相关论文: Construction of the generalized Cech complex

Community structure identification has been an important research topic in complex networks and there has been many algorithms proposed so far to detect community structures in complex networks, where most of the algorithms are not suitable…

\v{C}ech complexes reveal valuable topological information about point sets at a certain scale in arbitrary dimensions, but the sheer size of these complexes limits their practical impact. While recent work introduced approximation…

A multiplex is a collection of network layers, each representing a specific type of edges. This appears to be a genuine representation for many real-world systems. However, due to a variety of potential factors, such as limited budget and…

Complex networks are made up of vertices and edges. The edges, which may be directed or undirected, are equipped with positive weights. Modeling complex systems that consist of different types of objects leads to multilayer networks, in…

We characterise high-dimensional topology that arises from a random Cech complex constructed on the circle. Expected Euler characteristic curve is computed, where we observe limiting spikes. The spikes correspond to expected Betti numbers…

The analytical characterization of coverage probability in finite three-dimensional wireless networks has long remained an open problem, hindered by the loss of spatial independence in finite-node settings and the coupling between link…

Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally…

Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in…

The Calculus of Wrapped Compartments (CWC) is a recently proposed modelling language for the representation and simulation of biological systems behaviour. Although CWC has no explicit structure modelling a spatial geometry, its compartment…

Wireless network topologies change over time and maintaining routes requires frequent updates. Updates are costly in terms of consuming throughput available for data transmission, which is precious in wireless networks. In this paper, we…

Discovering and characterizing the large-scale topological features in empirical networks are crucial steps in understanding how complex systems function. However, most existing methods used to obtain the modular structure of networks…

The \v{C}ech complex is one of the most widely used tools in applied algebraic topology. Unfortunately, due to the inclusive nature of the \v{C}ech filtration, the number of simplices grows exponentially in the number of input points. A…

Nearest neighbor search is a basic computational tool used extensively in almost research domains of computer science specially when dealing with large amount of data. However, the use of nearest neighbor search is restricted for the…

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…

We propose a model for network community detection using topological data analysis, a branch of modern data science that leverages theory from algebraic topology to statistical analysis and machine learning. Specifically, we use cellular…

Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…

A multi-hop synchronous wirelss network is said to be unknown if the nodes have no knowledge of the topology. A basic task in wireless network is that of broadcasting a message (created by a fixed source node) to all nodes of the network.…

Modular structure is ubiquitous in real-world complex networks, and its detection is important because it gives insights in the structure-functionality Modular structure is ubiquitous in real-world complex networks, and its detection is…

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…

Inspired by the Statistical Physics of complex networks, wireless multihop ad hoc communication networks are considered in abstracted form. Since such engineered networks are able to modify their structure via topology control, we search…