## Workshop 3: Modeling and Analysis of Dynamic Social Networks

### Organizers

Ian Hamilton
EEOB/Mathematics, The Ohio State University
Keith Warren
Social Work, The Ohio State University

This event will be hosted in the MBI Auditorium, Jennings Hall 355

In recent years, the focus of social network theory in behavioral ecology and the social sciences has shifted to understanding the dynamics of social networks. Data analytical methods such as relational state models and others have been used to address patterns of network change over time as agents gain or lose ties and how network structure coevolves with the attributes of agents in real-world networks. Network models are beginning to incorporate data at multiple scales and multiple types of interactions.  New technologies have facilitated collection of large quantities of data in many systems allowing increasingly sophisticated analyses of changes in social structure over time.

Mathematical and empirical challenges arise because social networks are complex systems that emerge from, as well as influence, the interacting decisions of multiple, autonomous, objective-maximizing or goal-oriented agents.  Agents often have multiple types of relations, resulting in multilayer (multiplex) networks.  Current techniques for data analysis of dynamic networks are best suited to address enduring relationships, rather than momentary interactions, but many social interactions are better described by the latter.  Consequences of agent decisions to pursue interactions can depend on attributes at multiple levels, and decisions that maximize agent objectives may be in conflict with those of others or with beneficial outcomes for the network as a whole.  In humans and non-human animals, opportunities for interaction are constrained by factors such as location and mobility.  Social networks frequently involve a small number of agents, and stochastic processes are likely to be important influences on network dynamics.  Key emerging problems include how to incorporate multilayer and momentary data into network models, the roles of feedbacks between space use and network processes, how individual decisions interact with the evolution of network attributes, and the fitness or other consequences of such behaviors.

This workshop will consider these emerging problems with an interdisciplinary approach incorporating modeling and empirical work from the social sciences, behavioral biology, mathematics, and statistics. In addition, because many of the challenges inherent to the study of social network dynamics are not unique to such networks, this workshop aims to include perspectives from other areas of network research.

This MBI workshop is being co-sponsored by the National Institute of Statistical Sciences.

### Accepted Speakers

Benjamin Bolduc
Microbiology, The Ohio State University
Catherine Calder
Statistics, The Ohio State University
Benjamin Campbell
Political Science, The Ohio State University
Gerald Carter
Evolution, Ecology, and Organismal Biology, 300 Aronoff Lab
Skyler Cranmer
Political Science, The Ohio State University
Scott Duxbury
Sociology, The Ohio State University
Ian Hamilton
EEOB/Mathematics, The Ohio State University
Dana Haynie
Criminal Justice Research Center, The Ohio State University
Jennifer Hellmann
Animal Biology, University of Illinois at Urbana-Champaign
John Light
Mathematical Sociology, Oregon Research Institute
Facundo Memoli
math, The Ohio State University
Statistics, The Ohio State University
David Sivakoff
Statistics and Mathematics, The Ohio State University
Alexandria Volkening
Mathematical Biosciences Institute, The Ohio State University
Keith Warren
Social Work, The Ohio State University
Wednesday, November 7, 2018
Time Session
12:00 PM
01:00 PM

Lunch and Participant Collaboration

01:00 PM
01:30 PM

Introductory Remarks and Remarks by the Dean

01:30 PM
02:30 PM
Gerald Carter - Hypothesis-testing in animal social networks using null models

Dynamic networks allow researchers to study how social structure changes over time, which is at the center of many fundamental questions in biology. However, when data are limited or imprecise as in many field studies, there is a tradeoff between temporal resolution and estimating the network structure at each “snapshot” of time. This is important because in many animal studies the observed network is only a sample of the actual social structure at any given point in time. In this talk, I will review hypothesis-testing in animal social network analysis using null models based on permutations of the network nodes or the raw data (pre-network permutations). I will also discuss how resampling procedures can be used as power analyses using empirical examples of grooming in primates and food-sharing in vampire bats. I will then discuss some of the challenges for creating permutation-based null models for dynamic networks. Careful null models can control for nuisance factors that create social network structure as a mere byproduct of non-social spatial or temporal effects (such as individuals being “connected” due to simultaneous attraction to a particular place, rather than each other). Automated data collection allows for dynamic networks to be a practical tool in animal studies.

02:30 PM
03:30 PM
Benjamin Campbell - Detecting Heterogeneity and Inferring Latent Roles in Longitudinal Networks

Network analysis has typically examined the formation of whole networks while neglecting variation within or across networks. Actors within networks often adopt particular roles or have different incentives for tie formation. While cross-sectional approaches for inferring latent roles and detecting variation exist, there is a paucity of approaches for considering roles in longitudinal networks. This talk explores the conceptual dynamics of temporally observed roles while introducing a novel statistical tool, the ego-TERGM, capable of uncovering these latent dynamics. Estimated through an Expectation-Maximization algorithm, the ego-TERGM is quick and accurate in classifying roles within a broader temporal network. An application to the Kapferer strike network illustrates the model's utility.

