. Both deliverable components of this project were evaluated for their ability to enhance image quality when applied to clinical patient datasets and demonstrated qualitative and quantitative improvements over current state-of-the-art.

<p>Vid analys av fluider med akustisk spektroskopi finns ett behov av att finna multivariata metoder för att utifrån akustiska spektra prediktera storheter såsom viskositet och densitet. Användning av artificiella neurala nätverk och bayesiska nätverk för detta syfte utreds genom teoretiska och praktiska undersökningar. Förbehandling och uppdelning av data samt en handfull linjära och olinjära multivariata analysmetoder beskrivs och implementeras. Prediktionsfelen för de olika metoderna jämförs och PLS (Partial Least Squares) framstår som den starkaste kandidaten för att prediktera de sökta storheterna.</p> / <p>When analyzing fluids using acoustic spectrometry there is a need of finding multivariate methods for predicting properties such as viscosity and density from acoustic spectra. The utilization of artificial neural networks and Bayesian networks for this purpose is analyzed through theoretical and practical investigations. Preprocessing and division of data along with a handful of linear and non-linear multivariate methods of analysis are described and implemented. The errors of prediction for the different methods are compared and PLS (Partial Least Squares) appear to be the strongest candidate for predicting the sought-after properties.</p>