The concept as well as the collection of contributions to the present Special Issue found its main inspiration in the success of the ninth continuation of the series of international conferences devoted to the same subject. This inspiring meeting with informative homepage address http://www.math.zju.edu.cn/wjd took place in Zhejiang University in Hangzhou during June 21–24, 2010. As usual, the attention of cca 60 participants of the meeting (cf. the photo at frontispiece) transcended the strict scope of the PHHQP series, this time mainly towards the rich and quickly developing area of the so called effect algebras and other deeper layers of mathematical foundations of quantum physics. Within this overall framework our present special issue of IJTP offers a compact and well balanced sample of the results obtained in the subject areas covered by the meeting. The readership of our Special Issue will find here not only several up-to-date reports on the current state of development of the field but also, and predominantly, multiple carefully refereed samples of the original research written, naturally, not only by the direct participants of the conference. The latter paradox of the participation of non-participants is in fact not too surprising. Indeed, both the main subject areas covered by this Special Issue belong among the fresh and most quickly developing new subfields of quantum physics and related mathematics. For this reason the major part of the presented scientific material should be perceived as an integral part of the mainstream publication activity of the authors. In this sense both the Guest Editors would like to formulate and express their personal gratitude not only to all of the organizers of the ninth PHHQP meeting but, first of all, to all of the authors who accepted the challenge and who did contribute, to our Special Issue, with compact but still high-quality presentations of their most recent and interesting results.
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