Papers

Alex Arenas, Oriol Artime, Albert Díaz-Guilera, Sergio Gómez, Clara Granell

Annalen der PhysikAnnalen der Physik

Volume 538, Issue 9, September 2026, e70288

Many complex systems cannot be understood from network structure alone, nor from continuum descriptions in isolation, because their dynamics emerge from the reciprocal coupling between discrete interaction architectures and spatially extended physical fields. This perspective article surveys mathematical and computational frameworks for such network–field systems, focusing on models in which a graph is either itself the spatial substrate of a field or is embedded in a surrounding medium that mediates transport, signaling, forcing, or spatially distributed hazards. We first introduce a unified formalism for bidirectionally coupled network–field dynamics, emphasizing observation and injection operators that link node variables to continuum processes while preserving balance laws. We then examine two major modeling classes: fields evolving directly on metric graphs, where partial differential equations are posed on network geometries with vertex matching conditions; and hybrid discrete–continuous systems, where node dynamics are coupled to fields in the ambient domain, with particular attention to port-Hamiltonian formulations that provide energy-consistent interconnection principles. Within this common framework, we discuss representative modeling applications in neurobiology, including diffusion-mediated cellular communication and extracellular neural signaling, and in infrastructure systems, where network functionality depends on spatially distributed flows, loads, and hazards. Across these examples, a common picture emerges: the field is not merely an external environment, but an active dynamical layer that reshapes effective interactions, timescales, and collective behavior. By synthesizing concepts that are often developed separately across disciplines, this perspective article aims to clarify the mathematical structure, physical interpretation, and numerical challenges of coupled network–field models, and to highlight their role as a unifying language for spatially embedded complex systems.Many complex systems cannot be understood from network structure alone, nor from continuum descriptions in isolation, because their dynamics emerge from the reciprocal coupling between discrete interaction architectures and spatially extended physical fields. This perspective article surveys mathematical and computational frameworks for such network–field systems, focusing on models in which a graph is either itself the spatial substrate of a field or is embedded in a surrounding medium that mediates transport, signaling, forcing, or spatially distributed hazards. We first introduce a unified formalism for bidirectionally coupled network–field dynamics, emphasizing observation and injection operators that link node variables to continuum processes while preserving balance laws. We then examine two major modeling classes: fields evolving directly on metric graphs, where partial differential equations are posed on network geometries with vertex matching conditions; and hybrid discrete–continuous systems, where node dynamics are coupled to fields in the ambient domain, with particular attention to port-Hamiltonian formulations that provide energy-consistent interconnection principles. Within this common framework, we discuss representative modeling applications in neurobiology, including diffusion-mediated cellular communication and extracellular neural signaling, and in infrastructure systems, where network functionality depends on spatially distributed flows, loads, and hazards. Across these examples, a common picture emerges: the field is not merely an external environment, but an active dynamical layer that reshapes effective interactions, timescales, and collective behavior. By synthesizing concepts that are often developed separately across disciplines, this perspective article aims to clarify the mathematical structure, physical interpretation, and numerical challenges of coupled network–field models, and to highlight their role as a unifying language for spatially embedded complex systems.

Read the full article at: onlinelibrary.wiley.com

Michael Levin

Philosophies 2026, 11(5), 161

I argue that the emerging sciences of synthetic morphology and diverse intelligence suggest non-physicalist models of mind and show how they can be empirically investigated. Whence the anatomical, physiological, molecular-biological, and behavioral properties of engineered new beings that have never before existed, and do not have a history of selection? Understanding, predicting, and guiding new forms of life and mind requires characterizing a structured latent space of patterns. Developmental, synthetic, and behavioral biology should take seriously, and exploit, the kinds of non-physicalist ideas that are already a staple of Platonist mathematics. I propose the following hypotheses. (1) Patterns in this space span a highly variable degree of agency, comprising a spectrum ranging from static truths studied by mathematicians to active ones studied by behavioral scientists (i.e., some patterns on the same spectrum as mathematical truths are kinds of minds). (2) The relationship between mind and body is the same as the relationship between causally instructive mathematical facts and physics. (3) Living beings have no monopoly on the “free lunches” provided by the ingression of these patterns into the physical world. While traditional computationalist views of living and cognitive systems are insufficient, my framework erases artificial distinctions between organisms and machines, framing all physical constructs (natural or engineered) as being, to various degrees, in-formed by patterns from the latent space. I sketch a research program, already begun, inspired by these ideas. Such frameworks, while contradicting long-held assumptions of both mechanists and organicists, could have many implications for evolutionary biology, regenerative medicine, AI, and the ethics of synthbiosis with the forthcoming immense diversity of morally important beings.

