Papers

Erik Hoel

Complex systems can be described at myriad different scales, and their causal workings often have multiscale structure (e.g., a computer can be described at the microscale of its hardware circuitry, the mesoscale of its machine code, and the macroscale of its operating system). While scientists study and model systems across the full hierarchy of their scales, from microphysics to macroeconomics, there is debate about what the macroscales of systems can possibly add beyond mere compression. To resolve this longstanding issue, here a new theory of emergence is introduced wherein the different scales of a system are treated like slices of a higher-dimensional object. The theory can distinguish which of these scales possess unique causal contributions, and which are not causally relevant. Constructed from an axiomatic notion of causation, the theory's application is demonstrated in coarse-grains of Markov chains. It identifies all cases of macroscale causation: instances where reduction to a microscale is possible, yet lossy about causation. Furthermore, the theory posits a causal apportioning schema that calculates the causal contribution of each scale, showing what each uniquely adds. Finally, it reveals a novel measure of emergent complexity: how widely distributed a system's causal workings are across its hierarchy of scales.

Read the full article at: arxiv.org

Yueran Duan; Mateusz Nurek; Qing Guan; Radosław Michalski; Petter Holme

IEEE Transactions on Computational Social Systems

Temporality, a crucial characteristic in the formation of social relationships, was used to quantify the long-term time effects of networks for link prediction models, ignoring the heterogeneity of time effects on different time scales. In this work, we propose a novel approach to link prediction in temporal networks, extending existing methods with a cognitive mechanism that captures the dynamics of the interactions. Our approach computes the weight of the edges and their change over time, similar to memory traces in the human brain, by simulating the process of forgetting and strengthening connections depending on the intensity of interactions. We utilized five ground-truth datasets, which were used to predict social ties, missing events, and potential links.We found: 1) the cognitive mechanism enables more accurate capture of the heterogeneity of the temporal effect, leading to an average precision improvement of 9% compared to baselines with competitive area under curve (AUC); 2) the local structure and synchronous agent behavior contribute differently to different types of datasets; and 3) appropriately increasing the time intervals, which may reduce the negative impact from noise when dividing time windows to calculate the behavioral synchrony of agents, is effective for link prediction tasks.

Read the full article at: ieeexplore.ieee.org

Hao Wang

Human mobility, a pivotal aspect of urban dynamics, displays a profound and multifaceted relationship with urban sustainability. Despite considerable efforts analyzing mobility patterns over decades, the ranking dynamics of urban mobility has received limited attention. This study aims to contribute to the field by investigating changes in rank and size of hourly inflows to various locations across 60 Chinese cities throughout the day. We find that the rank-size distribution of hourly inflows over the course of the day is stable across cities. To uncover the microdynamics beneath the stable aggregate distribution amidst shifting location inflows, we analyzed consecutive-hour inflow size and ranking variations. Our findings reveal a dichotomy: locations with higher daily average inflow display a clear monotonic trend, with more pronounced increases or decreases in consecutive-hour inflow. In contrast, ranking variations exhibit a non-monotonic pattern, distinguished by the stability of not only the top and bottom rankings but also those in moderately-inflowed locations. Finally, we compare ranking dynamics across cities using a ranking metric, the rank turnover. The results advance our understanding of urban mobility dynamics, providing a basis for applications in urban planning and traffic engineering.

Read the full article at: arxiv.org

ELENA CANDELLONE, ERIK-JAN VAN KESTEREN, SOFIA CHELMI, and JAVIER GARCIA-BERNARDO

Advances in Complex SystemsVol. 28, No. 03, 2540002 (2025)

Decision-making processes often involve voting. Human interactions with exogenous entities such as legislations or products can be effectively modeled as two-mode (bipartite) signed networks — where people can either vote positively, negatively, or abstain from voting on the entities. Detecting communities in such networks could help us understand underlying properties: for example ideological camps or consumer preferences. While community detection is an established practice separately for bipartite and signed networks, it remains largely unexplored in the case of bipartite signed networks. In this paper, we systematically evaluate the efficacy of community detection methods on projected bipartite signed networks using a synthetic benchmark and real-world datasets. Our findings reveal that when no communities are present in the data, these methods often recover spurious user communities. When communities are present, the algorithms exhibit promising performance, although their performance is highly susceptible to parameter choice. This indicates that researchers using community detection methods in the context of bipartite signed networks should not take the communities found at face value: it is essential to assess the robustness of parameter choices or perform domain-specific external validation.

