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        <title>Frontiers in Complex Systems | Complex Systems Theory section | New and Recent Articles</title>
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        <description>RSS Feed for Complex Systems Theory section in the Frontiers in Complex Systems journal | New and Recent Articles</description>
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        <pubDate>2026-04-05T03:49:22.523+00:00</pubDate>
        <ttl>60</ttl>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2026.1808241</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2026.1808241</link>
        <title><![CDATA[Retraction: Toward a thermodynamic theory of evolution: a theoretical perspective on information entropy reduction and the emergence of complexity]]></title>
        <pubdate>2026-02-16T00:00:00Z</pubdate>
        <category>Retraction</category>
        
        <description></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1672525</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1672525</link>
        <title><![CDATA[On the evolutionary dynamics of complexity and consciousness]]></title>
        <pubdate>2026-01-06T00:00:00Z</pubdate>
        <category>Review</category>
        <author>Shimon Edelman</author>
        <description><![CDATA[The perennial debate about the possible directionality of evolution, as indicated by the apparent increase in the complexity of living systems over time, has recently witnessed renewed arguments in favor of the growth of complexity being “entropic,” that is, consistent with the growth of entropy as it is construed in thermodynamics. Here, I offer a brief review of formal treatments of complexity and of evolutionary mechanisms that are capable of causing it to increase. I then propose that both the evolutionary emergence and the individual learning of basic phenomenal awareness, a type of consciousness, are characterized by the same time-asymmetrical dynamics. Like life itself, biological consciousness arguably evolves towards greater complexity, and for the same reasons.]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1667670</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1667670</link>
        <title><![CDATA[Emergence as a science]]></title>
        <pubdate>2025-12-01T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Benyamin Lichtenstein</author>
        <description><![CDATA[Although this Special Issue calls for a theory of emergence, the present paper argues that the breadth of the phenomenon\a requires a science, within which various theories can be explored and tested. To identify a structure for such a science of emergence, I pursued an in-depth cross-disciplinary analysis of emergence and its emergents. The result was identifying 9 emergence Prototypes, each of which reflects a unique aspect or context of emergence. Further, within some Prototypes, decades of scientific research has led to one or more Principles that its scholars ascribe to. Finally, the potential of an emergence science is explored by introducing applications of emergence to Leadership, Entrepreneurship, and Sustainability.]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1612142</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1612142</link>
        <title><![CDATA[The value of information in multi-scale feedback systems]]></title>
        <pubdate>2025-08-29T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Louisa Jane Di Felice</author><author>Ada Diaconescu</author><author>Payam Zahadat</author><author>Patricia Mellodge</author>
        <description><![CDATA[Complex adaptive systems (CAS) can be described as system of information flows that dynamically interact across scales to adapt and survive. CAS often consist of many components that work toward a shared goal and interact across different informational scales through feedback loops, leading to their adaptation. In this context, understanding how information is transmitted among system components and across scales becomes crucial for understanding the behavior of CAS. Shannon entropy, a measure of syntactic information, is often used to quantify the size and rarity of messages transmitted between objects and observers, but it does not measure the value that information has for each observer. For this, semantic and pragmatic information have been conceptualized as describing the influence on an observer’s knowledge and actions. Building on this distinction, we describe the architecture of multi-scale information flows in CAS through the concept of multi-scale feedback systems and propose a series of syntactic, semantic, and pragmatic information measures to quantify the value of information flows for adaptation. While the measurement of values is necessarily context-dependent, we provide general guidelines on how to calculate semantic and pragmatic measures and concrete examples of their calculation through four case studies: a robotic collective model, a collective decision-making model, a task distribution model, and a hierarchical oscillator model. Our results contribute to an informational theory of complexity that aims to better understand the role played by information in the behavior of multi-scale feedback systems.]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1630050</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1630050</link>
        <title><![CDATA[RETRACTED: Toward a thermodynamic theory of evolution: a theoretical perspective on information entropy reduction and the emergence of complexity]]></title>
        <pubdate>2025-07-31T00:00:00Z</pubdate>
