Papers

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.

Read the full article at: arxiv.org

Elsa Andres, Romualdo Pastor-Satorras, Michele Starnini, and Márton Karsai

Phys. Rev. Research 7, 043088

Behavioral adoptions of individuals are influenced by their peers in different ways. While in some cases an individual may change behavior after a single incoming influence, in other cases multiple cumulated attempts of social influence are necessary for the same outcome. These two mechanisms, known as simple and complex contagion, often occur together in social contagion phenomena, yet their distinguishability based on the observable contagion dynamics is challenging. In this paper we define a social contagion model evolving on temporal networks where individuals can switch between contagion mechanisms. We explore three spreading scenarios: predominated by simple or complex contagion, or where the dominant mechanism changes during the unfolding process. We propose analytical and numerical methods relying on global spreading observables to identify which of these three scenarios characterizes a social spreading outbreak. This work offers insights into social contagion dynamics on temporal networks, without assuming prior knowledge about the contagion mechanism driving the adoptions of individuals.

Read the full article at: link.aps.org

Giulio Tononi, Melanie Boly

This overview of integrated information theory (IIT) emphasizes IIT's "consciousness-first" approach to what exists. Consciousness demonstrates to each of us that something exists--experience--and reveals its essential properties--the axioms of phenomenal existence. IIT formulates these properties operationally, yielding the postulates of physical existence. To exist intrinsically or absolutely, an entity must have cause-effect power upon itself, in a specific, unitary, definite and structured manner. IIT's explanatory identity claims that an entity's cause-effect structure accounts for all properties of an experience--essential and accidental--with no additional ingredients. These include the feeling of spatial extendedness, temporal flow, of objects binding general concepts with particular configurations of features, and of qualia such as colors and sounds. IIT's intrinsic ontology has implications for understanding meaning, perception, and free will, for assessing consciousness in patients, infants, other species, and artifacts, and for reassessing our place in nature.

Read the full article at: arxiv.org

David Dahmen, Axel Hutt, Giacomo Indiveri, Ann Kennedy, Jeremie Lefebvre, Luca Mazzucato, Adilson E. Motter, Rishikesh Narayanan, Melika Payvand , Henrike Planert , Richard Gast

Much effort has been spent clustering neurons into transcriptomic or functional cell types and characterizing the differences between them. Beyond subdividing neurons into categories, we must recognize that no two neurons are identical and that graded physiological or transcriptomic properties exist within cells of a given type. This often overlooked "within-type" heterogeneity is a specific neuronal implementation of what statistical physics refers to as "disorder" and exhibits rich computational properties, the identification of which may shed crucial insights into theories of brain function. In this perspective article, we address this gap by highlighting theoretical frameworks for the study of neural tissue heterogeneity and discussing the benefits and implications of within-type heterogeneity for neural network dynamics, computation, and self-organization.

Read the full article at: inria.hal.science

José Ignacio Arroyo, Amahury J. Lopez-Diaz, Alejandro Maass, Carlos Gershenson, Pablo Marquet, Geoffrey West, Christopher P. Kempes

Understanding the extent to which genetic correlations change in response to environmental factors, such as temperature, is a poorly explored question, despite the importance of understanding how different processes will change with climate warming. Despite correlations between thermal performance traits having been reported in the literature for a few taxa and performance tasks, such as population growth rate, a comprehensive global analysis of the entire tree of life and multiple performance tasks remains an open challenge. To advance in this open question, we compile a database of 1,300 thermal response curves, encompassing 38 variable types related to individuals’ performance (including per capita population growth rate, photosynthetic rate, among others) and 1,125 different species, ranging from viruses to mammals, encompassing all major lineages of the tree of life. Our analysis reveals that among all possible relationships between traits and optimal performance, four traits form a line with a high goodness-of-fit, while the remaining traits exhibit a polygonal pattern, either a triangle or a tetrahedron. We derive a thermodynamic framework that explains the relationships described by a curve or line (as opposed to a surface or polygon), highlighting the linear relationship between maximum and minimum temperatures, as well as between maximum and optimum temperatures. We also discuss other generic trait evolution models, which could account for the other significant sublinear relationships, as well as the more general model, Pareto optimality theory, which could account for relationships in the form of lines or polygons. Our theoretical framework and empirical evidence suggest that, based on a single data point (e.g., minimum temperature), all critical temperature limits and maximum performance boundaries can be predicted using the estimated parameter from this study. Our results reveal universal scaling relationships in thermal performance, which could be useful for predicting changes in performance under scenarios of climate warming.

