相关论文: Simplicial Homology for Future Cellular Networks

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…

Transistor topology optimization is a critical step in standard cell design, directly dictating diffusion sharing efficiency and downstream routability. However, identifying optimal topologies remains a persistent bottleneck, as…

Heterogeneous small cell networks with overlay femtocells and macrocell is a promising solution for future heterogeneous wireless cellular communications. However, great resilience is needed in heterogeneous small cells in case of…

High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…

Symmetries in a network connectivity regulate how the graph's functioning organizes into clustered states. Classical methods for tracing the symmetry group of a network require very high computational costs, and therefore they are of hard,…

Topological techniques have become a popular tool for studying information flows in neural networks. In particular, simplicial homology theory is used to analyze how cognitive representations of space emerge from large conglomerates of…

We consider simplicial complexes that are generated from the binomial random 3-uniform hypergraph by taking the downward-closure. We determine when this simplicial complex is homologically connected, meaning that its zero-th and first…

This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…

To improve the cellular energy efficiency, without sacrificing quality-of-service (QoS) at the users, the network topology must be densified to enable higher spatial reuse. We analyze a combination of two densification approaches, namely…

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…

The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e. a set of points along with a set of neighborhood relations. This setup does not require the definition of a metric and…

It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither…

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…

Hypergraphs have seen widespread application in network and data science communities in recent years. We present a survey of recent work to construct auxiliary structures from hypergraphs -- specifically simplicial, relative, and chain…

Optimizing activation and deactivation of base station transmissions provides an instrument for improving energy efficiency in cellular networks. In this paper, we study optimal cell clustering and scheduling of activation duration for each…

A central problem in topological data analysis is that of computing the homology of a given simplicial complex. Said complexes can have arbitrary large number of simplices, as can happen, for example, if the space is the Rips-Vietoris or…

Interference management has become a key factor in regulating transmissions in wireless communication networks. To support effective interference management schemes, it can be essential to have prior knowledge about the network topology. In…

A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a…

Persistent homology has been applied to brain network analysis for finding the shape of brain networks across multiple thresholds. In the persistent homology, the shape of networks is often quantified by the sequence of $k$-dimensional…

Multicell cooperation has recently attracted tremendous attention because of its ability to eliminate intercell interference and increase spectral efficiency. However, the enormous amount of information being exchanged, including channel…