        <category>Hypothesis and Theory</category>
        <author>Carlos Mendoza Montano</author>
        <description><![CDATA[Traditional evolutionary theory explains adaptation and diversification through random mutation and natural selection. While effective in accounting for trait variation and fitness optimization, this framework provides limited insight into the physical principles underlying the spontaneous emergence of complex, ordered systems. A complementary theory is proposed: that evolution is fundamentally driven by the reduction of informational entropy. Grounded in non-equilibrium thermodynamics, systems theory, and information theory, this perspective posits that living systems emerge as self-organizing structures that reduce internal uncertainty by extracting and compressing meaningful information from environmental noise. These systems increase in complexity by dissipating energy and exporting entropy, while constructing coherent, predictive internal architectures, fully in accordance with the second law of thermodynamics. Informational entropy reduction is conceptualized as operating in synergy with Darwinian mechanisms. It generates the structural and informational complexity upon which natural selection acts, whereas mutation and selection refine and stabilize those configurations that most effectively manage energy and information. This framework extends previous thermodynamic models by identifying informational coherence, not energy efficiency, as the primary evolutionary driver. Recently formalized metrics, Information Entropy Gradient (IEG), Entropy Reduction Rate (ERR), Compression Efficiency (CE), Normalized Information Compression Ratio (NICR), and Structural Entropy Reduction (SER), provide testable tools to evaluate entropy-reducing dynamics across biological and artificial systems. Empirical support is drawn from diverse domains, including autocatalytic networks in prebiotic chemistry, genome streamlining in microbial evolution, predictive coding in neural systems, and ecosystem-level energy-information coupling. Together, these examples demonstrate that informational entropy reduction is a pervasive, measurable feature of evolving systems. While this article presents a theoretical perspective rather than empirical results, it offers a unifying explanation for major evolutionary transitions, the emergence of cognition and consciousness, the rise of artificial intelligence, and the potential universality of life. By embedding evolution within general physical laws that couple energy dissipation to informational compression, this framework provides a generative foundation for interdisciplinary research on the origin and trajectory of complexity.]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1604132</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1604132</link>
        <title><![CDATA[Exploring interconnections among atoms, brain, society, and cosmos with network science and explainable machine learning]]></title>
        <pubdate>2025-06-30T00:00:00Z</pubdate>
        <category>Hypothesis and Theory</category>
        <author>Daniele Caligiore</author><author>Anna Monreale</author><author>Giulio Rossetti</author><author>Angela Bongiorno</author><author>Giuseppe Fisicaro</author>
        <description><![CDATA[This paper presents a methodology combining Network Science (NS) and Explainable Machine Learning (XML) that could hypothetically uncover shared principles across seemingly disparate scientific domains. As an example, it presents how the approach could be applied to four fields: materials science, neuroscience, social science, and cosmology. The study focuses on criticality, a phenomenon associated with the transition of complex systems between states, characterized by sudden and significant behavioral shifts. By proposing a five-step methodology—ranging from relational data collection to cross-domain analysis with XML—the paper offers a hypothetical framework for potentially identifying criticality-related features in these fields and transferring insights across disciplines. The results of domains cross-fertilization could support practical applications, such as improving neuroprosthetics and brain-machine interfaces by leveraging criticality in materials science and neuroscience or developing advanced materials for space exploration. The parallels between neural and social networks could deepen our understanding of human behavior, while studying cosmic and social systems may reveal shared dynamics in large-scale, interconnected structures. A key benefit could be the possibility of using transfer learning, that is XML models trained in one domain might be adapted for use in another with limited data. For instance, if common aspects of criticality in neuroscience and cosmology are identified, an algorithm trained on brain data could be repurposed to detect critical states in cosmic systems, even with limited cosmic data. This interdisciplinary approach advances theoretical frameworks and fosters practical innovations, laying the groundwork for future research that could transform our understanding of complex systems across diverse scientific fields.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1590952</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2025.1590952</link>
        <title><![CDATA[Cooperative behavior in pre-state societies: an agent based approach to the Axum civilization]]></title>
        <pubdate>2025-06-18T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Riccardo Vasellini</author><author>Gilda Ferrandino</author><author>Luisa Sernicola</author><author>Daniele Vilone</author><author>Chiara Mocenni</author>
