Related papers: Topological Measure Locating the Effective Crossov…
This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…
We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we…
We propose a novel model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the…
Hierarchy and centrality are two popular notions used to characterize the importance of entities in complex systems. Indeed, many complex systems exhibit a natural hierarchical structure, and centrality is a fundamental characteristic…
Clustering is typically measured by the ratio of triangles to all triples, open or closed. Generating clustered networks, and how clustering affects dynamics on networks, is reasonably well understood for certain classes of networks…
Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
Connectivity patterns of relevance in neuroscience and systems biology can be encoded in hierarchical modular networks (HMNs). Moreover, recent studies highlight the role of hierarchical modular organization in shaping brain activity…
Modularity is a popular measure of community structure. However, maximizing the modularity can lead to many competing partitions, with almost the same modularity, that are poorly correlated with each other. It can also produce illusory…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
This paper addresses the task of designing a modular neural network architecture that jointly solves different tasks. As an example we use the tasks of depth estimation and semantic segmentation given a single RGB image. The main focus of…
This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…
Community detection is a discovery tool used by network scientists to analyze the structure of real-world networks. It seeks to identify natural divisions that may exist in the input networks that partition the vertices into coherent…
In this paper, we propose a novel statistic of networks, the normalized clustering coefficient, which is a modified version of the clustering coefficient that is robust to network size, network density and degree heterogeneity under…
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…
A primary challenge in understanding collective behavior is characterizing the spatiotemporal dynamics of the group. We employ topological data analysis to explore the structure of honeybee aggregations that form during trophallaxis, which…
In turbulent flows, energy production is associated with highly organized structures, known as coherent structures. Since these structures are three-dimensional, their detection remains challenging in the most common situation, when…
In this paper we introduce a non-fuzzy measure which has been designed to rank the partitions of a network's nodes into overlapping communities. Such a measure can be useful for both quantifying clusters detected by various methods and…
Emergent effect is crucial to understanding the properties of complex systems that do not appear in their basic units, but there has been a lack of theories to measure and understand its mechanisms. In this paper, we consider emergence as a…