Networks

Hawkes processes has been a popular point process model for capturing mutual excitation of discrete events. In the network setting, this can capture the mutual influence between nodes, which has a wide range of applications in neural science, social networks, and crime data analysis. In this talk, I will present a statistical change-point detection framework to detect in real-time, a change in the influence using streaming discrete events.

This work introduces Graphon Mean Field Game (GMFG) theory for the analysis of

The Vector AutoRegressive (VAR) Model is a popular model for the analysis of a multivariate time series. It allows to investigate the impact changes in one time series have on other ones. A drawback of the VAR is the risk of overparametrization because the number of parameters increases quadratically with the number of included time series. This undermines the ability to identify important relationships in the data and to make accurate forecasts. In high dimensions, we therefore use sparse estimation.

Energy networks are becoming increasingly decentralized and exhibit new forms of coupling. For instance, during the polar vortex of 2014, sustained low temperatures in the Midwest region of the U.S. resulted in unusually high gas demands from buildings in urban areas. This led to shortages of natural gas that propagated to California, Massachusetts, and Texas. The gas shortages forced power plant shutdowns totaling 35 GW. At a value of lost load of 5,000 USD/MWh, such shortages represent economic losses of 175 million USD per hour.

A large variety of complex systems, from the brain to the weather networks and complex infrastructures, are formed by several networks that coexist, interact and coevolve forming a network of networks. Modeling such multilayer structures and characterizing the rich interplay between their structure and their dynamical behavior is crucial in order to understand and predict complex phenomena. In this talk I will present recent works on statistical mechanics of multiplex networks. Multiplex networks are formed by N nodes linked in different layers by different networks.

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Systems as diverse as the world wide web, Internet or the cell are described by highly interconnected networks with amazingly complex structure. Recent studies indicate that the evolution of these complex networks is governed by simple but generic laws, resulting in apparently universal architectural features. I will discuss this amazing order characterizing our interconnected world, and its implications to how we perceive the impact on communications and medicine.

Sensor networks are poised to impact society in fundamental ways analogous to the impact of the networked personal computers. The rapid development of small-scale sensors coupled with wireless ad hoc networking capability foreshadows a day when our physical surroundings will wake up with sensory data, assuming it does not drown in the data first. In this lecture, Professor Ghrist will describe a recent calculus for sensor network data, whose origins lie in the century-old theory of algebraic topology.

he reverse engineering of biological networks is an important and
interesting problem. Two examples of such networks are gene
regulatory networks, and the relationship of voxels in the brain. We
describe a method for determining possible wiring diagrams for such
networks. The method is based on computational algebra, and a key
part of the method uses computations involving monomial ideals in a
polynomial ring. To illustrate the algorithms, we apply the method
to data coming from fMRI scans of the brain.