This paper proposes new iterative methods for the efficient computation of the smallest eigenvalue of the symmetric nonlinear matrix eigenvalue problems of large order with a monotone dependence on the spectral parameter. Monotone nonlinear eigenvalue problems for differential equations have important applications in mechanics and physics. The discretization of these eigenvalue problems leads to ill-conditioned nonlinear eigenvalue problems with very large sparse matrices monotone depending on the spectral parameter. To compute the smallest eigenvalue of large matrix nonlinear eigenvalue problem, we suggest preconditioned iterative methods: preconditioned simple iteration method, preconditioned steepest descent method, and preconditioned conjugate gradient method. These methods use only matrix-vector multiplications, preconditioner-vector multiplications, linear operations with vectors and inner products of vectors. We investigate the convergence and derive grid-independent error estimates of these methods for computing eigenvalues. Numerical experiments demonstrate practical effectiveness of the proposed methods for a class of mechanical problems.

This paper deals with the variability of HRF, which may have crucial impact on outcomes of fMRI neuronal activation detection in some cases. There are three methods described - averaging, regression deconvolution and biconjugate gradient method - which provide HRF shape estimation. In frame of simulations regression method, which uses B-spline curves of 4-th order for window length of 30 s, was chosen as the most robust method. Deconvolution estimates was used as HRF models for classic analyse of fMRI data, concretely visual oddball paradigm, via general linear model. Enlargement of localizated areas was observed and after expert consultation with scientific employees from neurology clinic, outcomes was evaluated as relevant. Furthermore Matlab application, which provides confortable observation of HRF variability among brain areas, was made.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第17968号 / 情博第512号 / 新制||情||91(附属図書館) / 30798 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 中村 佳正, 教授 西村 直志, 准教授 山下 信雄 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24264号 / 情博第808号 / 新制||情||136(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 山下 信雄, 准教授 福田 秀美, 教授 太田 快人 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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Jump-diffusion models can under certain assumptions be expressed as partial integro-differential equations (PIDE). Such a PIDE typically involves a convection term and a nonlocal integral like for the here considered models of Merton and Kou. We transform the PIDE to eliminate the convection term, discretize it implicitly using finite differences and the second order backward difference formula (BDF2) on a uniform grid. The arising dense linear system is solved by an iterative method, either a splitting technique or a circulant preconditioned conjugate gradient method. Exploiting the Fast Fourier Transform (FFT) yields the solution in only $O(n\log n)$ operations and just some vectors need to be stored. Second order accuracy is obtained on the whole computational domain for Merton's model whereas for Kou's model first order is obtained on the whole computational domain and second order locally around the strike price. The solution for the PIDE with convection term can oscillate in a neighborhood of the strike price depending on the choice of parameters, whereas the solution obtained from the transformed problem is stabilized. / Master of Science

Hyperthermia is a cancer treatment modality that raises cancerous tissue to cytotoxic temperature levels for roughly 30 to 45 minutes. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol to be used in a hyperthermia treatment. This thesis presents a method to optimize a hyperthermia treatment heating protocol. An algorithm is developed which recovers a heating protocol that will cause a desired amount of thermal damage within a region of tissue. The optimization algorithm is validated experimentally on an albumen tissue phantom. The transient temperature distribution within the region is simulated using a two-dimensional, finite-difference model of the Pennes bioheat equation. The relationship between temperature and time is integrated to produce a damage field according to two different models; Henriques'' model and the thermal dose model (Moritz and Henriques (1947)), (Sapareto and Dewey (1984)). A minimization algorithm is developed which re duces the value of an objective function based on the squared difference between an optimal and calculated damage field. Either damage model can be used in the minimization algorithm. The adjoint problem in conjunction with the conjugate gradient method is used to minimize the objective function of the control problem. The flexibility of the minimization algorithm is proven experimentally and through a variety of simulations. With regards to the validation experiment, the optimal and recovered regions of permanent thermal damage are in good agreement for each test performed. A sensitivity analysis of the finite difference and damage models shows that the experimentally-obtained extent of damage is consistently within a tolerable error range. Excellent agreement between the optimal and recovered damage fields is also found in simulations of hyperthermia treatments on perfused tissue. A simplified and complex model of the human skin were created for use within the algorithm. Minimizations using both the Henriques'' model and the thermal dose model in the objective function are performed. The Henriques'' damage model was found to be more desirable for use in the minimization algorithm than the thermal dose model because it is less computationally intensive and includes a mechanism to predict the threshold of permanent thermal damage. The performance of the minimization algorithm was not hindered by adding complexity to the skin model. The method presented here for optimizing hyperthermia treatments is shown to be robust and merits further investigation using more complicated patient models. / Master of Science

Karst landscapes can serve as carbon sinks when carbon dioxide (CO2) reacts with water to form carbonic acid, which then weathers carbonate rocks. However, CO2 can also move through the subsurface via gas diffusion, a process that is not well-understood in karst systems. This study focused on quantifying CO2 diffusion within a karst sinkhole. The objectives of this study were to: 1) identify the depth of the zero-flux plane (i.e., depths of local maximum CO2 concentrations), analyze the distributions of concentration gradients, and investigate the validity of a uniform concentration gradient throughout the profile; and 2) assess the influences of vertical position and seasonality on CO2 fluxes within this sinkhole. The study site contained three locations within the sinkhole, including shoulder, backslope, and toeslope locations. Each location had three soil CO2 and three soil water content/temperature sensors placed at 20, 40, and 60 cm depths. Zero-flux planes were seldom detectable during the warm season (April-September) but were frequently found near the surface (20 or 40 cm) during the cool season (October-March). The common assumption of a uniform concentration gradient was often invalid based on relative concentrations between sensor pairs. As for the second objective, CO2 fluxes generally followed a trend of upward fluxes in warmer months that was partially offset by downward fluxes during the cooler months. These study results provide new insight into CO2 dynamics in a karst system, and suggest that subsurface processes such as chemical weathering and cave ventilation affect the direction and magnitude of CO2 fluxes. / Master of Science / Carbon dioxide (CO2) within soils is a larger pool of CO2 than atmospheric CO2. Therefore, the movement of CO2 within soils is important to understand, as soil CO2 may eventually diffuse through the soil and into the atmosphere. Soil CO2 movement is dependent on many factors such as soil water content, porosity, and temperature. Soil CO2 movement may vary between landscapes as well, due to chemical weathering processes being sinks of soil and atmospheric CO2. One type of important landscape is karst, which can be identified by easily soluble rocks, usually in the forms of limestone and dolomite rocks. In order to investigate the influences of karst landscapes on the movement of soil CO2, in this study I identified the depths of CO2 maximum concentrations and CO2 movement over time and by sinkhole slope position. The results from this study were that the depth of maximum CO2 concentration was deeper, > 40 cm, during the warmer months and often shallower, ≤ 40 cm, during the cooler months. The CO2 fluxes generally followed a trend of upward fluxes in warmer months that was partially offset by downward fluxes during the cooler months. The results from this study suggest that due to vertical differences in soil properties, temperature, chemical weathering of the karst rock, and cave ventilation the depth of the maximum CO2 concentration and the CO2 movement vary by season and sinkhole slope location. This study provides new insight to CO2 movement relative to karst landscapes while highlighting the importance of soil and geologic properties as influences that can alter the direction and magnitude of CO2 fluxes.