Vicky Chuqiao Yang, James Holehouse, Hyejin Youn, José Ignacio Arroyo, Sidney Redner, Geoffrey B. West, and Christopher P. Kempes

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.

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Sara Imari Walker
One of the longest standing open problems in science is how life arises from non-living matter. If it is possible to measure this transition in the lab, then it might be possible to understand the physical mechanisms by which the emergence of life occurs, which so far have evaded scientific understanding. A significant hurdle is the lack of standards or a framework for cross comparison across different experimental contexts and planetary environments. In this essay, I review current challenges in experimental approaches to origin of life chemistry, focusing on those associated with quantifying experimental selectivity versus de novo generation of molecular complexity, and I highlight new methods using molecular assembly theory to measure molecular complexity. This metrology-centered approach can enable rigorous testing of hypotheses about the cascade of major transitions in molecular order marking the emergence of life, while potentially bridging traditional divides between metabolism-first and genetics-first scenarios. Grounding the study of life's origins in measurable complexity has significant implications for the search for life beyond Earth, suggesting paths toward theory-driven detection of biological complexity in diverse planetary contexts. As the field moves forward, standardized measurements of molecular complexity may help unify currently disparate approaches to understanding how matter transforms to life. Much remains to be done in this exciting frontier.

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Costolo, Michael

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

Erik Hoel
Scientific theories of consciousness should be falsifiable and non-trivial. Recent research has given us formal tools to analyze these requirements of falsifiability and non-triviality for theories of consciousness. Surprisingly, many contemporary theories of consciousness fail to pass this bar, including theories based on causal structure but also (as I demonstrate) theories based on function. Herein, I show these requirements of falsifiability and non-triviality especially constrain the potential consciousness of contemporary Large Language Models (LLMs) because of their proximity to systems that are equivalent to LLMs in terms of input/output function; yet, for these functionally equivalent systems, there cannot be any falsifiable and non-trivial theory of consciousness that judges them conscious. This forms the basis of a disproof of contemporary LLM consciousness. I then show a positive result, which is that theories of consciousness based on (or requiring) continual learning do satisfy the stringent formal constraints for a theory of consciousness in humans. Intriguingly, this work supports a hypothesis: If continual learning is linked to consciousness in humans, the current limitations of LLMs (which do not continually learn) are intimately tied to their lack of consciousness.

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Sergey Gavrilets, Johannes Karl, and Michele J. Gelfand

PNAS 123 (7) e2522998123

People often get public opinion wrong, assuming their own views are unpopular when in fact many others share them. This widespread misperception, called pluralistic ignorance, can trap societies in harmful or outdated norms. We build a mathematical model showing how these misperceptions form and change over time, depending on whether cultures are “tight” (with strict norms) or “loose” (with flexible ones). Our results explain why support for issues like climate action or women’s rights is often underestimated, and why change happens faster in some societies than others. The model also points to practical solutions: in loose cultures, sharing accurate information works best, while in tight ones, lowering the costs of speaking up can spark social change.

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John E. Stewart

BioSystems Volume 262, April 2026, 105733

Our universe appears to be fine-tuned for life. But once life emerges, it does not evolve randomly. Evolution has a trajectory. Both evolvability and cooperative integration increase as evolution proceeds. Until now, this trajectory has largely been driven blindly by gene-based natural selection. But humans are developing cognitive capacities that are far superior than natural selection at adapting and evolving humanity. These capacities will enable humanity to use an understanding of evolution's future trajectory to guide its own evolution, avoiding the destructive selection that will otherwise reinforce the trajectory. Humans who help realize this potential will be fulfilling vital evolutionary roles that are meaningful and purposeful in a much larger scheme of things. The paper considers whether these roles remain meaningful when considered in the wider context of possible origins of the universe. But this analysis is faced with a potentially infinite number of origin hypotheses (including innumerable ‘God hypotheses’), which are not falsified by current knowledge. The paper addresses this challenge using methods that enable rational decision-making despite radical uncertainty. Broadly, this approach reinforces the conclusions reached by consideration of the evolutionary trajectory within the universe, and opens some new possibilities. Finally, the paper demonstrates that extending this analysis also largely overcomes Hume's critique of induction, placing scientific methodologies on a firmer footing. It achieves this by recognising that a universe which exhibits a trajectory towards increasing evolvability must contain discoverable regularities that provide adaptive advantages for evolvability.

