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3/14 Tuesday
14:00 - 15:00
Title A norm-based account of individual and collective identity and agency
Speaker Randall Harp (Vermont)
Abstract Many theories of intentional action are based upon the claim that actions are behaviors that are performed by agents for reasons. Being an individual agent, then, means being responsive to the normative force of reasons. As a parallel, I suggest that there are two ways that agents can constitute a group: agents can constitute a group in a descriptive sense, where the group consists of individual agents who share some descriptive property, or agents can constitute a group in a normative sense, where the group consists of agents who are collectively responsive to the normative force of reasons that they jointly construct and maintain. I suggest that normative groups are more robust and socially interesting, and I suggest ways of identifying normative groups across different models and contexts.
15:00 - 15:30
Title Effect of Network Topology on Phase Diagram: Multiplex Spin Model case
Speaker Cook Hyun Kim (KENTECH)
Abstract As a convenient tool for describing various kinds of phenomena, complex networks have received a lot of attention. However, since it is difficult to fully describe complex phenomena with single-layer networks, multi-layer networks have been introduced to overcome this limitation. In this study, motivated from the fact that a multi-layered network is needed to describe the opinion dynamics more realistically, the Ising spin model defined on the multi-layer network was studied. And we investigated the effect of the multi-layered network on the phase and phase transition phenomena. As a result, we revealed that various types of phase transitions and crossover phenomena could occur depending on the control parameters, which did not occur in the single-layer network structure. In particular, we confirmed that discontinuous phase transitions could occur successively as temperature decreases from the critical temperature. In particular, we confirmed that discontinuous phase transitions could occur successively as temperature decreases from the critical temperature. The properties of the Ising model in multi-layer networks are quite complex compared to that in case of the single-layer networks, and thus we used the Landau-Ginsberg framework to understand the critical phenomena of the multiplex spin model.
15:30 - 16:30
Title Various types of percolation transitions using different representations: graph, hypergraph, and simplicial complex representations
Speaker Byungnam Kahng (KENTECH)
Abstract Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently, however, different types of percolation transitions, continuous, discontinuous, hybrid, and infinite-order phase transitions, have been observed in complex systems. To illustrate such phenomena, considerable effort has been made to introduce models and construct theoretical frameworks. Moreover, percolation transitions can be described by different representations: graph, hypergraph, and simplicial complex. Depending on the representations, we can find different structural features of percolation clusters. I will explain features of each type of percolation transitions and each representation.
16:30 - 17:00
Title The critical role of higher-order components in contagion dynamics on hypergraphs
Speaker Jung-Ho Kim (Korea U.)
Abstract The presence of the giant component is a necessary condition for the emergence of collective behavior in complex networked systems. Unlike networks, hypergraphs have an important native feature that components of hypergraphs might be of higher order, which could be defined in terms of the number of common nodes between hyperedges. Although the extensive largest higher-order component (HOC) could be found ubiquitously in real-world hypergraphs, the role of the giant HOC in collective behavior on hypergraphs has yet to be elucidated. In this presentation, we demonstrate that the presence of the giant HOC fundamentally alters the outbreak patterns of higher-order contagion dynamics on real-world hypergraphs. We confirm it by using synthetic random hypergraphs containing adjustable and analytically calculable giant HOC.
17:00 - 18:00
Title [Collective] Action and [Network] Structure: Sociological Contexts
Speaker Wonjae Lee (KAIST)
Abstract American sociology has long focused on the concepts of action and structure as crucial tools for understanding the social world. Economics and physics have emerged as influential disciplines in refining and developing theories related to these concepts. As such, sociology has situated itself within an interdisciplinary framework to advance our understanding of social phenomena. Differences between sociological and economic/physics understandings of action and structure offer opportunities for interdisciplinary research to further advance our understanding.
