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Heterogeneity in the degree distribution is known to suppress global synchronization in complex networks of symmetrically coupled oscillators. Scale-free networks display a great deal of heterogeneity, containing a few nodes, termed hubs,…
We study the small-world networks recently introduced by Watts and Strogatz [Nature {\bf 393}, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local…
Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the co-evolving network voter model of opinion formation, studied by Holme and Newman [1].…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number of state variables that can be communicated instantaneously. When the edge…
We consider a modification of the adaptive contact process which, interpreted in the context of opinion dynamics, breaks the symmetry of the coevolutionary voter model by assigning to each node type a different strategy to promote…
Stochastic gradient descent (SGD) with mini-batching is a standard tool in large-scale optimization, yet its theoretical properties under heavy-tailed gradient noise remain largely unexplored. In this paper we study SGD with increasing…
We focus on non-consensus opinion models in which above a certain threshold two opinions coexist in a stable relationship. We revisit and extend the non-consensus opinion (NCO) model introduced by Shao. We generalize the NCO model by adding…
In this paper, we formulate and investigate a generalized consensus algorithm which makes an attempt to unify distributed averaging and maximizing algorithms considered in the literature. Each node iteratively updates its state as a…
In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…
Using a steady state process of node duplication and deletion we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. This occurs even though there is no growth involved and inherent preferential…
We investigate different opinion formation models on adaptive network topologies. Depending on the dynamical process, rewiring can either (i) lead to the elimination of interactions between agents in different states, and accelerate the…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
In this paper, randomized gossip-type matrix-weighted consensus algorithms are proposed for both leaderless and leader-follower topologies. First, we introduce the notion of expected matrix-weighted network, which captures the…
In this thesis we study synchronization phenomena in natural and artificial coupled multi-component systems, applicable to the scalability of parallel discrete-event simulation for systems with asynchronous dynamics. We analyze the…
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
An analytical study of the behavior of the voter model on the small-world topology is performed. In order to solve the equations for the dynamics, we consider an annealed version of the Watts-Strogatz (WS) network, where long-range…
We study the outcomes of information aggregation in online social networks. Our main result is that networks with certain realistic structural properties avoid information cascades and enable a population to effectively aggregate…
We explore the synchronization behavior in interdependent systems, where the one-dimensional (1D) network (the intranetwork coupling strength $J_{\rm I}$) is ferromagnetically intercoupled (the strength $J$) to the Watts-Strogatz (WS)…
Complex networks are a successful framework to describe collective behaviour in many applications, but a notable gap remains in the current literature, that of proving asymptotic convergence in networks of piecewise-smooth systems. Indeed,…