Quadratic forms with a strong regularity property on the representations of squares

A (positive definite and non-classic integral) quadratic form is called strongly $s$-regular if it satisfies a strong regularity property on the number of representations of squares of integers. In this article, we prove that for any integer $k \ge 2$, there are only finitely many isometry classes of strongly $s$-regular quadratic forms with rank $k$ if the minimum of the nonzero squares that are represented by them is fixed.Comment: 14 page

Improvement of Tropical Cyclone Track Forecast over the Western North Pacific Using a Machine Learning Method

Department of Urban and Environmental Engineering (Disaster Management Engineering)The accurate tropical cyclone (TC) track forecast is necessary to mitigate and prepare significant damage by a tropical cyclone. TC has been predicted by the numerical model, statistical model, and machine learning in previous researches. However, those models are separately used to predict the track of TC, and historical data with satellite image were used as input variables for machine learning without predicted data about the tropical cyclone in previous researches. In this study, we corrected the predicted track of TC by the regional climate model to ANN. TCs that occurred during the period from 2006 to 2015 over the western North Pacific were simulated by WRF, and TCs in this study include all categories of TCs except tropical depression (i.e., tropical storm, severe tropical storm, and typhoon) from June to November. We evaluated the performance of predicting TC track based on length, speed, and direction of forecast compared with observation. The simulated positions of TCs with historical data were used as variables for training and testing ANN targeted to TC position after 24-hour, 48-hour, and 72-hour. For optimizing the number of neurons in ANN, simulated TCs were divided into two parts, which are the TCs in 2006-2014 for ANN optimization and the TCs in 2015 for a blind test. Also, the output selection method, which has range based on the mean absolute error of WRF, was applied to exclude outlier of ANN results. By the output selection, the prediction error of ANN was more reduced than the prediction error of WRF. As a result, ANN can improve more the performance of WRF when the error of WRF was higher, and the error of ANN result, which wasn???t excluded by the output selection, increased less than ANN without applying output selection in the lower error of WRF. Also, cluster analysis was done in this study to investigate the effect of ANN depending on the location of predicted TC. This study used k-means clustering to divide the simulated TCs, and the TCs were divided into four parts, considering the silhouette coefficient value. The ANN with the output selection had better performance than WRF in cluster 1 (western Pacific) and cluster 2 (south of Korea) for 24-hour and 48-hour forecast. The ANN without the output selection had better performance than WRF in cluster 3 (Southeast Asia and China) and cluster 4 (south of Japan) for 72-hour forecast.clos

Prime-universal diagonal quadratic forms

A (positive definite and integral) quadratic form is said to be $\textit{prime-universal}$ if it represents all primes. Recently, Doyle and Williams in [2] classified all prime-universal diagonal ternary quadratic forms, and all prime-universal diagonal quaternary quadratic forms under two conjectures proposed by themselves. In this article, we classify all prime-universal diagonal quadratic forms regardless of ranks. Furthermore, we prove, so called, $67$-Theorem for a diagonal quadratic form to be prime-universal.Comment: 14 page

Guaranteeing the \~O(AGM/OUT) Runtime for Uniform Sampling and OUT Size Estimation over Joins

We propose a new method for estimating the number of answers OUT of a small join query Q in a large database D, and for uniform sampling over joins. Our method is the first to satisfy all the following statements. - Support arbitrary Q, which can be either acyclic or cyclic, and contain binary and non-binary relations. - Guarantee an arbitrary small error with a high probability always in \~O(AGM/OUT) time, where AGM is the AGM bound OUT (an upper bound of OUT), and \~O hides the polylogarithmic factor of input size. We also explain previous join size estimators in a unified framework. All methods including ours rely on certain indexes on relations in D, which take linear time to build offline. Additionally, we extend our method using generalized hypertree decompositions (GHDs) to achieve a lower complexity than \~O(AGM/OUT) when OUT is small, and present optimization techniques for improving estimation efficiency and accuracy.Comment: 19 page

Functionality-Driven Musculature Retargeting

We present a novel retargeting algorithm that transfers the musculature of a reference anatomical model to new bodies with different sizes, body proportions, muscle capability, and joint range of motion while preserving the functionality of the original musculature as closely as possible. The geometric configuration and physiological parameters of musculotendon units are estimated and optimized to adapt to new bodies. The range of motion around joints is estimated from a motion capture dataset and edited further for individual models. The retargeted model is simulation-ready, so we can physically simulate muscle-actuated motor skills with the model. Our system is capable of generating a wide variety of anatomical bodies that can be simulated to walk, run, jump and dance while maintaining balance under gravity. We will also demonstrate the construction of individualized musculoskeletal models from bi-planar X-ray images and medical examinations.Comment: 15 pages, 20 figure