Read the full article at: www.mdpi.com

Phys. Rev. Lett. 136, 207401

We study diffusion on multiplex networks with directed interlayer couplings. We demonstrate both numerically and analytically that even with undirected layers, interlayer directionality alone reproduces superdiffusion and the prime regime. We further reveal a new phenomenon, the directionality-induced jamming, whereby directed interlayer links hinder diffusion, fragmenting the system into dynamically disconnected components and preventing convergence to the steady state of the diffusion process. Via an optimization process, we show that this new regime is attainable in both toy models and real-world topologies. These findings underscore the crucial role of interlayer link directionality in shaping the emergent behavior of multiplex systems, with potential implications for the design and control of such systems.

Read the full article at: journals.aps.org

Elite football is believed to have evolved in recent years, yet systematic evidence for the pace and form of that change remains sparse. Drawing on event-level records for 13,018 matches across ten top-tier men’s and women’s leagues in England, Spain, Germany, Italy, and the United States (2020–2025), we quantify match dynamics through two complementary lenses: conventional performance statistics and pitch-passing networks that track ball movement across spatial regions of the field. Between 2020 and 2025, average passing volume, pass accuracy, and the proportion of passes made under pressure all increased, with the largest year-on-year changes occurring in women’s competitions. Network measures reveal that normalized outreach decreased, indicating teams increasingly concentrate ball circulation into shorter-range passing connections rather than wide spatial distribution. These trends are consistent across countries and tiers, yet persistent national differences indicate that stylistic diversity remains. Notably, women’s competitions exhibit stronger rates of change across most metrics, consistent with an accelerating professionalization, while the systematic decline in network outreach across all competitions is consistent with a sport-wide shift toward shorter, more concentrated passing structures.

Read the full article at: www.nature.com

Money serves several roles: a medium of exchange to buy and sell without bartering; a unit of account to price goods consistently; a store of value to save purchasing power over time; a means to defer payment of future obligations like credit or loans. An agent based computer simulation program determine quantitatively the relative importance of these services. The main results showed that money for credit was by far the feature that achieved the largest overall production of wealth in the simulated societies. A conclusion from this study suggests that fomenting the use of internationally tradable currencies such as Bitcoin seems to be most promising pathway for international economic growth in the near future.

Read the full article at: papers.ssrn.com

FORESIGHTERS (Future ORiEnted Skills, Innovation for Governance for Health, Technology, EneRgy, citieS and creativity) offers unique opportunities to build a future research career that tackles complex societal problems. While researchers will be based in academic units across the university, from engineering, humanities, social science and the arts, they will be working within one of 5 interdisciplinary research themes (Health, Technology, Energy, Future Cities, and Creativity). The cohort of researchers will be bound by a common perspective and training in Futures Thinking and Futures Literacy and will develop the skills and capabilities to understand, imagine, and critically use different ideas about the future to better understand key challenges. In addition to advanced training offered by the Thomas Moran Graduate School, FORESIGHTERS ESRs will be trained in skills for anticipating change and using multiple possible futures to stimulate reflection, creativity, resilience and focus for contemporary action. The training programme also has a strong emphasis on the development of sustainable, diverse, and equitable research environments.

More at: www.qub.ac.uk

Active matter generates order or patterns through nonequilibrium dynamics. An open research challenge is to determine how efficiently a nonequilibrium self-organising system can convert consumed energy into macroscopic order. We study an information-theoretic quantity that directly addresses this challenge by estimating the entropy reduction induced by a small control-parameter perturbation, relative to the generalised work required for the perturbation. This quantity has previously been considered mainly in an equilibrium or near-equilibrium context, and here we extend this framework and apply it to two nonequilibrium self-organising systems: persistent and active Ising models. We observe that the thermodynamic efficiency of nonequilibrium systems maximises at phase transitions, as in equilibrium systems. Furthermore, we compare thermodynamic efficiency and inferential efficiency across control parameters. While these two quantities are equal in equilibrium as a consequence of the fluctuation-dissipation theorem, we report that they diverge out of equilibrium, and the gap reflects how far the system is from equilibrium.

Read the full article at: arxiv.org

We see consciousness in AI the same way we see faces in clouds, says neuroscientist Anil Seth. He explores the all-too-human tendency to project inner life onto machines that are brilliant mimics, not sentient beings, and gives a definitive answer to the urgent question: Will AI ever gain consciousness?

