Related papers: Gradient systems on coupled cell networks
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
A network of coupled dynamical systems is represented by a graph whose vertices represent individual cells and whose edges represent couplings between cells. Motivated by the impact of synchronization results of the Kuramoto networks, we…
Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…
In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…
Networks with a prescribed power-law scaling in the spectrum of the graph Laplacian can be generated by evolutionary optimization. The Laplacian spectrum encodes the dynamical behavior of many important processes. Here, the networks are…
A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
We consider weighted coupled cell networks, that is networks where the interactions between any two cells have an associated weight that is a real valued number. Weighted networks are ubiquitous in real-world applications. We consider a…
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…
Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
We present a framework for simulating signal propagation in geometric networks (i.e. networks that can be mapped to geometric graphs in some space) and for developing algorithms that estimate (i.e. map) the state and functional topology of…
We consider a class of linear differential operators acting on vector-valued function spaces with general coupled boundary conditions. Unlike in the more usual case of so-called quantum graphs, the boundary conditions can be nonlinear.…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. In particular, we are interested in…
Dynamical systems with a coupled cell network structure can display synchronous solutions, spectral degeneracies and anomalous bifurcation behavior. We explain these phenomena here for homogeneous networks, by showing that every homogeneous…
In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
Directly parameterizing and learning gradients of functions has widespread significance, with specific applications in inverse problems, generative modeling, and optimal transport. This paper introduces gradient networks (GradNets): novel…