Read the full article at: www.mdpi.com

Marta Zava

Training a frontier artificial intelligence model costs hundreds of millions of dollars before a product exists, and few investors can write that cheque. This paper shows that the number who can falls as the fixed cost of a first training run rises, at a rate set by the concentration of the fund size distribution, so that doubling the cost removes about two thirds of the possible backers. The firms that compete are therefore selected by a small group of allocators before any customer has expressed a view. Three results follow. The price paid by the winner separates into a rational bid, a premium created by the fund's deployment clock, and an error from failing to adjust for adverse selection, and the sign of the price response to competition identifies which one dominates. Concentration trades breadth for depth, improving the funded set only when the skill advantage of the few outweighs the information lost through having fewer independent views, a loss that is small when investors think alike. And large upfront cheques reduce the value of stopping, so ventures funded under deployment pressure should fail later and larger rather than more often. The effective policy margin is access to compute rather than regulation of the capital market.Training a frontier artificial intelligence model costs hundreds of millions of dollars before a product exists, and few investors can write that cheque. This paper shows that the number who can falls as the fixed cost of a first training run rises, at a rate set by the concentration of the fund size distribution, so that doubling the cost removes about two thirds of the possible backers. The firms that compete are therefore selected by a small group of allocators before any customer has expressed a view. Three results follow. The price paid by the winner separates into a rational bid, a premium created by the fund's deployment clock, and an error from failing to adjust for adverse selection, and the sign of the price response to competition identifies which one dominates. Concentration trades breadth for depth, improving the funded set only when the skill advantage of the few outweighs the information lost through having fewer independent views, a loss that is small when investors think alike. And large upfront cheques reduce the value of stopping, so ventures funded under deployment pressure should fail later and larger rather than more often. The effective policy margin is access to compute rather than regulation of the capital market.

Read the full article at: papers.ssrn.com

John Stewart

An acceptable information-processing theory of consciousness should be able to identify the adaptive advantages that drove the emergence of consciousness during the evolution of life. It should also predict the specific dynamical architecture of information processing that would need to be instantiated in AI to produce consciousness and the superior adaptation it enables. Whether such an instantiation produces AI that is actually conscious and also more adaptable would provide the ultimate test of the theory. A prime candidate for such a theory is the Subject-Object Emergence Theory of consciousness. It argues that consciousness first evolved because it enabled organisms to achieve adaptive body-environment coordination without extensive trial-and-error learning. It postulates that the subject in an appropriate Subject-Object subsystem would be able to use depictive (iconic) visual representations of the relative positions of its body and the environment to guide motor actions that will produce adaptive body-environment coordination. The depictive representations will 'light up' for such a subject, producing subjective experience that is used to deliver adaptive benefits. Hand-eye coordination is a familiar example in humans-novel and intricate coordination tasks can be undertaken without additional reinforcement learning, provided focused conscious attention is employed to provide us (the subject) with relevant depictive images. The paper identifies how such a conscious Subject-Object subsystem could be instantiated in AI systems, enabling hand-eye and other body-environment coordination without the extensive reinforcement learning or complex computational programming needed at present. Drawing further on the Subject-Object theory of consciousness, the paper also identifies how these simple conscious subsystems evolved further in organisms to establish the conscious modelling that enables conscious planning, imagining, abduction and other higher cognitive functions. It demonstrates that current approaches to incorporating world modelling in AI will fail to achieve key elements of the general intelligence found in humans that require consciousness.

