HONS 2022

Program

When? July 14-15 2022, 08:00 - 12:00 EDT (14:00 - 18:0 CEST)

Where? (Online Event)

We are proud to present a high-quality program with speakers from different communities. Speakers who want to publish their talks after the satellite can send their slides via E-Mail.

JULY 14th	Presenter
14:00 - 14:10	Organizers Opening Statement
14:10 - 15:00	Keynote: Ginestra Bianconi ( Faculty of Mathematical Sciences,Quen Mary University of London, UK) Keynote Talk: Representing and modelling higher-order network data and topological signals Higher-order network data contains structural information on the higher-order interactions present in complex systems as well as information on topological signals, i.e. dynamical variables associated to nodes, links, triangles etc. Representing and modelling higher-order interactions and topological signals is key for extracting relevant information from data, for solving inference problems and for understanding the interplay between network topology, geometry and dynamics. In this talk I will present recent results combining statistical mechanics approaches with applied topology to address few central research questions arising in this context, including most relevantly: (i) establishing whether hypergraphs or simplicial complexes should be the preferred representation for higher-order network data; (ii) establishing frameworks to model and predict collective dynamics of topological signals.
15:00 - 15:30	Tim LaRock (Mathematical Institute,University of Oxford,UK) Invited Talk: Sequential Motifs in Observed Walks The structure of complex networks can be characterized by counting and analyzing network motifs, which are small graph structures that occur repeatedly in a network, such as triangles or chains. Recent work has generalized motifs to temporal and dynamic network data. However, existing techniques do not generalize to sequential or trajectory data, which represents entities walking through the nodes of a network, such as passengers moving through transportation networks. The unit of observation in these data is fundamentally different, since we analyze observations of walks (e.g., a trip from airport A to airport C through airport B), rather than independent observations of edges or snapshots of graphs over time. In this work, we define sequential motifs in trajectory data, which are small, directed, and sequenced-ordered graphs corresponding to patterns in observed sequences. We draw a connection between counting and analysis of sequential motifs and Higher-Order Network (HON) models. We show that by mapping edges of a HON, specifically a kth-order DeBruijn graph, to sequential motifs, we can count and evaluate their importance in observed data, and we test our proposed methodology with two datasets: (1) passengers navigating an airport network and (2) people navigating the Wikipedia article network. We find that the most prevalent and important sequential motifs correspond to intuitive patterns of traversal in the real systems, and show empirically that the heterogeneity of edge weights in an observed higher-order DeBruijn graph has implications for the distributions of sequential motifs we expect to see across our null models.
15:30 - 15:45	Short Break
15:45 - 16:15	Philip Leifeld (Department of Government, University of Essex, UK) Invited Talk: Identification of Social Influence in Bipartite Behaviour Cascades using Relational Event Models with Temporal Permutations Actors' behavior often takes the form of bipartite event cascades. Examples from the political domain include legislators sponsoring bills, countries ratifying treaties, and political actors stating beliefs in policy debates. Relational event models effectively analyze the interdependent nature of such cascades. Of primary interest is whether the behavior by an actor is caused by the recent behavior of similar actors. The inclusion of homophily statistics can test for such contagion, given one or more actor attributes or network relations. However, two competing causal pathways are generally confounded: social influence along the event sequence and independent but similar behavior as a consequence of shared attributes. The present article proposes a shuffle test to identify social influence and separate it from the effect of prior similarity. Monte Carlo simulations and an empirical example delineate the scope conditions of the shuffle test and demonstrate its efficacy under different mixture regimes of influence and similarity.
16:15 - 16:45	Amanda McGowan (Annenberg School of Communication, University of Pennsylvania, US) Invited Talk: Network analysis of within-person associations among physical activity, sleep, and wellbeing in college students’ daily lives How much we move throughout the day and sleep each night impacts our wellbeing. Physical activity, sleep, mood, and purpose in life are part of a system that reflects everyday wellbeing. An understanding of the dynamics within this system is key to informing interventions and policies with the most promise of influencing individual and population health. We used self-reported mood (happy, sad, angry, anxious) and physical activity periods collected twice per day via smartphone-based surveys over 28 days as college students (n = 226; M = 20.2 years, SD = 1.7 years, 75% women, 25% men) went about their daily lives. We