Speaker
Description
Dynamical systems analysis plays a crucial role in understanding the behavior of complex phenomena across various fields, including engineering, physics, and biology. However, the inherent complexity of these systems often presents significant challenges in their analysis, such as non-linearity and high-dimensionality. Topological methods have emerged as a powerful toolkit for addressing these difficulties, offering insights into the qualitative structure of dynamical systems without relying heavily on traditional metrics. By capturing the underlying shape and connectivity of data, these methods facilitate a deeper understanding of system dynamics. One noteworthy approach within the topological analysis that will be presented is the Euler Characteristic Profile. This method offers a robust framework for quantifying topological features and their evolution over time. Furthermore, we will illustrate its potential applicability in the analysis of biomedical data, highlighting how topological methods can deepen our understanding of intricate biological systems.