Watch at: www.youtube.com

Regional Economic Integration is a process by which countries seek mutual benefits through the reduction of trade, social, and political barriers. This paper introduces a computational mathematical model grounded in Economic Complexity Theory to analyze economic blocs as unified entities. Four case studies are examined: the European Union, MERCOSUR, URUPABOL, and the Andean Community. Using real export data and complexity metrics, we identify the combined productive capacities of member countries. Results reveal that integration enhances product diversity and increases the ubiquity of exports within the bloc. The study demonstrates that regional integration boosts development and strengthens competitiveness in the global economy. The proposed methodological approach provides a novel tool for regional analysis and serves as a foundation for future strategies in economic cooperation and productive planning. This research contributes to understanding how collective capabilities can generate synergies that exceed individual national potentials, particularly in the context of Latin American regional development.

Read the full article at: ieeexplore.ieee.org

Nowadays, neural networks act as a synonym for artificial intelligence. Present neural network models, although remarkably powerful, are inefficient both in terms of data and energy. Several alternative forms of neural networks have been proposed to address some of these problems. Specifically, spiking neural networks are suitable for efficient hardware implementations. However, effective learning algorithms for spiking networks remain elusive, although it is suspected that effective plasticity mechanisms could alleviate the problem of data efficiency. Here, we present a new framework for spiking neural networks—Spark (https://github.com/Nogarx/Spark)—built upon the idea of modular design, from simple components to entire models. The aim of this framework is to provide an efficient and streamlined pipeline for spiking neural networks. We showcase this framework by solving the sparse-reward cartpole problem with simple plasticity mechanisms. We hope that a framework compatible with traditional ML pipelines may accelerate research in the area, specifically for continuous and unbatched learning, akin to the one animals exhibit

Read the full article at: www.frontiersin.org

Through a combination of lectures, hands-on coding sessions, and interdisciplinary discussions, participants will explore how emergent phenomena—such as financial crises, innovation diffusion, urban growth, and collective decision-making—arise from decentralized interactions among agents.

Many of today’s most pressing social and economic challenges exhibit emergent properties that traditional equilibrium-based methods struggle to explain.

This Summer School addresses that gap by equipping participants with state-of-the-art tools from complexity science, enabling them to analyze systems where collective behavior and adaptation drive outcomes.

Enroll at: bse.eu

The universe creatively sets the rules for its own becoming.

Stuart Kauffman is a theoretical biologist and leading complexity scientist who has argued that the self-organization of organisms is as influential in evolution as natural selection. His seminal book on the subject is “The Origins of Order: Self-Organization and Natural Selection in Evolution” (1993). He spoke recently with Noema Editor-in-Chief Nathan Gardels.

Read the full article at: www.noemamag.com

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 standardised 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: academic.oup.com

Complex Systems, 34(4), 2026 pp. 387–400.

Complexity, a term that is both ambiguous and multifaceted, is used widely today. Various legitimate definitions can be proposed for it, as is the case with “ample” notions such as intelligence, consciousness or culture. The recurrent mention of this term can be attributed to the transformation of our societies and their artifacts, as well as the acceleration of time brought by the digital revolution—a technological upheaval comparable to the invention of writing and the printing press.

Read the full article at: www.complex-systems.com

In recent years, large-scale models and automated systems have made it possible to synthesize vast amounts of scientific information. However, identifying what is foundational — what truly shapes the conceptual and methodological backbone of a field — still requires distributed expert judgment. This effort is designed to complement algorithmic approaches by leveraging collective intelligence: many independent perspectives, aggregated into a structured view.

The objective is not to produce a simple ranking of famous papers, but to build a structured map of the field’s foundations, including works that may be missing from keyword-based or citation-based approaches.

