Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.Comment: 34 pages with 4 figures, Published in Neural Networks, 201

Ontology-driven conceptual modeling: A'systematic literature mapping and review

All rights reserved. Ontology-driven conceptual modeling (ODCM) is still a relatively new research domain in the field of information systems and there is still much discussion on how the research in ODCM should be performed and what the focus of this research should be. Therefore, this article aims to critically survey the existing literature in order to assess the kind of research that has been performed over the years, analyze the nature of the research contributions and establish its current state of the art by positioning, evaluating and interpreting relevant research to date that is related to ODCM. To understand and identify any gaps and research opportunities, our literature study is composed of both a systematic mapping study and a systematic review study. The mapping study aims at structuring and classifying the area that is being investigated in order to give a general overview of the research that has been performed in the field. A review study on the other hand is a more thorough and rigorous inquiry and provides recommendations based on the strength of the found evidence. Our results indicate that there are several research gaps that should be addressed and we further composed several research opportunities that are possible areas for future research