The Importance of Network Topology in Local Contribution Games

We consider a model of content contribution in peer-to-peer networks with linear quadratic payoffs and very general interaction patterns. We find that Nash equilibria of this game always exist; moreover, they are computable by solving a linear complementarity problem. The equilibrium is unique when goods are strategic complements or weak substitutes and contributions are proportional to a network centrality measure called the Bonacich index. In the case of public goods, the equilibrium is non-unique and characterized by k-order maximal independent sets. The structure of optimal networks is always star-like when the game exhibits strict or weak complements. Under public good scenarios, while star-like networks remain optimal in the best case, they also yield the worst-performing equilibria. We also discuss a network-based policy for improving the equilibrium performance of networks by the exclusion of a single player.Engineering and Applied Science

Connectivity, Coverage and Placement in Wireless Sensor Networks

Wireless communication between sensors allows the formation of flexible sensor networks, which can be deployed rapidly over wide or inaccessible areas. However, the need to gather data from all sensors in the network imposes constraints on the distances between sensors. This survey describes the state of the art in techniques for determining the minimum density and optimal locations of relay nodes and ordinary sensors to ensure connectivity, subject to various degrees of uncertainty in the locations of the nodes

An Inferential Framework for Network Hypothesis Tests: With Applications to Biological Networks

The analysis of weighted co-expression gene sets is gaining momentum in systems biology. In addition to substantial research directed toward inferring co-expression networks on the basis of microarray/high-throughput sequencing data, inferential methods are being developed to compare gene networks across one or more phenotypes. Common gene set hypothesis testing procedures are mostly confined to comparing average gene/node transcription levels between one or more groups and make limited use of additional network features, e.g., edges induced by significant partial correlations. Ignoring the gene set architecture disregards relevant network topological comparisons and can result in familiar

Statistical inference for some choice models

This thesis comprises two chapters that study the statistical inference problems for two types of choice models, namely, the discrete voter model and the Bradley-Terry models, respectively. In Chapter 1, we consider a discrete-time voter model process on a set of nodes, each being in one of two states, either 0 or 1. In each time step, each node adopts the state of a randomly sampled neighbour according to sampling probabilities, referred to as node interaction parameters. We study the maximum likelihood estimation of the node interaction parameters from observed node states for a given number of realizations of the voter model process. We present parameter estimation error bounds by interpreting the observation data as being generated according to an extended voter process that consists of cycles, each corresponding to a realization of the voter model process until absorption to a consensus state. We present new bounds for all moments and a probability tail bound for consensus time. We also present a sampling complexity lower bound for parameter estimation within a prescribed error tolerance for the class of locally stable estimators. In Chapter 2, we study the popular methods for inference of the Bradley-Terry model parameters, namely the gradient descent and MM algorithm, for maximum likelihood estimation and maximum a posteriori probability estimation. This class of models includes the Bradley-Terry model of paired comparisons, the Rao-Kupper model of paired comparisons allowing for tie outcomes, the Luce choice model, and the Plackett-Luce ranking model. We propose a simple modification of the classical gradient descent and MM algorithm with a parameter rescaling performed at each iteration step that avoids the observed slow convergence issue that we found in our previous work (Vojnovic et al. [2020]). We study the convergence rates of accelerated gradient descent and MM Algorithms for Bradley-Terry models. We also produce some experimental results using synthetic and real-world data to show that significant efficiency gains can be obtained by our new proposed method