Amahury J. López-Díaz, Pedro Juan Rivera Torres, Gerardo L. Febres, Carlos Gershenson

Discrete dynamical models underpin systems biology, but we still lack substrate-agnostic diagnostics for when such models can sustain genuinely open-ended evolution (OEE): the continual production of novel phenotypes rather than eventual settling. We introduce a simple, model-independent metric, {\Omega}, that quantifies OEE as the residence-time-weighted contribution of each attractor’s cycle length across the sequence of attractors realized over time. {\Omega} is zero for single-attractor dynamics and grows with the number and persistence of distinct cyclic phenotypes, separating enduring innovation from transient noise. Using Random Boolean Networks (RBNs) as a unifying testbed, we compare classical Boolean dynamics with biologically motivated non-classical mechanisms (probabilistic context switching, annealed rule mutation, paraconsistent logic, modal necessary/possible gating, and quantum-inspired superposition/entanglement) under homogeneous and heterogeneous updating schemes. Our results support the view that undecidability-adjacent, state-dependent mechanisms — implemented as contextual switching, conditional necessity/possibility, controlled contradictions, or correlated branching — are enabling conditions for sustained novelty. At the end of our manuscript we outline a practical extension of {\Omega} to continuous/hybrid state spaces, positioning {\Omega} as a portable benchmark for OEE in discrete biological modeling and a guide for engineering evolvable synthetic circuits.

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Alberto Aleta, Andreia Sofia Teixeira, Guilherme Ferraz de Arruda, Andrea Baronchelli, Alain Barrat, János Kertész, Albert Díaz-Guilera, Oriol Artime, Michele Starnini, Giovanni Petri, Márton Karsai, Siddharth Patwardhan, Alessandro Vespignani, Yamir Moreno, Santo Fortunato

Multilayer network science has emerged as a central framework for analysing interconnected and interdependent complex systems. Its relevance has grown substantially with the increasing availability of rich, heterogeneous data, which makes it possible to uncover and exploit the inherently multilayered organisation of many real-world networks. In this review, we summarise recent developments in the field. On the theoretical and methodological front, we outline core concepts and survey advances in community detection, dynamical processes, temporal networks, higher-order interactions, and machine-learning-based approaches. On the application side, we discuss progress across diverse domains, including interdependent infrastructures, spreading dynamics, computational social science, economic and financial systems, ecological and climate networks, science-of-science studies, network medicine, and network neuroscience. We conclude with a forward-looking perspective, emphasizing the need for standardized datasets and software, deeper integration of temporal and higher-order structures, and a transition toward genuinely predictive models of complex systems.

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Guest Editors: Thiago B. Murari, Marcelo A. Moret, Hernane B. de B. Pereira, Tarcísio M. Rocha Filho, José F. F. Mendes, Tiziana Di Matteo

Inspired by the Conference on Complex Systems 2023 (CCS2023) in Salvador, Brazil, this collection of EPJ B brings together 25 peer-reviewed articles covering a wide range of topics.
This collection highlights the interdisciplinary nature of the field, with contributions from physics, biology, economics, linguistics, and artificial intelligence, and serves as a reference for researchers addressing real-world challenges through systems-based thinking.

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Mohsen Raoufi, Heiko Hamann & Pawel Romanczuk
npj Complexity volume 2, Article number: 28 (2025)

Collective estimation is a variant of collective decision-making where agents reach consensus on a continuous quantity through social interactions. Achieving precise consensus is complex due to the co-evolution of opinions and the interaction network. While homophilic networks may facilitate estimation in well-connected systems, disproportionate interactions with like-minded neighbors lead to the emergence of echo chambers and prevent consensus. Our agent-based simulations confirm that, besides limited exposure to attitude-challenging opinions, seeking reaffirming information entrap agents in echo chambers. To overcome this, agents can adopt a stubborn state (Messengers) that carries data and connects clusters by physically transporting their opinion. We propose a generic approach based on a Dichotomous Markov Process, which governs probabilistic switching between behavioral states and generates diverse collective behaviors. We study a continuum between task specialization (no switching), to generalization (slow or rapid switching). Messengers help the collective escape local minima, break echo chambers, and promote consensus.

Read the full article at: www.nature.com

Michael Lissack

This paper presents a unified theoretical framework that reconciles four apparently disparate approaches: Quantum Bayesianism (QBism), Robert Rosen’s theory of Anticipatory Systems, the causal bubbles interpretation of quantum mechanics, and pragmatic constructivism through Hans Vaihinger’s philosophy of ‘as if.’ We demonstrate that these frameworks converge on a fundamental insight: reality emerges from a relational causal structure-the pattern of influences that determine what can affect what-rather than from external observation. The QBist agent exemplifies a Rosen Anticipatory System operating within a causal bubble, wherein the quantum wave function serves as a heuristic fiction-an ‘as if’ construct-used for anticipatory modeling within the agent’s architecture rather than for ontological description. This synthesis resolves longstanding quantum paradoxes, provides a naturalized account of final causality, and extends to encompass human cognition and artificial intelligence as distinct instantiations of the same anticipatory pattern. We argue that physical laws function as normative standards for coherent anticipation that acquire constraining force through selective pressure, and that this relational ontology bridges quantum physics, theoretical biology, epistemology, and cognitive science, dissolving apparent conflicts between these domains into perspectives on a shared structure.

Read the full article at: papers.ssrn.com