The stability analysis of synchronization in time-varying higher-order networked structures (simplicial complexes) is one the challenging problem due to presence group interactions. In this context, most previous studies have been done either on temporal pairwise networks or static simplicial complexes. Here, for first time, we propose a general framework study phenomenon We show that synchrono...

This manuscript focusses on algebraic shifting and its applications to f -vector theory of simplicial complexes and more general graded posets. It includes attempts to use algebraic shifting for solving the g-conjecture for simplicial spheres, which is considered by many as the main open problem in f -vector theory. While this goal has not been achieved, related results of independent interest ...

Abstract. Simplicial complexes represent useful and accurate models of complex networks and complex systems in general. We explore the properties of spectra of combinatorial Laplacian operator of simplicial complexes and show its relationship with connectivity properties of the Q-vector and with connectivities of cliques in the simplicial clique complex. We demonstrate the need for higher order...

We introduce toric complexes as polyhedral complexes consisting of rational cones together with a set of integral generators for each cone, and we define their associated face rings. Abstract simplicial complexes and rational fans can be considered as toric complexes, and the face ring for toric complexes extends Stanley and Reisner’s face ring for abstract simplicial complexes [20] and Stanley...

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...

The efficient representation and management of simplicial and cell complexes is an active research topic in several fields, including geometric modeling, computer graphics, scientific visualization, and geographic data processing. In this paper, we propose the Stellar tree, a topological data structure for performing efficient topological queries on simplicial and non-simplicial complexes. We p...

This manuscript focusses on algebraic shifting and its applications to f -vector theory of simplicial complexes and more general graded posets. It includes attempts to use algebraic shifting for solving the g-conjecture for simplicial spheres, which is considered by many as the main open problem in f -vector theory. While this goal has not been achieved, related results of independent interest ...