Related papers: Inferring symbolic dynamics of chaotic flows from …
We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between…
Persistent homology (PH) 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 widely applied. We demonstrate a general…
A new approach to analysis of the synchronization of chaotic oscillations in two (or more) coupled oscillators is described that makes it possible to reveal changes in the structure of attractors and detect the appearance of intermittency.…
We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky…
The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of non-equilibrium topological invariants is a central issue and usually necessitates the information of quantum…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Traditional risk measures in finance, predominantly based on the second moment of return distributions or tail risk heuristics (VaR/CVaR), fail to account for the intrinsic geometric structure of market dynamics. This paper introduces a…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…
We demonstrate how to use persistent homology for cosmological parameter inference in a tomographic cosmic shear survey. We obtain the first cosmological parameter constraints from persistent homology by applying our method to the…
Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces persistence diagrams, which have been successfully used in…
Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…
In this work, we uncover a layered organization of the state space in the Kuramoto-Sivashinsky equation with periodic boundary conditions, in which multiple invariant sets coexist at fixed system parameters and are selected by the initial…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…
A symbolic analysis of observed time series data requires making a discrete partition of a continuous state space containing observations of the dynamics. A particular kind of partition, called ``generating'', preserves all dynamical…
We use persistent homology and persistence images as an observable of three different variants of the two-dimensional XY model in order to identify and study their phase transitions. We examine models with the classical XY action, a…
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…
We use the theory of persistent homology to analyze a data set arising from the study of various aspects of democracy. Our results show that most "mature" democracies look more or less the same, in the sense that they form a single…
Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…