Computed Tomography (CT) is a non-invasive x-ray imaging method capable of reconstructing highly detailed cross-sectional interior maps of an object. CT is used in a range of medical applications such as detection of skeletal fractures, organ trauma and artery calcification. Reconstructing CT images requires the use of a forward operator, which is essentially a simulation of the scanning process. Photon-Counting CT is a rapidly developing alternative to conventional CT that promises higher spatial resolution, more accurate material separation and more robust reconstructions. A major difficulty in Photon-Counting CT is to model cross-talk between detectors. One way is to incorporate a wide point-spread function into the forward operator. Although this method works, it drastically slows down the reconstruction process.  In this thesis, we accelerate image reconstruction tasks for photon-counting CT by approximating the cross-talk component of the forward operator with a deep neural network, resulting in a learned forward operator. The learned operator reduces reconstruction error by an order of magnitude at the cost of a 20% increase in computation time, compared to ignoring cross-talk altogether. Furthermore, it generalises well to both unseen data and unseen detector settings. Our results indicate that a learned forward operator is a suitable way of approximating the forward operator in photon-counting CT. / Datortomografi (CT) är en icke-invasiv röntgenmetod som kan skapa högupplösta tvärsnittsbilder av objekt. CT används i en stor mängd tillämpningar, exempelvis vid detektion av frakturer, mjukvävnadstrauma och åderförkalkning. När man rekonstuerar tvärsnitt i CT krävs en simuleringsmodell som kallas framåtoperatorn. Fotonräknande CT är ett alternativ till konventionell CT som utlovar högre upplösning, mer precis uppdelning av material och högre robusthet i rekonstruktionerna. I fotonräknande CT är det viktigt att ta hänsyn till överhörning mellan detektorerna. Ett sätt är att inkorporera en punktspridningsfunktion i framåtoperatorn, vilket dessvärre saktar ned rekonstruktionsprocessen drastiskt.  I detta examensarbete approximerar vi överhörningseffekten mellan detektorer med ett djupt neuralt nätverk, med syfte att accelerera rekonstruktionsprocessen för fotonräknande spektral CT. Den inlärda framåtoperatorn reducerar rekonstruktionsfelet med en faktor tio på bekostnad av en 20-procentig ökning i beräkningstid, jämfört med en framåtoperator som inte modellerar överhörning. Vi visar att den inlärda framåtoperatorn generaliserar väl till data som den inte är tränad på, men även detektorinställningar den inte är van vid. Våra resultat tyder på att den inlärda framåtoperatorn är en lämplig approximationsmetod för framåtoperatorn i fotonräknande CT.

Photon counting computed tomography scanners constitute a major improvement of the field of computed tomography, opening various prospective and enabling the decomposition of computed tomography images into different materials. The material decomposition algorithm, mapping photon counts to material pathlengths, relies on a forward model with Poisson statistics. This model though suffers from noise and residual bias due to its sensitivity to calibration errors and specificities in single-pixel responses that are not captured by the material decomposition model.           This study proposes a pixel-specific and projection-based correction of the residual bias in the material decomposition estimates using artificial neural networks trained for each pixel of the detector. The neural network models were trained under supervised learning using material decomposition calibration data, scans of PE and PVC slabs of various thicknesses acquired for the calibration of the model. This method aims at the mapping of the singularities of the pixels’ responses and correct them in the projection domain. The trained models were evaluated on a set of evaluation slabs and on scans of a water phantom, in order to assess performances of homogeneity and bias correction.           The implemented solution exhibited promising results for the correction of residual bias in single pixels without impairment of the noise levels. An array of trained neural networks demonstrates its ability to correct calibration and evaluation slab data while conserving pixel-to-pixel difference. The application of the correction to the water phantom however offered nuanced results which call for further investigation of the identified issues and induced improvements of the model.

School cafeterias face significant challenges in maintaining operational efficiency while minimizing food waste within the educational sector. Currently, the methods available for counting dishes are predominantly manual or semi-manual. Accurately counting served plates is crucial for evaluating meal portions and planning food preparation, yet these methods frequently result in inaccuracies and inefficiencies. To address these challenges, this project introduces an innovative automated system for counting washed dishes used in the school’s dining hall. The system employs embedded systems equipped with a proper machine learning model to detect dishes placed in trays and count them at the washing station in the kitchens of schools. By automating the dish counting process, the system improves operational efficiency, reduces food waste, and provides precise data for meal planning, inventory management, and budget planning. Initial results show promising accuracy and efficiency, with the best model achieving an average precision of 0.71, a precision of 95.2%, and a recall of 70.5% using Google Cloud’s AutoML platform. However, further optimization is needed for real-world deployment. This project is constrained by limited time for labeling images and a budget of 300$. This project represents a collaboration between Linnaeus University, Kalmar Municipality, and SensIot Company, reflecting a shared commitment to sustainability through reduced food waste in educational institutions.