Read the full article at: www.biorxiv.org

See Also: A database of biological thermal performances

Thomas F. Varley, Vaibhav P. Pai, Caitlin Grasso, Jeantine Lunshof, Michael Levin & Josh Bongard

Communicative & Integrative Biology 

Volume 18, 2025 - Issue 1

Understanding how populations of cells collectively coordinate activity to produce the complex structures and behaviors that characterize multicellular organisms, and which coordinated activities, if any, survive processes that reshape cells and tissues into organoids, are fundamental issues in modern biology. Here, we show how techniques from complex systems and multivariate information theory provide a framework for inferring the structure of collective organization in non-neural tissue. Many of these techniques were developed in the context of theoretical neuroscience, where these statistics have been found to be altered during different cognitive, clinical, or behavioral states, and are generally thought to be informative about the underlying dynamics linking biology to cognition. Here, we show that these same patterns of coordinated activity are also present in the aneural tissues of evolutionarily distant biological systems: preparations of embryonic Xenopus laevis tissue (known as “basal Xenobots”). These similarities suggest that such patterns of activity either arose independently in these two systems (epithelial constructs and brains); are epiphenomenological byproducts of other dynamics conserved across vastly different configurations of life; or somehow directly support adaptive behavior across diverse living systems. Finally, these results provide unambiguous support for the hypothesis that, despite their apparent simplicity as collections of non-neural epithelial cells, Xenobots are in fact integrated, complex systems in their own right, with sophisticated internal information structures.

Read the full article at: www.tandfonline.com

Leila Hedayatifar, Alfredo J. Morales, Dominic E. Saadi, Rachel A. Rigg, Olha Buchel, Amir Akhavan, Egemen Sert, Aabir Abubaker Kar, Mehrzad Sasanpour, Irving R. Epstein & Yaneer Bar-Yam 

Scientific Reports volume 15, Article number: 33854 (2025)

Predicting dynamic behaviors is one of the goals of science in general as well as essential to many specific applications of human knowledge to real world systems. Here, we introduce an analytic approach using the sigmoid growth curve to model the dynamics of individual entities within complex systems. Despite the challenges posed by nonlinearity and unpredictability, we demonstrate that sigmoid-like trajectories frequently emerge in systems where entities undergo phases of acceleration and deceleration of growth. Through case studies of (1) customer purchasing behavior and (2) U.S. legislation adoption, we show that these patterns can be identified and used to predict an entity’s ultimate state well in advance of reaching it. This provides valuable insights for business leaders and policymakers. Moreover, our characterization of individual component dynamics offers a framework to reveal the aggregate behavior of the entire system. Moreover, our classification of entity lifepaths contributes to understanding system-level structure by revealing how individual-level dynamics scale to aggregate behaviors. This study offers a practical modeling framework that captures commonly observed growth dynamics in diverse complex systems and supports predictive decision-making.

Read the full article at: www.nature.com

compiled and edited by Ricard Solé, Chris Kempes and Susan Stepney
What is life, and how does it begin? This theme issue explores one of science’s deepest questions: how life can emerge from non-living matter. Researchers from many fields — from physics and chemistry to biology and artificial life — are working to uncover the basic principles that make life possible. Key themes include the role of energy and information in early cells, the plausibility of alternative forms of life, and efforts to recreate life-like systems in the lab. By bringing together diverse perspectives, this issue offers a fresh look at both the limits and possibilities for how life may arise, on Earth and beyond.

Read the full articles at: royalsocietypublishing.org

Petter Holme, Milena Tsvetkova

We review the historical development and current trends of artificially intelligent agents (agentic AI) in the social and behavioral sciences: from the first programmable computers, and social simulations soon thereafter, to today's experiments with large language models. This overview emphasizes the role of AI in the scientific process and the changes brought about, both through technological advancements and the broader evolution of science from around 1950 to the present. Some of the specific points we cover include: the challenges of presenting the first social simulation studies to a world unaware of computers, the rise of social systems science, intelligent game theoretic agents, the age of big data and the epistemic upheaval in its wake, and the current enthusiasm around applications of generative AI, and many other topics. A pervasive theme is how deeply entwined we are with the technologies we use to understand ourselves.