Read the full article at: www.worldscientific.com

Alex Gomez-Marin & Anil K. Seth 
Nature Neuroscience (2025)

The scientific study of consciousness was sanctioned as an orthodox field of study only three decades ago. Since then, a variety of prominent theories have flourished, including integrated information theory, which has been recently accused of being pseudoscience by more than 100 academics. Here we critically assess this charge and offer thoughts to elevate the clash into positive lessons for our field.

Read the full article at: www.nature.com

Seymour Garte, Perry Marshall, and Stuart Kauffman

Entropy 2025, 27(3), 280

The known laws of nature in the physical sciences are well expressed in the language of mathematics, a fact that caused Eugene Wigner to wonder at the “unreasonable effectiveness” of mathematical concepts to explain physical phenomena. The biological sciences, in contrast, have resisted the formulation of precise mathematical laws that model the complexity of the living world. The limits of mathematics in biology are discussed as stemming from the impossibility of constructing a deterministic “Laplacian” model and the failure of set theory to capture the creative nature of evolutionary processes in the biosphere. Indeed, biology transcends the limits of computation. This leads to a necessity of finding new formalisms to describe biological reality, with or without strictly mathematical approaches. In the former case, mathematical expressions that do not demand numerical equivalence (equations) provide useful information without exact predictions. Examples of approximations without equal signs are given. The ineffectiveness of mathematics in biology is an invitation to expand the limits of science and to see that the creativity of nature transcends mathematical formalism.

Read the full article at: www.mdpi.com

Franz Kuchling , Isha Singh , Mridushi Daga , Susan Zec , Alexandra Kunen and Michael Levin

JRS Interface February 2025 Volume 22Issue 223

The field of diverse intelligence explores the capacity of systems without complex brains to dynamically engage with changing environments, seeking fundamental principles of cognition and their evolutionary origins. However, there are many knowledge gaps around a general behavioural directive connecting aneural to neural organisms. This study tests predictions of the computational framework of active inference based on the free energy principle in neuroscience, applied to aneural biological processes. We demonstrate pattern recognition in the green algae Volvox using phototactic experiments with varied light pulse patterns, measuring their phototactic bias as a readout for their preferential ability to detect and adapt to one pattern over another. Results show Volvox adapt more readily to regular patterns than irregular ones and even exhibit memory properties, exhibiting a crucial component of basal intelligence. Pharmacological and electric shock-based interventions and photoadaptation simulations reveal how randomized stimuli interfere with normal photoadaptation through a structured dynamic interplay of colony rotation and calcium-mediated photoreceptor-to-flagellar information transfer, consistent with uncertainty minimization. The detection of functional uncertainty minimization in an aneural organism expands concepts like uncertainty minimization beyond neurons and provides insights and novel intervention tools applicable to other living systems, similar to early learning validations in simpler neural organisms.

Read the full article at: royalsocietypublishing.org

GUANGHUI YAN, JIE TANG, HUAYAN PEI, and WENWEN CHANG

Advances in Complex SystemsVol. 28, No. 01n02, 2550005 (2025)

Considering that rumors propagation is affected by many factors in real life, based on the SIRS infectious disease model in complex networks, an extended ISRI rumor propagation model is proposed by using the probability function to define the influence mechanisms such as trust mechanism, and suspicion mechanism. First, dynamic equations are established for homogeneous and heterogeneous networks, and the rumor and rumor-free equilibrium points in the two networks are analyzed, respectively. Then, the basic reproduction number R0 is obtained by using the next generation matrix and derivative calculation methods. Next, the lyapunov function is constructed to discuss the local stability and global stability of the equilibrium point, and the influence of different parameters on the basic reproduction number R0. In addition, we selected ER network and BA network and found that population flow has a significant impact on the speed and scale of rumor propagation. At the same time, the trust mechanism can improve the propagation speed and scale, while the skepticism mechanism can inhibit the propagation speed, and it is more obvious in the BA network. The interaction between these mechanisms further affects the propagation characteristics of rumors in the network.

