Related papers: A topological approach to the Cahn-Hilliard equati…
A universal topological marker has been proposed recently to map the topological invariants of Dirac models in any dimension and symmetry class to lattice sites. Using this topological marker, we examine the conditions under which the…
Vortex singularities in speckle patterns formed from random superpositions of waves are an inevitable consequence of destructive interference and are consequently generic and ubiquitous. Singularities are topologically stable, meaning they…
Emergence of self-similarity in hierarchical community structures is ubiquitous in complex systems. Yet, there is a dearth of universal quantification and general principles describing the formation of such structures. Here, we discover…
We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which…
The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
The application of modern topology optimization techniques to single physics systems has seen great advances in the last three decades. However, the application of these tools to sophisticated multiphysics systems such as fluid-structure…
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…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
A uniform derivation is presented of the self-consistent field equations in a finite basis set. Both restricted and unrestricted Hartree-Fock (HF) theory as well as various density functional (DF) approximations are considered. The unitary…
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…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
A theory has been presented previously in which the geometrical structure of a real four-dimensional space time manifold is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group. The group…
The topology and geometry of random fields - in terms of the Euler characteristic and the Minkowski functionals - has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial…
Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies basic topological features such as "holes," it lacks the…
We derive a new effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by 4-th order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly…
Cascades are self-reinforcing processes underlying the systemic risk of many complex systems. Understanding the universal aspects of these phenomena is of fundamental interest, yet typically bound to numerical observations in ad-hoc models…
Topological data analysis is an emerging field that applies the study of topological invariants to data. Perhaps the simplest of these invariants is the number of connected components or clusters. In this work, we explore a topological…
Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…
Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…
It is important that a spatial network's construction algorithm reproduces the structural properties of the original physical embedding. Here, we assess the Delaunay triangulation as a spatial network construction algorithm for seven…