Related papers: Network Horizon Dynamics I: Qualitative Aspects
The concept of node walk in graphs and complex networks has been addressed, consisting of one or more nodes that move into adjacent nodes, henceforth incorporating the respective connections. This type of dynamics is then applied to subsume…
Although two-dimensional periodic structures have functioned as the primary platform for exploring topological phenomena, recent advances have substantially expanded this research boundary to include more intricate, aperiodic structures:…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold…
Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like Trophic Analysis and non-normality. We propose a simple growing network model where the…
Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have…
Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the…
An object-oriented approach to implementing artificial neural networks is introduced in this article. The networks obtained in this way are highly connected in that they admit edges between nodes in any layers of the network, and dynamic,…
One of the defining features of complex networks is the connectivity properties that we observe emerging from local interactions. Recently, hypergraphs have emerged as a versatile tool to model networks with non-dyadic, higher-order…
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…
Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial and biological networks. At odds with empirical observation, these models predict that…
Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…
We propose and systematically evaluate three strategies for training dynamically-routed artificial neural networks: graphs of learned transformations through which different input signals may take different paths. Though some approaches…
We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…
This paper introduces a generalization of Convolutional Neural Networks (CNNs) to graphs with irregular linkage structures, especially heterogeneous graphs with typed nodes and schemas. We propose a novel spatial convolution operation to…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…