        <description><![CDATA[IntroductionThis study intends to test the hypothesis that, contrary to traditional interpretation, the social structure of the polity of Aksum–especially in its early stages–was not characterized by a vertical hierarchy with highly centralized administrative power, and that the leaders mentioned in the few available inscriptions were predominantly ritual leaders with religious rather than coercive political authority. This hypothesis, suggested by the available archaeological evidence, is grounded in Charles Stanish's model, which posits that pre-state societies could achieve cooperative behavior without the presence of coercive authority.MethodsUsing agent-based modeling applied to data inspired by the Aksum civilization, we examine the dynamics of cooperation in the presence and absence of a Public Goods Game.ResultsResults show that while cooperative behavior can emerge in the short term without coercive power, it may not be sustainable over the long term, suggesting a need for centralized authority to foster stable, complex societies.DiscussionThese findings provide insights into the evolutionary pathways that lead to state formation and complex social structures.]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1347930</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1347930</link>
        <title><![CDATA[Quantum logic automata generalizing the edge of chaos in complex systems]]></title>
        <pubdate>2024-08-06T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Yukio Pegio Gunji</author><author>Yoshihiko Ohzawa</author><author>Yuuki Tokuyama</author><author>Kentaro Eto</author>
        <description><![CDATA[BackgroundHistorically, although researchers in the science of complex systems proposed the idea of the edge of chaos and/or self-organized criticality as the essential feature of complex organization, they were not able to generalize this concept. Complex organization is regarded at the edge of chaos between the order phase and the chaos phase and a very rare case. Additionally, in cellular automata, the critical property is class IV, which is also rarely found. Therefore, there can be overestimation for natural selection. More recently, developments in cognitive and brain science have led to the free energy principle based on Bayesian inference, while quantum cognition has been established to explain various cognitive phenomena. Since Bayesian inference results in the perspective of a steady state, it can be described in Boolean logic. Considering that quantum logic consists of multiple Boolean logic in terms of lattice theory, the perspective of the free energy principle is the perspective of order, and the perspective of quantum logic might be the perspective of multiple worlds, which is strongly relevant for the edge of chaos.ProblemThe next question arises whether the perspective derived from quantum logic can be generalized for the complex behavior consisting of both order and chaos, instead of the edge of chaos or self-organized criticality, to reveal the property of critical behavior such as a power-law distribution.SolutionIn this study, we define quantum logic automata, which entail quantum logic (orthomodular lattice) in terms of lattice theory and have the features of a dynamical system. Because quantum logic automata are applied to a binary sequence, one can estimate the behavior of those automata with respect to patterns and a time series. Here, we show that most of a group of quantum logic automata display class IV-like behavior, in which oscillatory traveling waves collide with each other, leading to complex behavior; moreover, a time series of binary sequences displays 1/f noise. Therefore, one can see that quantum logic automata generalize and expand the idea of the edge of chaos.]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1306328</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1306328</link>
        <title><![CDATA[Scenarios—using the complexity frame of reference to inform the construction of available futures in the possibility space]]></title>
        <pubdate>2024-06-26T00:00:00Z</pubdate>
        <category>Review</category>
        <author>David Sidney Byrne</author>
        <description><![CDATA[The global socio-ecological system in the era of the Capitalocene—the world system created by the use of fossil fuels to provide energy for the development of a growth-oriented capitalist logic in all areas of production and consumption—is facing a set of interwoven sub-system crises that come together to make it extremely unlikely that the global system can continue in its present form. The whole system is in a state of crisis—a system state that cannot continue to exist and in which the system must either return to a previous system state—be resilient in the common usage of that word to mean “bouncing back”—or be transformed into a new relatively long-lasting but qualitatively different state. The most evident whole system crisis is, of course, a product of the impending climate transformation contingent upon global warming, but there are related crises of increasing social inequality, demographic structures, healthcare systems, fiscal and public expenditure processes, and urban systems in an urbanized world. These are all interwoven to constitute a polycrisis across the global socio-ecological world system. They are also manifested at all geographical levels and, in particular, at the level of city regions, which, in a predominantly urbanized world, are crucial levels for administration and action. The complex realist frame of reference can be used to inform the development of scenarios for the available alternative system states in the path-dependent possibility space. We have to start from where we are to get to where we want to go. Scenarios are not only descriptions of possible futures but also include a specification of the actions—the drivers—that shape the creation of specific kinds of futures in those available to us. The construction of scenarios should be done through a process of action research, involving a dialog among system scientists, key actors in governance systems, and civil society. The co-production of knowledge as a guide to action is essential.]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1367957</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1367957</link>
