Related papers: Homological percolation transitions in growing sim…
We examine the homological structure of the Barabasi-Albert model, focusing on the time evolution of $\Delta$-dimensional simplices and topological holes as functions of time $t$ and the attachment parameter $m$ (the number of edges added…
A complex system with many interacting individuals can be represented by a network consisting of nodes and links representing individuals and pairwise interactions, respectively. However, real-world systems grow with time and include many…
The prediction of critical transitions, such as extinction events, is vitally important to preserving vulnerable populations in the face of a rapidly changing climate and continuously increasing human resource usage. Predicting such events…
A hybrid percolation transition (HPT) exhibits both discontinuity of the order parameter and critical behavior at the transition point. Such dynamic transitions can occur in two ways: by cluster pruning with suppression of loop formation of…
Persistent homology is a fundamental tool in topological data analysis; however, it lacks methods to quantify the fragility or fineness of cycles, anticipate their formation or disappearance, or evaluate their stability beyond persistence.…
Persistent homology has been studied to better understand the structural properties and topology features of weighted networks. It can reveal hidden layers of information about the higher-order structures formed by non-pairwise interactions…
Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of…
We consider the topology of simplicial complexes with vertices the points of a random point process and faces determined by distance relationships between the vertices. In particular, we study the Betti numbers of these complexes as the…
Hybrid percolation transitions (HPTs) induced by cascading processes have been observed in diverse complex systems such as $k$-core percolation, breakdown on interdependent networks and cooperative epidemic spreading models. Much effort has…
In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree…
In this paper we discuss two general models of random simplicial complexes which we call the lower and the upper models. We show that these models are dual to each other with respect to combinatorial Alexander duality. The behaviour of the…
Simplicial complexes are increasingly used to understand the topology of complex systems as different as brain networks and social interactions. It is therefore of special interest to extend the study of percolation to simplicial complexes.…
Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the…
Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize social contagion processes such as opinion…
Percolation transition (PT) means the formation of a macroscopic-scale large cluster, which exhibits a continuous transition. However, when the growth of large clusters is globally suppressed, the type of PT is changed to a discontinuous…
We present a distributed algorithm to compute the first homology of a simplicial complex. Such algorithms are very useful in topological analysis of sensor networks, such as its coverage properties. We employ spanning trees to compute a…
We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…
Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of…
Given a chain complex with the only modification that each cell of the complex has a probability distribution assigned. We will call this complex - a random complex and what should be understood in practice, is that we have a classical…
Topological data analysis can extract effective information from higher-dimensional data. Its mathematical basis is persistent homology. The persistent homology can calculate topological features at different spatiotemporal scales of the…