03:30 PM
04:30 PM
David Sivakoff - Contact process with avoidance behavior

The (classical) contact process is a stochastic process on the vertices of a graph, which is a discrete, spatial model for the spread of a disease. The state of the contact process at time t is given by an infected subset of the vertices of the graph. At rate 1, each infected vertex becomes healthy, and therefore susceptible to reinfection. At rate lambda>0, each edge between an infected vertex and a healthy vertex transmits the infection, thus infecting the healthy vertex. The contact process has been thoroughly analyzed on the integer lattices and regular trees, where it is well-known to exhibit a phase transition: for large lambda, epidemics persist, while for smaller lambda, all vertices are eventually healthy. More recently, researchers have made progress in analyzing the behavior of the contact process on (finite) complex networks, where epidemics may persist for all lambda>0 on graphs with heavy-tailed' degree distributions. I will discuss recent progress on a version of the contact process in which the edges of the graph are also dynamic: at rate alpha, each edge from an infected vertex to a healthy vertex will deactivate; the edge will become active again when the infected vertex becomes healthy, and only active edges can transmit the infection. This emulates avoidance of infected individuals by healthy individuals. We demonstrate that the long-time qualitative behavior of this model may or may not differ from the classical contact process, depending on the underlying network topology. A technical obstacle is the lack of a certain type of monotonicity, which is present for the classical model. Based on joint work with Shirshendu Chatterjee and Matthew Wascher.

Thursday, November 8, 2018
Time Session
08:00 AM
09:00 AM

Breakfast and Daily Introduction

09:00 AM
10:00 AM
Skyler Cranmer - A Consistent Organizational Structure Across Multiple Functional Subnetworks of the Human Brain

A recurrent theme of both cognitive neuroscience and network neuroscience is that the brain has a consistent subnetwork structure that maps onto functional specialization for different cognitive tasks, such as vision, motor skills, and attention. Understanding how regions in these subnetworks relate is thus crucial to understanding the emergence of critical cognitive processes. However, the organizing principles that guide how regions within subnetworks communicate, and whether there is a common set of principles across subnetworks, remains unclear. This is partly due to available tools not being suited to precisely quantify the role that different organizational principles play in the organization of a subnetwork. Here, we apply the recently-developed correlation generalized exponential random graph model (cGERGM) to more completely quantify subnetwork structure. The cGERGM models a correlation network, such as those given in functional connectivity, as a function of activation motifs -- consistent patterns of coactivation (i.e., connectivity) between collections of nodes that describe how the regions within a network are organized (e.g., clustering) -- and anatomical properties -- relationships between the regions that are dictated by anatomy (e.g., Euclidean distance). Across nine functional subnetworks, we find remarkably consistent organizational properties guiding subnetwork architecture, suggesting a fundamental organizational basis for subnetwork communication. Specifically, all subnetworks displayed greater clustering than would be expected by chance, but lower preferential attachment (i.e., hub use), suggesting that human functional subnetworks follow a segregated highway structure rather than the small-world structure found in the whole-brain.

10:00 AM
11:00 AM
Kezia Manlove - Can a tripartite model help us understand temporal variation in social contact networks?

Understanding dynamics of social contact is a key precursor for modeling propagation of pathogens, genes, and information through societies. However, there is little consistency within the ecological community about what form of social contact network to use, when. In this talk, I'll propose a tripartite network model borrowing from Lagrangian descriptions of animal movement, that relates disparate ecological networks under a single unifying structure using nodes of type Individual, Location, and Time. I'll show how this tripartite network can be reduced to a variety of different commonly used ecological networks, including individual association networks, home-range overlap networks, and transportation-like networks; and then I'll argue that particular social structures generate consistent redundancies in information between these node types. I'll then demonstrate how information derived from alternative ecological metrics like group size or home range size distributions can be used to constrain the tripartite network's topology. Lastly, I'll outline two potential pathways for using the tripartite network to formally quantify information lost through network projection, one reliant on graph theory, and the other reliant on Shannon's information.

11:00 AM
12:00 PM
Catherine Calder - Community Detection in Co-Location Networks

Research on ‘neighborhood effects’ often focuses on linking features of social contexts or exposures to health, educational, and criminological outcomes. Traditionally, individuals are assigned a specific neighborhood, frequently operationalized by the census tract of residence, which may not contain the locations of routine activities. In order to better characterize the many social contexts to which adolescents and their caregivers are exposed, the Adolescent Health and Development in Context (AHDC) Study collected the locations of reported routine activities, as well as GPS-based space-time trajectories, of approximately 1,400 adolescents in Columbus, OH over two one-week periods. From these two types of data, co-location networks — two-mode networks linking individuals and the places they regularly spend time — can be constructed. In this presentation, we apply and extend statistical methodology for text mining, including latent Dirichlet allocation and non-negative matrix factorization methods, to the problem of community detection in co-location networks. Our findings reveal that both proximity of residence and homophily on race and socio-economic are associated with community membership, but communities tend to be more diverse than neighborhoods. We also report preliminary findings regarding differences in exposures to social context status across communities. This presentation is based on joint work with Wenna Xi and Chris Browning.

12:00 PM
01:00 PM

Lunch and Participant Collaboration

01:00 PM
02:00 PM
Jennifer Hellmann - Variation in within-group social networks due to within and between group characteristics in a group-living cichlid

In group-living species, natural selection should favor behavioral strategies that collectively give rise to structures that facilitate group persistence and minimize conflict among group members. However, the extent to which conflict is present in a group, as well as how conflict is resolved, varies widely among groups; some groups have relatively little conflict while others disband due to high levels of conflict. Here, we seek to understand how both within-group and between-group changes alter group stability and social network structure in the group-living cichlid, Neolamprologus pulcher. We find that network changes can be related to both within-group and between-group differences in social structure. First, we demonstrate that there are unique characteristics of groups that remain intact compared to those that disband. Second, we demonstrate that group characteristics and the presence of neighbors alter the target of conflict within the group, shifting how aggressive, submissive, and affiliative interactions are divided among individuals of different sizes and dominance statuses. Collectively, our results demonstrate that both within and between group social structure should play a key role in predicting conflict within groups and group persistence.

