Elucidation of information structure behind complex systems using continued fraction and scale invariant generalized exponential function

2015 Fiscal Year Final Research Report

• Project/Area Number: 25540106
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Soft computing
• Research Institution: Chiba University
• Principal Investigator: Suyari Hiroki 千葉大学, 融合科学研究科(研究院), 教授 (70246685)
• Research Collaborator: Naudts Jan アントワープ大学, 教授 ; Scarforne Antonio トリノ工科大学, 准教授
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: q-指数関数 / スケール不変 / 自己相似

Outline of Final Research Achievements

Power distribution is ubiquitous in complex systems such as chaos and fractals. A power distribution can be represented as a generalization of an exponential function, so that the information structure behind complex systems can be systematically expressed in terms of a generalized exponential function. In this work, using the self-similarity in the q-exponential function, the relation between continued fraction and q-exponential function is found, but the the relation to the multi-scaled cantor set is still missing. However, in the process of this work, we obtain the important result on the large deviation principle generalized for the q-exponential function. Concretely, we derive the generalized binomial distribution uniquely determined by the q-exponential function and obtain the alpha-divergence as the rate function for the first time.

Free Research Field

情報数理