        <title><![CDATA[Dynamical stability and chaos in artificial neural network trajectories along training]]></title>
        <pubdate>2024-05-17T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Kaloyan Danovski</author><author>Miguel C. Soriano</author><author>Lucas Lacasa</author>
        <description><![CDATA[The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network’s prediction, when confronted with a learning task. This iterative change can be naturally interpreted as a trajectory in network space–a time series of networks–and thus the training algorithm (e.g., gradient descent optimization of a suitable loss function) can be interpreted as a dynamical system in graph space. In order to illustrate this interpretation, here we study the dynamical properties of this process by analyzing through this lens the network trajectories of a shallow neural network, and its evolution through learning a simple classification task. We systematically consider different ranges of the learning rate and explore both the dynamical and orbital stability of the resulting network trajectories, finding hints of regular and chaotic behavior depending on the learning rate regime. Our findings are put in contrast to common wisdom on convergence properties of neural networks and dynamical systems theory. This work also contributes to the cross-fertilization of ideas between dynamical systems theory, network theory and machine learning.]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1329794</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2024.1329794</link>
        <title><![CDATA[What about adaptiveness? The case of organisational resilience and cognition]]></title>
        <pubdate>2024-02-15T00:00:00Z</pubdate>
        <category>Perspective</category>
        <author>Davide Secchi</author><author>Martin Neumann</author><author>Maria S. Festila</author><author>Rasmus Gahrn-Andersen</author>
        <description><![CDATA[This paper makes the very simple, perhaps straightforward point that adaptiveness cannot be taken for granted when analysing a complex system. The paradigm of Complex Adaptive Systems (CAS) theory makes it clear that a key feature of complex systems is the ability to adapt to changes in their environment. This is, indeed, relevant to many systems (e.g., living and social systems) since change is embedded in the way in which systems evolve over time. At the same time, adaptiveness is a strong assumption to make, since it prioritises change over stability and it can be a straight jacket, especially when it comes to studying complexity in the context of human social organising. By using a Case Study, this paper highlights the limits of a focus on adaptiveness and pushes for a more “neutral” perspective that allows researchers to appreciate a wider set of mechanisms, norms, and behaviours pertaining to complex social systems.]]></description>
      </item><item>
        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1329857</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1329857</link>
        <title><![CDATA[Complexity of the online distrust ecosystem and its evolution]]></title>
        <pubdate>2024-01-09T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Lucia Illari</author><author>Nicholas J. Restrepo</author><author>Neil F. Johnson</author>
        <description><![CDATA[Introduction: Collective human distrust—and its associated mis/disinformation—is one of the most complex phenomena of our time, given that approximately 70% of the global population is now online. Current examples include distrust of medical expertise, climate change science, democratic election outcomes—and even distrust of fact-checked events in the current Israel-Hamas and Ukraine-Russia conflicts.Methods: Here we adopt the perspective of the system being a complex dynamical network, in order to address these questions. We analyze a Facebook network of interconnected in-built communities (Facebook Page communities) totaling roughly 100 million users who, prior to the pandemic, were just focused on distrust of vaccines.Results: Mapping out this dynamical network from 2019 to 2023, we show that it has quickly self-healed in the wake of Facebook’s mitigation campaigns which include shutdowns. This confirms and extends our earlier finding that Facebook’s ramp-ups during COVID-19 were ineffective (e.g., November 2020). We also show that the post-pandemic network has expanded its topics and has developed a dynamic interplay between global and local discourses across local and global geographic scales.Discussion: Hence current interventions that target specific topics and geographical scales will be ineffective. Instead, our findings show that future interventions need to resonate across multiple topics and across multiple geographical scales. Unlike many recent studies, our findings do not rely on third-party black-box tools whose accuracy for rigorous scientific research is unproven, hence raising doubts about such studies’ conclusions–nor is our network built using fleeting hyperlink mentions which have questionable relevance.]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1284458</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1284458</link>