Read the full article at: arxiv.org

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.

Read the full issue at: epjb.epj.org

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

Guido Caldarelli, Oriol Artime, Giulia Fischetti, Stefano Guarino, Andrzej Nowak, Fabio Saracco, Petter Holme, Manlio de Domenico
The boundaries between physical and social networks have narrowed with the advent of the Internet and its pervasive platforms. This has given rise to a complex adaptive information ecosystem where individuals and machines compete for attention, leading to emergent collective phenomena. The flow of information in this ecosystem is often non-trivial and involves complex user strategies from the forging or strategic amplification of manipulative content to large-scale coordinated behavior that trigger misinformation cascades, echo-chamber reinforcement, and opinion polarization. We argue that statistical physics provides a suitable and necessary framework for analyzing the unfolding of these complex dynamics on socio-technological systems. This review systematically covers the foundational and applied aspects of this framework. The review is structured to first establish the theoretical foundation for analyzing these complex systems, examining both structural models of complex networks and physical models of social dynamics (e.g., epidemic and spin models). We then ground these concepts by describing the modern media ecosystem where these dynamics currently unfold, including a comparative analysis of platforms and the challenge of information disorders. The central sections proceed to apply this framework to two central phenomena: first, by analyzing the collective dynamics of information spreading, with a dedicated focus on the models, the main empirical insights, and the unique traits characterizing misinformation; and second, by reviewing current models of opinion dynamics, spanning discrete, continuous, and coevolutionary approaches. In summary, we review both empirical findings based on massive data analytics and theoretical advances, highlighting the valuable insights obtained from physics-based efforts to investigate these phenomena of high societal impact.

Read the full article at: arxiv.org

Fernando Diaz-Diaz, Elena Candellone, Miguel A. Gonzalez-Casado, Emma Fraxanet, Antoine Vendeville, Irene Ferri, Andreia Sofia Teixeira

Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This polarity reshapes how we think about structure and dynamics in complex systems: a negative tie is not simply a missing positive one but a constraint that generates tension, and possibly asymmetry. Across disciplines, from sociology to neuroscience and machine learning, signed networks provide a shared language to formalise duality, balance, and opposition as integral components of system behaviour. This review provides a comprehensive and foundational summary of signed network theory. It formalises the mathematical principles of signed graphs and surveys signed-network-specific measures, including signed degree distributions, clustering, centralities, motifs, and Laplacians. It revisits balance theory, tracing its cognitive and structural formulations and their connections to frustration. Structural aspects of signed networks are examined, analysing key topics such as null models, node embeddings, sign prediction, and community detection. Subsequent sections address dynamical processes on and of signed networks, such as opinion dynamics, contagion models, and data-driven approaches for studying evolving networks. Practical challenges in constructing, inferring and validating signed data from real-world systems are also highlighted, and we offer an overview of currently available datasets. We also address common pitfalls and challenges that arise when modelling or analysing signed data. Overall, this review integrates theoretical foundations, methodological approaches, and cross-domain examples, providing a structured entry point and a reference framework for researchers interested in the study of signed networks in complex systems.

Read the full article at: arxiv.org

Luiz H. A. Monteiro

Complexities 2025, 1(1), 2

Defining a complex system and evaluating its complexity typically requires an interdisciplinary approach, integrating information theory, signal processing techniques, principles of dynamical systems, algorithm length analysis, and network science. This overview presents the main characteristics of complex systems and outlines several metrics commonly used to quantify their complexity. Simple examples are provided to illustrate the key concepts. Speculative ideas regarding these topics are also discussed here.

Read the full article at: www.mdpi.com

Renli Wu, Christopher Esposito, and James Evans

PNAS 122 (44) e2414893122

China’s emergence as one of the world’s top producers of high-quality science raises critical questions about its trajectory toward achieving scientific leadership. Traditional methods for evaluating the power of national scientific ecosystems, however, often overlook the nuances of a country’s global influence. In this perspective, we introduce a framework that highlights shifting power dynamics in international scientific collaborations, focusing on whether leadership positions in international scientific teams are moving from one country to another. Using rich sociological data from nearly 6 million scientific publications, we document a marked shift in team leadership from Western countries to China. In particular, the share of team leaders involved in U.S-China scientific collaborations that were affiliated with Chinese institutions grew from 30% of the total in 2010 to 45% in 2023. We further explore the implications of China’s rise by forecasting when Chinese scientists are projected to achieve parity in leadership vis-à-vis the United States, including in 11 critical technology areas that are focal points of technological development, and by analyzing how a potential decoupling of U.S.-Chinese science might affect Chinese scientific leadership. We conclude by considering the impacts of China’s growing investments in the training of young scientists in countries participating in the Belt and Road Initiative.

