京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24041号 / 情博第797号 / 新制||情||135(附属図書館) / 京都大学大学院情報学研究科システム科学専攻 / (主査)教授 加納 学, 教授 下平 英寿, 教授 石井 信 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

In this project, we are aiming to solve option pricing and hedging problems numerically via Backward Stochastic Differential Equations (BSDEs). We use Markovian BSDEs to formulate nonlinear pricing and hedging problems of both European and American option types. This method of formulation is crucial for pricing financial instruments since it enables consideration of market imperfections and computations in high dimensions. We conduct numerical experiments of the pricing and hedging problems, where there is a higher interest rate for borrowing than lending, using the least squares Monte Carlo and deep neural network methods. Moreover, based on the experiment results, we point out which method to chooseover the other depending on the the problem at hand.

More than 350,000 anterior cruciate ligament (ACL) injuries occur every year in the United States. A torn ACL is typically replaced with an allograft or autograft tendon (patellar, quadriceps or hamstring), with the choice of tissue generally dictated by surgeon preference. Despite the number of ACL reconstructions performed every year, the process of ligamentization, transformation of a tendon graft to a healthy functional ligament, is poorly understood. Previous research studies have relied on mechanical, biochemical and histological studies. However, these methods are destructive. Clinically, magnetic resonance imaging (MRI) is the most common method of graft evaluation, but it lacks adequate resolution and molecular specificity. There is a need for objective methodology to study the ligament repair process that would ideally be non- or minimally invasive. Development of such a method could lead to a better understanding of the effects of therapeutic interventions and rehabilitation protocols in animal models of ligamentization, and ultimately, in clinical studies. Fourier transform infrared (FT-IR) spectroscopy is a technique sensitive to molecular structure and composition in tissues. FT-IR fiber optic probes combined with arthroscopy could prove to be an important tool where minimally invasive tissue assessment is required, such as assessment of graft composition during the ligamentization process. Spectroscopic methods have been used to differentiate normal and diseased connective tissues, but have not been applied to investigate ligamentization, or to investigate differences in tendons and ligaments. In the proposed studies, we hypothesize that infrared spectroscopy can provide molecular information about the compositional differences between tendons and ligaments, which can serve as a foundation to non-destructively monitor the tissue transformation that occurs during ligamentization. / Bioengineering

In the past 30 years zero-valent iron (ZVI) has become an increasingly popular reducing agent technology for remediating environmental contaminants prone to chemical degradation. Azo dyes and chlorinated organic compounds (COCs) are two classes of such contaminants, both of which include toxic compounds with known carcinogenic potential. ZVI has been successfully applied to the surfaces of permeable reactive barriers, as well as grown into nanoscale particles (nZVI) and applied in-situ to chemically reduce these contaminants into more environmentally benign compounds. However, the reactivity of ZVI and nZVI in these technologies is limited by their finite supply of electrons for facilitating chemical reduction, and the tendency of nZVI particles to homo-aggregate in solution and form colloids with reduced surface area to volume ratio, and thus reduced reactivity. The goal of this project was to combine reactive nanoparticle and membrane technologies to create an electro-catalytic permeable reactive barrier that overcomes the weaknesses of nZVI for the enhanced electrochemical filtration of azo dyes in solution. Specifically, nZVI was successfully grown and stabilized in a network of functionalized carbon nanotubes (CNTs) and deposited into an electrically conductive thin film on the surface of a polymeric microfiltration support membrane. Under a cathodic applied voltage, this thin film facilitated the direct reduction of the methyl orange (MO) azo dye in solution, and regenerated nZVI reactivity for enhanced electro-catalytic operation. The electro-catalytic performance of these nZVI-CNT membrane surface composites to remove MO was validated, modelled, and optimized in a batch system, as well as tested in a dead-end continuous flow cell system. In the batch experiments, systems with nZVI and a -2 V applied potential demonstrated synergistic enhancement of MO removal, which indicated the regeneration of nZVI reactivity and allowed for the complete removal of 0.25 mM MO batches within 2-3 hours. Partial least squares regression (PLSR) modelling was used to determine the impact of each experimental parameter in the batch system and provided the means for an optimization leading to maximized MO removal. Finally, tests in a continuous system yielded rates of MO removal 1.6 times greater than those of the batch system in a single pass, and demonstrated ~87% molar removal of MO at fluxes of approximately 422 lmh. The work herein lays the foundation for a promising technology that, if further developed, could be applied to remediate azo dyes and COCs in textile industry effluents and groundwater sites respectively. / Thesis / Master of Applied Science (MASc)

