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京都大学 / 新制・課程博士 / 博士(理学) / 甲第23682号 / 理博第4772号 / 新制||理||1684(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 矢野 孝次, 教授 泉 正己, 教授 日野 正訓 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This submission is officially titled as a project. The author has also produced a second project relating to the same topic, titled "Part B: Power Transient in a CANDU Reactor" / This report consists of two separate studies. The first part deals with the calculation of the tube thickness of the Bruce B adjuster rods. The incremental cross-section for four tube thicknesses were obtained using the SUPERCELL Method. The tube thicknesses were then calculated so that the flux distributions at steady state full power and the corresponding total reactivity worth of the adjuster rods were in agreement with the reference design valves. The second part deals with the modifications made to the three-dimensionalSORGHUM code to permit calculations of steady-state flux distributions in asubcritical assembly in the presence of a constant non-fission meutron source. / Thesis / Master of Engineering (ME)

This study assessed the utility of an object-oriented approach to deciduous and coniferous forest volume and above ground biomass estimation, based solely on small-footprint, multiple return lidar data. The study area is located in Appomattox Buckingham State Forest in the Piedmont physiographic province of Virginia, U.S.A, at 78°41’ W, 37°25’ N. Vegetation is composed of various coniferous, deciduous, and mixed forest stands. The eCognition segmentation algorithm was used to derive objects from a lidar-based canopy height model (CHM). New segment selection criteria, based on between- and within-segment CHM variance, and average field plot size, were developed. Horizontal point samples were used to measure in-field volume and biomass, for 2-class (deciduous-coniferous) and 3-class (deciduous-coniferous-mixed) forest schemes. Per-segment lidar distributional parameters, e.g., mean, range, and percentiles, were extracted from the lidar data and used as input to volume and biomass regression analysis. Discriminant classification was performed using lidar point height and CHM distributions. There was no evident difference between the two-class and three-class approaches, based on similar adjusted R2 values. Two-class forest definition was preferred due to its simplicity. Two-class adjusted R2 and root mean square error (RMSE) values for deciduous volume (0.59; 51.15 m3/ha) and biomass (0.58; 37.41 Mg/ha) were improvements over those found in another plot-based study for the same study area. Although coniferous RMSE values for volume (38.03 m3/ha) and biomass (17.15 Mg/ha) were comparable to published results, adjusted R2 values (0.66 and 0.59) were lower. This was attributed to more variability and a narrower range (6.94 - 350.93 m3/ha) in measured values. Classification accuracy for discriminant classification based on lidar point height distributions (89.2%) was a significant improvement over CHM-based classification (79%). A lack of modeling and classification differences between average segment sizes was attributed to the hierarchical nature of the segmentation algorithm. However, segment-based modeling was distinctly better than modeling based on existing forest stands, with values of 0.42 and 62.36 m3/ha (volume) and 0.46 and 41.18 Mg/ha (biomass) for adjusted R2 and RMSE, respectively. Modeling results and classification accuracies indicated that an object-oriented approach, based solely on lidar data, has potential for full-scale forest inventory applications. / Ph. D.

