We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

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Modern Applied Statistics With S

Even though human movement and mobility patterns have a high degree of freedom and variation, they also exhibit structural patterns due to geographic and social constraints. Using cell phone location data, as well as data from two online location-based social networks, we aim to understand what basic laws govern human motion and dynamics. We find that humans experience a combination of periodic movement that is geographically limited and seemingly random jumps correlated with their social networks. Short-ranged travel is periodic both spatially and temporally and not effected by the social network structure, while long-distance travel is more influenced by social network ties. We show that social relationships can explain about 10% to 30% of all human movement, while periodic behavior explains 50% to 70%. Based on our findings, we develop a model of human mobility that combines periodic short range movements with travel due to the social network structure. We show that our model reliably predicts the locations and dynamics of future human movement and gives an order of magnitude better performance than present models of human mobility.

/pdf/friendship-and-mobility-user-movement-in-location-based-2u0rrxuc9l.pdf

Friendship and mobility: user movement in location-based social networks

Amazon’s Mechanical Turk is an online labor market where requesters post jobs and workers choose which jobs to do for pay. The central purpose of this paper is to demonstrate how to use this website for conducting behavioral research and lower the barrier to entry for researchers who could beneﬁt from this platform. We describe general techniques that apply to a variety of types of research and experiments across disciplines. We begin by discussing some of the advantages of doing experiments on Mechanical Turk, such as easy access to a large, stable, and diverse subject pool, the low cost of doing experiments and faster iteration between developing theory and executing experiments. We will discuss how the behavior of workers compares to experts and to laboratory subjects. Then, we illustrate the mechanics of putting a task on Mechanical Turk including recruiting subjects, executing the task, and reviewing the work that was submitted. We also provide solutions to common problems that a researcher might face when executing their research on this platform including techniques for conducting synchronous experiments, methods to ensure high quality work, how to keep data private, and how to maintain code security.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1798687_code1554670.pdf?abstractid=1691163&mirid=1&type=2

Conducting Behavioral Research on Amazon's Mechanical Turk

Amazon’s Mechanical Turk is an online labor market where requesters post jobs and workers choose which jobs to do for pay. The central purpose of this article is to demonstrate how to use this Web site for conducting behavioral research and to lower the barrier to entry for researchers who could benefit from this platform. We describe general techniques that apply to a variety of types of research and experiments across disciplines. We begin by discussing some of the advantages of doing experiments on Mechanical Turk, such as easy access to a large, stable, and diverse subject pool, the low cost of doing experiments, and faster iteration between developing theory and executing experiments. While other methods of conducting behavioral research may be comparable to or even better than Mechanical Turk on one or more of the axes outlined above, we will show that when taken as a whole Mechanical Turk can be a useful tool for many researchers. We will discuss how the behavior of workers compares with that of experts and laboratory subjects. Then we will illustrate the mechanics of putting a task on Mechanical Turk, including recruiting subjects, executing the task, and reviewing the work that was submitted. We also provide solutions to common problems that a researcher might face when executing their research on this platform, including techniques for conducting synchronous experiments, methods for ensuring high-quality work, how to keep data private, and how to maintain code security.

/pdf/conducting-behavioral-research-on-amazon-s-mechanical-turk-1xjwv92e5j.pdf

Conducting behavioral research on Amazon's Mechanical Turk.

A fundamental open question in the analysis of social networks is to understand the interplay between similarity and social ties. People are similar to their neighbors in a social network for two distinct reasons: first, they grow to resemble their current friends due to social influence; and second, they tend to form new links to others who are already like them, a process often termed selection by sociologists. While both factors are present in everyday social processes, they are in tension: social influence can push systems toward uniformity of behavior, while selection can lead to fragmentation. As such, it is important to understand the relative effects of these forces, and this has been a challenge due to the difficulty of isolating and quantifying them in real settings.We develop techniques for identifying and modeling the interactions between social influence and selection, using data from online communities where both social interaction and changes in behavior over time can be measured. We find clear feedback effects between the two factors, with rising similarity between two individuals serving, in aggregate, as an indicator of future interaction -- but with similarity then continuing to increase steadily, although at a slower rate, for long periods after initial interactions. We also consider the relative value of similarity and social influence in modeling future behavior. For instance, to predict the activities that an individual is likely to do next, is it more useful to know the current activities of their friends, or of the people most similar to them?

/pdf/feedback-effects-between-similarity-and-social-influence-in-4ud2r9fgi7.pdf

Feedback effects between similarity and social influence in online communities

In recent years the MapReduce framework has emerged as one of the most widely used parallel computing platforms for processing data on terabyte and petabyte scales. Used daily at companies such as Yahoo!, Google, Amazon, and Facebook, and adopted more recently by several universities, it allows for easy parallelization of data intensive computations over many machines. One key feature of MapReduce that differentiates it from previous models of parallel computation is that it interleaves sequential and parallel computation. We propose a model of efficient computation using the MapReduce paradigm. Since MapReduce is designed for computations over massive data sets, our model limits the number of machines and the memory per machine to be substantially sublinear in the size of the input. On the other hand, we place very loose restrictions on the computational power of of any individual machine---our model allows each machine to perform sequential computations in time polynomial in the size of the original input.We compare MapReduce to the PRAM model of computation. We prove a simulation lemma showing that a large class of PRAM algorithms can be efficiently simulated via MapReduce. The strength of MapReduce, however, lies in the fact that it uses both sequential and parallel computation. We demonstrate how algorithms can take advantage of this fact to compute an MST of a dense graph in only two rounds, as opposed to Ω(log(n)) rounds needed in the standard PRAM model. We show how to evaluate a wide class of functions using the MapReduce framework. We conclude by applying this result to show how to compute some basic algorithmic problems such as undirected s-t connectivity in the MapReduce framework.

https://epubs.siam.org/doi/pdf/10.1137/1.9781611973075.76

A model of computation for MapReduce

We investigate the extent to which social ties between people can be inferred from co-occurrence in time and space: Given that two people have been in approximately the same geographic locale at approximately the same time, on multiple occasions, how likely are they to know each other? Furthermore, how does this likelihood depend on the spatial and temporal proximity of the co-occurrences? Such issues arise in data originating in both online and offline domains as well as settings that capture interfaces between online and offline behavior. Here we develop a framework for quantifying the answers to such questions, and we apply this framework to publicly available data from a social media site, finding that even a very small number of co-occurrences can result in a high empirical likelihood of a social tie. We then present probabilistic models showing how such large probabilities can arise from a natural model of proximity and co-occurrence in the presence of social ties. In addition to providing a method for establishing some of the first quantifiable estimates of these measures, our findings have potential privacy implications, particularly for the ways in which social structures can be inferred from public online records that capture individuals’ physical locations over time.

https://www.pnas.org/content/pnas/107/52/22436.full.pdf

Siddharth Suri

Papers

Conducting Behavioral Research on Amazon's Mechanical Turk

Conducting behavioral research on Amazon's Mechanical Turk.

Feedback effects between similarity and social influence in online communities

A model of computation for MapReduce

Inferring social ties from geographic coincidences