Read the full article at: www.worldscientific.com

Manuel Baltieri, Martin Biehl, Matteo Capucci, Nathaniel Virgo

The internal model principle, originally proposed in the theory of control of linear systems, nowadays represents a more general class of results in control theory and cybernetics. The central claim of these results is that, under suitable assumptions, if a system (a controller) can regulate against a class of external inputs (from the environment), it is because the system contains a model of the system causing these inputs, which can be used to generate signals counteracting them. Similar claims on the role of internal models appear also in cognitive science, especially in modern Bayesian treatments of cognitive agents, often suggesting that a system (a human subject, or some other agent) models its environment to adapt against disturbances and perform goal-directed behaviour. It is however unclear whether the Bayesian internal models discussed in cognitive science bear any formal relation to the internal models invoked in standard treatments of control theory. Here, we first review the internal model principle and present a precise formulation of it using concepts inspired by categorical systems theory. This leads to a formal definition of `model' generalising its use in the internal model principle. Although this notion of model is not a priori related to the notion of Bayesian reasoning, we show that it can be seen as a special case of possibilistic Bayesian filtering. This result is based on a recent line of work formalising, using Markov categories, a notion of `interpretation', describing when a system can be interpreted as performing Bayesian filtering on an outside world in a consistent way.

Read the full article at: arxiv.org

Guozheng Lin, Ramon Escobedo, Xu Li, Tingting Xue, Zhangang Han, Clément Sire, Vishwesha Guttal, Guy Theraulaz

How do animal groups dynamically adjust their collective behavior in response to environmental changes is an open and challenging question. Here, we investigate the mechanisms that allow fish schools to tune their collective state under stress, testing the hypothesis that these systems operate near criticality, a state maximizing sensitivity, responsiveness, and adaptability. We combine experiments and data-driven computational modeling to study how group size and stress influence the collective behavior of rummy-nose tetras (Hemigrammus rhodostomus). We quantify the collective state of fish schools using polarization, milling, and cohesion metrics and use a burst-and-coast model to infer the social interaction parameters that drive these behaviors. Our results indicate that group size modulates stress levels, with smaller groups experiencing higher baseline stress, likely due to a reduced social buffering effect. Under stress, fish adjust the strength of their social interactions in a way that leads the group into a critical state, thus enhancing its sensitivity to perturbations and facilitating rapid adaptation. However, large groups require an external stressor to enter the critical regime, whereas small groups are already near this state. Unlike previous studies suggesting that fish adjust their interaction network structure under risk, our results suggest that the intensity of social interactions, rather than network structure, governs collective state transitions. This simpler mechanism reduces cognitive demands while enabling dynamic adaptation. By revealing how stress and group size drive self-organization toward criticality, our study provides fundamental insights into the adaptability of collective biological systems and the emergent properties in animal groups.

Read the full article at: www.biorxiv.org

M. A. Polo-González, A. P. Riascos, L. K. Eraso-Hernandez

In this paper, we introduce a mathematical framework to assess the impact of damage, defined as the reduction of weight in a specific link, on identical oscillator systems governed by the Kuramoto model and coupled through weighted networks. We analyze how weight modifications in a single link affect the system when its global function is to achieve the synchronization of coupled oscillators starting from random initial phases. We introduce different measures that allow the identification of cases where damage enhances synchronization (antifragile response), deteriorates it (fragile response), or has no significant impact. Using numerical solutions of the Kuramoto model, we investigate the effects of damage on network links where antifragility emerges. Our analysis includes lollipop graphs of varying sizes and a comprehensive evaluation and all the edges of 109 non-isomorphic graphs with six nodes. The approach is general and can be applied to study antifragility in other oscillator systems with different coupling mechanisms, offering a pathway for the quantitative exploration of antifragility in diverse complex systems.

Read the full article at: arxiv.org

Viktor Stojkoski, and César Hidalgo, “Optimizing Economic Complexity”, TSE Working Paper, n. 24-1623, March 2025.

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 a method to identify diversification opportunities based on the minimization of a cost function that captures the constraints imposed by an economy’s pattern of specialization and show that this ECI optimization algorithm produces recommendations that are substantially different from those obtained using relatedness-complexity diagrams. This method advances the use of economic complexity methods to explore questions of strategic diversification.