02:00 PM
03:00 PM
Facundo Memoli - Stable Signatures for Dynamic Networks via Zigzag Persistence

When studying flocking/swarming behaviors in animals one is interested in quantifying and comparing the dynamics of the clustering induced by the coalescence and disbanding of animals in different groups. In a similar vein, studying the dynamics of social networks leads to the problem of characterizing groups/communities as they form and disperse throughout time.

Motivated by this, we study the problem of obtaining persistent homology based summaries of time-dependent data. Given a finite dynamic graph (DG), we first construct a zigzag persistence module arising from linearizing the dynamic transitive graph naturally induced from the input DG. Based on standard results, we then obtain a persistence diagram or barcode from this zigzag persistence module. We prove that these barcodes are stable under perturbations in the input DG under a suitable distance between DGs that we identify.

More precisely, our stability theorem can be interpreted as providing a lower bound for the distance between DGs. Since it relies on barcodes, and their bottleneck distance, this lower bound can be computed in polynomial time from the DG inputs.

Along the way, we propose a summarization of dynamic graphs that captures their time-dependent clustering features which we call formigrams. These set-valued functions generalize the notion of dendrogram, a prevalent tool for hierarchical clustering. In order to elucidate the relationship between our distance between two DGs and the bottleneck distance between their associated barcodes, we exploit recent advances in the stability of zigzag persistence due to Botnan and Lesnick, and to Bjerkevik.

This is joint work with Woojin Kim.

https://research.math.osu.edu/networks/formigrams/

03:00 PM
04:00 PM
Scott Duxbury - Attack Tolerance of Dynamic Networks

Interconnected systems in physical, biological, and social sciences are often at risk of attacks from exogenous sources. As a result, a growing number of studies focus on network attack tolerance. In general, this body of research assumes that damage to cross-sectional networks persists over time and has almost ubiquitously focused on attack strategies targeting integral vertices or edges. At issue, however, is that many networks are dynamic, especially in the social sciences, and capable of adaptive responses to attacks. Relatedly, network attack strategies may be diffuse, targeting an array of weak links, rather than high profile vertices. Together, these two omissions limit researchers€™ ability to reach firm conclusions or derive policy recommendations from past research. Expanding on this prior work, we examine data collected from an online drug trafficking network comprised of roughly 7,400 actors and 17,000 illicit drug transactions observed over 14 months. We use these data to develop an agent-based simulation experiment evaluating how the drug trafficking network responds to targeted and diffuse attacks. Results show that the network suffers substantial damage from diffuse attacks and that conventional methods for evaluating network robustness do a poor job of representing this type of damage. In particular, cross-sectional measures of network robustness in the simulated output networks suggest that the networks actually grow stronger in the aftermath of a diffuse attack, despite losing a substantial portion of edges and vertices. Pertinent to policy, these results indicate that the diffuse attack strategy evaluated in this study is an effective tactic for curbing online drug trafficking€”an issue which has vexed law enforcement for some time.

Friday, November 9, 2018
Time Session
08:00 AM
09:00 AM

Breakfast and Daily Introduction

09:00 AM
10:00 AM
Subhadeep Paul - Community detection with realistic network models: a superimposed SBM and a hyperbolic space model

Detecting communities or a group of vertices that are similar to each other in a complex network is a well-studied problem in network science. Methods for community detection include model-based approaches, namely, based on the stochastic block model and its variants, latent space models, as well as model-free approaches including spectral, modularity and matrix factorization methods. The stochastic block model is the most commonly employed model of complex networks with community structure. However, the model fails to explain many observed properties of networks including, heterogeneous and power-law degree distribution (scale-free), strong local clustering especially triadic closures (transitivity) in an otherwise sparse graph, hierarchical nature of connections (core-periphery structure). The goals of this project are to develop models for networks with community structure that explain observed properties of real-world networks better. We propose a superimposed stochastic block model (SupSBM) and a hyperbolic latent space network community model (Hypcomm) for this purpose. We analyze the performance of a higher-order spectral clustering algorithm under the SupSBM. We also develop computationally efficient Variational EM, and Laplacian spectral embedding algorithms to estimate the latent positions and the communities in the Hypcomm model.

10:00 AM
11:00 AM
Alexandria Volkening - Forecasting U.S. elections with compartmental models

U.S. election prediction involves polling likely voters, making assumptions about voter turnout, and accounting for various features such as state demographics and voting history. While political elections in the United States are decided at the state level, errors in forecasting are correlated between states. With the goal of better understanding these correlations and exploring how states influence each other, we develop a framework for forecasting elections in the U.S. from the perspective of dynamical systems. Through a simple approach that borrows ideas from epidemiology, we show how to combine a compartmental model with public polling data from HuffPost and RealClearPolitics to forecast gubernatorial, senatorial, and presidential elections at the state level. Our results for the 2012 and 2016 U.S. races are largely in agreement with those of popular pollsters, and we use our new model to explore how subjective choices about uncertainty impact results. We conclude by forecasting the senatorial and gubernatorial races in the 2018 U.S. midterm elections of 6 November 2018. This is joint work with Daniel F. Linder (Augusta University), Mason A. Porter (UCLA), and Grzegorz A. Rempala (Ohio State).

