We have recently presented evidence that in configurations dominating the regularized pure-glue QCD path integral, the topological charge density constructed from overlap Dirac operator organizes into an ordered space-time structure. It was pointed out that, among other properties, this structure exhibits two important features: it is lowdimensional and geometrically global, i.e. consisting of ...

the atom bond connectivity index of a graph is a new topological index was defined by e.estrada as abc(g)  uve (dg(u) dg(v) 2) / dg(u)dg(v) , where g d ( u ) denotes degreeof vertex u. in this paper we present some bounds of this new topological index.

Image analysis by topological gradient approach is a technique based upon the historic application of the topological asymptotic expansion to crack localization problem from boundary measurements. This paper aims at reviewing this methodology through various applications in image processing; in particular image restoration with edge detection, classification and segmentation problems for both g...

The topological characterization of nonequilibrium matter is highly nontrivial because familiar approaches designed for equilibrium phases may not apply. In the presence crystal symmetry, Floquet insulator states cannot be easily distinguished from normal insulators by a set symmetry eigenvalues at high points in Brillouin zone. This work advocates physically motivated, easy-to-implement approa...

Simplicial complexes are discrete representations of topological spaces that are practical for computational studies. The first three Betti-numbers (indicating the number of components, tunnels and voids), as well as the topological persistence of each such feature, is welldefined and can be efficiently computed for simplicial complexes embedded in 2D and 3D [1, 2]. We introduce a novel represe...