Related papers: Gradient systems on coupled cell networks
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…
We explore a systematic approach to studying the dynamics of evolving networks at a coarse-grained, system level. We emphasize the importance of finding good observables (network properties) in terms of which coarse grained models can be…
Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…
Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks (CTLNs) in order to…
We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…
Graphs are a powerful tool for representing and analyzing unstructured, non-Euclidean data ubiquitous in the healthcare domain. Two prominent examples are molecule property prediction and brain connectome analysis. Importantly, recent works…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
A biological regulatory network can be modeled as a discrete function that contains all available information on network component interactions. From this function we can derive a graph representation of the network structure as well as of…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…
Power grid networks, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted…
Biological systems and processes are networks of complex nonlinear regulatory interactions between nucleic acids, proteins, and metabolites. A natural way in which to represent these interaction networks is through the use of a graph. In…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a class of ' cellular networks'…
Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present…
This work provides a comprehensive derivation of the parameter gradients for GATv2 [4], a widely used implementation of Graph Attention Networks (GATs). GATs have proven to be powerful frameworks for processing graph-structured data and,…