3/15 Wednesday
09:30 - 10:30
Title Limits of Individual Consent and Models of Distributed Consent in Online Social Networks
Speaker Juniper Lovato (Vermont)
Abstract Personal data are not discrete in socially-networked digital environments. A user who consents to allow access to their profile can expose the personal data of their network connections to non-consented access. Therefore, the traditional consent model (informed and individual) is not appropriate in social networks where informed consent may not be possible for all users affected by data processing and where information is distributed across users. Here, we outline the adequacy of consent for data transactions. Informed by the shortcomings of individual consent, we introduce both a platform-specific model of "distributed consent'' and a cross-platform model of a "consent passport.'' In both models, individuals and groups can coordinate by giving consent conditional on that of their network connections. We simulate the impact of these distributed consent models on the observability of social networks and find that low adoption would allow macroscopic subsets of networks to preserve their connectivity and privacy. [link to paper]
10:30 - 11:30
Title Understanding the structural effects in complex systems
Speaker Mi Jin Lee (Hanyang)
Abstract Various systems have their own underlying interaction structures which are usually expressed in terms of network sciences. The networked structures play an essential role of the emergence of a wide range of intriguing macroscopic phenomena. Focusing on the growth of infected clusters in an epidemic spreading, we want to understand the structural effects in complex systems. For reliable prediction of an epidemic or information spreading pattern in complex systems, the mean infection time is suggested as a better measure than cluster size. We show that the mean infection time can be evaluated by use of the scaling behaviors of the boundary area of the infected cluster. This enables us to find a nonexponential but algebraic spreading phase in the intermediate stage on strongly heterogeneous networks. This slow spreading originates from small-degree nodes left susceptible, while most hubs are already infected in the early exponential-spreading stage. Our results offer a way to quantify the temporal pattern of spread under structural heterogeneity. Furthermore, how to identify influential nodes in the spreading phenomena is an important question, and it is well known that the k-core score of the node is crucial. In other words, in general, detecting the core or essential structure of the embedding network helps us grasp the properties of the system, so this talk will end up with a brief introduction of relative research.
11:30 - 12:00
Title Growing scale-free hypergraph models with group-based growth rule
Speaker Dahae Roh (Korea U.)
Abstract In higher-order representations, a node can be considered to choose not only a node to interact with but also a community to participate in. Given that, a family of growing hypergraph models is presented taking into account contributions of both node and hyperedge in growth process. Depending on the model specifics, a node or a hyperedge could be selected either at random or preferentially. In one hand, a node can be merged into one of the pre-existing communities (the M-model), such as becoming a member of an association. On the other hand, another group can be created involving a new node and all the nodes participating in one of the pre-existing groups (the C-model), like creating new project group or collaboration. In the M-model, the resulting hyperdegree distribution P(k) and hyperedge size distribution P(s) follow either exponential or asymptotic power law and both are solved exactly. The C-model is studied also in probabilistic-mixture model, resulting P(k) ∼ k^{−γ} (2 ≤ γ ≤ 3) and exponential-like P(s). For hyperedge-random process in C-model, asymptotic P(k) and P(s) are solved exactly.
14:00 - 15:00
Title Interplay of individual and group dynamics in the study of contagions and cooperation.
Speaker Laurent Hébert-Dufresne (Vermont)
Abstract Models of dynamics in complex systems deviate from classic mathematical models by considering the heterogeneity of the agents involved. However, many of these dynamics are shaped by the decisions and behaviours of groups more than by the decisions and behaviours of individuals. Here, we will introduce a new family of mathematicals models of cooperation ("good dynamics") and contagions ("bad dynamics") moderated by groups and their dynamics. These groups can represent institutions like public health agencies or local communities with their own norms and culture. We show how these group-based models can produce complex dynamics without requiring very complex mechanisms. Our results will hopefully inspire more work to simplify our mathematical descriptions and ground our models in empirical results. More importantly, we hope to shift conceptual efforts away from agent-based perspectives and towards much needed group-based models.
15:00 - 15:30
Title Contagion dynamics on hypergraphs with nested hyperedges
Speaker Jihye Kim (Korea U.)
Abstract In complex social systems encoded as hypergraphs, higher-order (i.e., group) interactions taking place among more than two individuals can be represented as hyperedges connecting any number of nodes. In hypergraphs, some hyperedges can include other hyperedges within them. We refer to the hyperedge the nodes within which are connected by other hyperedges but no other hyperedges accommodate it as a subset in a hypergraph as the facet. In this paper, we say that a hyperedge is nested, if it connects a proper subset of the nodes in a facet. To quantify the hyperedge-nestedness and to investigate its effects on a simplicial susceptible-infected-susceptible (SIS) dynamics in hypergraphs, here we propose a nested-hypergraph model and an analytical framework called the facet approximation (FA). We formulate the FA and apply it to the proposed nested-hypergraph model with facets of size three. Solving the self-consistency equations derived from the FA, we obtain the stationary-state fraction of infected nodes for the simplicial SIS model; we further show how the hyperedge-nestedness changes the phase diagram. Monte Carlo simulations support the FA results.
