Related papers: Topological Woodward-Hoffmann classification for c…

We present a characterization of topological phases in photonic lattices. Our theory relies on a formal equivalence between the singular value decomposition of the non-Hermitian coupling matrix and the diagonalization of an effective…

The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological (SPT) phases, especially for interacting systems. In this paper, we systematically…

Topology optimization techniques have been applied in integrated optics and nanophotonics for the inverse design of devices with shapes that cannot be conceived by human intuition. At optical frequencies, these techniques have only been…

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…

Aliphatic hydrocarbons, such as normal alkanes, constitute a naturally abundant source of carbon atoms. Of special interest is the formation of cyclic and aromatic products from aliphatic reactants. Combining scanning tunneling microscopy…

Topology is an important degree of freedom in characterizing electronic systems. Recently, it also brings new theoretical frontiers and many potential applications in photonics. However, the verification of the topological nature is highly…

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

Topological indices play an important role in mathematical chemistry especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). Recent research indicates that the augmented…

We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

The celebrated tenfold-way of Altland-Zirnbauer symmetry classes discern any quantum system by its pattern of non-spatial symmetries. It lays at the core of the periodic table of topological insulators and superconductors which provided a…

We describe a construction of the cyclotomic structure on topological Hochschild homology ($THH$) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis takes place entirely in the category of equivariant…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

It is well known that (1+1)-D bosonic symmetry-protected topological (SPT) phases with symmetry group $G$ can be identified by the projective representation of the symmetry at the edge. Here, we generalize this result to higher dimensions.…

Bio-orthogonal click chemistry based on [3 + 2] dipolar cycloadditions has had a profound impact on the field of biochemistry and significant effort has been devoted to identify promising new candidate reactions for this purpose. To gauge…

We determine the optimum topology of quasi-one dimensional nonlinear optical structures using generalized quantum graph models. Quantum graphs are relational graphs endowed with a metric and a multiparticle Hamiltonian acting on the edges,…

Bottom-up layout algorithms for compound graphs are suitable for presenting the microscale view of models and are often used in model-driven engineering. However, they have difficulties at the macroscale where maintaining the overview of…

We present a systematic investigation of the thermodynamic topology for a broad class of asymptotically charged Anti-de Sitter (AdS) black holes in Einstein-Maxwell-Dilaton (EMD) theories, examining how scalar coupling parameters and…

We study the electronic properties of coupled parallel Polyyne chains in a couple of symmetric stacking arrangements, namely the AA stacking and the stacking AB, with the single and triple carbon bonds of one chain aligned (AA) and…

We investigate the topologies of random geometric complexes built over random points sampled on Riemannian manifolds in the so-called "thermodynamic" regime. We prove the existence of universal limit laws for the topologies; namely, the…