Read the full article at: www.sciencedirect.com

Giovanni Pezzulo, Michael Levin
Achieving advanced machine intelligence remains a central challenge in AI research, often approached through scaling neural architectures and generative models. However, biological systems offer a broader repertoire of strategies for adaptive, goal-directed behavior - strategies that emerged long before nervous systems evolved. This paper advocates a genuinely life-inspired approach to machine intelligence, drawing on principles from biology that enable robustness, autonomy, and open-ended problem-solving across scales. We frame intelligence as flexible problem-solving, following William James, and develop the concept of "cognitive light cones" to characterize the continuum of intelligence in living systems and machines. We argue that biological evolution has discovered a scalable recipe for intelligence - and the progressive expansion of organisms' "cognitive light cone", predictive and control capacities. To explain how this is possible, we distill five design principles - multiscale autonomy, growth through self-assemblage of active components, continuous reconstruction of capabilities, exploitation of physical and embodied constraints, and pervasive signaling enabling self-organization and top-down control from goals - that underpin life's ability to navigate creatively diverse problem spaces. We discuss how these principles contrast with current AI paradigms and outline pathways for integrating them into future autonomous, embodied, and resilient artificial systems.

Read the full article at: arxiv.org

Fernando Rodriguez-Vergara and Phil Husbands

Mathematics 2026, 14(3), 535

According to the Church–Turing thesis, the limit of what is computable is bounded by Turing machines. Following from this, given that general computable functions formally describe the notion of recursive mechanisms, it is sometimes argued that every organismic process that specifies consistent cognitive responses should be both limited to Turing machine capabilities and amenable to formalization. There is, however, a deep intuitive conviction permeating contemporary cognitive science, according to which mental phenomena, such as consciousness and agency, cannot be explained by resorting to this kind of framework. In spite of some exceptions, the overall tacit assumption is that whatever the mind is, it exceeds the reach of what is described by notions of computability. This issue, namely the nature of the relation between cognition and computation, becomes particularly pertinent and increasingly more relevant as a possible source of better understanding the inner workings of the mind, as well as the limits of artificial implementations thereof. Moreover, although it is often overlooked or omitted so as to simplify our models, it will probably define, or so we argue, the direction of future research on artificial life, cognitive science, artificial intelligence, and related fields.

Read the full article at: www.mdpi.com

Alberto Robledo

Complexities 2026, 2(1), 3

We detail a procedure to transform the current empirical stage in the study of complex systems into a predictive phenomenological one. Our approach starts with the statistical-mechanical Landau-Ginzburg equation for dissipative processes, such as kinetics of phase change. Then, it imposes discrete time evolution to explicit back feeding, and adopts a power-law driving force to incorporate the onset of chaos, or, alternatively, criticality, the guiding principles of complexity. One obtains, in closed analytical form, a nonlinear renormalization-group (RG) fixed-point map descriptive of any of the three known (one-dimensional) transitions to or out of chaos. Furthermore, its Lyapunov function is shown to be the thermodynamic potential in q-statistics, because the regular or multifractal attractors at the transitions to chaos impose a severe impediment to access the system’s built-in configurations, leaving only a subset of vanishing measure available. To test the pertinence of our approach, we refer to the following complex systems issues: (i) Basic questions, such as demonstration of paradigms equivalence, illustration of self-organization, thermodynamic viewpoint of diversity, biological or other. (ii) Derivation of empirical laws, e.g., ranked data distributions (Zipf law), biological regularities (Kleiber law), river and cosmological structures (Hack law). (iii) Complex systems methods, for example, evolutionary game theory, self-similar networks, central-limit theorem questions. (iv) Condensed-matter physics complex problems (and their analogs in other disciplines), like, critical fluctuations (catastrophes), glass formation (traffic jams), localization transition (foraging, collective motion).

