Bastian studied mathematics at the University of Münster for both his bachelor’s degree, with a minor in economics, and his master’s degree, with minor in psychology. During his bachelor studies, as part of which he also spent time at Universitat de Barcelona, Bastian focused mainly on pure mathematics, and wrote his bachelor thesis on the edge of analytic and algebraic number theory. While working towards his master’s degree, he was part of the workgroup “methods in bioelectromagnetism”, headed by PD Dr. Carsten Wolters, and became familiar with brain research, especially concerning epilepsy, both mathematically and medically. Bastian’s research there concerned inverse problems, specifically simulation studies based on a Hierarchical Bayesian Modeling approach. His minor studies in psychology enabled him to amplify his background on methodologies of brain imaging, as well as to learn about cognitive processes and mechanisms in the brain. In order to understand the underlying mathematical concepts of brain dynamics, Bastian wrote his Master’s thesis on synchronization patterns of non-locally coupled oscillators, focussing mainly on their bifurcation and stability analysis, under the supervision of Prof. Dr. Michael Herrmann.
In 2015 Bastian started his PhD research project, entitled “Frequency-doubling bifurcations in neuronal networks – a means of cross-frequency interactions” which is jointly supervised by Profs. Andreas Daffertshofer and Bob van Dijk at Vrije Universiteit Amsterdam and Profs. Aneta Stefanovska and Peter McClintock at the University of Lancaster. Bastian’s research interests are broad, but his interest in the dynamics of complex systems drive him to try and discover out more about mathematical and physical concepts that underlie our world, and to draw crosslinks between different areas. Specifically to COSMOS, he hopes to pursue the brain and networks research in order to find out how information is transmitted, how different subnetworks interact with each other, and what leads to specifically known phenomena.
He successfully completed his PhD in December 2018.
Pietras B., Deschle N., and Daffertshofer A. “First-order phase transitions in the Kuramoto model with compact bimodal frequency distributions” Phys. Rev. E 98, 062219 (2019) LINK
Daffertshofer A., Ton R., Pietras B., Kringelbach M. L., Deco G. “Scale-freeness or partial synchronization in neural mass phase oscillator networks: Pick one of two” NeuroImage, 180, Part B (2018) 428-441 LINK
Pietras B., N. Deschle, A. Daffertshofer “Equivalence of coupled networks and networks with multimodal frequency distributions: Conditions for the bimodal and trimodal case”, Phys. Rev. E 94, 052211 (2016) LINK
Pietras B. “Exact low-dimensional mean-field dynamics of neuronal networks – networks of spiking neurons”. SIAM Conference on Dynamical Systems, Snowbird, Utah, May 2017 Talk
Pietras B. “The Ott-Antonsen ansatz — theory and applications”. COSMOS Retreat, Wittenberg, March 2017 Talk
Deschle N., Devalle F., Goldschmidt J., Pietras B., Topcu, C. “Identification of dynamics – oscillations, synchronization and the Kuramoto model”. 2nd COSMOS Workshop, Amsterdam, Dec. 2016 Talk
Pietras B., Daffertshofer A. “Ott-Antonsen attractiveness for parameter-dependent systems”, Multistability and tipping. Dresden, Germany, Oct 2016, Poster
Pietras B., Deschle N., Daffertshofer A. “Multimodal or coupled networks: just a matter of taste?” Multistability and tipping. Dresden, Germany, Oct 2016, Poster
Pietras B., Deschle N., Daffertshofer A. “Multimodal or coupled networks: just a matter of taste?” Multistability and tipping. Dresden, Germany, Sept 2016 Talk
Deschle N., Pietras B., Daffertshofer A. “Estimation of relaxation times in coupled oscillatory networks” Statphys26 Satellite: Complex Networks: from theory to interdisciplinary applications. Marseille July 2016. Poster.
Pietras B., Daffertshofer A. “Ott-Antonsen attractiveness for parameter-dependent systems”, Patterns of Dynamics. Berlin, Germany, July 2016 TALK
Pietras B., Deschle N., Daffertshofer A. “Multimodal or coupled networks: just a matter of taste?” Dynamics Days Europe. Corfu, Greece, June 2016 TALK
Pietras B., Deschle N., Daffertshofer A. “Coupled networks and networks with bimodal frequency distributions are equivalent” Second International Conference on Mathematical Neuroscience (ICMNS 2016), Juan les Pins, France, May 2016, Poster
Pietras B. “Phase-reduction techniques near and away from bifurcation points” Problems and challenges: multiple scales and coherent structures. Münster, Germany, Apr 2016 Talk
Pietras B., Deschle N., Daffertshofer A. “Coupled networks and networks with bimodal frequency distribution are equivalent” International conference on biological oscillations (ESGCO 2016). Lancaster, UK, Apr 2016 Poster