15:30 - 16:30
Title Tie Formation and Group Formation in Strategic Interactions
Speaker Yunkyu Sohn (SNU)
Abstract I discuss the mechanisms of tie formation and group formation among decision makers in strategic interactions.
16:30 - 17:00
Title Influential teams and core structure of the higher-order networks
Speaker Jongshin Lee (KENTECH)
Abstract Recent advances in higher-order networks enlarge the human understanding of numerous complex systems, especially systems with team or group interaction structures. Similar to the graph case, a question arises about how we can select the influential or robust structure of the higher-order networks. In this presentation, we focus on the betweenness centrality (BC) for the former and the core decomposition for the latter. For each case, we propose procedures to obtain the BC values and the core structures using the bipartite graph representation. Next, we will be statistical physicists; unraveling the scaling behavior of these team structures enables us to have a new perspective on unexplored interactions. In the BC world, we analyze the BC distribution of hyperedges to figure out the highly influential teams. Unlike Barabasi-Albert (BA) networks, which exhibit the power-law BC distributions, a hypergraph model extending the BA network does not show that power-law distribution. Exploring how to get the power-law BC distribution of teams in the real-world coauthorship network, an exciting result is uncovered: a team with a widely connected member is highly influential. In the core decomposition process, we analytically and numerically scrutinize the percolation transition and critical phenomena. Most cases show the hybrid percolation transition, signified by the coinciding jump of the order parameter and the critical phenomena at the transition point. However, continuous percolation transition occurs for a particular case. Furthermore, not only the transition type but also the critical dynamics differs. For this particular case, we find the novel degree-dependent power-law relaxation dynamics. Our methods discussed will contribute to selecting high-impact teams or modular structures, which are sparsely connected to the periphery part, but highly interconnected within their respective structures.
[1] J. Lee, Y. Lee, S. M. Oh, and B. Kahng, Betweenness centrality of teams in social networks, Chaos 31, 061108 (2021).
[2] J. Lee, K.-I. Goh, D.-S. Lee, and B. Kahng, (k, q)-core decomposition of hypergraphs, arXiv:2301.06712 (2023).
17:00 - 18:00
Title Exploring The Network Origin of Creativity: The Post-AI Culture
Speaker Juyong Park (KAIST)
Abstract We discuss the meaning of creativity, and how high-order combinations of extant elements can provide an exponentially large “search space” for finding original and meaningful solutions to problems.
3/16 Thursday
09:30 - 10:30
Title The role of structure in higher-order dynamics
Speaker Alice Patania (Vermont)
Abstract Simplicial complexes are higher-order combinatorial structures that generalize graphs and encode not only pairwise relationships but also higher-order interactions between vertices. They have been used to represent real-world complex systems in various domains of data science. In this talk, we will introduce some basic concepts and tools of simplicial complexes, such as homology and cohomology, which measure the topological features of these structures. We will also explore the connection between differential equations and simplicial complexes using Hodge theory, which provides a way to decompose higher-order dynamics on these spaces. Finally, we will discuss some open problems and directions for future research on simplicial complexes and their applications.
10:30 - 11:00
Title Dynamics and control of higher-order epidemics
Speaker Bukyoung Jhun (SNU)
Abstract Complex contagion processes that cannot be reduced to a superposition of simple pair-wise contagion processes have been observed in a wide range of social systems. Hypergraph offers a platform to study higher-order interactions among constituents and dynamical behavior such as the spread of information or disease. Here, we introduce our studies on the phase transition and control of higher-order epidemics. We show that the phase transition from the absorbing to the endemic epidemic state is continuous (hybrid) when the effect of hubs is dominant (weak) [1]. We compare this result with a similar phenomenon in open quantum systems which has a distinct origin [2]. We also extend the pair-based mean-field theory to hypergraphs and develop effective epidemic control strategies in hypergraphs [3]. The effectiveness of such strategies indicates the necessity of scientific, data-driven, systematic policy-making for epidemic containment. This work is done in collaboration with Minjae Jo and B. Kahng.
[1] B. Jhun, M. Jo, and B. Kahng, J. Stat. Mech. 2019, 123207 (2019).
[2] B. Jhun, M. Jo, and B. Kahng, Chaos Solitons Fractals 160, 112262 (2022).
[3] B. Jhun, Phys. Rev. Res. 3, 033282 (2021).