Read the full article at: www.mdpi.com

Advances in artificial intelligence (AI) offer the prospect of manipulating beliefs and behaviors on a population-wide level (1). Large language models (LLMs) and autonomous agents (2) let influence campaigns reach unprecedented scale and precision. Generative tools can expand propaganda output without sacrificing credibility (3) and inexpensively create falsehoods that are rated as more human-like than those written by humans (3, 4). Techniques meant to refine AI reasoning, such as chain-of-thought prompting, can be used to generate more convincing falsehoods. Enabled by these capabilities, a disruptive threat is emerging: swarms of collaborative, malicious AI agents. Fusing LLM reasoning with multiagent architectures (2), these systems are capable of coordinating autonomously, infiltrating communities, and fabricating consensus efficiently. By adaptively mimicking human social dynamics, they threaten democracy. Because the resulting harms stem from design, commercial incentives, and governance, we prioritize interventions at multiple leverage points, focusing on pragmatic mechanisms over voluntary compliance.

DANIEL THILO SCHROEDER, MEEYOUNG CHA, ANDREA BARONCHELLI, NICK BOSTROM, NICHOLAS A. CHRISTAKIS, DAVID GARCIA, AMIT GOLDENBERG, YARA KYRYCHENKO, KEVIN LEYTON-BROWN, NINA LUTZ, GARY MARCUS, FILIPPO MENCZER, GORDON PENNYCOOK, DAVID G. RAND, MARIA RESSA, FRANK SCHWEITZER, DAWN SONG, CHRISTOPHER SUMMERFIELD, AUDREY TANG, JAY J. VAN BAVEL, SANDER VAN DER LINDEN, AND JONAS R. KUNST

SCIENCE 22 Jan 2026 Vol 391, Issue 6783 pp. 354-357

Read the full article at: www.science.org

Lucas Lacasa
In network science, collective dynamics of complex systems are typically modelled as (nonlinear, often including many-body) vertex-level update rules evolving over a graph interaction structure. In recent years, frameworks that explicitly model such higher-order interactions in the interaction backbone (i.e. hypergraphs) have been advanced, somehow shifting the imputation of the effective nonlinearity from the dynamics to the interaction structure. In this work we discuss such structural--dynamical representation duality, and investigate how and when a nonlinear dynamics defined on the vertex set of a graph allows an equivalent representation in terms of a linear dynamics defined on the state space of a sufficiently richer, higher-order interaction structure. Using Carleman linearisation arguments, we show that finite polynomial dynamics defined in the |V| vertices of a graph admit an exact representation as linear dynamics on the state space of an hb-graph of order |V|, a combinatorial structure that extends hypergraphs by allowing vertex multiplicity, where the specific shape of the nonlinearity indicates whether the hb-graph is either finite or infinite (in terms of the number of hb-edges). For more general analytic nonlinearities, exact linear representation always require an hb-graph of infinite size, and its finite-size truncation provides an approximate representation of the original nonlinear graph-based dynamics.

Read the full article at: arxiv.org

ONERVA KORHONEN

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

How and why do complex chemical and biological systems self-organize into ordered states far from thermodynamic equilibrium? Despite advances in thermodynamics, kinetics, and information theory, a unifying principle that links organization and efficiency across scales has remained elusive. In open systems, productive-event trajectories are conditioned on starting at a source and ending at a sink. This work proposes a stochastic–dissipative least-action triad framework in which (i) a path-ensemble weighting biases trajectories by their action cost, (ii) feedback processes sharpen this distribution, and (iii) the ensemble evolves toward a least-average-action attractor, decreasing during self-organization and increasing during decay. A parametric cross-scale metric—Average Action Efficiency (AAE)—is defined, which is inversely proportional to the average action per productive event. Under reinforcing feedback, identities derived from the exponential-family path measure show that the average action decreases and AAE rises monotonically. In future extensions, this formulation could help bridge quantum, classical, and biological regimes while remaining computationally tractable, because its empirical version relies on aggregate energetic and timing data rather than enumerating individual trajectories. AAE reaches a local maximum at a non-equilibrium steady state under fixed operational context, consistent with the present formulation, and connections to thermodynamic and informational measures are made. A companion article (Part II) details empirical estimation strategies and applications (Georgiev, 2025a).

