Optical bound states in the continuum (BICs) have recently been realized in photonic crystal slabs, where the disappearance of out-of-plane radiation turns leaky resonances into guided modes with infinite lifetimes. We show that such BICs are vortex centers in the polarization directions of far-field radiation. They carry conserved and quantized topological charges, defined by the winding numbe...

We study fourfold rotation-invariant gapped topological systems with time-reversal symmetry in two and three dimensions (d=2, 3). We show that in both cases nontrivial topology is manifested by the presence of the (d-2)-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wann...

This paper shows an image/video application using topological invariants for human gait recognition. Using a background subtraction approach, a stack of silhouettes is extracted from a subsequence and glued through their gravity centers, forming a 3D digital image I . From this 3D representation, the border simplicial complex ∂K(I) is obtained. We order the triangles of ∂K(I) obtaining a sequen...

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

Controlling topological defects in 3D liquid crystal phases is a crucial element in the development of novel devices, from blue-phase displays to passive biochemical sensors. However, it remains challenging to realize the 3D topological conditions necessary to robustly and arbitrarily direct the formation of defects. Here, using a series of short pillar arrays as topological templates, we demon...

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

Apparent Michaelis constants for nucleotides in transcription of yeast tRNA gene by homologous RNA polymerase III with auxiliary protein factors, were found to be remarkably higher in initiation than in elongation of RNA chain. This supports presumptions regarding topological similarities between catalytic centers of bacterial and eukaryotic RNA polymerases.

Several novel data center networking (DCN) topologies have been proposed to improve the topological properties of data centers. Unfortunately, it is ignored that whether these topologies are suited for the online applications and infrastructure services running on the corresponding data centers. In this paper, we propose a novel DCN topology, named HyperFat-tree Network (HFN). HFN incarnates th...