Related papers: Continuum Limits for Adaptive Network Dynamics

Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such…

Building on recent work by Medvedev (2014) we establish new connections between a basic consensus model, called the voting model, and the theory of graph limits. We show that in the voting model if consensus is attained in the continuum…

This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this…

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…

Reuse of data in adaptive workflows poses challenges regarding overfitting and the statistical validity of results. Previous work has demonstrated that interacting with data via differentially private algorithms can mitigate overfitting,…

Network structures are extremely important to the study of political science. Much of the data in its subfields are naturally represented as networks. This includes trade, diplomatic and conflict relationships. The social structure of…

We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…

Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of…

Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of…

We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…

Many experiments have been performed that use evolutionary algorithms for learning the topology and connection weights of a neural network that controls a robot or virtual agent. These experiments are not only performed to better understand…

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…

In recent years, the state-of-the-art in deep learning has been dominated by very large models that have been pre-trained on vast amounts of data. The paradigm is very simple: investing more computational resources (optimally) leads to…

This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…

A Markovian model of the evolution of intermittent connections of various classes in a communication network is established and investigated. Any connection evolves in a way which depends only on its class and the state of the network, in…

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…

We study information processing in populations of Boolean networks with evolving connectivity and systematically explore the interplay between the learning capability, robustness, the network topology, and the task complexity. We solve a…

The maximum achievable capacity from source to destination in a network is limited by the min-cut max-flow bound; this serves as a converse limit. In practice, link capacities often fluctuate due to dynamic network conditions. In this work,…

We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…

Over the last years, a great deal of attention has been focused on complex networked systems, characterized by intricate structure and dynamics. The latter has been often represented in terms of overall statistics (e.g. average and standard…