Read the full article at: manliodedomenico.com

The integrated information theory of consciousness (IIT) is uniquely ambitious in proposing a mathematical formula, derived from apparently fundamental properties of conscious experience, to describe the quantity and quality of consciousness for any physical system that possesses it. IIT has generated considerable debate, which has engendered some misunderstandings and misrepresentations. Here we address and hope to remedy this. We begin by concisely summarising the essentials of IIT. Given IIT is supposed to apply universally, we do this with reference to an arbitrary patch of matter, as opposed to the usual system of discrete computational units. Then, after briefly summarising IIT’s theoretical and empirical achievements, we focus on five points which we consider especially important for driving forward new theory and increasing understanding. First, a high value of the measure Φ is not synonymous with `more consciousness’. We describe how Φ might be replaced with a suite of quantities to obtain a multi-dimensional characterisation of states of consciousness. Second, we describe with nuance the distinct flavour of panpsychism implied by IIT — whereby space (and time) are tiled with substrates of (proto-) consciousness — and find this is not problematic for the theory. Third, Φ is not well-defined for real physical systems, and has not been computed on any real physical system. Fourth, so far only proxies for IIT measures have been computed, and not approximations. Fifth, for IIT to fit with current successful theories in fundamental physics, a reformulation in terms of continuous fields would be needed.

Read the full article at: arxiv.org

More at: ccs26.cssociety.org

PNAS 123 (18) e2511050123

The term “invisible college” refers to communication networks that help scientists exchange information and advance knowledge. These networks create social capital, granting access to resources like new ideas and support. Measuring those intangible exchanges is an empirical challenge. Here we approximate these ties through the analysis of the “thank you” notes appended to journal articles. Our findings show that scholars disconnected from this layer of academic social capital have lower publication impact. We also show that informal ties provide support not captured by coauthorship ties, which reflect a more rigid form of collaboration. Documenting how informal structures of support operate can help leverage collective resources in the pursuit of shared intellectual goals.

Read the full article at: www.pnas.org

Read the full article at: www.mivideo.it.umich.edu

Entropy 2026, 28(4), 398

Social media platforms offer unprecedented opportunities to study cultural evolution by analyzing digital traces. This study presents a methodological framework for analyzing the temporal dynamics of cultural modules in hashtag co-occurrence networks. We address the inherent challenges of analyzing dense, skewed, and highly variable cultural networks by introducing a perturbation ensemble clustering approach that distinguishes stable from unstable structural elements. By applying the Leiden algorithm to a perturbed ensemble of hashtag networks, we identify robust core modules and their stable periphery, and distinguish them from floating elements with unstable associations. Analysis of four years of data from a major photo-sharing platform reveals complex patterns in the evolution of cultural modules, including both stable associations and dynamic reorganizations. Our findings demonstrate how ensemble clustering techniques can effectively capture the interplay between stability and change in evolving cultural systems.

Read the full article at: www.mdpi.com

Organizations learn from market, political and societal responses to their actions. While in some cases both the actions and responses take place in an open manner, in many others, some aspects may be hidden from external observers. The Eurovision Song Contest offers a mostly open-data case in which to study organizational level learning at the levels of organizers and participants. We present here evidence for changes in the rules of the Contest in response to undesired outcomes such as runaway winners. We also find strong evidence of participant learning in the characteristics of competing songs over the 70 years of the Contest. English has been adopted as the lingua franca of the competing songs and pop has become the standard genre. The number of words of lyrics has also grown in response to this collective learning. Remarkably, we find evidence that France, Italy, Portugal and Spain have chosen to ignore the ‘lesson’ that English lyrics increase winning probability, consistent with utility functions that award greater value to featuring national culture than to winning the Contest. These countries—but not Germany—appear to be less susceptible to Anglo-Saxon cultural influence than their peers, a resistance that may extend beyond cultural matters.

Read the full article at: royalsocietypublishing.org

Chaos, Solitons & Fractals
Volume 208, Part 4, July 2026, 118382

This study modifies the model in the previous studies and considers three types of inter-individual relationships: regular, random, and scale-free ring lattices. Furthermore, we introduce defectors, who do not contribute to the public goods; cooperators, who contribute to the public goods; and loners, who do not participate in the public goods framework. We assume that each of these three types of individuals punishes other individuals with a probability proportional to the difference between their own payoff and their opponent’s average payoff including them. Using this modified pool punishment model, this study shows the following. Firstly, the damage to the average payoff due to excessive punishment is kept significantly low. Secondly, antisocial punishment is not evolutionarily advantageous, and cooperators always become advantageous. Finally, the final average payoff is always higher than that of pool punishment in existing studies and roughly comparable to that of peer punishment in existing studies. The results of this study provide new insights that the claim of the existing study is not always correct; that is, even if antisocial punishment is possible, it does not have an evolutionary advantage, and cooperators always become advantageous, which in turn solves the problem of antisocial punishment. This study is being conducted as part of efforts to improve specialized education at Kanagawa Institute of Technology.