Read the full article at: papers.ssrn.com

Marcus Schref, Udo Schilcher, and Christian Bettstetter
Phys. Rev. E 114, 024216 – Published 18 August, 2026

Swarmalator systems intertwine two forms of collective behavior, swarming and synchronization, leading to the emergence of specific space-time patterns. Scaling the model to real-world phenomena and technical applications is problematic due to the assumption of global coupling among all swarmalators, which is impractical under physical constraints on interaction range. Conversely, purely local coupling was shown to be infeasible. To address this gap, we introduce and evaluate the concept of multihop coupling for swarmalators, which preserves the locality of physical interactions but propagates state information throughout the network via hop-limited and probabilistic flooding. It is demonstrated that convergence to the original emergent patterns can be achieved in a reliable and fast manner while keeping overhead low. A practical guideline for selecting the range, hop limit, and forwarding probability is provided. The range required for convergence can be approximated by the connectivity threshold of random geometric graphs.

Read the full article at: journals.aps.org

Andrew J. King ∙ Ella G. Henry ∙ Simon Garnier ∙ William L. Allen ∙ Robert J.P. Heathcote ∙ Marco Fele ∙ Marina Papadopoulou ∙ Daniel W.E. Sankey ∙ Ines Fürtbauer

Trends in Ecology and Evolution

Collective behaviour is widespread in the animal kingdom and can enhance individual
fitness. Yet not all collective behaviours are adaptations. Instead, some may be nonadaptive
or ‘evolutionary spandrels’—traits that originated as by-products in the sense proposed
by Stephen Jay Gould and Richard Lewontin. Here, we argue that self-organising processes
provide a route through which evolutionary spandrels in collective animal behaviour
can occur, and we provide three examples: spatial organisation in primate groups,
division of labour in ants, and insect chorusing. We then consider how such outcomes
may be co-opted into adaptive roles through exaptation and conclude by outlining the
challenges associated with testing adaptive and nonadaptive hypotheses in collective
behaviour research using individual-based studies, phylogenetic comparative analyses,
and agent-based models.

Read the full article at: www.cell.com

Mario Franco, Zeinab Davoudmanesh, Sean P. Maley, Fernanda Sánchez-Puig, Carlos Gershenson

Seventy years of artificial intelligence are usually told as a long preamble followed by a revolution beginning around 2012. We organize the period differently, around a question the field has answered differently at different times: what kind of thing is intelligence, such that a machine could have it? Read that way, the human contribution does not withdraw as systems learn more; it relocates, and mostly to places our instruments do not record. Whether the recent acceleration is a change in kind or a change in budget is, we suspect, the more interesting question, and not one that benchmark curves can settle.

Read the full article at: www.preprints.org

Zyri Bajrami
Matter, energy, and information, on the one hand, and the interplay between natural selection and self-organization, on the other, have given rise to modules, which constitute the fundamental units of interaction, organization, and function, as well as the primary targets of natural selection throughout chemical, biological, and cultural evolution. Based on the forms of structural information that enable their emergence, modules can be classified into huit types: (a) chemical modules (l) genetic and epigenetic modules, (c) cell, (d) neural, (f) mental modules, (g) moduloma (m) and affordance modules (n). Through interactions among modules and between modules and their environment, semantic (meaningful) modular information emerges. It is this semantic information that enables modules to acquire and maintain stability as both physical and abstract entities. The emergence and persistence of both material and immaterial (abstract) modules occur only at a specific point in time, when structural information is matched with the corresponding energy. This relationship is described by the law of modular stability. Modules acquire and preserve stability when the structural information responsible for establishing the relationships among the elements of their structure, considered as systems, corresponds to the energy required to maintain those relationships, while semantic modular information reaches its maximum value. One of the principal implications of this law is that the creative role of natural selection and modular stability is expressed primarily during the first stage of module formation, when the module is established as a replicator, rather than during the second stage, when it functions as an interactor and its fitness is determined.

Read the full article at: www.preprints.org

Tomás Cicchini, Ollin D. Langle-Chimal, Marta C. González, Ines Caridi & Leonardo Ermann

Discover Cities

Volume 3, article number 139 (2026)

Public transportation systems are vital for urban mobility, yet their robustness against disruptions remains underexplored, particularly in Latin American cities. This study quantifies the structural and functional robustness of public transport networks in Mexico City, Rio de Janeiro, and Buenos Aires, revealing that Rio de Janeiro exhibits the highest resilience due to its structural redundancy, while also establishing a strong correlation between structural connectivity and trip feasibility across the cities.