11:00 AM
12:00 PM
Benjamin Bolduc - vConTACT2: Leveraging network analytics to classify novel viruses

Viruses of bacteria and archaea are likely to be critical to all natural, engineered and human ecosystems, and yet their study is hampered by the lack of a universal or scalable taxonomic framework. Here, we introduce vConTACT 2.0, a network-based application to establish prokaryotic virus taxonomy that scales to thousands of uncultivated virus genomes/fragments, and integrates confidence scores for all taxonomic predictions. Performance tests using vConTACT 2.0 demonstrate near-identical correspondence to the current official viral taxonomy (>85% genus-rank assignments at 96% accuracy) through an integrated distance-based hierarchical approach. Beyond €œknown viruses€?, we used vConTACT 2.0 to automatically assign 1,364 previously unclassified reference viruses to tentative taxa, and scaled it to modern metagenomic datasets for which the reference network was robust to adding 16,000 viral metagenomic contigs. Together these efforts provide a systematic reference network and an accurate, scalable taxonomic analysis tool that is critically needed for the research community.

12:00 PM
01:00 PM

Lunch and Participant Collaboration

01:00 PM
02:00 PM
Elizabeth Hobson - Using dynamics of network interactions to infer social rules

In many social species across both humans and other animals, individuals both create their social worlds through interaction decisions and are then subject to and constrained by these social constructs, which can affect an individual’s future actions. Understanding how much individuals know about their social worlds is critical in understanding these potential feedbacks. However, it is difficult to determine how much knowledge individuals have of the social structures in which they live. I present several dynamic network-based methods that provide ways to detect and quantify the extent to which individuals use of social knowledge to make decisions about how to socially interact. These methods can then be used to gain insight into the types of social information that individuals pay attention to as well as the cognitive abilities that may underly social decisions. This approach provides new potential for broad comparative analyses to better understand the evolution of complex sociocultural traits.

02:00 PM
03:00 PM
John Light - Stochastic Actor-Oriented Modeling of Social Network Dynamics

Many systems of scientific interest can be naturally thought of as networks of evolving relationships, for instance, linkages between neurons in the brain, computers on the internet, or adolescents in a high school. The last 20 years or so have seen rapid progress in methods for the empirical study of network evolution. The Stochastic Actor-Oriented Model (SAOM) framework is one of the most popular such approaches in the behavioral sciences, and is a particularly natural way to represent systems in which tie formation and maintenance depend on characteristics of some set of potentially interconnected nodes, and where also the interconnections, once formed, can €œfeed back€? and affect nodal characteristics. In Part 1 of this presentation, I will describe the basic structure of a SAOM as a set of interrelated continuous-time Markov processes, and show how transition probabilities can be specified as functions of linkage and nodal data. In Part 2, an empirical application will be given, where the goal was to detect indirect (€œspillover€?) effects on alcohol use of an intervention with a subset of heavy drinkers in a college freshmen class.