        <title><![CDATA[When may a system be referred to as complex?—an entropic perspective]]></title>
        <pubdate>2023-11-06T00:00:00Z</pubdate>
        <category>Hypothesis and Theory</category>
        <author>Constantino Tsallis</author>
        <description><![CDATA[Defining complexity is hard and far from unique—like defining beauty, intelligence, creativity, and many other such abstract concepts. In contrast, describing concrete complex systems is a sensibly simpler task. We focus here on such an issue from the perspective of entropic functionals, either additive or nonadditive. Indeed, for the systems currently referred to as simple, the statistical mechanics and associated (additive) entropy is that of Boltzmann–Gibbs, formulated 150 years ago. This formalism constitutes a pillar of contemporary theoretical physics and is typically grounded on strong chaos, mixing, ergodicity, and similar hypotheses, which typically emerge for systems with short-range space–time generic correlations. It fails, however, for the so-called complex systems, where generic long-range space–time correlations prevail, typically grounded on weak chaos. Many such nontrivial systems are satisfactorily handled within a generalization of the Boltzmann–Gibbs theory, namely, nonextensive statistical mechanics, introduced in 1988 and grounded on nonadditive entropies. Illustrations are presented in terms of D-dimensional simplexes such as nodes (D = 0), bonds (D = 1), plaquettes (D = 2), polyhedra (D = 3, …), and higher-order ones. A regularly updated bibliography is available at http://tsallis.cat.cbpf.br/biblio.htm.]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1235202</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1235202</link>
        <title><![CDATA[Unifying complexity science and machine learning]]></title>
        <pubdate>2023-10-18T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>David C. Krakauer</author>
        <description><![CDATA[Complexity science and machine learning are two complementary approaches to discovering and encoding regularities in irreducibly high dimensional phenomena. Whereas complexity science represents a coarse-grained paradigm of understanding, machine learning is a fine-grained paradigm of prediction. Both approaches seek to solve the “Wigner-Reversal” or the unreasonable ineffectiveness of mathematics in the adaptive domain where broken symmetries and broken ergodicity dominate. In order to integrate these paradigms I introduce the idea of “Meta-Ockham” which 1) moves minimality from the description of a model for a phenomenon to a description of a process for generating a model and 2) describes low dimensional features–schema–in these models. Reinforcement learning and natural selection are both parsimonious in this revised sense of minimal processes that parameterize arbitrarily high-dimensional inductive models containing latent, low-dimensional, regularities. I describe these models as “super-Humean” and discuss the scientic value of analyzing their latent dimensions as encoding functional schema. ]]></description>
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        <guid isPermaLink="true">https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1111486</guid>
        <link>https://www.frontiersin.org/articles/10.3389/fcpxs.2023.1111486</link>
        <title><![CDATA[Heterogeneity extends criticality]]></title>
        <pubdate>2023-05-03T00:00:00Z</pubdate>
        <category>Original Research</category>
        <author>Fernanda Sánchez-Puig</author><author>Octavio Zapata</author><author>Omar K. Pineda</author><author>Gerardo Iñiguez</author><author>Carlos Gershenson</author>
        <description><![CDATA[Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between order and chaos. In classic models of complex systems where structure and dynamics are considered homogeneous, criticality is restricted to phase transitions, leading either to robust (ordered) or fragile (chaotic) phases for most of the parameter space. Many real-world complex systems, however, are not homogeneous. Some elements change in time faster than others, with slower elements (usually the most relevant) providing robustness, and faster ones being adaptive. Structural patterns of connectivity are also typically heterogeneous, characterized by few elements with many interactions and most elements with only a few. Here we take a few traditionally homogeneous dynamical models and explore their heterogeneous versions, finding evidence that heterogeneity extends criticality. Thus, parameter fine-tuning is not necessary to reach a phase transition and obtain the benefits of (homogeneous) criticality. Simply adding heterogeneity can extend criticality, making the search/evolution of complex systems faster and more reliable. Our results add theoretical support for the ubiquitous presence of heterogeneity in physical, biological, social, and technological systems, as natural selection can exploit heterogeneity to evolve complexity “for free”. In artificial systems and biological design, heterogeneity may also be used to extend the parameter range that allows for criticality.]]></description>
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