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Habilitation
Applicability of ordinal-array-based indicators to strange nonchaotic attractors
(Universität Kassel, 2017-06-12)
Time series are useful for modeling systems behavior, for predicting some events (catastrophes, epidemics, weather, ...) or for classification purposes (pattern recognition, pattern analysis). Among the existing data analysis algorithms, ordinal pattern based algorithms have been shown effective when dealing with simulation data. However, when applied to quasi-periodically forced systems, they fail to detect SNA and tori as regular dynamics. In this work we address this concern by defining ordinal array (OA) based ...
Dissertation
Computing Quot Schemes
(2017-02-27)
The main goal of this thesis is to develop computational methods which allow effective computations on Hilbert and Quot schemes. At first we introduce marked bases over modules. They may be considered as a form of Gröbner basis which do not depend on a term order. Instead, one chooses for each generator some term as head module term such that the head module terms generate a prescribed monomial module. We show that the involutive normal form algorithm with respect to Pommaret division will terminate if the prescribed ...