Name Email Affiliation
Bayer, Joseph bayer.66@osu.edu School of Communication, The Ohio State University
Bolduc, Benjamin bolduc.10@osu.edu Microbiology, The Ohio State University
Box-Steffensmeier, Janet steffensmeier.2@osu.edu Department of Political Science, The Ohio State University
Calder, Catherine calder.13@osu.edu Statistics, The Ohio State University
Campbell, Benjamin campbell.1721@osu.edu Political Science, The Ohio State University
Cao, Qiuchang cao.847@buckeyemail.osu.edu College of Social Work, The Ohio State University
Carter, Gerald ggc.bats@gmail.com Evolution, Ecology, and Organismal Biology, 300 Aronoff Lab
Chen, Jing chen.4046@osu.edu Educational Studies, Crane Center for Early Childhood Research and Policy
Correa Duran, Fabio correaduran.1@osu.edu Anthropology, The Ohio State University
Cranmer, Skyler cranmer.12@osu.edu Political Science, The Ohio State University
Doogan, Nate doogan.1@osu.edu Government Resource Center, The Ohio State University
Doogan, Nathan nathan.doogan@osumc.edu Ohio Colleges of Medicine Government Resource Center, The Ohio State University
Downey, Sean downey.205@osu.edu Anthropology, The Ohio State University
Duxbury, Scott duxbury.5@osu.edu Sociology, The Ohio State University
Guerrero Montero, Deyssi guerreromontero.1@osu.edu Electrical & Computer Engr., The Ohio State University
Hamilton, Ian hamilton.598@osu.edu EEOB/Mathematics, The Ohio State University
Hamilton, Matthew hamilton.1323@osu.edu Sch of Environ & Natural Res, The Ohio State University
Haynie, Dana haynie.7@osu.edu Criminal Justice Research Center, The Ohio State University
Hellmann, Jennifer jehellmann45@gmail.com Animal Biology, University of Illinois at Urbana-Champaign
Hobson, Elizabeth ehobson@santafe.edu Santa Fe Institute, Santa Fe Institute
Howard, Kristen howard.1231@osu.edu Psychology, The Ohio State University
Islam, Md rafiul.islam@ttu.edu Mathematics and Statistics, Texas Tech University
Karamoko, Matthieu karamoko.1@osu.edu Industry Liaison Office - Business Intelligence & Mapping, The Ohio State University
Kent, Daniel kent.249@osu.edu Political Science, The Ohio State University
Kim, Woojin kim.5235@osu.edu Mathematics, The Ohio State University
Kurtek, Sebastian kurtek.1@stat.osu.edu Statistics, The Ohio State University
Light, John jlight@ori.org Mathematical Sociology, Oregon Research Institute
Lo, Meng-Ting lo.194@osu.edu EHE Research Methodology Ctr, The Ohio State University
Logan, Jessica Logan.251@osu.edu College of Education and Human Ecology, The Ohio State University
Luo, Hengrui luo.619@osu.edu Statistics, Ohio State University
Manlove, Kezia kezia.manlove@gmail.com Wildland Resources, Utah State University
McCormack-Mager, Meredith mccormack-mager.1@osu.edu Biostatistics, The Ohio State University
Melamed, David melamed.9@osu.edu Sociology, Ohio State
Memoli, Facundo memoli@math.osu.edu math, The Ohio State University
Mendel, Catherine mendel.9@osu.edu Evolution and Ecology, The Ohio State University
Morgan, Jason jason.w.morgan@gmail.com Behavioral Intelligence, Wiretap
Muhanna, Waleed muhanna.1@osu.edu Accounting & MIS, The Ohio State University
Nguyen, Ha Khanh nguyen.1833@buckeyemail.osu.edu Statistics, The Ohio State University
Paul, Subhadeep paul.963@osu.edu Statistics, The Ohio State University
Razik, Imran razik.2@osu.edu Evolution, Ecology and Organismal Biology, The Ohio State University
Sivakoff, David sivakoff.2@osu.edu Statistics and Mathematics, The Ohio State University
Volkening, Alexandria volkening.2@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Wan, Zhengchao wan.252@osu.edu Department of Mathematics, The Ohio State University
Wang, Selena wang.10171@osu.edu Psychology, The Ohio State University
Warren, Keith warren.193@osu.edu Social Work, The Ohio State University
Xi, Wenna xi.34@osu.edu Biostatistics, The Ohio State University
Yi, Hongtao yi.201@osu.edu John Glenn College of Public Affairs, The Ohio State University
Zhou, Ling zhou.2568@osu.edu Mathematics, Ohio State University
vConTACT2: Leveraging network analytics to classify novel viruses

Viruses of bacteria and archaea are likely to be critical to all natural, engineered and human ecosystems, and yet their study is hampered by the lack of a universal or scalable taxonomic framework. Here, we introduce vConTACT 2.0, a network-based application to establish prokaryotic virus taxonomy that scales to thousands of uncultivated virus genomes/fragments, and integrates confidence scores for all taxonomic predictions. Performance tests using vConTACT 2.0 demonstrate near-identical correspondence to the current official viral taxonomy (>85% genus-rank assignments at 96% accuracy) through an integrated distance-based hierarchical approach. Beyond â€œknown virusesâ€?, we used vConTACT 2.0 to automatically assign 1,364 previously unclassified reference viruses to tentative taxa, and scaled it to modern metagenomic datasets for which the reference network was robust to adding 16,000 viral metagenomic contigs. Together these efforts provide a systematic reference network and an accurate, scalable taxonomic analysis tool that is critically needed for the research community.

Community Detection in Co-Location Networks

Research on ‘neighborhood effects’ often focuses on linking features of social contexts or exposures to health, educational, and criminological outcomes. Traditionally, individuals are assigned a specific neighborhood, frequently operationalized by the census tract of residence, which may not contain the locations of routine activities. In order to better characterize the many social contexts to which adolescents and their caregivers are exposed, the Adolescent Health and Development in Context (AHDC) Study collected the locations of reported routine activities, as well as GPS-based space-time trajectories, of approximately 1,400 adolescents in Columbus, OH over two one-week periods. From these two types of data, co-location networks — two-mode networks linking individuals and the places they regularly spend time — can be constructed. In this presentation, we apply and extend statistical methodology for text mining, including latent Dirichlet allocation and non-negative matrix factorization methods, to the problem of community detection in co-location networks. Our findings reveal that both proximity of residence and homophily on race and socio-economic are associated with community membership, but communities tend to be more diverse than neighborhoods. We also report preliminary findings regarding differences in exposures to social context status across communities. This presentation is based on joint work with Wenna Xi and Chris Browning.

Detecting Heterogeneity and Inferring Latent Roles in Longitudinal Networks

Network analysis has typically examined the formation of whole networks while neglecting variation within or across networks. Actors within networks often adopt particular roles or have different incentives for tie formation. While cross-sectional approaches for inferring latent roles and detecting variation exist, there is a paucity of approaches for considering roles in longitudinal networks. This talk explores the conceptual dynamics of temporally observed roles while introducing a novel statistical tool, the ego-TERGM, capable of uncovering these latent dynamics. Estimated through an Expectation-Maximization algorithm, the ego-TERGM is quick and accurate in classifying roles within a broader temporal network. An application to the Kapferer strike network illustrates the model's utility.

