Related papers: Topological persistence and dynamical heterogeneit…
Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…
Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information in a parameterized version of the Betti numbers, i.e. the…
We study nonequilibrium dynamics of SU(2) lattice gauge theory in Minkowski space-time in a classical-statistical regime, where characteristic gluon occupancies are much larger than unity. In this strongly correlated system far from…
Persistent homology provides a robust methodology to infer topological structures from point cloud data. Here we explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point…
The problem of (point) forecasting $ \textit{univariate} $ time series is considered. Most approaches, ranging from traditional statistical methods to recent learning-based techniques with neural networks, directly operate on raw time…
Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…
We discuss the spatiotemporal behavior of local density and its relation to dynamical heterogeneity in a highly supercooled liquid by using molecular dynamics simulations of a binary mixture with different particle sizes in two dimensions.…
This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the…
Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the…
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding to a homological feature supported over that interval or,…
Multiparameter persistence modules come up naturally in topological data analysis and topological robotics. Given a metric graph $(X,\delta)$, the second configuration space of $(X,\delta)$ with proximity parameters (for example, the…
Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…
Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…
In the present study, we performed molecular-dynamics simulations and investigated dynamical heterogeneity in a supercooled liquid under a steady shear flow. Dynamical heterogeneity can be characterized by three quantities: the correlation…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…