Related papers: Graph Structure of the Generalized Tent Map over R…
Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in…
Recent progress in research on Deep Graph Networks (DGNs) has led to a maturation of the domain of learning on graphs. Despite the growth of this research field, there are still important challenges that are yet unsolved. Specifically,…
Recently, methods that represent data as a graph, such as graph neural networks (GNNs) have been successfully used to learn data representations and structures to solve classification and link prediction problems. The applications of such…
Inductive spatial temporal prediction can generalize historical data to predict unseen data, crucial for highly dynamic scenarios (e.g., traffic systems, stock markets). However, external events (e.g., urban structural growth, market crash)…
Spin wave equations in the non-equilibrium precessing state of a ferromagnetic system are found. They show a spin-wave instability towards growing domains of stable magnetization. Precession of the uniform magnetization mode is described by…
This paper concerns the link between the dynamical behaviour of a dynamical system and the dynamical behaviour of its numerical simulations. Here, we model numerical truncation as a spatial discretization of the system. Some previous works…
Many biological systems collectively construct complex, adaptive, and functional architectures, where function emerges from bottom-up building processes rather than top-down planning or centralized control. However, general strategies for…
We present a domain decomposition strategy for developing structure-preserving finite element discretizations from data when exact governing equations are unknown. On subdomains, trainable Whitney form elements are used to identify…
Decentralized generalized approximate message-passing (GAMP) is proposed for compressed sensing from distributed generalized linear measurements in a tree-structured network. Consensus propagation is used to realize average consensus…
We numerically study the dynamics of extended domain walls in homogeneous ferromagnets driven by a uniform magnetic field at zero temperature. Using both micromagnetic Landau-Lifshitz-Gilbert simulations and a collective-coordinate…
The chaotic phenomenon of intermittency is modeled by a simple map of the unit interval, the Farey map. The long term dynamical behaviour of a point under iteration of the map is translated into a spin system via symbolic dynamics. Methods…
In this paper we give an elementary treatment of the dynamics of skew tent maps. We divide the two-parameter space into six regions. Two of these regions are further subdivided into infinitely many regions. All of the regions are given…
Graph neural networks (GNNs) have achieved remarkable success in various domains, yet they often struggle with domain adaptation due to significant structural distribution shifts and insufficient exploration of transferable patterns. One of…
Temporal graph networks (TGNs) have gained prominence as models for embedding dynamic interactions, but little is known about their theoretical underpinnings. We establish fundamental results about the representational power and limits of…
Dynamic graphs are formulated in continuous-time or discrete-time dynamic graphs. They differ in temporal granularity: Continuous-Time Dynamic Graphs (CTDGs) exhibit rapid, localized changes, while Discrete-Time Dynamic Graphs (DTDGs) show…
Time series of graphs are increasingly prevalent in modern data and pose unique challenges to visual exploration and pattern extraction. This paper describes the development and application of matrix factorizations for exploration and…
We tackle the problem of visual localization under changing conditions, such as time of day, weather, and seasons. Recent learned local features based on deep neural networks have shown superior performance over classical hand-crafted local…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to practical…
With the growing amount of available temporal real-world network data, an important question is how to efficiently study these data. One can simply model a temporal network as either a single aggregate static network, or as a series of…