added once per day reports of sleep duration, sleep quality, and purpose in life. Multilevel vector autoregression was used to construct networks that describe within-person associations within this system of wellbeing on the same day, next day, and up to 2 days later. We find that the beneficial effects of physical activity and sleep on wellbeing are relatively short-term (up to one day later), yet a sense of purpose in life has slightly longer positive effects on wellbeing, bleeding into the next few days. Socioecological and family systems theories highlight the importance of extending this system of wellbeing to examine the influence of higher-order dependencies. For instance, college students’ wellbeing is likely influenced by their social relations and neighborhoods in which they live. A continued challenge in moving forward the notion of a wellbeing system is how we can best represent naturalistic dynamics within these complex systems so that we can simulate and control the nodes, useful for personalized interventions and testing feasibility of health-enhancing programs. Coauthors: Zachary M. Boyd, PhD;2 Yoona Kang, PhD;1 Logan Bennett;1 Peter J. Mucha, PhD;3 Kevin N. Ochsner, PhD;4 Dani S. Bassett, PhD;7-12 Emily B. Falk, PhD;1,5,6,14 & David M. Lydon-Staley, PhD1,7,13 1Annenberg School for Communication, University of Pennsylvania, Philadelphia, PA, USA 2Department of Mathematics, Brigham Young University, Provo, UT, USA 3Department of Mathematics, Dartmouth College, Hanover, NH, USA 4Department of Psychology, Columbia University, New York City, NY, USA 5Department of Psychology, University of Pennsylvania, Philadelphia, PA, USA 6Marketing Department, Wharton School, University of Pennsylvania, PA, USA 7Department of Bioengineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA, USA 8Department of Physics & Astronomy, College of Arts and Sciences, University of Pennsylvania, Philadelphia, PA, USA 9Department of Electrical & Systems Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA, USA 10Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA 11Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA 12Santa Fe Institute, Santa Fe, NM, USA 13Leonard Davis Institute of Health Economics, University of Pennsylvania, Philadelphia, PA, USA 14Operations, Information and Decisions, Wharton School, University of Pennsylvania, Philadelphia, PA, USA
16:45 - 17:15	Leah Keating (Department of Mathematics and Statistics, University of Limerick, Ireland) Invited Talk: Modelling dynamics on clustered networks using multi-type branching processes. Online social networks such as Twitter, Facebook, Instagram and TikTok serve as media for the spread of information between their users. We are interested in developing models for this information diffusion to gain a greater understanding of its drivers. Some models for the spread of online behaviour and information assume that the information behaves similarly to a virus, where infection is equally likely after each exposure, these dynamics are known as a simple contagion. In a simple contagion, the exposures are independent of each other. However, online adoption of some behaviour and content has been empirically observed to be more likely after multiple exposures from their network neighbours [1-2], the exposures are not independent of each other, we refer to this as a complex contagion. Analytically tractable descriptions of complex contagions have been developed for continuous-time dynamics. These extend mean-field and pair approximation methods to account for clustering in the network topologies [3]; however, no such analogous treatments for discrete-time cascade processes exist using branching processes. We describe a novel definition of complex contagion adoption dynamics and show how to construct multi-type branching processes which account for clustering on networks [4]. We achieve this by tracking the evolution of a cascade via different classes of clique motifs which contain different numbers of active, inactive and removed nodes. This description allows for accurate analytical calculation of cascade sizes, determination of critical behaviour and we also describe how the branching process description allows us, using probability generating functions, to derive full distributions of cascade sizes and other quantities of interest from the model. [1] D. Centola, The spread of behavior in an online social network experiment, Science 329, 1194 (2010). [2] D. M. Romero, B. Meeder, and J. Kleinberg, Differences in the mechanics of information diffusion across topics: idioms, political hashtags, and complex contagion on twitter, in Proceedings of the 20th international conference on World wide web (2011) pp. 695–704. [3] D. J. P. O’Sullivan, G. J. O’Keeffe, P. G. Fennell, and J. P. Gleeson, Mathematical modeling of complex contagion on clustered networks, Frontiers in Physics 3,10.3389/fphy.2015.00071 (2015). [4] Keating, L.A., Gleeson, J.P. and O’Sullivan, D. J.P. Multitype branching process method for modeling complex contagion on clustered networks. Physical Review E, 105(3), 034306 (2022).
17:15 - 17:30	Short Break
	DEMO Session
17:30 - 18:00	Nicholas Landry (The Vermont Complex Systems Center, US) Leo Torres (MPI for Mathematics in the Sciences,Leipzig,DE) Demo: XGI: compleX Group Interactions, a python package for higher-order networks TBA XGI