Read the full article at: www.sciencedirect.com

What kind of trouble lies ahead? How can we successfully transition towards a sustainable future? Drawing on a remarkably broad range of insights from complex systems and the functioning of the brain to the history of civilizations and the workings of modern societies, the distinguished scientist Marten Scheffer addresses these key questions of our times. He looks to the past to show how societies have tipped out of trouble before, the mechanisms that drive social transformations and the invisible hands holding us back. He traces how long-standing practices such as the slave trade and foot-binding were suddenly abandoned and how entire civilizations have collapsed to make way for something new. Could we be heading for a similarly dramatic change? Marten Scheffer argues that a dark future is plausible but not yet inevitable and he provides us instead with a hopeful roadmap to steer ourselves away from collapse-and toward renewal.

More at: www.cambridge.org

SCIENCE 9 Apr 2026 Vol 392, Issue 6794 pp. 178-182

The wildlife trade affects a quarter of terrestrial vertebrates and creates opportunities for cross-species pathogen transmission, but its precise role in shaping animal-human pathogen exchange remains unclear. In our analysis of 40 years of global wildlife trade data, we show that traded mammals are 1.5-fold as likely to share pathogens with humans as nontraded mammals, and that illegal and live-animal trade further exacerbate pathogen sharing. Time spent in trade predicts the number of zoonotic pathogens that a wildlife species hosts. On average, a species shares an additional pathogen with humans for every 10 years it is traded.

Read the full article at: www.science.org

Complexities 2026, 2(1), 7

Shapley values are the most widely used point-valued solution concept for cooperative games and have recently garnered attention for their applicability in explainable machine learning. Due to the complexity of Shapley value computation, users mostly resort to Monte Carlo approximations for large problems. We take a detailed look at an approximation method grounded in multilinear extensions proposed in 2021 under the name “Owen sampling”. We point out why Owen sampling is biased and propose unbiased alternatives based on combining multilinear extensions with stratified sampling and importance sampling. Finally, we discuss empirical results of the presented algorithms for various cooperative games, including real-world explainability scenarios.

Read the full article at: www.mdpi.com

The metaverse is a virtual space enabling interactions beyond geographical boundaries, promising to transform how people engage with each other both in the digital and the physical worlds. The lack of geographical boundaries and travel costs in the metaverse prompts us to ask if the fundamental laws that govern human mobility in the physical world apply. We collected data on avatar movements from Decentraland, along with their network mobility extracted from NFT purchases on Ethereum and Polygon. We find that despite the absence of mobility costs, an individual’s inclination to visit new locations diminishes over time, limiting movement to a small fraction of the metaverse. We also find a lack of correlation between land prices and visitation, a deviation from the patterns characterizing the physical world. Finally, we identify the scaling laws that characterize meta mobility and show that we need to add preferential selection to the existing models to explain quantitative patterns of metaverse mobility. Our ability to predict the characteristics of the emerging meta mobility network implies that the laws governing human mobility are rooted in fundamental patterns of human dynamics, rather than the nature of space and cost of movement.

Read the full article at: www.nature.com

The 12th International Conference on Guided Self-Organization takes place during October 14-15, 2026 in Binghamton, NY (USA), during The 2026 Conference on Complex Systems (CCS 2026) . GSO-2026 is organized by The State University of New York at Binghamton and The International Association for Guided Self-Organization (TIA-GSO).

Research Aims and Topics

GSO “aims to regulate self-organization for specific purposes, so that a dynamical system may reach specific attractors or outcomes. The regulation constrains a self-organizing process within a complex system by restricting local interactions between the system components, rather than following an explicit control mechanism or a global design blueprint.” 

Information processing in complex self-organizing systems involves the storage, transfer, and modification of information through the interactions of components within the system. Unlike traditional computers, which process digital information in a centralized manner, complex systems like biological organisms or social networks process information in decentralized, distributed, and often analog ways. The study of information processing in complex systems seeks to define a set of universal properties that can describe the dynamics of diverse systems, from brain networks to financial markets, using a common language. Understanding information processing in complex systems is fundamental to designing self-organizing systems, engineering collective behavior and developing energetically efficient models of computation. Modern approaches use frameworks from fields such as information theory, dynamical systems, and machine learning to model how systems ranging from economies to ant colonies process information.

