Tadashi Imaizumi, School of Management & Information Sciences, Tama University, Tokyo, Japan Akinori Okada, Rikkyo University, Toshima-ku, Japan Sadaaki Miyamoto, University of Tsukuba, Ibaraki, Japan Fumitake Sakaori, Department of Mathematics, Chuo University, Tokyo, Japan Yoshiro Yamamoto, Department of Mathematics, Tokai University, Kanagawa, Japan Maurizio Vichi, Department of Statistical Sciences, Sapienza University of Rome, Roma RM, Italy