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

这一行动资助蒙大拿州立大学的凯利·斯彭德洛夫在2013年夏天在日本京都的京都大学进行数学和物理科学领域的研究项目。 该项目的标题是“计算复杂系统中出现的关键转变的特征”。“主持人是Hiroshi Kokubu。复杂的动态系统，从生理系统和金融市场到地球气候模型，通常会表现出临界阈值-通常称为临界点-系统可能会从一种状态到另一种状态彻底改变其行为。 例如，在生理学上，有自发的系统性故障，如哮喘发作或癫痫发作，以及某些疾病的突然发作和进展;在生态学上，有野生动物种群的崩溃或环境的灾难性荒漠化;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，在发生之前预测这种关键转变是非常困难的：从经验上讲，系统在达到临界点之前可能会显示出很小的变化;从理论上讲，已经证明全球动力学的变化可以在相空间和参数空间的所有尺度上发生。此外，复杂系统的模型通常是不精确的，参数很少确切知道，计算可能包含各种大小的误差。尽管存在这一困难，但最近的工作表明，存在着通用的预警信号，而不是针对任何特定类别的系统。利用这些通用指标，该项目实施了一种新的分析形式，基于动力系统理论和应用代数拓扑学的思想，旨在揭示关键转变发生之前的基本特征或签名。EAPSI奖学金的更广泛影响包括为研究员提供美国以外的第一手研究经验;介绍各自所在地的科学，科学政策和科学基础设施;以及社会，文化和语言的方向。 这些活动符合NSF的目标，即在科学家，工程师和教育工作者的职业生涯早期进行国际合作教育，从而确保具有全球意识的美国科学工作者。 此外，所有开发的代码都被纳入了东道科学家目前参与的一个现有开放源码项目。 在这个项目中强调开源框架是特别重要的，因为作为一个正在进行的网站和源代码库的一部分，工作的结果是公开的，不受学术机构，货币成本，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.