The ComplexData project aims at advancing our understanding of the statistical treatment of varied types of complex data by generating new theory and methods, and to obtain progress in concrete current biophysical problems through the implementation of the new tools developed. Complex Data constitute data where the basic object of observation cannot be described in the standard Euclidean context of statistics, but rather needs to be thought of as an element of an abstract mathematical space with special properties. Scientific progress has, in recent years, begun to generate an increasing number of new and complex types of data that require statistical understanding and analysis. Four such types of data that are arising in the context of current scientific research and that the project will be focusing on are: random integral transforms, random unlabelled shapes, random flows of functions, and random tensor fields. In these unconventional contexts for statistics, the strategy of the project will be to carefully exploit the special aspects involved due to geometry, dimension and randomness in order to be able to either adapt and synthesize existing statistical methods, or to generate new statistical ideas altogether. However, the project will not restrict itself to merely studying the theoretical aspects of complex data, but will be truly interdisciplinary. The connecting thread among all the above data types is that their study is motivated by, and will be applied to concrete practical problems arising in the study of biological structure, dynamics, and function: biophysics. For this reason, the programme will be in interaction with local and international contacts from this field. In particular, the theoretical/methodological output of the four programme research foci will be applied to gain insights in the following corresponding four application areas: electron microscopy, protein homology, DNA molecular dynamics, brain imaging.
Fields of science
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