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

这项行动资助蒙大拿州立大学的Kelly Spendlove于2013年夏天在日本京都大学开展数学和物理科学领域的研究项目。该项目名为“计算复杂系统中出现的关键转变的特征”。主持的科学家是Hiroshi Kokubu。复杂的动力系统，从生理系统和金融市场到地球气候模型，经常表现出临界阈值——通常被称为引爆点——在这个临界点上，系统的行为可能从一种状态彻底转变为另一种状态。例如，在生理学上，有自发的系统性衰竭，如哮喘发作或癫痫发作，以及某些疾病的突然发作和进展；在生态学中，有野生动物种群的崩溃或灾难性的环境荒漠化；在地球气候系统中，海洋环流或气候可能发生突变。众所周知，在这种关键转变发生之前进行预测是非常困难的：根据经验，系统在达到临界点之前可能几乎没有变化；从理论上讲，已经证明了在相空间和参数空间的所有尺度上都可以发生全局动力学的变化。此外，复杂系统的模型通常是不精确的，参数很少确切地知道，计算可能包含各种大小的误差。尽管有这种困难，最近的工作现在表明存在一般的早期预警信号，而不是针对任何特定类别的系统。利用这些通用指标，本项目基于动力系统理论和应用代数拓扑的思想，实现了一种新颖的分析形式，旨在揭示关键转变发生之前的基本特征或特征。EAPSI奖学金的广泛影响包括为研究员提供美国以外的第一手研究经验；介绍该地区的科学、科学政策和科学基础设施；以及对社会、文化和语言的了解。这些活动符合美国国家科学基金会的目标，即在其科学家、工程师和教育工作者的职业生涯早期培养国际合作，从而确保美国科学劳动力具有全球意识。此外，所有开发的代码都被整合到宿主科学家目前参与的现有开源项目中。在这个项目中，对开源框架的强调是特别重要的，因为作为一个正在进行的网站和源代码存储库的一部分，工作的结果是公开的，不受学术机构、金钱成本甚至科学学科的阻碍。

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.