<p><br></p><p dir="ltr">The complexity of modern financial markets poses substantial challenges for analyzing time-series data, as traditional diffusion models often fail to capture the intricate dynamics of real-world market behavior. This dissertation develops data-driven, non-Markovian methodologies to overcome these limitations, enhancing the analysis of dependencies in financial and insurance data. The research employs advanced stochastic models and machine learning techniques to address critical phenomena in finance and insurance. Notable findings include the following: a Hawkes process framework is introduced to model cascading health transitions, capturing how past events amplify the likelihood of future occurrences (Chapter 3); a discrete-time Hawkes process is used to quantify time-varying lead-lag relationships between intraday and overnight returns, uncovering predictive dynamics in asset price movements (Chapter 4); and attention-based models are applied to high-dimensional, spatiotemporal limit order book (LOB) data, enabling robust analysis and forecasting of its complex structure and behavior (Chapter 5). These findings highlight the limitations of traditional Markovian models, particularly in representing memory-dependent systems, high-frequency data, and multi-state processes. By advancing non-Markovian methods, this dissertation provides practical tools for analyzing momentum effects, cascading health transitions, and intricate market microstructures. These contributions establish a robust analytical foundation for understanding memory-dependent dynamics in finance and insurance, addressing key limitations of Markovian assumptions and opening new avenues for research and application.</p>

The goal in medical x-ray imaging is to obtain the image quality requiredfor a given detection task, while ensuring that the patient dose is kept as lowas reasonably achievable. The two most common strategies for dose reductionare: optimizing incident x-ray beams and utilizing energy informationof transmitted beams with new detector techniques (spectral imaging). Inthis thesis, dose optimization schemes were investigated in two x-ray imagingsystems: digital mammography and computed tomography (CT). In digital mammography, the usefulness of anti-scatter grids was investigatedas a function of breast thickness with varying geometries and experimentalconditions. The general conclusion is that keeping the grid is optimalfor breasts thicker than 5 cm, whereas the dose can be reduced without a gridfor thinner breasts. A photon-counting silicon-strip detector developed for spectral mammographywas characterized using synchrotron radiation. Energy resolution, ΔE/Ein, was measured to vary between 0.11-0.23 in the energy range 15-40 keV, which is better than the energy resolution of 0.12-0.35 measured inthe state-of-the-art photon-counting mammography system. Pulse pileup hasshown little effect on energy resolution. In CT, the performance of a segmented silicon-strip detector developedfor spectral CT was evaluated and a theoretical comparison was made withthe state-of-the-art CT detector for some clinically relevant imaging tasks.The results indicate that the proposed photon-counting silicon CT detector issuperior to the state-of-the-art CT detector, especially for high-contrast andhigh-resolution imaging tasks. The beam quality was optimized for the proposed photon-counting spectralCT detector in two head imaging cases: non-enhanced imaging and Kedgeimaging. For non-enhanced imaging, a 120-kVp spectrum filtered by 2half value layer (HVL) copper (Z = 29) provides the best performance. Wheniodine is used in K-edge imaging, the optimal filter is 2 HVL iodine (Z = 53)and the optimal kVps are 60-75 kVp. In the case of gadolinium imaging, theradiation dose can be minimized at 120 kVp filtered by 2 HVL thulium (Z =69). / <p>QC 20160401</p>

The purpose of this study is to observe some factors that may affect the understanding of subtraction with borrowing. The study is done in a foreign environment, in Kenya. Factors that will be looked into are: the classroom environment, the situation of learning in a second language. The study will also observe factors that can cause an erroneous answer and what those may look like. Within this area manipulatives will be mentioned. The study has used a qualitative as well as quantitative approach. The qualitative method has been accomplished through interviews and observations, the quantitative method through tests given to the learners. For the analysis of the observations, Cobb’s and Yackel’s model (1995) of the mathematical classroom has been used. The study is interpreted from a sociocultural perspective focusing interaction. The result in this study shows that the interaction in the classroom is important to the individual learning, perceptions of mathematics and the expectations on the individual. Learning in a second language can be a barrier. The use of manipulatives can work as a scaffold, but it can also hinder the learner to develop a deeper understanding. / Syftet med studien är att studera faktorer som kan påverka förståelsen av subtraktion med växling. Studien är gjord i en annan lärmiljö, i Kenya. Faktorer som kommer att uppmärksammas är lärmiljön i klassrummet och att inlärningen sker på ett för eleven andra språk. Studien kommer också att uppmärksamma faktorer som kan bidra till ett felaktigt svar och hur de kan se ut. Inom detta område kommer laborativt material nämnas. Studien har både ett kvalitativt och kvantitativt tillvägagångssätt. Den kvalitativa metoden har genomförts genom intervjuer och observationer, den kvantitativa metoden med hjälp av elevtester. Cobbs och Yackels (1995) modell över matematik klassrummet har använts som analysmaterial. Studien tolkas utifrån ett sociokulturellt perspektiv. Focus är på interaktionen.   Resultaten i studien visar att interaktionen I klassrummet är viktigt för det individuella lärandet, uppfattningen om matematik och förväntningar på individen. Undervisning på ett andra språk kan bli ett hinder. Användandet av laborativt material kan fungera som ett stöd, men kan också hindra utvecklandet av en djupare förståelse.

