Related papers: The Evolution of Complex Networks: A New Framework
We derive upper bounds on the complexity of ReLU neural networks approximating the solution of a linear system given the matrix and the right-hand side. We focus on matrices which are symmetric positive definite and sparse, as they appear…
In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…
Traditionally, network analysis is based on local properties of vertices, like their degree or clustering, and their statistical behavior across the network in question. This paper develops an approach which is different in two respects. We…
Studying the invertibility of deep neural networks (DNNs) provides a principled approach to better understand the behavior of these powerful models. Despite being a promising diagnostic tool, a consistent theory on their invertibility is…
Previous work has shown that the dynamical regime of Recurrent Neural Networks (RNNs) - ranging from oscillatory to chaotic and fixpoint behavior - can be controlled by the global distribution of weights in connection matrices with…
We study a novel model for evolution of complex networks. We introduce information filtering for reduction of the number of available nodes to a randomly chosen sample, as stochastic component of evolution. New nodes are attached to the…
We propose a novel methodology for discovering the presence of relationships realized as binary time series between variables in high dimension. To make it visually intuitive, we regard the existence of a relationship as an edge connection,…
Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these…
Modern communication networks have become very complicated and highly dynamic, which makes them hard to model, predict and control. In this paper, we develop a novel experience-driven approach that can learn to well control a communication…
In the interdisciplinary field of network science, a complex-valued network, with edges assigned complex weights, provides a more nuanced representation of relationships by capturing both the magnitude and phase of interactions.…
Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real world systems. Using random matrix analysis of a weighted…
Real-data networks often appear to have strong modularity, or network-of-networks structure, in which subgraphs of various size and consistency occur. Finding the respective subgraph structure is of great importance, in particular for…
Besides the complexity in time or in number of messages, a common approach for analyzing distributed algorithms is to look at the assumptions they make on the underlying network. We investigate this question from the perspective of network…
Deep neural networks are revolutionizing the way complex systems are developed. However, these automatically-generated networks are opaque to humans, making it difficult to reason about them and guarantee their correctness. Here, we propose…
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the…
Many dynamical processes of complex systems can be understood as the dynamics of a group of nodes interacting on a given network structure. However, finding such interaction structure and node dynamics from time series of node behaviours is…
Graph-theoretical analyses of complex brain networks is a rapidly evolving field with a strong impact for neuroscientific and related clinical research. Due to a number of confounding variables, however, a reliable and meaningful…
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…
We present a new approach to the calculation of measures in weighted networks, based on the translation of a weighted network into an ensemble of edges. This leads to a straightforward generalization of any measure defined on unweighted…
We adopt the statistical framework on robustness proposed by Watson and Holmes in 2016 and then tackle the practical challenges that hinder its applicability to network models. The goal is to evaluate how the quality of an inference for a…