Read the full article at: www.tse-fr.eu

Roland den Boef & René van Woudenberg

Foundations of Science Volume 30, pages 55–72, (2025)

The humanistic disciplines aim to offer explanations of a wide variety of phenomena. Philosophical theories of explanation have focused mostly on explanations in the natural sciences; a much discussed theory of explanation is the causal theory of explanation. Recently it has come to be recognized that the sciences sometimes offer respectable explanations that are non-causal. This paper broadens the discussion by discussing explanations that are offered in the fields of history, linguistics, literary theory, and archaeology that do not seem to fit the causal theory of explanation. We conducted an exploratory survey in acclaimed humanities textbooks to find explicitly so-called explanations and analyze their nature. The survey suggests that non-causal explanations are an integral part of the humanities and that they are of distinct kinds. This paper describes three kinds that are suggested by our survey: teleological, formal, and normative explanations. We suggest that such humanistic explanations strengthen the case for explanatory pluralism.

Read the full article at: link.springer.com

Jaume Ojer, Michele Starnini, and Romualdo Pastor-Satorras

Phys. Rev. Research 7, 013207

Understanding the mechanisms to mitigate opinion polarization in our society is crucial to minimizing social division and ultimately strengthening democracy. Due to the challenge of collecting long-term reliable empirical data, researchers have been mostly focused on a theoretical understanding of the process of opinion depolarization. To this aim, realistic yet simple models prove valuable, especially when multiple topics are discussed at the same time, which may result in entangled opinion dynamics. In this paper, we propose the multidimensional social compass model, based on two competing key ingredients: DeGroot learning, driven by the social influence exerted across multiple topics, and the preference of individuals to maintain their initial opinions. The interplay between these two mechanisms triggers a phase transition from polarization to consensus, determined by a threshold value of social influence. We analytically study the nature of the depolarization transition and its threshold, depending on the number of topics discussed, the possible correlations between initial opinions, the topology of the underlying social networks, and the correlations between the initial opinion distribution and the network's structure. Theoretical predictions are validated by running numerical simulations on both synthetic and real social networks. We rely on several simplifying assumptions to explore different scenarios, such as a mean-field approximation for high dimension or orthogonal initial orientations. We uncover an upper critical dimension (𝐷𝑐=5 topics) for uncorrelated initial opinions, distinguishing between discontinuous and continuous phase transitions. For the simplest 𝐷=2 case and correlated initial opinions, we found that the depolarization threshold can vanish if the underlying connectivity is heterogeneous, as predicted by perturbation theory. Such an effect is due to the presence of hubs, which promote consensus in the population. We test this hypothesis by designing a rewiring algorithm that increases the structural heterogeneity of the underlying network, showing that the depolarization threshold decreases. Finally, we demonstrate that if hubs share the same initial opinion, the depolarization dynamics is significantly hindered. Our findings contribute to understanding the mechanisms to mitigate polarization in real-world scenarios, suggesting which settings can promote the depolarization process. The presence of very popular individuals on online social networks and the alignment of their opinions, in particular, may play a pivotal role in the multidimensional depolarization dynamics.

Read the full article at: link.aps.org

Five years ago this week, the World Health Organization declared the COVID-19 pandemic, and the world has never been the same. What began in December 2019 as a cluster of patients in Wuhan, China, with a mysterious pneumonia-like illness exploded into an existential threat that has killed more than 7 million people. Life changed for everyone, practically overnight. Millions of workers lost their jobs as businesses shuttered, and those who were fortunate enough to work remotely had to adjust quickly to digitalization. Supply chains were disrupted, and economies were in turmoil. Health care professionals faced unprecedented challenges caring for the sick while trying to protect themselves amid a shortage of equipment. The real estate market, particularly in the United States, transformed dramatically as prices rose along with interest rates. No country, no industry, no individual was left unaffected by the pandemic, in ways both large and small.

We asked several Wharton professors to reflect on these profound changes and how they continue to shape the world. Keep reading for their responses.

Read the full article at: knowledge.wharton.upenn.edu

Pedro Márquez-Zacarías, Andrés Ortiz-Muñoz, Emma P. Bingham

Living systems are thermodynamically open but closed in their organization. In other words, even though their material components turn over constantly, a material-independent property persists, which we call organization. Moreover, organization comes from within organisms themselves, which requires us to explain how this self-organization is established and maintained. In this paper we propose a mathematical and conceptual framework to understand the kinds of organized systems that living systems are, aiming to explain how self-organization emerges from more basic elemental processes. Additionally, we map our own notions to existing traditions in theoretical biology and philosophy, aiming to bring the main formal ideas into conceptual congruence.