This project utilised a novel solvent-free continuous cocrystallisation (SFCC) method to manufacture pharmaceutical co-crystals. The objectives were to optimize the process towards achieving high co-crystal yields and to understand the behaviour of co-crystals under different conditions. Particular attention was paid to the development of near infrared (NIR) spectroscopy as a process analytical technology (PAT). Twin screw, hot melt extrusion was the base technique of the SFCC process. Changing parameters such as temperature, screw speed and screw geometry was important for improving the co-crystal yield. The level of mixing and shear was directly influenced by the screw geometry, whilst the screw speed was an important parameter for controlling the residence time of the material during hot melt extrusion. Ibuprofen – nicotinamide 1:1 cocrystals and carbamazepine – nicotinamide 1:1 co-crystals were successfully manufactured using the SFCC method. Characterisation techniques were important for this project, and NIR spectroscopy proved to be a convenient, accurate analytical technique for identifying the formation of co-crystals along the extruder barrel. Separate thermal and model shear deformation studies were also carried out to determine the effect of temperature and shear on co-crystal formation for several different pharmaceutical co-crystal pairs. Finally, NIR spectroscopy was used to create two partial least squares regression models, for predicting the 1:1 co-crystal yield of ibuprofen – nicotinamide and carbamazepine – nicotinamide, when in a powder mixture with the respective pure API. It is believed that the prediction models created in this project can be used to facilitate future in-line PAT studies of pharmaceutical co-crystals during different manufacturing processes. / Engineering and Physical Sciences Research Council (EPSRC)

No / The purpose of this work was to explore NIR spectroscopy as a PAT tool to monitor the formation of ibuprofen and nicotinamide cocrystals during extrusion based solvent free continuous cocrystallization (SFCC). Drug and co-former were gravimetrically fed into a heated co-rotating twin screw extruder to form cocrystals. Real-time process monitoring was performed using a high temperature NIR probe in the extruder die to assess cocrystal content and subsequently compared to off-line powder X-ray diffraction measurements. The effect of processing variables, such as temperature and mixing intensity, on the extent of cocrystal formation was investigated. NIR spectroscopy was sensitive to cocrystal formation with the appearance of new peaks and peak shifts, particularly in the 4800-5200 cm(-1) wave-number region. PXRD confirmed an increased conversion of the mixture into cocrystal with increase in barrel temperature and screw mixing intensity. A decrease in screw rotation speed also provided improved cocrystal yield due to the material experiencing longer residence times within the process. A partial least squares analysis in this region of NIR spectrum correlated well with PXRD data, providing a best fit with cocrystal conversion when a limited range of process conditions were considered, for example a single set temperature. The study suggests that NIR spectroscopy could be used to monitor cocrystal purity on an industrial scale using this continuous, solvent-free process.

