09:30 to 10:30 Tom Britton (Stockholm University)A network epidemic model with preventive rewiring: comparative analysis of the initial phase Co-authors: Joan Saldana (Universitat de Girona), David Juher (Universitat de Girona)  This talk is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate ω (and reconnect to non-infectious individuals with probability α or else simply drop the edge if α=0), so-called preventive rewiring. The models are denoted SIR-ω and SEIR-ω, and we focus attention on the early stages of an outbreak, where we derive expression for the basic reproduction number R0 and the expected degree of the infectious nodes E(DI) using two different approximation approaches. The first approach approximates the early spread of an epidemic by a branching process, whereas the second one uses pair approximation. The expressions are compared with the corresponding empirical means obtained from stochastic simulations of SIR-ω and SEIR-ω epidemics on Poisson and scale-free networks. To appear in Bull Math Biol. INI 1 10:30 to 11:15 Morning Coffee 11:15 to 12:00 Maria Deijfen Birds of a feather or opposites attract - effects in network modelling We study properties of some standard network models when the population is split into two types and the connection pattern between the types is varied. The studied models are generalizations of the Erdös-Renyi graph, the configuration model and a preferential attachment graph. For the Erdös-Renyi graph and the configuration model, the focus is on the component structure. We derive expressions for the critical parameter, indicating when there is a giant component in the graph, and study the size of the largest component by aid of simulations. For the preferential attachment model, we analyze the degree distributions of the two types and derive explicit expressions for the degree exponents. Joint work with Robert Fitzner (Eindhoven University of Technology). INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:45 to 14:45 Susan Holmes (Stanford University)Study of the dynamics of bacterial communities in the Human Microbiome Co-authors: Kris Sankaran (Stanford), Julia Fukuyama (Stanford), Lan Nguyen (Stanford), Diana Proctor (Stanford), David Relman (Stanford), Sergio Bacallado (Cambridge), Boyu Ren (Stanford), Pratheepa Jeganathan (Stanford)  The human microbiome is a complex assembly of bacteria that are sensitive to many perturbations. In several longitudinal analyses we study perturbations of bacterial community networks over time. For this, we have developed specific tools for modeling the vaginal, intestinal and oral microbiomes under these different perturbations (pregnancy, hypo-salivation inducing medications and antibiotics are some examples).  A suite of statistical tools written in R based on a Bioconductor package (phyloseq) allows for easy normalization, visualization and statistical testing of the longitudinal multi-table data composed of 16sRNA reads combined with clinical data, transcriptomic and metabolomic profiles. Challenges we have had to address include information leaks, the heterogeneity of the data, multiplicity of choices during the analyses and validation of results.  Each different body site requires a different modeling strategy as some sites form tight communities easily modeled with Stochastic Block Models whereas others show more diverse assemblies that require complex latent variable models. Related Links http://statweb.stanford.edu/~susan/ - Website. INI 1 14:45 to 15:30 Danielle Bassett (University of Pennsylvania)Dynamic networks in the human brain Each area of the human brain plays a unique role in processing information gleaned from the external world and in driving our responses to that external world via behavior. However, the brain is far from a set of disconnected building blocks. Instead, parts of the brain communicate with one another in complex spatiotemporal patterns that enable human behavior. Understanding this spatio-temporal complexity requires a paradigmatic shift in our conceptual approaches, empirical thrusts, and quantitative methods. In this talk, I will describe the recent use of tools from network science to understand the structure and function of the human brain. With these novel approaches, we can begin to characterize the connectome’’, a model representation of neurobiological data that encapsulates both constituent elements of the brain (network nodes) and their interactions with one another (network edges). In a critical innovation, we imbue network edges with temporal dependence to capture the dynamics of the ever-reconfiguring brain communication patterns that support cognition. I will recount the utility of dynamic network approaches in not only understanding, but also predicting individual differences in adaptive functions such as learning, and in delineating healthy versus diseased brain communication dynamics. An emerging frontier, dynamic network neuroscience provides a powerful new conceptual and mathematical framework with which to understand adaptive human capabilities because it embraces the inherently evolving, interconnected nature of neurophysiological phenomena underlying human thought. INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 16:45 Stéphane Robin (INRA - Institut National de la Recherche Agronomique)Detecting change-points in the structure of a network: Exact Bayesian inference Joint work with Loïc Schwaller We consider the problem of change-point detection in multivariate time-series, typically the expression of a set of genes, or the activity of a set of brain regions over time. We adopt the framework of graphical models to described the dependency between the series. We are interested in the situation where the graphical model is affected by abrupt changes throughout time. In the above examples, such changes correspond to gene or brain region rewiring. We demonstrate that it is possible to perform exact Bayesian inference whenever one considers a simple class of undirected graphs called spanning trees as possible structures. We are then able to integrate on both the graph and segmentation spaces at the same time by combining classical dynamic programming with algebraic results pertaining to spanning trees. In particular, we show that quantities such as posterior distributions for change-points or posterior edge probabilities over time can efficiently be obtained. We illustrate our results on both synthetic and experimental data arising from molecular biology and neuroscience. INI 1 16:45 to 17:30 Harry Crane (Rutgers, The State University of New Jersey)Markov process models for time-varying networks Many models for dynamic networks, such as the preferential attachment model, describe evolution by sequential addition of vertices and/or edges. Such models are not suited to networks whose connectivity varies over time, as in social relationships and other kinds of temporally varying interactions. For modeling in this latter setting, I develop the general theory of exchangeable Markov processes for time-varying networks and discuss relevant consequences. INI 1