Read the full article at: link.springer.com

Klaus Jaffe

Infodynamics explores how the interactions between information and energy generates useful work, offering a framework for understanding cognition. It views consciousness as an adaptive mechanism that enables an entity, biological or artificial, to construct an internal map of itself and integrate it into its environmental models (Weltanschauung). When these models incorporate the perceived internal states of others, empathy emerges. Empathy in turn allows to secure synergistic social cooperation to build robust new social structures. By focusing on the utility of information, infodynamics uncovers how consciousness and empathy serve as evolutionary tools to enhance survival odds and stabilize social structures. This approach provides an actionable methodology for detecting consciousness in living or artificial entities, that allows optimizing the design of advanced artificial intelligence, and of future educational systems. Both will drive cultural and eventually biological evolution.

Read the full article at: papers.ssrn.com

Cameron Brooks, Estelle Janin, Gage Siebert, Cole Mathis, Orit Peleg & Sara Imari Walker 
Scientific Reports (2026)

The Search for Extraterrestrial Intelligence (SETI) has historically been a search for aliens like us, shaped by human-centric ideas of intelligence, communication, and technology. However, humans are not the only instance of an intelligent, communicating species on Earth, and thus not the only guide to how we might think about ETI. Here, we explore how non-human communication systems could complement existing SETI strategies, usually focused on complex, potentially decodable signals, using firefly communication as an illustrative example. Fireflies communicate their presence through evolved flash patterns that are distinguishable from complex visual backgrounds. Drawing on this strategy, we present a firefly-inspired model for detecting potential technosignatures within environments dominated by ordered astronomical phenomena, such as pulsars. Using pulsar data from the Australia Telescope National Facility, we generate simulated pulse sequences that exhibit evolved dissimilarity from the surrounding pulsar population of Earth, which would constitute a signature of intelligence embodied in a relatively simple signal. This approach shifts focus from anthropocentric assumptions about intelligence toward recognizing communication through its fundamental structural properties, specifically evolutionarily optimized contrast with natural backgrounds. Our model demonstrates that alien signals need not be inherently complicated nor must we decipher their meaning to identify them; rather, signals might be distinguishable as products of engineering or evolutionary design. We discuss implications for broadening SETI methodologies and leveraging the diverse forms of intelligence found on Earth.

Read the full article at: www.nature.com

Sebastian Sander-Oest

Synthese Volume 208, article number 143 (2026)

Self-assembly and self-organization are central concepts in theories of how patterns form in natural systems. However, literature on the topic has for long been riddled with inconsistent uses of these concepts, which often conflate their meaning or define them idiosyncratically. This is problematic as it struggles to make sense of the ubiquitous interaction between self-assembly and self-organization in chemistry and biology. The thermodynamic account is an attempt to draw up clear definitions of the concepts using thermodynamics as the appropriate framework for distinguishing the two concepts from each other. In this paper, I challenge this account and argue that self-assembly shouldn’t primarily be understood in terms of thermodynamics. I offer a philosophical analysis of core conceptual challenges for self-assembly and self-organization and argue that the thermodynamic approach follows a misguided conceptualization strategy. Drawing on recent philosophical work on scientific definitions, I propose an alternative account that treats the concept as a conceptual tool that directs our attention towards the kinds of features that are explanatorily relevant for the pattern-formation process and towards the features the resulting pattern itself will possess.Self-assembly and self-organization are central concepts in theories of how patterns form in natural systems. However, literature on the topic has for long been riddled with inconsistent uses of these concepts, which often conflate their meaning or define them idiosyncratically. This is problematic as it struggles to make sense of the ubiquitous interaction between self-assembly and self-organization in chemistry and biology. The thermodynamic account is an attempt to draw up clear definitions of the concepts using thermodynamics as the appropriate framework for distinguishing the two concepts from each other. In this paper, I challenge this account and argue that self-assembly shouldn’t primarily be understood in terms of thermodynamics. I offer a philosophical analysis of core conceptual challenges for self-assembly and self-organization and argue that the thermodynamic approach follows a misguided conceptualization strategy. Drawing on recent philosophical work on scientific definitions, I propose an alternative account that treats the concept as a conceptual tool that directs our attention towards the kinds of features that are explanatorily relevant for the pattern-formation process and towards the features the resulting pattern itself will possess.

