03.04.16 - 08.04.16, Seminar 16142

Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis

Diese Seminarbeschreibung wurde vor dem Seminar auf unseren Webseiten veröffentlicht und bei der Einladung zum Seminar verwendet.

Motivation

Multivalued data sets are generated by modern technology, such as advanced imaging methods and computational simulations, and in many applications, ranging from medicine and neuroscience to fluid dynamics and structural mechanics. In all these disciplines, we are encountering not only fields of scalars or vectors, but also of more complex quantities, often expressed as second-order or higher-order tensors, or as other higher order descriptors. Moreover, we are frequently dealing with multiple quantities that relate to different aspects of the same phenomenon, and that have to be analyzed jointly in order to understand their relationships.

Proper tools for visualization, data processing, statistical analysis and predictive modeling of multi-valued data are urgently needed, but are still hard to come by. Recent years have seen rapid scientific progress in diverse related applications and also on fundamental theoretical and algorithmic questions related to proper treatment of such data, spread over different disciplines. The goal of this workshop is to bring together scientists working on computer science, applied mathematics, physics, engineering, neuroscience, and medicine, thus enabling interdisciplinary exchange to bridge the gap between the applications and the fundamental scientific developments. This includes making sure that practitioners are aware of available methodology, and that researchers working on theory and algorithms understand what the most pressing challenges are on the application side.

In particular, we aim to address issues related to:

  • Modern variants of diffusion MRI, including the use of multiple gradient pulses and flexible gradient waveforms.
  • Graph-based representations of data from neuroimaging.
  • Data from engineering disciplines, in which information is frequently encoded in tensor fields, which are rarely analyzed by practitioners.
  • Decompositions and approximations of higher order tensors to support data analysis.
  • Visual representations of state-of-the-art mathematical models for data within the scope of the seminar.
  • Accounting for data uncertainty, model uncertainty, or measurement artifacts in the visualization of higher order descriptors.
  • Statistical distributions and hypothesis tests for structured data, tensorial random variables, and higher order descriptors.
  • Effective and computationally efficient kernels to enable predictive modeling of multivalued, tensorial, and higher-order data.
  • Using Finsler geometry for the quantitative and visual analysis of higher order descriptors, especially those arising in diffusion MR imaging.
  • Approximative or compressed representations of higher order data.

This Dagstuhl Seminar is the sixth in a series of stimulating, highly interdisciplinary Dagstuhl seminars. Previous seminars resulted in various collaborations and books that reflect the excitement and inspiration generated by these seminars. The charming atmosphere of Schloss Dagstuhl will prove once more to be a powerful catalyst that initiates vivid discussions, fruitful exchange of expertise, and lasting scientific relations between the participating researchers.