Hypothesis-testing in animal social networks using null models

Dynamic networks allow researchers to study how social structure changes over time, which is at the center of many fundamental questions in biology. However, when data are limited or imprecise as in many field studies, there is a tradeoff between temporal resolution and estimating the network structure at each “snapshot” of time. This is important because in many animal studies the observed network is only a sample of the actual social structure at any given point in time. In this talk, I will review hypothesis-testing in animal social network analysis using null models based on permutations of the network nodes or the raw data (pre-network permutations). I will also discuss how resampling procedures can be used as power analyses using empirical examples of grooming in primates and food-sharing in vampire bats. I will then discuss some of the challenges for creating permutation-based null models for dynamic networks. Careful null models can control for nuisance factors that create social network structure as a mere byproduct of non-social spatial or temporal effects (such as individuals being “connected” due to simultaneous attraction to a particular place, rather than each other). Automated data collection allows for dynamic networks to be a practical tool in animal studies.

A Consistent Organizational Structure Across Multiple Functional Subnetworks of the Human Brain

A recurrent theme of both cognitive neuroscience and network neuroscience is that the brain has a consistent subnetwork structure that maps onto functional specialization for different cognitive tasks, such as vision, motor skills, and attention. Understanding how regions in these subnetworks relate is thus crucial to understanding the emergence of critical cognitive processes. However, the organizing principles that guide how regions within subnetworks communicate, and whether there is a common set of principles across subnetworks, remains unclear. This is partly due to available tools not being suited to precisely quantify the role that different organizational principles play in the organization of a subnetwork. Here, we apply the recently-developed correlation generalized exponential random graph model (cGERGM) to more completely quantify subnetwork structure. The cGERGM models a correlation network, such as those given in functional connectivity, as a function of activation motifs -- consistent patterns of coactivation (i.e., connectivity) between collections of nodes that describe how the regions within a network are organized (e.g., clustering) -- and anatomical properties -- relationships between the regions that are dictated by anatomy (e.g., Euclidean distance). Across nine functional subnetworks, we find remarkably consistent organizational properties guiding subnetwork architecture, suggesting a fundamental organizational basis for subnetwork communication. Specifically, all subnetworks displayed greater clustering than would be expected by chance, but lower preferential attachment (i.e., hub use), suggesting that human functional subnetworks follow a segregated highway structure rather than the small-world structure found in the whole-brain.

A Consistent Organizational Structure Across Multiple Functional Subnetworks of the Human Brain

A recurrent theme of both cognitive neuroscience and network neuroscience is that the brain has a consistent subnetwork structure that maps onto functional specialization for different cognitive tasks, such as vision, motor skills, and attention. Understanding how regions in these subnetworks relate is thus crucial to understanding the emergence of critical cognitive processes. However, the organizing principles that guide how regions within subnetworks communicate, and whether there is a common set of principles across subnetworks, remains unclear. This is partly due to available tools not being suited to precisely quantify the role that different organizational principles play in the organization of a subnetwork. Here, we apply the recently-developed correlation generalized exponential random graph model (cGERGM) to more completely quantify subnetwork structure. The cGERGM models a correlation network, such as those given in functional connectivity, as a function of activation motifs -- consistent patterns of coactivation (i.e., connectivity) between collections of nodes that describe how the regions within a network are organized (e.g., clustering) -- and anatomical properties -- relationships between the regions that are dictated by anatomy (e.g., Euclidean distance). Across nine functional subnetworks, we find remarkably consistent organizational properties guiding subnetwork architecture, suggesting a fundamental organizational basis for subnetwork communication. Specifically, all subnetworks displayed greater clustering than would be expected by chance, but lower preferential attachment (i.e., hub use), suggesting that human functional subnetworks follow a segregated highway structure rather than the small-world structure found in the whole-brain.

Attack Tolerance of Dynamic Networks

Interconnected systems in physical, biological, and social sciences are often at risk of attacks from exogenous sources. As a result, a growing number of studies focus on network attack tolerance. In general, this body of research assumes that damage to cross-sectional networks persists over time and has almost ubiquitously focused on attack strategies targeting integral vertices or edges. At issue, however, is that many networks are dynamic, especially in the social sciences, and capable of adaptive responses to attacks. Relatedly, network attack strategies may be diffuse, targeting an array of weak links, rather than high profile vertices. Together, these two omissions limit researchersâ€™ ability to reach firm conclusions or derive policy recommendations from past research. Expanding on this prior work, we examine data collected from an online drug trafficking network comprised of roughly 7,400 actors and 17,000 illicit drug transactions observed over 14 months. We use these data to develop an agent-based simulation experiment evaluating how the drug trafficking network responds to targeted and diffuse attacks. Results show that the network suffers substantial damage from diffuse attacks and that conventional methods for evaluating network robustness do a poor job of representing this type of damage. In particular, cross-sectional measures of network robustness in the simulated output networks suggest that the networks actually grow stronger in the aftermath of a diffuse attack, despite losing a substantial portion of edges and vertices. Pertinent to policy, these results indicate that the diffuse attack strategy evaluated in this study is an effective tactic for curbing online drug traffickingâ€”an issue which has vexed law enforcement for some time.