11:00 - 11:30
Title COVID-19 epidemic under the K-quarantine model
Speaker Hoyoun Choi (SNU)
Abstract The COVID-19 pandemic is still ongoing worldwide, and the damage it has caused is unprecedented. In early times, South Korea had adopted a local quarantine strategy rather than a global lockdown for prevention. This approach not only minimizes economic damage but also efficiently prevents the spread of the disease. In this study, the spread of COVID-19 under local quarantine measures is modeled using the Susceptible-Exposed-Infected-Recovered model on complex networks. In this network approach, the links connected to infected and so quarantined people are disconnected and then reinstated when they are released. These link dynamics leads to time-dependent reproduction number. Numerical simulations are performed on networks with reaction rates estimated from empirical data. The temporal pattern of the accumulated number of confirmed cases is then reproduced. The results show that a large number of asymptomatic infected patients are detected as they are quarantined together with infected patients. Additionally, possible consequences of the breakdown of local quarantine measures and social distancing are considered.
11:30 - 12:30
Title Understanding transient dynamics leading to synchrony from the perspective of percolation transition
Speaker Young Sul Cho (JBNU)
Abstract Transient dynamics leading to the synchrony of a type of pulse-coupled oscillators, so-called scrambler oscillators, has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the evolution of the cluster size distribution for general cluster sizes has not been fully understood yet. In this presentation, we study the evolution of the cluster size distribution from the perspective of a percolation model by regarding the number of aggregations as the number of attached bonds. Specifically, we derive the scaling form of the cluster size distribution with specific values of the critical exponents using the property that the characteristic cluster size diverges as the percolation threshold is approached from below. Through simulation, it is confirmed that the scaling form well explains the evolution of the cluster size distribution. Based on the distribution behavior, we find that a giant cluster of all oscillators is formed discontinuously at the threshold and also that further aggregation does not occur like in a one-dimensional bond percolation model. Finally, we discuss the origin of the discontinuous formation of the giant cluster from the perspective of global suppression in explosive percolation models. For this, we approximate the aggregation process as a cluster–cluster aggregation with a given collision kernel.
3/17 Friday
09:30 - 10:30
Title Collective interactions in coevolutionary dynamics of networks
Speaker Byungjoon Min (CBNU)
Abstract Understanding the role of collective interactions in coevolutionary dynamics is crucial for pre- dicting the behavior of complex systems, from social networks to biological ecosystems. In this presentation, we explores the coevolutionary dynamics of group interactions and the evolution of network topology. Specifically, we study two models beyond pair-wise interactions: i) a coevolving non-linear voter model and ii) a coevolving threshold cascade model. We show that collective in- teractions between agents lead to diverse dynamical consequences and can play an important role in coevolutionary dynamics.
10:30 - 11:30
Title Statistical Modeling and Inference for Higher-Order Network Science
Speaker Jean-Gabriel Young (Vermont)
Abstract One of the main modeling tasks in higher-order network science is to reproduce, explain, and predict the structure of empirical systems. Higher-order descriptions afford us much welcomed flexibility in our models, as they allow us to explicitly incorporate the fundamental difference between dyadic and group relations in models. But with great flexibility come even greater challenges, both statistical and computational. In this talk, I will give an overview of statistical modeling techniques for higher-order systems, highlighting where complications arise in going from dyads to larger groups. I will discuss foundational structure models formulated in the simplicial complexes and hypergraphs representations, their connection with data, statistical computing techniques for estimating these models and discuss the problem of measurements.
11:30 - 12:00
Title Hidden Multiscale Organization in Real Multiplex Networks
Speaker Gangmin Son (KAIST)
Abstract Hidden geometry serves as a powerful framework to investigate complex networks at different resolutions. Here, we reveal the multiscale organization in real multiplex networks and its crucial role in cascading dynamics by introducing an extended framework. Our extension yields the spectrum of interlayer geometric correlation while zooming out from a multiplex network. Notably, we observe U-shaped spectra in real multiplex networks, i.e., the interlayer correlation breaks down significantly when the microscopic details are washed out to a certain scale. We demonstrate that these nontrivial behaviors can be reproduced by a model with clan structure, where the organization within clans is preserved across layers while that between clans is not. Moreover, we uncover the intimate relationship between clan structure and cascading dynamics. Our findings expand the role of hidden geometry in multiplex networks and shed light on the interplay between multiscale organization and function in real interdependent systems.