Topological data analysis refers to approaches for systematically and reliably computing
abstract 'shapes' of complex data sets. There are various applications of topological data …

We explore the evolution of daily returns of four major US stock market indices during the
technology crash of 2000, and the financial crisis of 2007–2009. Our methodology is based …

We analyze four major cryptocurrencies (Bitcoin, Ethereum, Litecoin, and Ripple) before the
digital asset market crash at the beginning of 2018. We also analyze Bitcoin before some of …

Persistent homology is a recently developed theory in the field of algebraic topology to study
shapes of datasets. It is an effective data analysis tool that is robust to noise and has been …

A comprehensive theoretical and numerical analysis of the dynamical features of a fractional-
order delay financial risk system (FDRS) is presented in this paper. Applying the …

Research has found that the vividness of conscious experience is related to brain dynamics.
Despite both being anaesthetics, propofol and ketamine produce different subjective states …

The study of phase transitions using data-driven approaches is challenging, especially
when little prior knowledge of the system is available. Topological data analysis is an …

Traditionally, computation of Lyapunov exponents has been the marque method for
identifying chaos in a time series. Recently, new methods have emerged for systems with …

Topological Data Analysis (TDA) is the collection of mathematical tools that capture the
structure of shapes in data. Despite computational topology and computational geometry …

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in
and are driven by temporally varying environments. Such systems can show multiple …