We investigate the condition on transmission radius needed to achieve connectivity in duty-cycled wireless sensor networks (briefly, DC-WSN). First, we settle a conjecture of Das et. al. (2012) and prove that the connectivity condition on Random Geom
etric Graphs (RGG), given by Gupta and Kumar (1989), can be used to derive a weak sufficient condition to achieve connectivity in DC-WSN. To find a stronger result, we define a new vertex-based random connection model which is of independent interest. Following a proof technique of Penrose (1991) we prove that when the density of the nodes approaches infinity then a finite component of size greater than 1 exists with probability 0 in this model. We use this result to obtain an optimal condition on node transmission radius which is both necessary and sufficient to achieve connectivity and is hence optimal. The optimality of such a radius is also tested via simulation for two specific duty-cycle schemes, called the contiguous and the random selection duty-cycle scheme. Finally, we design a minimum-radius duty-cycling scheme that achieves connectivity with a transmission radius arbitrarily close to the one required in Random Geometric Graphs. The overhead in this case is that we have to spend some time computing the schedule.
We propose a stochastic model for the diffusion of topics entering a social network modeled by a Watts-Strogatz graph. Our model sets into play an implicit competition between these topics as they vie for the attention of users in the network. The dy
namics of our model are based on notions taken from real-world OSNs like Twitter where users either adopt an exogenous topic or copy topics from their neighbors leading to endogenous propagation. When instantiated correctly, the model achieves a viral regime where a few topics garner unusually good response from the network, closely mimicking the behavior of real-world OSNs. Our main contribution is our description of how clusters of proximate users that have spoken on the topic merge to form a large giant component making a topic go viral. This demonstrates that it is not weak ties but actually strong ties that play a major part in virality. We further validate our model and our hypotheses about its behavior by comparing our simulation results with the results of a measurement study conducted on real data taken from Twitter.
We present the first comprehensive characterization of the diffusion of ideas on Twitter, studying more than 4000 topics that include both popular and less popular topics. On a data set containing approximately 10 million users and a comprehensive sc
raping of all the tweets posted by these users between June 2009 and August 2009 (approximately 200 million tweets), we perform a rigorous temporal and spatial analysis, investigating the time-evolving properties of the subgraphs formed by the users discussing each topic. We focus on two different notions of the spatial: the network topology formed by follower-following links on Twitter, and the geospatial location of the users. We investigate the effect of initiators on the popularity of topics and find that users with a high number of followers have a strong impact on popularity. We deduce that topics become popular when disjoint clusters of users discussing them begin to merge and form one giant component that grows to cover a significant fraction of the network. Our geospatial analysis shows that highly popular topics are those that cross regional boundaries aggressively.
We argue that relationships between Web pages are functions of the users intent. We identify a class of Web tasks - information-gathering - that can be facilitated by a search engine that provides links to pages which are related to the page the user
is currently viewing. We define three kinds of intentional relationships that correspond to whether the user is a) seeking sources of information, b) reading pages which provide information, or c) surfing through pages as part of an extended information-gathering process. We show that these three relationships can be productively mined using a combination of textual and link information and provide three scoring mechanisms that correspond to them: {em SeekRel}, {em FactRel} and {em SurfRel}. These scoring mechanisms incorporate both textual and link information. We build a set of capacitated subnetworks - each corresponding to a particular keyword - that mirror the interconnection structure of the World Wide Web. The scores are computed by computing flows on these subnetworks. The capacities of the links are derived from the {em hub} and {em authority} values of the nodes they connect, following the work of Kleinberg (1998) on assigning authority to pages in hyperlinked environments. We evaluated our scoring mechanism by running experiments on four data sets taken from the Web. We present user evaluations of the relevance of the top results returned by our scoring mechanisms and compare those to the top results returned by Googles Similar Pages feature, and the {em Companion} algorithm proposed by Dean and Henzinger (1999).