Digital Particle Image Velocimetry (DPIV) is a planar measurement technique to measure the velocity within a fluid by correlating the motion of flow tracers over a sequence of images recorded with a camera-laser system. Sophisticated digital processing algorithms are required to provide a high enough accuracy for quantitative DPIV results. This study explores the potential of a variety of cross-correlation filters to improve the accuracy and robustness of the DPIV estimation. These techniques incorporate the use of the Phase Transform (PHAT) Generalized Cross Correlation (GCC) filter applied to the image cross-correlation. The use of spatial windowing is subsequently examined and shown to be ideally suited for the use of phase correlation estimators, due to their invariance to the loss of correlation effects. The Robust Phase Correlation (RPC) estimator is introduced, with the coupled use of the phase correlation and spatial windowing. The RPC estimator additionally incorporates the use of a spectral filter designed from an analytical decomposition of the DPIV Signal-to-Noise Ratio (SNR). This estimator is validated in a variety of artificial image simulations, the JPIV standard image project, and experimental images, which indicate reductions in error on the order of 50% when correlating low SNR images. Two variations of the RPC estimator are also introduced, the Gaussian Transformed Phase Correlation (GTPC): designed to optimize the subpixel interpolation, and the Spectral Phase Correlation (SPC): estimates the image shift directly from the phase content of the correlation. While these estimators are designed for DPIV, the methodology described here provides a universal framework for digital signal correlation analysis, which could be extended to a variety of other systems. / Master of Science

This paper investigates the feasibility of a rendezvous with an uncooperative space object using only optical sensors and takes a closer look at the performance of different algorithms used to estimate an object’s orbit. The ability to perform a rendezvous with an uncooperative target is critical for a wide variety of future missions, such as space debris removal. The main satellite, referred to as chaser, has to determine precisely the orbit of the space object of interest, referred to as target. After some elements of mission analysis, this report dives into the angles-only method of Initial Orbit Determination developed by Gooding, which is a method well suited for space-based observations. It gives access to the osculating orbit at the time of measurements. Then, the estimated orbit is refined using a Batch Least Squares algorithm. The accuracy of the orbit determination depends on the number and precision of the measurements. An optimal strategy for the distribution of the measurements on orbit is to take measurements regularly throughout the whole orbit. The constraints of eclipses and ground stations contacts are taken into account. Finally, the Rendezvous and Proximity Operations are explored in a mission scenario. / Detta examensarbete undersöker möjligheten av ett rendezvous med ett icke-samarbetsvilligt rymdobjekt som endast använder optiska sensorer och tar en närmare titt på prestandan hos olika algoritmer som används för att uppskatta ett objekts omloppsbana. Förmågan att utföra ett möte med ett icke samarbetsvilligt mål är avgörande för en mängd olika framtida uppdrag, till exempel borttagning av rymdskrot. Den viktigaste satelliten, kallad chaser, måste exakt bestämma omloppsbanan för rymdföremål av intresse, kallad target. Efter några element av uppdragsanalys, dyker denna rapport in i den vinkelbaserade metoden för initial omloppsbestämning som utvecklats av Gooding, som är en metod som är väl lämpad för rymdbaserade observationer. Den ger tillgång till den osulerande banan vid tidpunkten för mätningarna. Därefter förfinas den beräknade omloppsbanan med hjälp av minstakvadratmetoden. Noggrannheten i omloppsbestämningen beror på antalet mätningar och deras precision. En optimal strategi för fördelningen av mätningarna i omloppsbana är att göra mätningar regelbundet över hela omloppsbanan. Begränsningarna i förmörkelser och markstationernas kontakter beaktas. Slutligen utforskas mötes- och närhetsoperationer i ett uppdragsscenario.

<p dir="ltr">This thesis presents advances in numerical methods for partial differential equations (PDEs) and optimization problems, with a focus on improving efficiency, stability, and accuracy across various applications. We begin by addressing 3D Poisson-type equations, developing a GPU-accelerated spectral-element method that utilizes the tensor product structure to achieve extremely fast performance. This approach enables solving problems with over one billion degrees of freedom in less than one second on modern GPUs, with applications to Schrödinger and Cahn<i>–</i>Hilliard equations demonstrated. Next, we focus on parabolic PDEs, specifically the Cahn<i>–</i>Hilliard equation with dynamical boundary conditions. We propose an efficient energy-stable numerical scheme using a unified framework to handle both Allen<i>–</i>Cahn and Cahn<i>–</i>Hilliard type boundary conditions. The scheme employs a scalar auxiliary variable (SAV) approach to achieve linear, second-order, and unconditionally energy stable properties. Shifting to a machine learning perspective for PDEs, we introduce an unsupervised learning-based numerical method for solving elliptic PDEs. This approach uses deep neural networks to approximate PDE solutions and employs least-squares functionals as loss functions, with a focus on first-order system least-squares formulations. In the realm of optimization, we present an efficient and robust SAV based algorithm for discrete gradient systems. This method modifies the standard SAV approach and incorporates relaxation and adaptive strategies to achieve fast convergence for minimization problems while maintaining unconditional energy stability. Finally, we address optimization in the context of machine learning by developing a structure-guided Gauss<i>–</i>Newton method for shallow ReLU neural network optimization. This approach exploits both the least-squares and neural network structures to create an efficient iterative solver, demonstrating superior performance on challenging function approximation problems. Throughout the thesis, we provide theoretical analysis, efficient numerical implementations, and extensive computational experiments to validate the proposed methods. </p>

