Related papers: Continuum Limits for Adaptive Network Dynamics
An effective aggregation of node features into a graph-level representation via readout functions is an essential step in numerous learning tasks involving graph neural networks. Typically, readouts are simple and non-adaptive functions…
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…
The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
Real-world network systems are inherently dynamic, with network topologies undergoing continuous changes over time. Previous works often focus on static networks or rely on complete prior knowledge of evolving topologies, whereas real-world…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
Despite their widespread utility across domains, basic network models face fundamental limitations when applied to complex biological systems, particularly in neuroscience. This paper critically examines these limitations and explores…
Many physical systems -- such as optical waveguide lattices and dense neuronal or vascular networks -- can be modeled by metric graphs, where slender "wires" (edges) support wave or diffusion equations subject to Kirchhoff conditions at the…
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…
It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network…
Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
The co-evolution of structure and dynamics, known as adaptivity, is a fundamental property in various systems and drives diverse emergent behaviors. However, the adaptivity in previous works is primarily stemmed from pairwise situations,…
We consider the population dynamics of a set of species whose network of catalytic interactions is described by a directed graph. The relationship between the attractors of this dynamics and the underlying graph theoretic structures like…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…