One of the most important factors that influences a stream's hydraulic and ecological health is the streambed's sediment size distribution. This distribution affects streambed stability, sediment transport rates, and flood levels by defining the roughness of the stream channel. Adverse effects on water quality and wildlife can be expected when excessive fine sediments enter a stream. Many chemicals and toxic materials are transported through streams by binding to fine sediments. Increases in fine sediments also seriously impact the survival of fish species present in the stream. Fine sediments fill tiny spaces between larger particles thereby denying fish embryos the necessary fresh water to survive. Reforestation, constructed wetlands, and slope stabilization are a few management practices typically utilized to reduce the amount of sediment entering a stream. To effectively gauge the success of these techniques, the sediment size distribution of the stream must be monitored. Gravel bed streams are typically stratified vertically, in terms of particle size, in three layers, with each layer having its own distinct grain size distribution. The top two layers of the stream bed, the pavement and subpavement, are the most significant in determining the characteristics of the stream. These top two layers are only as thick as the largest particle size contained within each layer. This vertical stratification by particle size makes it difficult to characterize the grain size distribution of the surface layer. The traditional bulk or volume sampling procedure removes a specified volume of material from the stream bed. However, if the bed exhibits vertical stratification, the volume sample will mix different populations, resulting in inaccurate sample results. To obtain accurate results for the pavement size distribution, a surface oriented sampling technique must be employed. The most common types of surface oriented sampling are grid and areal sampling. Due to limitations in the sampling techniques, grid samples typically truncate the sample at the finer grain sizes, while areal samples typically truncate the sample at the coarser grain sizes. When combined with an analysis technique, either frequency-by-number or frequency-by-weight, the sample results can be represented in terms of a cumulative grain size distribution. However, the results of different sampling and analysis procedures can lead to biased results, which are not equivalent to traditional volume sampling results. Different conversions, dependent on both the sampling and analysis technique, are employed to remove the bias from surface sample results. The topic of the present study is to determine the accuracy of sediment samples obtained by the different sampling techniques. Knowing the accuracy of a sample is imperative if the sample results are to be meaningful. Different methods are discussed for placing confidence intervals on grid sample results based on statistical distributions. The binomial distribution and its approximation with the normal distribution have been suggested for these confidence intervals in previous studies. In this study, the use of the multinomial distribution for these confidence intervals is also explored. The multinomial distribution seems to best represent the grid sampling process. Based on analyses of the different distributions, recommendations are made. Additionally, figures are given to estimate the grid sample size necessary to achieve a required accuracy for each distribution. This type of sample size determination figure is extremely useful when preparing for grid sampling in the field. Accuracy and sample size determination for areal and volume samples present difficulties not encountered with grid sampling. The variability in number of particles contained in the sample coupled with the wide range of particle sizes present make direct statistical analysis impossible. Limited studies have been reported on the necessary volume to sample for gravel deposits. The majority of these studies make recommendations based on empirical results that may not be applicable to different size distributions. Even fewer studies have been published that address the issue of areal sample size. However, using grid sample results as a basis, a technique is presented to estimate the necessary sizes for areal and volume samples. These areal and volume sample sizes are designed to match the accuracy of the original grid sample for a specified grain size percentile of interest. Obtaining grid and areal results with the same accuracy can be useful when considering hybrid samples. A hybrid sample represents a combination of grid and areal sample results that give a final grain size distribution curve that is not truncated. Laboratory experiments were performed on synthetic stream beds to test these theories. The synthetic stream beds were created using both glass beads and natural sediments. Reducing sampling errors and obtaining accurate samples in the field are also briefly discussed. Additionally, recommendations are also made for using the most efficient sampling technique to achieve the required accuracy. / Master of Science

Regarding quantifying uncertainties in prediction, two projects with different perspectives and application backgrounds are presented in this dissertation. The goal of the first project is to predict the corporate default risks based on large-scale time-to-event and covariate data in the context of controlling credit risks. Specifically, we propose a competing risks model to incorporate exits of companies due to default and other reasons. Because of the stochastic and dynamic nature of the corporate risks, we incorporate both company-level and market-level covariate processes into the event intensities. We propose a parsimonious Markovian time series model and a dynamic factor model (DFM) to efficiently capture the mean and correlation structure of the high-dimensional covariate dynamics. For estimating parameters in the DFM, we derive an expectation maximization (EM) algorithm in explicit forms under necessary constraints. For multi-period default risks, we consider both the corporate-level and the market-level predictions. We also develop prediction interval (PI) procedures that synthetically take uncertainties in the future observation, parameter estimation, and the future covariate processes into account. In the second project, to quantify the uncertainties in the maximum likelihood (ML) estimators and compute the exact tolerance interval (TI) factors regarding the nominal confidence level, we propose algorithms for two-sided control-the-center and control-both-tails TI for complete or Type II censored data following the (log)-location-scale family of distributions. Our approaches are based on pivotal properties of ML estimators of parameters for the (log)-location-scale family and utilize the Monte-Carlo simulations. While for Type I censored data, only approximate pivotal quantities exist. An adjusted procedure is developed to compute the approximate factors. The observed CP is shown to be asymptotically accurate by our simulation study. Our proposed methods are illustrated using real-data examples. / Ph. D.

