Related papers: Concentration and mean field approximation results…
The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
Markov Chain Monte Carlo (MCMC) has been the de facto technique for sampling and inference of large graphs such as online social networks. At the heart of MCMC lies the ability to construct an ergodic Markov chain that attains any given…
We investigate both analytically and numerically the ensemble of minimum-weight loops and paths in the negative-weight percolation model on random graphs with fixed connectivity and bimodal weight distribution. This allows us to study the…
Distributed quantized weight-balancing and average consensus over fixed digraphs are considered. A digraph with non-negative weights associated to its edges is weight-balanced if, for each node, the sum of the weights of its out-going edges…
Via operator theoretic methods, we formalize the concentration phenomenon for a given observable `$r$' of a discrete time Markov chain with `$\mu_{\pi}$' as invariant ergodic measure, possibly having support on an unbounded state space. The…
We analyze a class of distributed quantized consensus algorithms for arbitrary static networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network,…
Concentration inequalities for subgraph counts in random geometric graphs built over Poisson point processes are proved. The estimates give upper bounds for the probabilities $\mathbb{P}(N\geq M +r)$ and $\mathbb{P}(N\leq M - r)$ where $M$…
Motivated by applications of distributed linear estimation, distributed control and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically,…
Concentration inequalities are widely used for analyzing machine learning algorithms. However, current concentration inequalities cannot be applied to some of the most popular deep neural networks, notably in natural language processing.…
We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged.…
We propose a notion of graph convergence that interpolates between the Benjamini--Schramm convergence of bounded degree graphs and the dense graph convergence developed by L\'aszl\'o Lov\'asz and his coauthors. We prove that spectra of…
We study a non-exchangeable multi-agent system and rigorously derive a strong form of the mean-field limit. The convergence of the connection weights and the initial data implies convergence of large-scale dynamics toward a deterministic…
We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…
We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…
We consider the problem of inferring a matching hidden in a weighted random $k$-hypergraph. We assume that the hyperedges' weights are random and distributed according to two different densities conditioning on the fact that they belong to…
This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM). The generalized concentrability condition establishes a framework that interpolates…
The mean-field limit of interacting diffusions without exchangeability, caused by weighted interactions and non-i.i.d. initial values, are investigated. The weights could be signed and unbounded. The result applies to a large class of…