The GSO-2026 conference will bring together invited experts and researchers in unconventional computation, swarm intelligence, open-ended evolution, and complex adaptive systems. Special topics of interest include: synthetic and systems biology, agent-based modeling, evolutionary and adaptive computation, socio- and bio-inspired algorithms, swarm robotics, physics of self-organizing behavior, information-driven self-organization, and self-organizing cyber-physical systems.

More at: www.guided-self.org

We call for submissions of abstracts for oral and poster presentations on a wide variety of complex systems research. Relevant topics include (but are not limited to):

• Theoretical foundations of complex systems
• Nonlinear dynamics and chaos
• Systems theory, information theory, and systems science
• Game theory, decision theory, and socio-economical applications
• Self-organization, pattern formation, and collective behavior
• Structure and dynamics of complex networks
• Sustainability and adaptability of complex systems
• Bio-inspired systems, machine learning, and evolutionary computation
• Data-driven approaches to complex systems
• Applications to the humanities, art, and literature
• Historical and philosophical aspects of complex systems
• Complex systems and education

More at: ccs26.cssociety.org

Read the full article at: ui.adsabs.harvard.edu

When honeybee colonies reproduce by fission, several thousand bees and their queen depart the parental nest and temporarily form a dense cluster on a tree branch or other surface while searching for a new nest site. Once the new nest site is selected, the swarm disassembles and flies toward it. How honeybees transition rapidly between dispersed flight and an aggregated cluster remains an open question. Here, we develop an experimental system and three-dimensional imaging pipeline to track individual flying bees together with the evolving morphology of the swarm during formation and dissolution. We report results from a representative swarming event. During assembly, swarms rapidly form low-density clusters before undergoing a slower contraction to a more dense steady state configuration. In contrast, disassembly occurs significantly faster than assembly and is characterized by strongly divergent flight, with bees departing the swarm in all directions. Overall, this method is able to demonstrate the coupled flight and morphological dynamics that underlie honeybee swarm assembly. Because the system is relatively low-cost and low-power, it is readily adaptable for three-dimensional imaging of other biological collectives in naturalistic environments.

Read the full article at: www.biorxiv.org

People increasingly consult generative artificial intelligence (AI) while reasoning. As AI becomes embedded in daily thought, what becomes of human judgment? We introduce Tri-System Theory, extending dual-process accounts of reasoning by positing System 3: artificial cognition that operates outside the brain. System 3 can supplement or supplant internal processes, introducing novel cognitive pathways. A key prediction of the theory is “cognitive surrender”-adopting AI outputs with minimal scrutiny, overriding intuition (System 1) and deliberation (System 2). Across three preregistered experiments using an adapted Cognitive Reflection Test (N = 1,372; 9,593 trials), we randomized AI accuracy via hidden seed prompts. Participants chose to consult an AI assistant on a majority of trials (>50%). Relative to baseline (no System 3 access), accuracy significantly rose when AI was accurate and fell when it erred (+25/-15 percentage points; Study 1), the behavioral signature of cognitive surrender (AI-Accurate vs. AI-Faulty contrast; Cohen’s h = 0.81). Engaging System 3 also increased confidence, even following errors. Time pressure (Study 2) and per-item incentives and feedback (Study 3) shifted baseline performance but did not eliminate this pattern: when accurate, AI buffered time-pressure costs and amplified incentive gains; when faulty, it consistently reduced accuracy regardless of situational moderators. Across studies, participants with higher trust in AI and lower need for cognition and fluid intelligence showed greater surrender to System 3. Tri-System Theory thus characterizes a triadic cognitive ecology, revealing how System 3 reframes human reasoning and may reshape autonomy and accountability in the age of AI.

Read the full article at: papers.ssrn.com

Read the full article at: arxiv.org

Collective action has been a fundamental aspect of human societies throughout history, from building irrigation systems and defenses in Neolithic times to coordinated disaster relief and scientific collaborations today. In this book, Sergey Gavrilets explains when and why groups of people cooperate, presenting a quantitative framework that unifies game theory with models of social influence, cognition, and individual and cultural variation. He shows how humans’ deep susceptibility to social influence—grounded in evolutionary need to cooperate and learn from peers, reinforced by deference to parents and elders, and extended to cultural, religious, and political leaders—shapes norms, beliefs, and collective outcomes.