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

Viktor Stojkoski, César A. Hidalgo

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.

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Ivan Shpurov and Tom Froese Phys. Rev. E 113, 024405

The collective behavior of numerous animal species, including insects, exhibits scale-free behavior indicative of the critical (second-order) phase transition. Previous research uncovered such phenomena in the behavior of honeybees, most notably the long-range correlations in space and time. Furthermore, it was demonstrated that the bee activity in the hive manifests the hallmarks of the jamming process. We follow up by presenting a discrete model of the system that faithfully replicates some of the key features found in the data, such as the divergence of correlation length and scale-free distribution of jammed clusters. The dependence of the correlation length on the control parameter, density, is demonstrated for both the real data and the model. We conclude with a brief discussion on the contribution of the insights provided by the model to our understanding of the insects' collective behavior.

Read the full article at: link.aps.org

Federico Naldini, Fabio Oddi, Leo D'Amato, Grégory Marlière, Vito Trianni, Paola Pellegrini
Improving traffic management in case of perturbation is one of the main challenges in today's railway research. The great majority of the existing literature proposes approaches to make centralized decisions to minimize delay propagation. In this paper, we propose a new paradigm to the same aim: we design and implement a modular process to allow trains to self-organize. This process consists in having trains identifying their neighbors, formulating traffic management hypotheses, checking their compatibility and selecting the best ones through a consensus mechanism. Finally, these hypotheses are merged into a directly applicable traffic plan. In a thorough experimental analysis on a portion of the Italian network, we compare the results of self-organization with those of a state-of-the-art centralized approach. In particular, we make this comparison mimicking a realistic deployment thanks to a closed-loop framework including a microscopic railway simulator. The results indicate that self-organization achieves better results than the centralized algorithm, specifically thanks to the definition and exploitation of the instance decomposition allowed by the proposed approach.

Read the full article at: arxiv.org

Tiago P. Peixoto, Leto Peel, Thilo Gross, Manlio De Domenico
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on "higher-order networks" that graph-based representations are fundamentally limited to "pairwise" interactions, requiring hypergraph formulations to capture richer dependencies. We clarify this issue by emphasizing two frequently overlooked facts. First, graph-based models are not restricted to pairwise interactions, as they naturally accommodate interactions that depend simultaneously on multiple adjacent nodes. Second, hypergraph formulations are strict special cases of more general graph-based representations, as they impose additional constraints on the allowable interactions between adjacent elements rather than expanding the space of possibilities. We show that key phenomenology commonly attributed to hypergraphs -- such as abrupt transitions -- can, in general, be recovered exactly using graph models, even locally tree-like ones, and thus do not constitute a class of phenomena that is inherently contingent on hypergraphs models. Finally, we argue that the broad relevance of hypergraphs for applications that is sometimes claimed in the literature is not supported by evidence. Instead it is likely grounded in misconceptions that network models cannot accommodate multibody interactions or that certain phenomena can only be captured with hypergraphs. We argue that clearly distinguishing between multivariate interactions, parametrized by graphs, and the functions that define them enables a more unified and flexible foundation for modeling interacting systems.

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The Effects of Remote Working on Scientific Collaboration and Impact

Sara Venturini, Satyaki Sikdar, Martina Mazzarello, Francesco Rinaldi, Francesco Tudisco, Paolo Santi, Santo Fortunato, Carlo Ratti
The COVID-19 pandemic shifted academic collaboration from in-person to remote interactions. This study explores, for the first time, the effects on scientific collaborations and impact of such a shift, comparing research output before, during, and after the pandemic. Using large-scale bibliometric data, we track the evolution of collaboration networks and the resulting impact of research over time. Our findings are twofold: first, the geographic distribution of collaborations significantly shifted, with a notable increase in cross-border partnerships after 2020, indicating a reduction in the constraints of geographic proximity. Second, despite the expansion of collaboration networks, there was a concerning decline in citation impact, suggesting that the absence of spontaneous in-person interactions-which traditionally foster deep discussions and idea exchange-negatively affected research quality. As hybrid work models in academia gain traction, this study highlights the need for universities and research organizations to carefully consider the balance between remote and in-person engagement.

Read the full article at: arxiv.org