Read the full article at: www.pnas.org

Xiangyi Meng, Benjamin Piazza, Csaba Both, Baruch Barzel, Albert-László Barabási

The brain's connectome and the vascular system are examples of physical networks whose tangible nature influences their structure, layout, and ultimately their function. The material resources required to build and maintain these networks have inspired decades of research into wiring economy, offering testable predictions about their expected architecture and organisation. Here we empirically explore the local branching geometry of a wide range of physical networks, uncovering systematic violations of the long-standing predictions of length and volume minimisation. This leads to the hypothesis that predicting the true material cost of physical networks requires us to account for their full three-dimensional geometry, resulting in a largely intractable optimisation problem. We discover, however, an exact mapping of surface minimisation onto high-dimensional Feynman diagrams in string theory, predicting that with increasing link thickness, a locally tree-like network undergoes a transition into configurations that can no longer be explained by length minimisation. Specifically, surface minimisation predicts the emergence of trifurcations and branching angles in excellent agreement with the local tree organisation of physical networks across a wide range of application domains. Finally, we predict the existence of stable orthogonal sprouts, which not only are prevalent in real networks but also play a key functional role, improving synapse formation in the brain and nutrient access in plants and fungi.

Read the full article at: arxiv.org

Dirk Helbing

This review article reflects on emerging societies using a data-driven, cybernetic governance approach. Such an approach implies great opportunities, but also considerable challenges and potential ethical issues, requiring scientific and pubic debate. We will start by discussing the role of the Internet of Things for cyber-physical systems and smart societies. After this, we will introduce converging technologies, which are able to connect information technologies with nano-, bio-, and other technologies. While these technologies are currently less known to the wider public, they can be game changers for societies. Among the possible applications, we will pay particular attention to the "Internet of Bodies" and to nano-neurotechnologies. The former can be used in the context of precision medicine, while the latter may eventually enable interactions with the real world just by thought. Both approaches use digital twins and have enormous opportunities , but the risks of accidental damage or intentional misuse are high. As it turns out, quantum technologies have further interesting implications, which may change emerging cybernetic societies as well. Last but not least we will discuss ethical issues and further challenges of cybernetic societies, leading to a call for action.

Read the full article at: www.researchgate.net

J. A. Scott Kelso

The European Physical Journal Special Topics

This tribute to Hermann Haken, the great theoretical physicist, explores the idea—based on a reconsideration of the experiments that led to the HKB model—that intentions (an emergent ‘mental force’) are hidden~exposed in order parameter fluctuations that arise due to special boundary conditions or rate-independent constraints on the basic coordination dynamics of human brain and behavior.

Read the full article at: link.springer.com

bel Jansma, Erik Hoel

One of the reasons complex systems are complex is because they have multiscale structure. How does this multiscale structure come about? We argue that it reflects an emergent hierarchy of scales that contribute to the system's causal workings. An example is how a computer can be described at the level of its hardware circuitry but also its software. But we show that many systems, even simple ones, have such an emergent hierarchy, built from a small subset of all their possible scales of description. Formally, we extend the theory of causal emergence (2.0) so as to analyze the causal contributions across the full multiscale structure of a system rather than just over a single path that traverses the system's scales. Our methods reveal that systems can be classified as being causally top-heavy or bottom-heavy, or their emergent hierarchies can be highly complex. We argue that this provides a more specific notion of scale-freeness (here, when causation is spread equally across the scales of a system) than the standard network science terminology. More broadly, we provide the mathematical tools to quantify this complexity and provide diverse examples of the taxonomy of emergent hierarchies. Finally, we demonstrate the ability to engineer not just degree of emergence in a system, but how that emergence is distributed across the multiscale structure.

Read the full article at: arxiv.org