Papers
Topics
Authors
Recent
Search
2000 character limit reached

Synergistic signatures of group mechanisms in higher-order systems

Published 21 Jan 2024 in physics.soc-ph and cond-mat.stat-mech | (2401.11588v2)

Abstract: The interplay between causal mechanisms and emerging collective behaviors is a central aspect of understanding, controlling, and predicting complex networked systems. In our work, we investigate the relationship between higher-order mechanisms and higher-order behavioral observables in two representative models with group interactions: a simplicial Ising model and a social contagion model. In both systems, we find that group (higher-order) interactions show emergent synergistic (higher-order) behavior. The emergent synergy appears only at the group level and depends in a complex, non-linear way on the trade-off between the strengths of the low- and higher-order mechanisms and is invisible to low-order behavioral observables. Our work sets the basis for systematically investigating the relation between causal mechanisms and behavioral patterns in complex networked systems with group interactions, offering a robust methodological framework to tackle this challenging task.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (21)
  1. U. Grenander and M. I. Miller, Journal of the Royal Statistical Society: Series B (Methodological) 56, 549 (1994).
  2. J. D. Sterman, System Dynamics Review 10, 291 (1994).
  3. S. V. Scarpino and G. Petri, Nature communications 10, 898 (2019).
  4. T. P. Peixoto, Physical Review X 8, 041011 (2018).
  5. B. Prasse and P. Van Mieghem, Proceedings of the National Academy of Sciences 119, e2205517119 (2022).
  6. A.-L. Barabási, Nature Physics 8, 14 (2012).
  7. T. P. Peixoto, Physical Review Letters 123, 128301 (2019).
  8. K. Huang, Introduction to statistical physics (CRC press, 2009).
  9. S. N. Dorogovtsev, A. V. Goltsev, and J. F. Mendes, Reviews of Modern Physics 80, 1275 (2008).
  10. P. L. Williams and R. D. Beer, Nonnegative decomposition of multivariate information (2010), arXiv:1004.2515 [cs.IT] .
  11. V. Griffith and C. Koch, in Guided self-organization: inception (Springer, 2014) pp. 159–190.
  12. T. Schreiber, Physical Review Letters 85, 461 (2000).
  13. D. Merlini, Lettere al Nuovo Cimento (1971-1985) 8, 623 (1973).
  14. M. E. Newman and G. T. Barkema, Monte Carlo methods in statistical physics (Clarendon Press, 1999).
  15. Triplets of random nodes behave similarly to 3-cliques, moreover it is of interest to discriminate between true and spurious three-body couplings.
  16. T. M. Cover, Elements of information theory (John Wiley & Sons, 1999).
  17. The statistical distance is half of the L1superscript𝐿1L^{1}italic_L start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT distance between the two discrete distributions.
  18. The Ising model on a Erdős–Rényi random graph is well described by the know results for the mean-field Ising model [21], which has critical temperature given by Tcr./J=qsubscript𝑇cr𝐽𝑞T_{\rm cr.}/J=qitalic_T start_POSTSUBSCRIPT roman_cr . end_POSTSUBSCRIPT / italic_J = italic_q where q𝑞qitalic_q is the coordination number of the lattice. Fixing the temperature T=1𝑇1T=1italic_T = 1 and with q=⟨k1⟩𝑞delimited-⟨⟩subscript𝑘1q=\langle k_{1}\rangleitalic_q = ⟨ italic_k start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ⟩ in our Hamiltonian Eq. (Dynamical systems with higher-order mechanisms.) we obtain the critical value of the pairwise coupling: J1cr.=1superscriptsubscript𝐽1cr1J_{1}^{\rm cr.}=1italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT roman_cr . end_POSTSUPERSCRIPT = 1.
  19. S. Piaggesi, A. Panisson, and G. Petri, in Learning on Graphs Conference (PMLR, 2022) pp. 55–1.
  20. A. Levina, V. Priesemann, and J. Zierenberg, Nature Reviews Physics 4, 770 (2022).
  21. V. Thibeault, A. Allard, and P. Desrosiers, Nature Physics , 1 (2024).
Citations (2)
View on Semantic Scholar

Summary

  • The paper introduces a framework that quantifies emergent synergistic behavior through higher-order interactions in complex networks.
  • It utilizes extended simplicial Ising and contagion models to capture group mechanisms, revealing nonlinear dependencies between interaction strength and system dynamics.
  • The study shows that traditional pairwise metrics overlook key dynamics, highlighting the need for measures like total dynamical O-information in network analysis.

Synergistic Signatures of Group Mechanisms in Higher-Order Systems

The paper "Synergistic signatures of group mechanisms in higher-order systems" addresses the complexity of networked systems by examining the interplay between causal mechanisms and emergent collective behaviors. It posits that higher-order interactions in systems, such as simplicial complexes, can generate emergent behaviors not explainable by pairwise interactions alone. The research establishes a framework for analyzing these relationships, critical for understanding, controlling, and predicting system dynamics.

The study focuses on two representative models featuring group interactions: the simplicial Ising model and a social contagion model. In both, the authors explore how group interactions manifest emergent synergistic behavior and assess how the prevalence of this behavior scales with the strength of higher-order interactions.

Methodological Approach

The methodology involves leveraging simplicial complexes to capture the multi-node interactions typical of higher-order networks. The analyses employ two extended dynamical models:

  1. Simplicial Ising Model: A generalization of the classic Ising model incorporating group interactions, quantified by a Hamiltonian encompassing higher-order terms among simplices.
  2. Simplicial Contagion Model: An evolution of the traditional SIS model, adapted to include group infection dynamics within simplicial complexes.

Higher-order behaviors are quantified using the total dynamical O-information, a metric that extends previous measures like transfer entropy to capture information-sharing among variable groups. This measure distinguishes between redundant and synergistic information distribution, highlighting interactions that traditional pairwise metrics might overlook.

Numerical Results and Key Findings

The research provides robust numerical evidence supporting its hypotheses. Specifically, it identifies that higher-order mechanisms can promote significant synergistic behaviors, as revealed by enhanced synergistic O-information. The results also underscore the inadequacy of lower-order metrics in capturing the complexity inherent in group interactions, revealing a nuanced dependency of higher-order behaviors on the strength of higher-order mechanisms. Two pivotal findings are:

  • Emergent Synergistic Interactions: The study reveals that as the strength of higher-order interactions increases, the systems exhibit increasingly significant synergistic behavior, especially in genuine higher-order groupings such as 2-simplices.
  • System-Specific Dependency: The degree to which higher-order interactions influence observed behaviors is system-dependent, with varying non-linear relationships noted between different parameters in the Ising and contagion models.

Implications and Future Directions

The implications of these findings are two-fold. Theoretically, the paper enhances the understanding of complex system dynamics by linking behavior to mechanistic underpinnings in a non-trivial manner. Practically, the results could inform the design of interventions in complex systems, whether in controlling spreading processes or in optimizing the performance of networked infrastructures.

Future work could extend this analysis to larger systems and different network topologies to determine how these findings generalize. Additionally, integrating real-world data could validate the models' predictive capabilities, thereby bridging theoretical and applied research in network science. This involves further exploration of the interplay between low- and higher-order interactions, which may contribute significantly to advancements in fields like computational neuroscience, epidemiology, and beyond.

The study offers a comprehensive framework for advancing the frontier of knowledge in higher-order network dynamics, presenting potent tools for both academic inquiry and practical application in understanding complex systems.

Paper to Video (Beta)

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Generate

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Tweets

Sign up for free to view the 7 tweets with 95 likes about this paper.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up for Free