Read the full article at: link.springer.com

Tim Gebbie

Complex systems are often organised into hierarchies whose internal interactions are stronger or faster than interactions across levels. When markets are treated as genuinely multilevel systems it becomes natural to represent them as systems with hierarchical causality. Here we show that reflexivity can be formulated within such a discrete hierarchical causal system; but one in which a higher-level actor state restricts the lower-level transition kernels that remain admissible. Then event dynamics can be separated from calendar embeddings: a set-valued actor-conditioned correspondence can be used to define the admissible family of event kernels, while joint state and waiting-time laws can be used to determine compatible timing to then natural demonstrate reflexivity. A selected event-state law need not determine a unique calendar embedding. Locally, uniqueness of the joint event or timing specification requires uniqueness of both the admissible event kernel and its compatible timing law. Reflexivity is thus the endogenous closure of a hierarchical constraint loop, while timing and projection can generate calendar-time memory or causal ambiguity even for Markov event dynamics.

Read the full article at: arxiv.org

Ryosuke Takata, Yujin Tang, Yingtao Tian, Norihiro Maruyama, Hiroki Kojima, Takashi Ikegami,

Collective Intelligence

This study simulates the dynamics of a collection of clonal agents responding to chemical gradients (chemotaxis) to demonstrate the evolution of individual variation. To build our multi-agent simulation, we first optimized single agents that rely on a neural network to perform chemotaxis. We then constructed multi-agent simulations using clones of these evolved individuals. We find that mutual interactions lead to the emergence of behavioral variation. We also find population-level performance degradation during later evolutionary stages, despite maintained high individual performance and simplified neural architectures. This decline occurred because agents developed reduced sensory-motor coupling. This latter finding demonstrates that incentives for individual variation worked against the collective interest.

Read the full article at: journals.sagepub.com

Ilya Horiguchi, Hiroki Sayama

Hash Chemistry is a family of minimalistic evolutionary models in which a deterministic hash function assigns a scalar score to entities of arbitrary size, opening a combinatorially vast possibility space (a ``cardinality leap''). Since its introduction, the idea has been realized in several settings, from the original spatial formulation to a fast non-spatial variant and then to structural cellular models. Here we review the Hash Chemistry family as a coherent modeling framework and use it to explore how minimal systems can demonstrate the mechanisms behind multiscale open-ended evolutionary dynamics. The most recent model, Structural Cellular Hash Chemistry (SCHC), successfully demonstrated multiscale ecological interaction/adaptation and complexity growth of replicators in a computationally efficient manner. In this study, we first extend SCHC to incorporate spatial locality and dyadicity of competitive interactions among replicating structures. We show this extension substantially enhances SCHC's evolutionary dynamics. Furthermore, we explore SCHC in a significantly larger spatial domain using a GPU-accelerated implementation. We show that the size of the space acts as a control parameter for a stochastic, nucleation-like transition between a compact-replicator regime and a runaway size-dominance regime, and we separate the responsible mechanism into a non-spatial, size-biased sampling feedback and a finite-size spatial effect. Altogether, these results illustrate the rich potential of Hash Chemistry as a minimal, mechanistically transparent testbed for studying open-ended evolution across scales.

Read the full article at: arxiv.org

Ariel Flint, Luca Maria Aiello, Romualdo Pastor-Satorras, and Andrea Baronchelli

PNAS August 18, 2026 123 (34) e2531697123

Large language models (LLMs) are increasingly deployed in large numbers, and their interactions make collective behavior harder to anticipate than that of a single model. While most studies compare one model with a collective of fixed size, we ask a key yet overlooked question: What is the role of group size? We show that interaction among LLMs can magnify individual biases, generate new ones, or even overturn individual preferences, and that, crucially, these effects scale in unexpected, nonlinear ways with group size. Our results demonstrate that more is different for LLM populations: The number of interacting agents is a key driver of the dynamics, with implications for the design and governance of multi-agent AI systems.

Read the full article at: www.pnas.org

Mohammed, Sudaff; Al-Hinkawi, Wahda Shuker; and Hasan, Nada Abdulmueen (2025) "The Role of Swarm Intelligence Systems in Shaping Urban Development Policies," Iraqi Journal of Architecture and Planning: Vol. 24: Iss. 1, Article 3.

