Related papers: Elements, topology, and T-shirts
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…
We investigate active particles that exhibit long-range interactions only restricted by a field of view, which is characterized by an angle $\beta$. We show that constraining attractive interactions to a field of view leads to the emergence…
Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…
This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…
Chirality manifests across multiple scales, yielding unique phenomena that break mirror symmetry. In chiral materials, unexpectedly large spin-filtering or photogalvanic effects have been observed even in materials composed of light…
A primary hypothesis that drives scientific and engineering studies is that data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) and signal processing (e.g.,…
Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected…
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…
Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide…
We discuss the higher-order topological field theory and response of topological crystalline insulators with no other symmetries. We show how the topology and geometry of the system is organised in terms of the elasticity tetrads which are…
Topologically nontrivial states are common in symmetry broken phases at macroscopic scales. Low dimensional systems bring them to a microscopic level where solitons emerge as single particles. The earliest and latest applications are…
Knitted and woven textile structures are examples of doubly periodic structures in a thickened plane made out of intertwining strands of yarn. Factoring out the group of translation symmetries of such a structure gives rise to a link…
Recent advancements in the field of topological band theory have significantly contributed to our understanding of intriguing topological phenomena observed in various classical and quantum systems, encompassing both wave and dissipative…
We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the…
We prove a criterion for $k-$formality of arrangements, using a complex constructed from vector spaces introduced in \cite{bt}. As an application, we give a simple description of $k-$formality of graphic arrangements: Let $G$ be a connected…
In recent years, low-dimensional materials with tetragonal $P4/nmm$ (orthorhombic $Pnma$) space group having square-net (chain-like) substructure of $p$-block elements have been studied extensively. By using a first-principles calculation…
The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given…
The edge states of a two-dimensional quantum spin Hall (QSH) insulator form a one-dimensional helical metal which is responsible for the transport property of the QSH insulator. Conceptually, such a one-dimensional helical metal can be…
Non-Hermiticity enriches the contents of topological classification of matter including exceptional points, bulk-edge correspondence and skin effect. Gain and loss can be described by imaginary diagonal elements in Hamiltonians and the…
Soft elastic filaments that can be stretched, bent and twisted exhibit a range of topologically and geometrically complex morphologies that include plectonemes, solenoids, knot-like and braid-like structures. We combine numerical…