JULY 15th	Presenter
14:00 - 14:45	Keynote: Mustafa Hajij (Department of Mathematics and Computer Science, Santa Clara University,US ) Keynote Talk: A unifying deep learning framework with higher order attention networks Over the past decade, deep learning has been remarkably successful at solving a massive set of problems on data types including images and sequential data. This success drove the extension of deep learning to other discrete domains such as sets, point clouds ,graphs ,3D shapes, and discrete manifolds. While many of the extended schemes have successfully tackled notable challenges in each particular domain, the plethora of fragmented frameworks have created or resurfaced many long-standing problems in deep learning such as explainability, expressiveness and generalizability. Moreover, theoretical development proven over one discrete domain does not naturally apply to the other domains. Finally, the lack of a cohesive mathematical framework has created many ad hoc and inorganic implementations and ultimately limited the set of practitioners that can potentially benefit from deep learning technologies. In this talk I will talk about generalized higher-order domains called combinatorial complexes (CCs) and utilize them to build a new class of attention-based neural networks called higher-order attention networks (HOANs). CCs generalize many discrete domains that are of practical importance such as point clouds, 3D shapes, (hyper)graphs, simplicial complexes, and cell complexes. The topological structure of a CC encodes arbitrary higher-order interactions among elements of the CC. By exploiting the rich combinatorial and topological structure of CCs, HOANs define a new class of higher-order message passing attention-based networks that unify existing higher-order models based on hypergraphs and cell complexes. I will show how this new framework forms novel links between higher-order deep learning and more mature fields such as topological data analysis and geometric data processing. Moreover, I will demonstrate how HOANs can be used to define traditional deep learning operations such as higher-order pooling. I will illustrate the reducibility of any CC to a special graph called the Hasse graph, which allows the characterization of certain aspects of HOANs and other higher order models in terms of graph-based models. Finally the predictive capacity of HOANs will be demonstrated in shape analysis and in graph learning, competing against state-of-the-art task-specific neural networks.
14:45 - 15:15	Jelena Smiljanic (Department of Physics, Umeå University, Sweden) Invited Talk: Mapping regularized higher-order network flows To capture modular regularities in sequence data or data describing interactions across multiple layers, the flow-based community detection method, known as the map equation, uses higher-order network flow models. Unlike first-order models, where each node has a single community assignment, higher-order models allow nodes to be assigned to several communities and identify overlapping communities. The map equation performs well when enough data are provided, but in the case of insufficient data, it is prone to overfit and requires flow regularization. Because higher-order models have higher complexity than first-order models, with degrees of freedom that grow exponentially with their order, the risk to overfit becomes more pronounced as we increase order, requiring considerably more data to detect reliable communities. We have recently proposed a Bayesian approach that overcomes the problem of overfitting in plain networks with incomplete data, that is, memoryless networks with one layer. Here we extend the idea behind the Bayesian estimate of the transition rates for plain networks to regularize flows in memory and multilayer networks. Our results in synthetic networks with planted community structures show that the map equation with regularized higher-order flows outperforms the standard map equation and enables more robust community detection in sparse empirical data.
15:15 - 15:45	Unai Alvarez-Rodriguez (Data Analytics Group, University of Zurich, CH ) Contributed Talk: Inference of time-ordered multibody interactions We introduce time-ordered multibody interactions to describe complex systems manifesting temporal as well as multibody dependencies. First, we show how the dynamics of multivariate Markov chains can be decomposed in ensembles of time-ordered multibody interactions. Then, we present an algorithm to extract combined interactions from data and a measure to characterize the complexity of interaction ensembles. Finally, we experimentally validate the robustness of our algorithm against statistical errors and its efficiency at obtaining simple interaction ensembles.
15:45 - 16:00	Short Break
16:00 - 16:30	Xie He (Department of Mathematics, Darthmouth College, US) Invited Talk: Learning to Predict: A Topological Stacking Link Prediction Method for Temporal Networks Link prediction has become an essential tool for speeding up the collection of and filling in incomplete network data. However, links change over time. With rapid increases in the availability of temporal network data and improved methods for analyzing these data, there is a crucial need to study temporal topological structures and predict missing links in temporal networks. We find across that various temporal topological features, in addition to high computational cost, fail to improve link prediction accuracy compared to stacked static features. We then construct a temporal stacking link prediction method with 41 static features to avoid verbose feature engineering. We demonstrate that the temporal stacking achieves the theoretically optimal AUC for link prediction in two temporal block models. Finally, we empirically illustrate that the temporal stacking with incorporated predictors out-performs single predictors on 19 real-world temporal network datasets from different domains.
16:30 - 17:00	Alexander Christensen (Data Science Institute,Vanderbilt University,US) Contributed Talk: Advances in the Louvain Algorithm for Hierarchical Community Detection in Psychological Data Psychological data usually follow a hierarchical organization, with lower order traits (e.g., spatial scanning and mental rotation) nested within higher order ones (e.g., visual processing). This feature has often been neglected in applied research, especially in exploratory settings, hindering progress in areas like intelligence, personality, and psychopathology. Using Gaussian Graphical Models combined with the Louvain community detection algorithm and consensus clustering, we present a two-stage approach we call hierarchical exploratory graph analysis (hierEGA) to estimate hierarchical community structures. We introduce a novel approach to aggregate nodes in the Louvain algorithm, using latent weighted scores, rather than summing edges, to form aggregate nodes. An exhaustive Monte Carlo simulation tested the accuracy of hierEGA to detect the correct number of lower and higher order communities. hierEGA displayed a good hit rate for the number of lower-order communities and a close to perfect hit rate for the number of higher-order communities. Our approach to aggregate nodes in the Louvain algorithm significantly outperformed the original Louvain algorithm. Furthermore, it remained robust to conditions commonly encountered in psychological research, like low sample size and noisy data. Therefore, we regard hierEGA as a reliable tool for the estimation of hierarchical structures in psychological data and beyond.
17:00 - 17:15	Short Break

17:15 - 18:00	PANEL (Moderator:Ingo Scholtes Center for Artificial Intelligence and Data Science (CAIDAS), Julius-Maximilians-Universität Würzburg,DE)