Mathematical Sciences: Archetypal Analysis of Complex Spatio-Temporal Data

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9510284 Stone This work is supported by a Research Planning Grant for Women Scientists and Engineers Award. A major area of current interest in the field of dynamiaal systems is the understanding, prediction, and modeling of complex spatio-temporal dynamics. With the advent of high-speed, large capacity computers, more complex methods from statistics have become practical in the analysis of data from dynamical systems. One of the goals of this project is to compare and contrast two methods, Karhunen-Loeve (KL) decomposition and Archetypes, in their application to several experimental dynamical systems, both physical and numerical. Another goal is to propose a method that builds on Archetypal analysis for data with translating coherent structures, by finding archetypes that move with the traveling structure, in an objective manner. The shape of the structure itself is extracted (or possibly shapes, if the structure itself is varying as well as translating) as well as information on how the structure is moving across the spatial domain. A third goal is to determine the feasibility of using archetypes as a basis upon which to perform a Galerkin projection of the governing equations (when they exist), for modeling purposes. The National Science Foundation's mandate to ensure the vitality of the Nation's scientific enterprise includes concern for the quality, composition, distribution and effectiveness of the human resource base in science and engineering. Within this context, the Foundation is committed to enhancing the current rate of participation of women in science and engineering careers, in general, and as active participants in all of its programs. Research Planning Grant awards are made: (1) to help increase the number of new women investigators participating in NSF's research programs; and, (2) to facilitate preliminary studies and other activities related to the development of competitive research projects and proposals by women who have not previously had independent Federal research funding. Research Planning Grants are one-time awards that may be used for preliminary work to determine the feasibility of a proposed line of inquiry, and/or for other activities that will facilitate proposal development.