Disrupting Darknet Drug Markets

Interconnected systems in physical, biological, and social sciences are often at risk of attacks from exogenous sources. As a result, a growing number of studies focus on network attack tolerance. In general, this body of research assumes that damage to cross-sectional networks persists over time and has almost ubiquitously focused on attack strategies targeting integral vertices or edges. At issue, however, is that many networks are dynamic, especially in the social sciences, and capable of adaptive responses to attacks. Relatedly, network attack strategies may be diffuse, targeting an array of weak links, rather than high profile vertices. Together, these two omissions limit researchers’ ability to reach firm conclusions or derive policy recommendations from past research. Expanding on this prior work, we examine data collected from an online drug trafficking network comprised of roughly 7,400 actors and 17,000 drug transactions observed over 14 months. We use these data to develop an agent-based simulation experiment evaluating how the drug trafficking network responds to diffuse attacks. Results show that the network suffers substantial damage from diffuse attacks and that conventional methods for evaluating network robustness do a poor job of representing this type of damage. In particular, cross-sectional measures of network robustness in the simulated output networks suggest that the networks actually grow stronger in the aftermath of a diffuse attack, despite losing a substantial portion of edges and vertices. Pertinent to policy, these results indicate that the diffuse attack strategy evaluated in this study is an effective tactic for curbing online drug trafficking—an issue which has vexed law enforcement for some time.

Variation in within-group social networks due to within and between group characteristics in a group-living cichlid

In group-living species, natural selection should favor behavioral strategies that collectively give rise to structures that facilitate group persistence and minimize conflict among group members. However, the extent to which conflict is present in a group, as well as how conflict is resolved, varies widely among groups; some groups have relatively little conflict while others disband due to high levels of conflict. Here, we seek to understand how both within-group and between-group changes alter group stability and social network structure in the group-living cichlid, Neolamprologus pulcher. We find that network changes can be related to both within-group and between-group differences in social structure. First, we demonstrate that there are unique characteristics of groups that remain intact compared to those that disband. Second, we demonstrate that group characteristics and the presence of neighbors alter the target of conflict within the group, shifting how aggressive, submissive, and affiliative interactions are divided among individuals of different sizes and dominance statuses. Collectively, our results demonstrate that both within and between group social structure should play a key role in predicting conflict within groups and group persistence.

Using dynamics of network interactions to infer social rules

In many social species across both humans and other animals, individuals both create their social worlds through interaction decisions and are then subject to and constrained by these social constructs, which can affect an individual’s future actions. Understanding how much individuals know about their social worlds is critical in understanding these potential feedbacks. However, it is difficult to determine how much knowledge individuals have of the social structures in which they live. I present several dynamic network-based methods that provide ways to detect and quantify the extent to which individuals use of social knowledge to make decisions about how to socially interact. These methods can then be used to gain insight into the types of social information that individuals pay attention to as well as the cognitive abilities that may underly social decisions. This approach provides new potential for broad comparative analyses to better understand the evolution of complex sociocultural traits.

Stochastic Actor-Oriented Modeling of Social Network Dynamics

Many systems of scientific interest can be naturally thought of as networks of evolving relationships, for instance, linkages between neurons in the brain, computers on the internet, or adolescents in a high school. The last 20 years or so have seen rapid progress in methods for the empirical study of network evolution. The Stochastic Actor-Oriented Model (SAOM) framework is one of the most popular such approaches in the behavioral sciences, and is a particularly natural way to represent systems in which tie formation and maintenance depend on characteristics of some set of potentially interconnected nodes, and where also the interconnections, once formed, can â€œfeed backâ€? and affect nodal characteristics. In Part 1 of this presentation, I will describe the basic structure of a SAOM as a set of interrelated continuous-time Markov processes, and show how transition probabilities can be specified as functions of linkage and nodal data. In Part 2, an empirical application will be given, where the goal was to detect indirect (â€œspilloverâ€?) effects on alcohol use of an intervention with a subset of heavy drinkers in a college freshmen class.

Can a tripartite model help us understand temporal variation in social contact networks?

Understanding dynamics of social contact is a key precursor for modeling propagation of pathogens, genes, and information through societies. However, there is little consistency within the ecological community about what form of social contact network to use, when. In this talk, I'll propose a tripartite network model borrowing from Lagrangian descriptions of animal movement, that relates disparate ecological networks under a single unifying structure using nodes of type Individual, Location, and Time. I'll show how this tripartite network can be reduced to a variety of different commonly used ecological networks, including individual association networks, home-range overlap networks, and transportation-like networks; and then I'll argue that particular social structures generate consistent redundancies in information between these node types. I'll then demonstrate how information derived from alternative ecological metrics like group size or home range size distributions can be used to constrain the tripartite network's topology. Lastly, I'll outline two potential pathways for using the tripartite network to formally quantify information lost through network projection, one reliant on graph theory, and the other reliant on Shannon's information.

Stable Signatures for Dynamic Networks via Zigzag Persistence

When studying flocking/swarming behaviors in animals one is interested in quantifying and comparing the dynamics of the clustering induced by the coalescence and disbanding of animals in different groups. In a similar vein, studying the dynamics of social networks leads to the problem of characterizing groups/communities as they form and disperse throughout time.

Motivated by this, we study the problem of obtaining persistent homology based summaries of time-dependent data. Given a finite dynamic graph (DG), we first construct a zigzag persistence module arising from linearizing the dynamic transitive graph naturally induced from the input DG. Based on standard results, we then obtain a persistence diagram or barcode from this zigzag persistence module. We prove that these barcodes are stable under perturbations in the input DG under a suitable distance between DGs that we identify.