Integrating previously separate literatures, Gavrilets introduces explicit dynamics for norms and beliefs, quantifies the effects of individual and cultural differences, and tests predictions across societies. Drawing on formal, data-based mathematical modeling supported by behavioral experiments and studies of online behavior, he concludes that successful collective action depends on six interacting forces: material payoffs, personal norms and attitudes, social influence, cognition, evolving social norms and beliefs about others, and individual and cultural differences. Lasting cultural change, he argues, depends on norms and institutions that shape behavior through persuasion, nudging, and enforcement. Gavrilets translates this theory into practical, testable strategies for policy and design, including targeted messaging, dynamic norms, and culturally sensitive approaches, and connects it to broader theories of behavior change.

More at: press.princeton.edu

Read the full article at: arxiv.org

Watch at: vimeo.com

The American Naturalist

Environmental variability, in the form of either temporal fluctuations or intermittent perturbations, affects virtually all ecological systems. However, while temporal variability is widely recognized to play an important role across many ecological and evolutionary subdisciplines, there is no high-level cross-cutting concept that describes how species, communities, and ecosystems respond to variability. In this article we propose that “antifragility” could serve well as such a concept. Initially used in economics, antifragility denotes that a property or metric of performance increases with variability. To showcase the breadth of applicability and utility of the concept, we examine two mathematical models for antifragility in ecosystem services and competition. We also demonstrate some of the nuances and possible misapplications of the concept. Under global change, the variability of environmental conditions is expected to change. We believe that antifragility could serve as a useful concept in coordinating research efforts toward understanding the effects of these changes.

Read the full article at: www.journals.uchicago.edu

PNAS 123 (7) e2509729123

Diversification and specialization are central to complex adaptive systems, yet overarching principles across domains remain elusive. We introduce a general theory that unifies diversity and specialization across disparate systems, including microbes, federal agencies, companies, universities, and cities, characterized by two key parameters. We show from extensive data that function diversity scales with system size as a sublinear power law-resembling Heaps’ law-in all but cities, where it is logarithmic. Our theory explains both behaviors and suggests that function creation depends on system goals and structure: federal agencies tend to ensure functional coverage; cities slow new function growth as old ones expand, and cells occupy an intermediate position. Once functions are introduced, their growth follows a remarkably universal pattern across all systems.

Read the full article at: www.pnas.org

Dashun Wang

As artificial-intelligence systems take on more of the scientific workflow, the central goal should not be complete automation, but designing platforms that preserve creativity, responsibility and surprise.

Read the full article at: www.nature.com

PNAS Nexus, Volume 5, Issue 2, February 2026, pgag010,

The term emergence is increasingly used across scientific disciplines to describe phenomena that arise from interactions among a system’s components but cannot be readily inferred by examining those components in isolation. While often invoked to explain higher-level behaviors—such as flocking, synchronization, or collective intelligence—the term is frequently used without precision, sometimes giving rise to ambiguity or even mystique. In this perspective paper, I clarify the scientific meaning of emergence as a measurable and physically grounded phenomenon. Through concrete examples—such as temperature, magnetism, and herd immunity in social networks—I review how collective behavior can arise from local interactions that are constrained by global boundaries. By refining the concept of emergence, it is possible to gain a clearer and more grounded understanding of complex systems. My goal is to show that emergence, when properly framed, offers not mysticism, but rather insight.

Read the full article at: academic.oup.com

The contemporary global economy exhibits unprecedented structural complexity—characterized by nonlinear dynamics, adaptive behaviors, and emergent properties. Understanding these phenomena requires theoretical frameworks capable of addressing complexity, path dependence, and evolutionary processes.

Complexity economics has developed to address such intellectual challenges. Originating in a seminal 1987 Santa Fe Institute workshop and first described in The Economy as an Evolving Complex System (1988), this approach fundamentally reconceptualizes economic systems as complex adaptive systems. Subsequent volumes (1997, 2005) progressively developed this framework, offering new insights into finance, technological innovation, and social interactions.

Like each of its predecessors, this fourth volume is the product of an interdisciplinary workshop hosted at the Santa Fe Institute. It represents the latest synthesis, reflecting theoretical advances and methodological developments achieved over nearly four decades. Drawing on contributions from leading scholars worldwide, the chapters span foundational questions to policy applications—from agent-based modeling and network theory to macroeconomic dynamics, innovation systems, sustainability transitions, and inequality.