This bachelor thesis investigates inequalities present within the elementary schools of Helsingborg during the period from 2013 to 2023. Through statistical analysis, it explores various dimensions of difference among students, considering factors such as gender, school affiliation, academic performance, and whether or not one recently arrived in the country. The study relies on data sourced from the Helsingborg municipality and addresses two main questions: the extent and nature of inequalities in Helsingborg’s schools and how these inequalities have evolved over the specified period. Two definitions of inequality are utilised: “Differences between groups” (e.g., between boys and girls) and “Differences within the same group” (indicated by high standard deviation within a group). These differences are quantified using three metrics: the sum of students’ grades (merit value), the number of classes passed, and whether or not the student qualified for further education (gymnasium). The methodology includes nonparametric hypothesis tests and regression analysis. The tests employed are Kruskal-Wallis’ test, Dunn’s test, χ2 test for independence, and Fisher’s exact test, with appropriate corrections. Standard linear regression is also applied. The findings highlight disparities in academic achievement and access to higher education. Notable results include a significant dichotomy between newly arrived students and other students across all performance metrics. There were no significant changes in inequality over the time period.

Social media and user engagement are bigger than ever. Users are presented with various types of content curated by algorithms, which partially dictate what is shown to them. These algorithms lack transparency and clarity for the user. In this thesis we have developed a toolset to tail fit data of user engagement to show what behaviours this data actually shows. We want to see the differences between categories of content and show how user engagement in social media behaves. From our study we have found that there are differences between how users engage with different leanings within political content andcontents of differing credibility. We have also found that more narrow metrics in choosingdata can present different results and behaviours. From this we can determine that choice of data is crucial when working with tails. Future work is imperative to keep creating understanding for these social media platforms and how users engage with different types of content. To keep up with the constantly changing environment of social media new tools and methods will needed to create understanding for our most used platforms for public interaction.

The primary objective of this dissertation is to extend the classical Principal Components Analysis (PCA), aiming to reduce the dimensionality of a large number of Normal interrelated variables, in two directions. The first is to go beyond the static (contemporaneous or synchronous) covariance matrix among these interrelated variables to include certain forms of temporal (over time) dependence. The second direction takes the form of extending the PCA model beyond the Normal multivariate distribution to the Elliptically Symmetric family of distributions, which includes the Normal, the Student's t, the Laplace and the Pearson type II distributions as special cases. The result of these extensions is called the Generalized principal component analysis (GPCA). The GPCA is illustrated using both Monte Carlo simulations as well as an empirical study, in an attempt to demonstrate the enhanced reliability of these more general factor models in the context of out-of-sample forecasting. The empirical study examines the predictive capacity of the GPCA method in the context of Exchange Rate Forecasting, showing how the GPCA method dominates forecasts based on existing standard methods, including the random walk models, with or without including macroeconomic fundamentals. / Ph. D. / Factor models are employed to capture the hidden factors behind the movement among a set of variables. It uses the variation and co-variation between these variables to construct a fewer latent variables that can explain the variation in the data in hand. The principal component analysis (PCA) is the most popular among these factor models. I have developed new Factor models that are employed to reduce the dimensionality of a large set of data by extracting a small number of independent/latent factors which represent a large proportion of the variability in the particular data set. These factor models, called the generalized principal component analysis (GPCA), are extensions of the classical principal component analysis (PCA), which can account for both contemporaneous and temporal dependence based on non-Gaussian multivariate distributions. Using Monte Carlo simulations along with an empirical study, I demonstrate the enhanced reliability of my methodology in the context of out-of-sample forecasting. In the empirical study, I examine the predictability power of the GPCA method in the context of “Exchange Rate Forecasting”. I find that the GPCA method dominates forecasts based on existing standard methods as well as random walk models, with or without including macroeconomic fundamentals.