2.1 Designing an appropriate loss function V (yi, f(xi)) In the case where the classification function, f(x), and the training point, yi, have the same sign, we have classified correctly, yif(xi) ≥ 0, and want the loss function V to be small or zero. When there is an incorrect classification, yif(xi) < 0, we want the loss function V to be larger. When first considering this problem, a natural i...

1 Graduate Institute of Opto-Mechatronics, National Chung Cheng University, No. 168, University Rd., Min-Hsiung, Chia-Yi 621, Taiwan 2 ITRI South, Industrial Technology Research Institute, No. 8, Gongyan Rd., Liujia District, Tainan 734, Taiwan 3 Department of Mechanical Engineering, National Chung Cheng University, No. 168, University Rd., Min-Hsiung, Chia-Yi 621, Taiwan 4 Department of Mechan...

where J (t, y) = {i : Ti = t, Yi = y} represents the set of respondents with Ti = t and Yi = y. However, this likelihood function is difficult to maximize because it consists of many mixture components. Thus, following Imai (2011), we develop an EM algorithm by treating Z∗ i,J+t as partially missing data for each t = 1, . . . ,K. This leads to the following complete-data likelihood function, Lc...

In this paper we describe new classes of periodic solutions for point vortices on a plane and a sphere. They correspond to similar solutions (so-called choreographies) in celestial mechanics. 1 Equations of motion and first integrals for vortices on a plane For n point vortices with Cartesian coordinates (xi, yi) and intensities Γi, the Hamiltonian equations of the motion are Γiẋi = ∂H ∂yi , Γi...

[To my wife Jialin Yi] iv ACKNOWLEDGEMENTS I would like to express my sincere appreciation to my advisor, Dr. Without their guidance and help, I could have never have completed this dissertation. I would also like to thank Dr. David Sjoquist, who generously allowed me to use the tax revenue dataset from Georgia Department of Revenue. Finally, I extend my special thanks to my wife, Jialin Yi, wh...

Junjie Xiao,* Dandan Liang,* Yangyang Zhang,* Yi Liu, Hong Zhang, Ying Liu, Li Li, Xingqun Liang, Yunfu Sun, and Yi-Han Chen Key Laboratory of Arrhythmias, Ministry of Education, China (East Hospital, Tongji University School of Medicine); Department of Cardiology, East Hospital, Tongji University School of Medicine; Institute of Medical Genetics, Tongji University, Shanghai; Department of Card...

The aim of the paper is to study a global structure of solutions of four differential inequalities αiy i(t)yi+1 ≥ 0, yi+1(t) = 0 ⇒ y ′ i(t) = 0, i = 1, 2, 3, 4 , αi ∈ {−1, 1}, α1α2α3α4 = −1 with respect to their zeros. The structure of an oscillatory solution is described, and the number of points with trivial Cauchy conditions is investigated.

(3) yc = c1y1 + . . .+ cnyn , ci constants, where the yi are n solutions to (2) which are linearly independent, meaning that none of them can be expressed as a linear combination of the others, i.e., by a relation of the form (the left side could also be any of the other yi): yn = a1y1 + . . .+ an−1yn−1 , ai constants. Once the associated homogeneous equation (2) has been solved by finding n in...

Tsung-Chia Chen 1,*, Chia-Jung Chang 1, Jui-Pin Hung 2, Rong-Mao Lee 1 and Cheng-Chi Wang 2 1 Department of Mechanical Engineering, National Chin-Yi University of Technology, Taichung 41170, Taiwan; [email protected] (C.-J.C.); [email protected] (R.-M.L.) 2 Institute of Precision Manufacturing, National Chin-Yi University of Technology, Taichung 41170, Taiwan; [email protected] (J.-P.H....

For this problem we assume that the set of training examples {(xi, yi)} are drawn from two classes such that yi = ±1. For such two-class classifcation problems, the form of yihm(xi) is particularly simple; if an example is correctly classified, then yihm(xi) = 1. If an example is misclassified, then yihm(xi) = −1. As a result, Equation 3 can be decomposed as Zm = W (m−1) + e −αm + W (m−1) − e α...