Cette thèse s'inscrit dans le domaine des problèmes inverses en traitement du signal. Elle est consacrée à la conception d'algorithmes de restauration et de séparation de signaux parcimonieux et à leur application à l'approximation de courbes de forces en microscopie de force atomique (AFM), où la notion de parcimonie est liée au nombre de points de discontinuité dans le signal (sauts, changements de pente, changements de courbure). Du point de vue méthodologique, des algorithmes sous-optimaux sont proposés pour le problème de l'approximation parcimonieuse basée sur la pseudo-norme l0 : l'algorithme Single Best Replacement (SBR) est un algorithme itératif de type « ajout-retrait » inspiré d'algorithmes existants pour la restauration de signaux Bernoulli-Gaussiens. L'algorithme Continuation Single Best Replacement (CSBR) est un algorithme permettant de fournir des approximations à des degrés de parcimonie variables. Nous proposons aussi un algorithme de séparation de sources parcimonieuses à partir de mélanges avec retards, basé sur l'application préalable de l'algorithme CSBR sur chacun des mélanges, puis sur une procédure d'appariement des pics présents dans les différents mélanges. La microscopie de force atomique est une technologie récente permettant de mesurer des forces d'interaction entre nano-objets. L'analyse de courbes de forces repose sur des modèles paramétriques par morceaux. Nous proposons un algorithme permettant de détecter les régions d'intérêt (les morceaux) où chaque modèle s'applique puis d'estimer par moindres carrés les paramètres physiques (élasticité, force d'adhésion, topographie, etc.) dans chaque région. Nous proposons finalement une autre approche qui modélise une courbe de force comme un mélange de signaux sources parcimonieux retardées. La recherche des signaux sources dans une image force-volume s'effectue à partir d'un grand nombre de mélanges car il y autant de mélanges que de pixels dans l'image / This thesis handles several inverse problems occurring in sparse signal processing. The main contributions include the conception of algorithms dedicated to the restoration and the separation of sparse signals, and their application to force curve approximation in Atomic Force Microscopy (AFM), where the notion of sparsity is related to the number of discontinuity points in the signal (jumps, change of slope, change of curvature).In the signal processing viewpoint, we propose sub-optimal algorithms dedicated to the sparse signal approximation problem based on the l0 pseudo-norm : the Single Best Replacement algorithm (SBR) is an iterative "forward-backward" algorithm inspired from existing Bernoulli-Gaussian signal restoration algorithms. The Continuation Single Best Replacement algorithm (CSBR) is an extension providing approximations at various sparsity levels. We also address the problem of sparse source separation from delayed mixtures. The proposed algorithm is based on the prior application of CSBR on every mixture followed by a matching procedure which attributes a label for each peak occurring in each mixture.Atomic Force Microscopy (AFM) is a recent technology enabling to measure interaction forces between nano-objects. The force-curve analysis relies on piecewise parametric models. We address the detection of the regions of interest (the pieces) where each model holds and the subsequent estimation of physical parameters (elasticity, adhesion forces, topography, etc.) in each region by least-squares optimization. We finally propose an alternative approach in which a force curve is modeled as a mixture of delayed sparse sources. The research of the source signals and the delays from a force-volume image is done based on a large number of mixtures since there are as many mixtures as the number of image pixels