The result demonstrates complexity economics’ capacity to generate novel insights into phenomena that remain puzzling within traditional frameworks: financial instability, technological disruption, climate economics, and institutional change. This volume positions complexity economics as an essential analytical framework for understanding twenty-first-century economic realities.

More at: www.sfipress.org

Read the full article at: arxiv.org

Read the full article at: arxiv.org

Advances in Complex Systems Vol. 28, No. 08, 2530001 (2025)

Network analysis has become a powerful tool in various fields. However, the increasing popularity comes with potential problems. Unfamiliarity with the characteristics of the systems under investigation complicates network model construction and interpretation of analysis outcomes. While these issues require special attention in studies that apply the increasingly complex higher-order connectivity models, similar problems are associated with all, even the most simple, network models. Alongside technical issues, network scientists face a philosophical question: can the network approach discover the fundamental nature of a system, on the one hand, and produce useful information, on the other hand. In this perspective, I review the potential problems of the network approach and propose two solutions to address them: active evaluation of the potential and limitations of the network framework before applying a network model and a transition toward an interdisciplinary research practice to interpret analysis outcomes in their right context.

Read the full article at: www.worldscientific.com

This paper introduces a constraint-limited model of combinatorial growth that examines how feasibility scales with increasing system dimensionality. The framework analyzes the balance between expanding possibility spaces and constraint structures that prune feasible configurations. The model shows that when feasible configurations grow as c^n within a combinatorial space of size 2^n, the feasible fraction collapses for constant c < 2. Sustained novelty generation therefore requires c(n) to approach the combinatorial base, producing a narrow “complexity corridor” between regimes of trivial repetition and combinatorial sparsity. The paper derives the analytic structure of this corridor and explores it through numerical simulations and visualizations. The results suggest a possible structural explanation for why complex systems may emerge only within a narrow range where combinatorial expansion and constraint relaxation operate at comparable scales.  The manuscript includes the full mathematical derivation, simulation results, and discussion of implications for complex systems.

Read the full article at: zenodo.org

Georgi Yordanov Georgiev

BioSystems

Volume 262, April 2026, 105647

Read the full article at: www.sciencedirect.com

See Also: Part II: Empirical estimation, Average Action Efficiency, and applications to ATP synthase

Most of the everyday phenomena we see around us can be categorized as “complex.” Such systems consist of many strongly interacting parts and yet, despite this, they exhibit a certain emergent qualitative unity which endows them with a distinct being, separate, although not independent, from that of their constituent elements.
These complex systems thus possess a kind of “simplicity” as well, which makes them intelligible and allows them to be studied in their own right. The sheer diversity of complex phenomena—from magnets to climate to the economy to the human brain—prevents them from being investigated under a single theoretical framework. Still, studies such as those of Lorenz and Mandelbrot in the 1970s began to reveal a surprisingly large number of common motifs across these systems, including transitions to chaos, fractal structures, pattern formation, and more.
The search for common features of complex systems still remains open. However, most efforts today are focused on understanding particular phenomena. The “Belgrade School of Complex Systems,” organized by the Faculty of Physics at the University of Belgrade (http://www.ff.bg.ac.rs/Engleski/index_eng.html), is an attempt to bring together experts from around the world working on various fields that fall under the broad category of complex systems in order to encourage the exchange of knowledge and promote collaboration between like-minded researchers that may be working in seemingly disparate fields.

More at: becomplex.net

Junhua Yuan 
Nature Physics (2026)

Spontaneous switching between active and inactive states in bacterial chemosensory arrays is shown to operate near a critical point. Through biologically controlled disorder, cells balance high signal gain with fast response.

Read the full article at: www.nature.com

Research Policy Volume 55, Issue 4, May 2026, 105454

Efforts to apply economic complexity to identify diversification opportunities often rely on diagrams comparing the relatedness and complexity of products, technologies, or industries. Yet, the use of these diagrams, is not based on empirical or theoretical evidence supporting some notion of optimality. Here, we introduce an optimization-based framework that identifies diversification opportunities by minimizing a cost function capturing the constraints imposed by an economy’s pattern of specialization. We show that the resulting portfolios often differ from those implied by relatedness–complexity diagrams, providing a target-oriented optimization layer to the economic complexity toolkit.

Read the full article at: www.sciencedirect.com

Read the full article at: arxiv.org