Read the full article at: arxiv.org

In math and computer science, researchers have long understood that some questions are fundamentally unanswerable. Now physicists are exploring how even ordinary physical systems put hard limits on what we can predict, even in principle.

Read the full article at: www.quantamagazine.org

Keith Y Patarroyo, Abhishek Sharma, Ian Seet, Ignas Packmore, Sara I. Walker, Leroy Cronin

Quantifying the evolution and complexity of materials is of importance in many areas of science and engineering, where a central open challenge is developing experimental complexity measurements to distinguish random structures from evolved or engineered materials. Assembly Theory (AT) was developed to measure complexity produced by selection, evolution and technology. Here, we extend the fundamentals of AT to quantify complexity in inorganic molecules and solid-state periodic objects such as crystals, minerals and microprocessors, showing how the framework of AT can be used to distinguish naturally formed materials from evolved and engineered ones by quantifying the amount of assembly using the assembly equation defined by AT. We show how tracking the Assembly of repeated structures within a material allows us formalizing the complexity of materials in a manner accessible to measurement. We confirm the physical relevance of our formal approach, by applying it to phase transformations in crystals using the HCP to FCC transformation as a model system. To explore this approach, we introduce random stacking faults in closed-packed systems simplified to one-dimensional strings and demonstrate how Assembly can track the phase transformation. We then compare the Assembly of closed-packed structures with random or engineered faults, demonstrating its utility in distinguishing engineered materials from randomly structured ones. Our results have implications for the study of pre-genetic minerals at the origin of life, optimization of material design in the trade-off between complexity and function, and new approaches to explore material technosignatures which can be unambiguously identified as products of engineered design.

Read the full article at: arxiv.org

Ben Piazza, Dániel L. Barabási, André Ferreira Castro, Giulia Menichetti, Albert-László Barabási

The brain has long been conceptualized as a network of neurons connected by synapses. However, attempts to describe the connectome using established network science models have yielded conflicting outcomes, leaving the architecture of neural networks unresolved. Here, by performing a comparative analysis of eight experimentally mapped connectomes, we find that their degree distributions cannot be captured by the well-established random or scale-free models. Instead, the node degrees and strengths are well approximated by lognormal distributions, although these lack a mechanistic explanation in the context of the brain. By acknowledging the physical network nature of the brain, we show that neuron size is governed by a multiplicative process, which allows us to analytically derive the lognormal nature of the neuron length distribution. Our framework not only predicts the degree and strength distributions across each of the eight connectomes, but also yields a series of novel and empirically falsifiable relationships between different neuron characteristics. The resulting multiplicative network represents a novel architecture for network science, whose distinctive quantitative features bridge critical gaps between neural structure and function, with implications for brain dynamics, robustness, and synchronization.

Read the full article at: www.biorxiv.org

Colin J. Carlson, Cole B. Brookson, Daniel J. Becker, Caroline A. Cummings, Rory Gibb, Fletcher W. Halliday, Alexis M. Heckley, Zheng Y. X. Huang, Torre Lavelle, Hailey Robertson, Amanda Vicente-Santos, Ciara M. Weets & Timothée Poisot 

Nature Reviews Biodiversity volume 1, pages 32–49 (2025)

Emerging infectious diseases, biodiversity loss, and anthropogenic environmental change are interconnected crises with massive social and ecological costs. In this Review, we discuss how pathogens and parasites are responding to global change, and the implications for pandemic prevention and biodiversity conservation. Ecological and evolutionary principles help to explain why both pandemics and wildlife die-offs are becoming more common; why land-use change and biodiversity loss are often followed by an increase in zoonotic and vector-borne diseases; and why some species, such as bats, host so many emerging pathogens. To prevent the next pandemic, scientists should focus on monitoring and limiting the spread of a handful of high-risk viruses, especially at key interfaces such as farms and live-animal markets. But to address the much broader set of infectious disease risks associated with the Anthropocene, decision-makers will need to develop comprehensive strategies that include pathogen surveillance across species and ecosystems; conservation-based interventions to reduce human–animal contact and protect wildlife health; health system strengthening; and global improvements in epidemic preparedness and response. Scientists can contribute to these efforts by filling global gaps in disease data, and by expanding the evidence base for disease–driver relationships and ecological interventions.

Read the full article at: www.nature.com