Related papers: Boundary value problems in consensus networks
When dealing with large graphs, such as those that arise in the context of online social networks, a subset of nodes may be labeled. These labels can indicate demographic values, interest, beliefs or other characteristics of the nodes…
Average consensus algorithms compute the global average of sensor data in a distributed fashion using local sensor nodes. Simple execution, decentralized philosophy make these algorithms suitable for WSN scenarios. Most of the researchers…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
Average consensus algorithms can be implemented over wireless sensor networks (WSN), where global statistics can be computed using communications among sensor nodes locally. Simple execution, robustness to global topology changes due to…
We consider the convergence time for solving the binary consensus problem using the interval consensus algorithm proposed by B\' en\' ezit, Thiran and Vetterli (2009). In the binary consensus problem, each node initially holds one of two…
Disagreements are common in online discussions. Disagreement may foster collaboration and improve the quality of a discussion under some conditions. Although there exist methods for recognizing disagreement, a deeper understanding of…
Comparing weighted networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges of that network. This problem arises in the analysis of both weighted and unweighted…
How hard is it to achieve consensus in a social network under uncertainty? In this paper we model this problem as a social graph of agents where each vertex is initially colored red or blue. The goal of the agents is to achieve consensus,…
Graph Convolutional Networks (GCNs) are one of the most popular architectures that are used to solve classification problems accompanied by graphical information. We present a rigorous theoretical understanding of the effects of graph…
We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered…
Theoretical computer science plays an important role in the understanding of social networks and their properties. We can model information rippling throughout social networks, or the opinions of social media users for example, using graph…
The aim of this paper is to analyze a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks formed by agents with first-order dynamics. In particular, in the analyzed class a single evaluation of a…
In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to…
We investigate the performance of linear consensus algorithms subject to a scaling of the underlying network size. Specifically, we model networked systems with $n^{\text{th}}$ order integrator dynamics over families of undirected, weighted…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
Social norms can facilitate societal coexistence in groups by providing an implicitly shared set of expectations and behavioral guidelines. However, different social groups can hold different norms, and lacking an overarching normative…
We describe a protocol for the average consensus problem on any fixed undirected graph whose convergence time scales linearly in the total number nodes $n$. The protocol is completely distributed, with the exception of requiring all nodes…
Networks created from real-world data contain some inaccuracies or noise, manifested as small changes in the network structure. An important question is whether these small changes can significantly affect the analysis results. In this…
In this paper, we study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed…
Graph neural networks (GNNs) learn node representations by passing and aggregating messages between neighboring nodes. GNNs have been applied successfully in several application domains and achieved promising performance. However, GNNs…