Swarm intelligence is a nature-inspired complex system that draws from the behaviours of social creatures such as ants and birds. This system functions through simple behavioural rules enacted by autonomous, intelligent agents. Existing literature indicates that swarm intelligence possesses a wide range of principles and characteristics derived from the theories of Biomimicry, complex adaptive systems, and parametric and generative design. While the previous studies have intensively addressed the computational aspects of intelligence, a comprehensive conceptual framework is essential for analysing complex urban forms and structures. Therefore, this research develops and applies a conceptual model of swarm intelligence by examining several projects across the following dimensions: growth strategies, mechanisms, and logic; primary and final characteristics; and the types and classifications of the system’s agents. The research emphasises the integration of theoretical and practical aspects of swarm intelligence to inform urban growth policies and promote more sustainable urban forms and structures.

Read the full article at: iqjap.uotechnology.edu.iq

Evgeny Ivanko, Aleksey Belousov

BioSystems
Volume 261, March 2026, 105711

We study the development of model biotic communities in which species play the role of environment for each other. Each experiment starts with the appearance of a single species in an abiotic environment. The properties of this initial species (together with the size of the abiotic environment) are the independent parameters of the experiment. In the following phase of macroevolutionary “unwrapping” each existing species can change its abundance (according to its current fitness) and give rise to new species (as a result of mutation). During this process, the destiny of the species becomes increasingly determined by the influence of other species rather than by the abiotic environment. With the mechanics described, artificial biotic communities experience adaptive radiation from single species to complex networks that coevolve in adaptive landscapes of their own making.
Using a number of metrics, we track the evolution of biotic communities in the hope of discovering interesting properties and patterns. We have tried to provide plausible explanations for the experiment results wherever possible. However, the main purpose of this work is not to answer questions, but rather to raise new ones, to provoke thoughts and analogies among readers with different backgrounds.

Read the full article at: www.sciencedirect.com

Peter A. Corning

BioSystems
Volume 266, August 2026, 105845

Charles Darwin's theory of evolution was seriously deficient. Although his concept of natural selection was an important contribution – highlighting the fundamental fact that life on Earth is a contingent, always at-risk enterprise – he failed to acknowledge the fact that all living systems – from the smallest single-celled bacteria to humankind – are also shaped by their evolved purposiveness (teleonomy). Their initiatives and activities – their “agency” – has exercised an important influence over the trajectory of life on Earth, as one of Darwin's predecessors, Jean-Baptiste de Lamarck, appreciated. Lamarck proposed that changes in an animal's “habits”, stimulated by environmental changes, have been a primary source of evolutionary change over time. Darwin also portrayed evolution as a fundamentally competitive process (the “struggle for existence” in Darwin's term), as did many of his contemporaries. Today we know that life has also been a multi-faceted cooperative (synergistic) enterprise and that this has been of overriding importance in the evolution of complexity over time. Teleonomy and cooperative functional effects (synergy) have shaped natural selection in many different ways. Indeed, we now know that there have been many influences in evolution. My proposed Inclusive Synthesis is also open-ended, because it is expected that still more has yet to be learned about biological evolution; it is an ongoing work-in-progress rather than a completed theoretical edifice. “Teleonomic Selection” (after Corning) and “Synergistic Selection” (after John Maynard Smith) have played important parts in evolution. It's time for a more inclusive theory.

Read the full article at: www.sciencedirect.com

Karina Kofman, et al.

Organisms. Journal of Biological Sciences

Life is one of the most fascinating features of the physical world. Despite centuries of scientific study, experts still disagree about the definition, and even the possibility or utility of a definition, of this field. In a recent paper, we used AI to analyze the conceptual space formed by definitions of life given by a select set of modern workers in the life sciences and related fields. However, some of the most interesting material emerged as real-time conversations among those polled. In order to ensure that these ideas are not lost to the peer-reviewed scientific record, we here provide a minimally-edited (largely verbatim) transcript of the email chain among leading thinkers, containing numerous clarifications, disagreements, and challenges that enrich the topic of Life. It is our hope that this case study serves as an example for future papers, since the exchange of ideas among scientists is at least as interesting and valuable as formal scientific manuscripts written from a single perspective.

Read the full article at: rosa.uniroma1.it