In this paper, we are interested in modeling diffusion of innovations on social networks. We focus on a scenario where innovation emerges at a small number of nodes in the society, and each individual needs certain portion of his neighbors (thresholds) to adopt the innovation before he does so. We analyze the dynamics of the diffusion process under deterministic topologies and threshold values. We show that the diffusion process depends on both the topology and threshold values through so called coherent sets. We investigate several interesting topologies, and utilize coherent set argument to determine the behavior of the process on these topologies.

We consider the problem of coordinating a group of mobile nodes communicating through a wireless medium. The objective of the network is the alignment of all the nodes towards a common direction through local interactions, without the need for global knowledge such as the network topology or the maximum degree of the network, or even local parameters, such as the number of neighbors. The key feature of our algorithm is that each node state update is done through voting, where the probability of each vote is biased by the state of the node neighbors. We propose two possible physical implementations for our algorithm. The first is based on the explicit exchange of packetized messages, while the second is a cross-layer approach. Our analysis unveils key convergence properties of this simple class of alignment algorithms, via analytical and simulated results.

Given a network of N nodes with the i-th sensor's observation xiisin RM, the matrix containing all Euclidean distances among measurements ||xi- xj|| foralli, j isin {1,..., N} is a useful description of the data. While reconstructing a distance matrix has wide range of applications, we are particularly interested in the manifold reconstruction and its dimensionality reduction for data fusion and query. To make this map available to the all of the nodes in the network, we propose a fully decentralized consensus gossiping algorithm which is based on local neighbor communications, and does not require the existence of a central entity. The main advantage of our solution is that it is insensitive to changes in the network topology and it is fully decentralized. We describe the proposed algorithm in detail, study its complexity in terms of the number of inter-node radio transmissions and showcase its performance numerically.

Average consensus algorithms are gossiping protocols for averaging original sensor measurements via near neighbor communications. In this paper, we consider the average consensus algorithm under communication rate constraints. Without any communication rate restrictions, the algorithm ideally allows every node state to converge to the initial average in the limit. Noting that brute force quantization does not guarantee convergence due to error propagation effects, in our recent work we proposed two source coding methods which use side information (predictive coding and Wyner-Ziv coding) to achieve convergence with vanishing quantization rates in the case of block coding. In this work, we focus on a simplified predictive coding scheme with variable quantization rates over the iterations and on a communication network with regular topology. We characterize the asymptotic rate which allows to achieve a bounded convergence in terms of the initial conditions (i. e, the rate at the first iteration, and the initial state correlation), and the connectivity of the network. Moreover, we study the optimal rate allocation among the average consensus iterations subject to the constraints that the total number of quantization bits is fixed.

Motivated by applications to wireless sensor, peer-to-peer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and for computing in an arbitrarily connected network of nodes. Specifically, we propose a broadcasting-based gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcast gossip algorithms almost surely converge to a consensus. In addition, the random consensus value is, in expectation, equal to the desired value, i.e., the average of initial node measurements. However, the broadcast gossip algorithms do not converge to the initial average in absolute sense because of the fact that the sum is not preserved at every iteration. We provide theoretical results on the mean square error performance of the broadcast gossip algorithms. The results indicate that the mean square error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithms required to achieve a given distance to consensus through numerical simulations.

In this paper we consider the problem of transmitting quantized data while performing an average consensus algorithm. Average consensus algorithms are protocols to compute the average value of all sensor measurements via near neighbors communications. The main motivation for our work is the observation that consensus algorithms offer the perfect example of network communications where there is an increasing correlation between the data exchanged, as the system updates its computations. Henceforth, it is possible to utilize previously exchanged data and current side information to reduce significantly the demands of quantization bit rate for a certain precision. We analyze the case of a network with a topology built as that of a random geometric graph and with links that are assumed to be reliable at a constant bit rate. Numerically we show that in consensus algorithms, increasing number of iterations does not have the effect of increasing the error variance. Thus, we conclude that noisy recursions lead to a consensus if the data correlation is exploited in the messages source encoders and decoders. We briefly state the theoretical results which are parallel to our numerical experiments.