Examples of Matrix Factorizations from SYZ

We find matrix factorization corresponding to an anti-diagonal in ${\mathbb C}P^1 \times {\mathbb C}P^1$, and circle fibers in weighted projective lines using the idea of Chan and Leung of Strominger-Yau-Zaslow transformations. For the tear drop orbifolds, we apply this idea to find matrix factorizations for two types of potential, the usual Hori-Vafa potential or the bulk deformed (orbi)-potential. We also show that the direct sum of anti-diagonal with its shift, is equivalent to the direct sum of central torus fibers with holonomy $(1,-1)$ and $(-1,1)$ in the Fukaya category of ${\mathbb C}P^1 \times {\mathbb C}P^1$, which was predicted by Kapustin and Li from B-model calculations

Monte Carlo Analysis of the Accelerator-Driven System at Kyoto University Research Reactor Institute

An accelerator-driven system consists of a subcritical reactor and a controllable external neutron source. The reactor in an accelerator-driven system can sustain fission reactions in a subcritical state using an external neutron source, which is an intrinsic safety feature of the system. The system can provide efficient transmutations of nuclear wastes such as minor actinides and long-lived fission products and generate electricity. Recently at Kyoto University Research Reactor Institute (KURRI; Kyoto, Japan), a series of reactor physics experiments was conducted with the Kyoto University Critical Assembly and a Cockcroft-Walton type accelerator, which generates the external neutron source by deuterium-tritium reactions. In this paper, neutronic analyses of a series of experiments have been re-estimated by using the latest Monte Carlo code and nuclear data libraries. This feasibility study is presented through the comparison of Monte Carlo simulation results with measurements.clos

Robust design of control charts for autocorrelated processes with model uncertainty

Statistical process control (SPC) procedures suitable for autocorrelated processes have been extensively investigated in recent years. The most popular method is the residual-based control chart. To implement this method, a time series model, which is usually an autoregressive moving average (ARMA) model, of the process is required. However, the model must be estimated from data in practice and the resulting ARMA modeling errors are unavoidable. Residual-based control charts are known to be sensitive to ARMA modeling errors and often suffer from inflated false alarm rates. As an alternative, control charts can be applied directly to the autocorrelated data with widened control limits. The widened amount is determined by the autocorrelation function of the process. The alternative method, however, can not be also free from the effects of modeling errors because it relies on an accurate process model to be effective. To compare robustness to the ARMA modeling errors between the preceding two kinds of methods for control charting autocorrelated data, this dissertation investigates the sensitivity analytically. Then, two robust design procedures for residual-based control charts are developed from the result of the sensitivity analysis. The first approach for robust design uses the worst-case (maximum) variance of a chart statistic to guarantee the initial specification of control charts. The second robust design method uses the expected variance of the chart statistic. The resulting control limits are widened by an amount that depends on the variance of chart statistic - maximum or expected - as a function of (among other things) the parameter estimation error covariances

Prediction of monthly Arctic sea ice concentrations using satellite and reanalysis data based on convolutional neural networks

Changes in Arctic sea ice affect atmospheric circulation, ocean current, and polar ecosystems. There have been unprecedented decreases in the amount of Arctic sea ice due to global warming. In this study, a novel 1-month sea ice concentration (SIC) prediction model is proposed, with eight predictors using a deep-learning approach, convolutional neural networks (CNNs). This monthly SIC prediction model based on CNNs is shown to perform better predictions (mean absolute error - MAE - of 2.28 %, anomaly correlation coefficient - ACC - of 0.98, root-mean-square error - RMSE - of 5.76 %, normalized RMSE - nRMSE - of 16.15 %, and NSE - Nash-Sutcliffe efficiency - of 0.97) than a random-forest-based (RF-based) model (MAE of 2.45 %, ACC of 0.98, RMSE of 6.61 %, nRMSE of 18.64 %, and NSE of 0.96) and the persistence model based on the monthly trend (MAE of 4.31 %, ACC of 0.95, RMSE of 10.54 %, nRMSE of 29.17 %, and NSE of 0.89) through hindcast validations. The spatio-temporal analysis also confirmed the superiority of the CNN model. The CNN model showed good SIC prediction results in extreme cases that recorded unforeseen sea ice plummets in 2007 and 2012 with RMSEs of less than 5.0 %. This study also examined the importance of the input variables through a sensitivity analysis. In both the CNN and RF models, the variables of past SICs were identified as the most sensitive factor in predicting SICs. For both models, the SIC-related variables generally contributed more to predict SICs over ice-covered areas, while other meteorological and oceanographic variables were more sensitive to the prediction of SICs in marginal ice zones. The proposed 1-month SIC prediction model provides valuable information which can be used in various applications, such as Arctic shipping-route planning, management of the fishing industry, and long-term sea ice forecasting and dynamics

Arctic lead detection using a waveform mixture algorithm from CryoSat-2 data

We propose a waveform mixture algorithm to detect leads from CryoSat-2 data, which is novel and different from the existing threshold-based lead detection methods. The waveform mixture algorithm adopts the concept of spectral mixture analysis, which is widely used in the field of hyperspectral image analysis. This lead detection method was evaluated with high-resolution (250 m) MODIS images and showed comparable and promising performance in detecting leads when compared to the previous methods. The robustness of the proposed approach also lies in the fact that it does not require the rescaling of parameters (i.e., stack standard deviation, stack skewness, stack kurtosis, pulse peakiness, and backscatter sigma(0)), as it directly uses L1B waveform data, unlike the existing threshold-based methods. Monthly lead fraction maps were produced by the waveform mixture algorithm, which shows interannual variability of recent sea ice cover during 2011-2016, excluding the summer season (i.e., June to September). We also compared the lead fraction maps to other lead fraction maps generated from previously published data sets, resulting in similar spatiotemporal patterns