Related papers: Persistent topology of the reionization bubble net…
The reionization of intergalactic hydrogen has received intense theoretical scrutiny over the past two decades. Here, we approach the process formally as a percolation process and phase transition. Using semi-numeric simulations, we…
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology,…
We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving…
We use the photon flux and absorption tracer algorithm presented in Katz et al.~2018, to characterise the contribution of haloes of different mass and stars of different age and metallicity to the reionization of the Universe. We employ a…
This paper extends the possibility to examine the underlying curvature of data through the lens of topology by using the Betti curves, tools of Persistent Homology, as key topological descriptors, building on the clique topology approach.…
Two types of osmolytes, i.e., trimethylamin N-oxide (TMAO) and urea, demonstrate dramatically different properties in a protein folding process. Even with the great progresses in revealing the potential underlying mechanism of these two…
Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, and biological networks. The primary challenge in this domain is measuring…
The persistent homology transform (PHT) represents a shape with a multiset of persistence diagrams parameterized by the sphere of directions in the ambient space. In this work, we describe a finite set of diagrams that discretize the PHT…
Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…
The optical depth parameterisation is typically used to study the 21-cm signals associated with the properties of the neutral hydrogen (HI) gas and the ionisation morphology during the Epoch of Reionisation (EoR), without solving the…
We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…
Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…
One of the key observables of the reionization era is the distribution of neutral and ionized gas. Recently, Furlanetto, Zaldarriaga, & Hernquist developed a simple analytic model to describe the growth of HII regions during this era. Here,…
This study introduces a pore morphology algorithm that emphasizes the central role of topology in multiphase flow through porous media. Analysis of drainage in lattice-based pore networks identifies two key quantities, the percolation…
Topology provides an essential concept for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing realistic applications is that the level of protection displayed in real systems is…
We consider interface modes in block disordered subwavelength resonator chains in one dimension. Based on the capacitance operator formulation, which provides a first-order approximation of the spectral properties of dimer-type block…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…
The bubble size distribution of ionized hydrogen regions probes the information about the morphology of \HII\ bubbles during the reionization. Conventionally, the \HII\ bubble size distribution can be derived from the tomographic imaging…
We give an exhaustive characterization of the topology of band structures in class AI, using nonsymmorphic space group 33 ($Pna2_1$) as a representative example where a great variety of symmetry protected line-nodal structures can be…
The persistence diagram is a central object in the study of persistent homology and has also been investigated in the context of random topology. The more recent notion of the verbose diagram (a.k.a. verbose barcode) is a refinement of the…