NSF East Asia and Pacific Summer Institute (EAPSI) for FY 2013 in Japan

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This action funds Kelly Spendlove of Montana State University to conduct a research project in the Math and Physical Sciences area during the summer of 2013 at Kyoto University in Kyoto, Japan. The project is entitled "Computing the Signatures of Critical Transitions Arising in a Complex System." The host scientist is Hiroshi Kokubu. Complex dynamical systems, which range from physiological systems and financial markets to models of the Earth's climate, often exhibit critical thresholds - commonly entitled tipping points - at which the system may radically shift its behavior from one state to another. For instance, in physiology, there are spontaneous systemic failures such as asthma attacks or epileptic seizures, as well as the sudden onset and progression of certain diseases; in ecology there is the collapse of wildlife populations or catastrophic desertification of environments; in the Earth climate system, abrupt shifts in ocean circulation or climate may occur. It is notoriously difficult to predict such critical transitions before they happen: empirically, systems may show little change before reaching a tipping point; theoretically, it has been proven that changes in global dynamics can occur on all scales in both phase space and parameter space. Moreover, models of complex systems are typically imprecise, parameters are rarely known exactly and computations may contain errors of various magnitudes. In spite of this difficulty, recent work now suggests the existence of generic early-warning signals, not specific to any particular class of system. Utilizing such generic indicators, this project implements a novel form of analysis, based on ideas from dynamical systems theory and applied algebraic topology, aiming to uncover the fundamental characteristics - or signature - of critical transitions before they occur.Broader impacts of an EAPSI fellowship include providing the Fellow a first-hand research experience outside the U.S.; an introduction to the science, science policy, and scientific infrastructure of the respective location; and an orientation to the society, culture and language. These activities meet the NSF goal to educate for international collaborations early in the career of its scientists, engineers, and educators, thus ensuring a globally aware U.S. scientific workforce. Furthermore, all developed code is being incorporated within an existing open-source project with which the host scientist is currently involved. The emphasis on an open-source framework in this project is particularly important, since as part of an on-going website and source-code repository the results of the work are publicly available, unhindered by academic institution, monetary cost and even scientific discipline.