This longitudinal study tracks how 5- to 7-year-olds perform with early number skills. The aim of this study is to diagnose at-risk mathematics students by distinguishing the skills that, if not mastered by the end of Kindergarten, lead to greater difficulty in mathematics in 1st grade. This study’s methodology is mixed as it follows an exploratory and inductive path in light of its use of a hypothesis, an interpretive path in light of its interest in the individual student, and a positivist path in light of its focus on developing rules from analyzed data. An oral diagnostic test based on a comprehensive collection of early number skills was used to test students as Kindergarteners and again as 1st graders. The test results created benchmarks, revealing how the majority of the students performed with early number skills. The test results also revealed that each early number skill is highly, moderately, or minimally predictive in terms of student placement by the end of 1st grade. When comparing the individual skill scores of each Kindergarten student to his/her total test results of 1st grade, the predictive power of each skill emerged. Performing poorly with skills that are minimally predictive did not seem to have an impact on how the Kindergarten student finished in 1st grade; performing poorly with moderately predictive skills had a greater impact on 1st grade placement; performing poorly with highly predictive skills in Kindergarten increased the likelihood that the student would finish in the lower attaining group in 1st grade. A third result of the test showed that certain skills serve as preconditions for other skills; success with certain skills usually meant success with other skills. These connections between skills point to a learning model called in this study “simultaneous pathways,” indicating that there are connections between certain skills, and that students can be learning on several pathways simultaneously. The impact of the predictive power of early number skills is that diagnosis becomes more effective. Early diagnosis means early remediation which may prevent at-risk students from falling further behind their peers. The benchmarks developed by this research will help teachers assess their students because they will know the general skill level of Kindergarteners and 1st graders. This oral diagnostic test informs curriculum development. If test results show that students are missing the skills that are highly predictive, teachers can address those gaps in order to insure mastery.

This thesis explores the use of single-photon avalanche diodes (SPADs) for visible light communications (VLC). The high sensitivity of SPADs can potentially enhance the performance of VLC receivers. However, a SPAD-based system has challenges that need to be addressed before it can be considered as a viable option for VLC. The first challenge is the susceptibility of SPAD-based receivers to variations in ambient light. The high sensitivity of SPADs is advantageous for signal detection, but also makes SPADs vulnerable to variations in ambient light. In this thesis, the performance of a SPAD-based receiver is investigated under changing lighting conditions. Analytical expressions to quantify performance are derived, and an experiment is conducted to gain further understanding of system performance. It is shown that a SPAD-based receiver is highly sensitive to illumination changes when on-off keying (OOK) is employed, and that pulse-position modulation (PPM) is a preferred modulation scheme as it is more robust. The second challenge is broadcasting to SPAD-based receivers with different capabilities. A traditional broadcasting scheme is time-sharing, whereby a transmitter sends data to receivers in an alternating manner. Broadcasting to SPAD-based receivers is challenging as receivers may have diverse capabilities. In this thesis, a new multiresolution modulation scheme is proposed, which can potentially improve system performance over the traditional timesharing approach. The performance of the proposed scheme is analyzed, and a proof-of-concept experiment is performed to demonstrate its viability.

Název práce: Obecná enumerace číselných rozklad· Autor: Jaroslav Hančl Katedra: Katedra aplikované matematiky Vedoucí diplomové práce: doc. RNDr. Martin Klazar, Dr., KAM MFF UK Abstrakt: Předložená diplomová práce se zabývá asymptotikami počítacích funkcí ideál· číselných rozklad·. Jejím hlavním cílem je zjistit největší možný asympto- tický r·st počítací funkce rozkladového ideálu, která je nekonečněkrát rovna nule. Autor se na základě znalosti asymptotik vybraných rozkladových ideál· snaží po- mocí kombinatorických a základních analytických metod odvodit odhady hledané asymptotiky. Výsledkem je za prvé slabší horní odhad, za druhé poměrně silný dolní odhad a za třetí, pro speciální třídu rozkladových ideál· je nalezen největší asymptotický r·st. Klíčová slova: íselné rozklady, asymptotika rozklad·, rozkladové ideály, počítací funkce, kombinatorická enumerace. 1

NP search problems and reductions among them Renáta Ševčíková In the thesis we study the class of Total NP search problems. More attention is devoted to study the subclasses of Total NP search problems and reductions among them. We combine some known methods: the search trees and their relation to re- ductions, the Nullstellensatz refutation and the degree lower bound based on design to show that two classes of relativized NP search problems based on Mod-p counting principle and Mod-q counting principle, where p and q are different primes, are not reducible to each other. This thesis is finished by a new separation result for p = 2 and q = 3.