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TUTORIALS : NOVEMBER 29, 2016
ERNESTO ESTRADA: Consensus dynamics on networks. Theory and applications
Consensus is well documented across the social sciences, with examples ranging from behavioral flocking in popular cultural styles, emotional contagion, collective decision making, pedestrians’ walking behavior, and others. We can model consensus in a social group by encoding the state of each individual at a given time in a vector. The group reaches consensus at when the difference in the “opinions” for every pair of individuals is asymptotically zero, and the collective dynamics of the system is modeled by a diffusion equation dominated by the graph Laplacian. Decisions in groups trying to reach consensus are frequently influenced by a small proportion of the group who guides or dictates the behavior of the entire network. In this situation a group of leaders indicates and/or initiates the route to the consensus, and the rest of the group readily follows their attitudes. The study of leadership in social groups has always intrigued researchers in the social and behavioral sciences. Specifically, the way in which leaders emerge in social groups is not well understood. Leaders may emerge either randomly in response to particular historical circumstances or from the individual having the most prominent position (centrality) in the social network at any time. In this tutorial I will introduce the theoretical model of consensus in a network, for the general case of undirected as well as directed ones. First, I will introduce the mathematical concepts of the model, and show when in every case there is a consensus in the network. I will also introduce some properties of the Laplacian matrix for networks that will help to understand the main results of the model. Then, I will introduce a controllability problem and its solution in networks consisting of leaders and followers. Following this initial part I will how to use Matlab to model a consensus process in a given network (codes will be provided to participants). At this point I will motive the necessity of considering the indirect influence of peers apart from the direct peers pressure. In mathematical terms I will make a generalization of the Laplacian matrix on graphs to consider the k-path Laplacians and their transform. Using this transformed k-path Laplacians I will show how to study a few interesting topics on networks, such as the controllability of networks, the selection of leaders, the diffusion of innovations under direct+indirect peers pressure. Finally, I will prove and illustrate how the consensus and diffusion of innovations can be superdiffusive or ballistic in complex networks under the effect of direct and indirect peers pressure. Some examples, such as diffusion of methods among high schools or the adoption of a biotechnological product among farmers will be used in the tutorial.
Professor Estrada has an internationally leading reputation for shaping and developing the study of complex networks. His expertise ranges in the areas of network structure, algebraic network theory, dynamical systems on networks and the study of random models of networks. He has a distinguished track record of high-quality publications, which has attracted more than 8, 500 citations. His h-index (number of papers with at least h citations) is 53. His publications are in the areas of network theory and its applications to social, ecological, engineering, physical, chemical and biological real-world problems. Professor Estrada has published two text books on network sciences both published by Oxford University Press in 2011 and 2015, respectively. He has demonstrated a continuous international leadership in his field where he has been invited and plenary speaker at the major conferences in network sciences and applied mathematics. His research interests include the use of matrix functions; random geometric networks; generalised Laplacian operators for networks; generalised diffusion models for networks; study of indirect peer pressure over consensus dynamics on networks; applications of network sciences to oil and gas exploration; spatial efficiency of networks; Euclidean geometrical embedding of networks, among many others.
BRUNO GONCALVES: A practical introduction to Machine Learning (with Python)
The data deluge we currently witnessing presents both opportunities and challenges. Never before have so many aspects of our world been so thoroughly quantified as now and never before has data been so plentiful. On the other hand, the complexity of the analyses required to extract useful information from these piles of data is also rapidly increasing rendering more traditional and simpler approaches simply unfeasible or unable to provide new insights.
In this tutorial we provide a practical introduction to some of the most important algorithms of machine learning that are relevant to the field of Complex Networks in general, with a particular emphasis on the analysis and modeling of empirical data. The goal is to provide the fundamental concepts necessary to make sense of the more sophisticated data analysis approaches that are currently appearing in the literature and to provide a field guide to the advantages an disadvantages of each algorithm.
In particular, we will cover unsupervised learning algorithms such as K-means, Expectation-Maximization, and supervised ones like Support Vector Machines, Neural Networks and Deep Learning. Participants are expected to have a basic understanding of calculus and linear algebra as well as working proficiency with the Python programming language.
Bruno Gonçalves is a Data Science fellow at NYU's Center for Data Science while on leave from a tenured faculty position at Aix-Marseille Université. He has a strong expertise in using large scale datasets for the analysis of human behavior. After completing his joint PhD in Physics, MSc in C.S. at Emory University in Atlanta, GA in 2008 he joined the Center for Complex Networks and Systems Research at Indiana University as a Research Associate. From September 2011 until August 2012 he was an Associate Research Scientist at the Laboratory for the Modeling of Biological and Technical Systems at Northeastern University. Since 2008 he has been pursuing the use of Data Science and Machine Learning to study human behavior. By processing and analyzing large datasets from Twitter, Wikipedia, web access logs, and Yahoo! Meme he studied how we can observe both large scale and individual human behavior in an obtrusive and widespread manner. The main applications have been to the study of Computational Linguistics, Information Diffusion, Behavioral Change and Epidemic Spreading. He is the author of 60+ publications with over 3800+ Google Scholar citations and an h-index of 26. In 2015 he was awarded the Complex Systems Society's 2015 Junior Scientific Award for "outstanding contributions in Complex Systems Science" and he is the editor of the book Social Phenomena: From Data Analysis to Models (Springer, 2015).