More precisely, our stability theorem can be interpreted as providing a lower bound for the distance between DGs. Since it relies on barcodes, and their bottleneck distance, this lower bound can be computed in polynomial time from the DG inputs.

Along the way, we propose a summarization of dynamic graphs that captures their time-dependent clustering features which we call formigrams. These set-valued functions generalize the notion of dendrogram, a prevalent tool for hierarchical clustering. In order to elucidate the relationship between our distance between two DGs and the bottleneck distance between their associated barcodes, we exploit recent advances in the stability of zigzag persistence due to Botnan and Lesnick, and to Bjerkevik.

This is joint work with Woojin Kim.

https://research.math.osu.edu/networks/formigrams/

Community detection with realistic network models: a superimposed SBM and a hyperbolic space model

Detecting communities or a group of vertices that are similar to each other in a complex network is a well-studied problem in network science. Methods for community detection include model-based approaches, namely, based on the stochastic block model and its variants, latent space models, as well as model-free approaches including spectral, modularity and matrix factorization methods. The stochastic block model is the most commonly employed model of complex networks with community structure. However, the model fails to explain many observed properties of networks including, heterogeneous and power-law degree distribution (scale-free), strong local clustering especially triadic closures (transitivity) in an otherwise sparse graph, hierarchical nature of connections (core-periphery structure). The goals of this project are to develop models for networks with community structure that explain observed properties of real-world networks better. We propose a superimposed stochastic block model (SupSBM) and a hyperbolic latent space network community model (Hypcomm) for this purpose. We analyze the performance of a higher-order spectral clustering algorithm under the SupSBM. We also develop computationally efficient Variational EM, and Laplacian spectral embedding algorithms to estimate the latent positions and the communities in the Hypcomm model.

Contact process with avoidance behavior

The (classical) contact process is a stochastic process on the vertices of a graph, which is a discrete, spatial model for the spread of a disease. The state of the contact process at time t is given by an infected subset of the vertices of the graph. At rate 1, each infected vertex becomes healthy, and therefore susceptible to reinfection. At rate lambda>0, each edge between an infected vertex and a healthy vertex transmits the infection, thus infecting the healthy vertex. The contact process has been thoroughly analyzed on the integer lattices and regular trees, where it is well-known to exhibit a phase transition: for large lambda, epidemics persist, while for smaller lambda, all vertices are eventually healthy. More recently, researchers have made progress in analyzing the behavior of the contact process on (finite) complex networks, where epidemics may persist for all lambda>0 on graphs with heavy-tailed' degree distributions. I will discuss recent progress on a version of the contact process in which the edges of the graph are also dynamic: at rate alpha, each edge from an infected vertex to a healthy vertex will deactivate; the edge will become active again when the infected vertex becomes healthy, and only active edges can transmit the infection. This emulates avoidance of infected individuals by healthy individuals. We demonstrate that the long-time qualitative behavior of this model may or may not differ from the classical contact process, depending on the underlying network topology. A technical obstacle is the lack of a certain type of monotonicity, which is present for the classical model. Based on joint work with Shirshendu Chatterjee and Matthew Wascher.

Forecasting U.S. elections with compartmental models

U.S. election prediction involves polling likely voters, making assumptions about voter turnout, and accounting for various features such as state demographics and voting history. While political elections in the United States are decided at the state level, errors in forecasting are correlated between states. With the goal of better understanding these correlations and exploring how states influence each other, we develop a framework for forecasting elections in the U.S. from the perspective of dynamical systems. Through a simple approach that borrows ideas from epidemiology, we show how to combine a compartmental model with public polling data from HuffPost and RealClearPolitics to forecast gubernatorial, senatorial, and presidential elections at the state level. Our results for the 2012 and 2016 U.S. races are largely in agreement with those of popular pollsters, and we use our new model to explore how subjective choices about uncertainty impact results. We conclude by forecasting the senatorial and gubernatorial races in the 2018 U.S. midterm elections of 6 November 2018. This is joint work with Daniel F. Linder (Augusta University), Mason A. Porter (UCLA), and Grzegorz A. Rempala (Ohio State).

Attack Tolerance of Dynamic Networks
Scott Duxbury

Interconnected systems in physical, biological, and social sciences are often at risk of attacks from exogenous sources. As a result, a growing number of studies focus on network attack tolerance. In general, this body of research assumes th

Many systems of scientific interest can be naturally thought of as networks of evolving relationships, for instance, linkages between neurons in the brain, computers on the internet, or adolescents in a high school. The last 20 years or so h

Viruses of bacteria and archaea are likely to be critical to all natural, engineered and human ecosystems, and yet their study is hampered by the lack of a universal or scalable taxonomic framework. Here, we introduce vConTACT 2.0, a network

Detecting communities or a group of vertices that are similar to each other in a complex network is a well-studied problem in network science. Methods for community detection include model-based approaches, namely, based on the stochastic bl

When studying flocking/swarming behaviors in animals one is interested in quantifying and comparing the dynamics of the clustering induced by the coalescence and disbanding of animals in different groups. In a similar vein, studying the dyna

In group-living species, natural selection should favor behavioral strategies that collectively give rise to structures that facilitate group persistence and minimize conflict among group members. However, the extent to which conflict is pre

Understanding dynamics of social contact is a key precursor for modeling propagation of pathogens, genes, and information through societies. However, there is little consistency within the ecological community about what form of social conta

Videos

### Print

Full Schedule Participant List