Galen J. Wilkerson
The origin of life poses a problem of combinatorial feasibility: How can temporally supported functional organization arise in exponentially branching assembly spaces when unguided exploration behaves as a memoryless random walk? We show that nonlinear threshold-cascade dynamics in connected interaction networks provide a minimal, substrate-agnostic mechanism that can soften this obstruction. Below a critical connectivity threshold, cascades die out locally and structured input-output response mappings remain sparse and transient-a “functional desert” in which accumulation is dynamically unsupported. Near the critical percolation threshold, system-spanning cascades emerge, enabling discriminative functional responses. We illustrate this transition using a minimal toy model and generalize the argument to arbitrary networked systems. Also near criticality, cascades introduce finite-timescale structural and functional coherence, directional bias, and weak dynamical path-dependence into otherwise memoryless exploration, allowing biased accumulation. This connectivity-driven transition-functional percolation-requires only generic ingredients: interacting units, nonlinear thresholds, influence transmission, and non-zero coherence times. The mechanism does not explain specific biochemical pathways, but it identifies a necessary dynamical regime in which structured functional organization can emerge and be temporarily supported, providing a physical foundation for how combinatorial feasibility barriers can be crossed through network dynamics alone.

Read the full article at: arxiv.org

Marco A. Rosas Pulido, Roberto Murcio, Omar R. Vázquez, Carlos Gershenson
Intricate interactions among firms, institutions, and spatial structures shape urban economic systems. In this study, we propose a framework based on three structural dimensions — abundance, diversity, and longevity (ADL) of economic units — as proxies of urban economic complexity and resilience. Using a decade of georeferenced firm-level data from Mexico City, we analyze the relationships among ADL variables using regression, spatial correlation, and time-series clustering. Our results reveal nonlinear dynamics across urban space, with powerlaw behavior in central zones and logarithmic saturation in peripheral areas, suggesting differentiated growth regimes. Notably, firm longevity modulates the relationship between abundance and diversity, particularly in periurban transition zones. These spatial patterns point to an emerging polycentric restructuring within a traditionally monocentric metropolis. By integrating economic complexity theory with spatial analysis, our approach provides a scalable method to assess the adaptive capacity of urban economies. This has implications for understanding informality, designing inclusive urban policies, and navigating structural transitions in rapidly urbanizing regions.

Read the full article at: arxiv.org

Erik Hoel

Patterns, Volume 7, Issue 1101472January 09, 2026

Complex systems can be described at myriad different scales, and their causal workings often have a 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 long-standing issue, here, a new theory of emergence is introduced that can distinguish which scales irreducibly contribute to a system’s causal workings. The theory’s application is demonstrated in coarse grains of Markov chains, revealing a novel measure of emergent complexity: how widely distributed a system’s causal contributions are across its hierarchy of scales.

Read the full article at: www.cell.com

Nick Holton, Marianne Cottin, Adam Wright, Michael Mannino, Dayanne S. Antonio, Marcelo Bigliassi

Antifragility challenges conventional thinking by proposing that adversity is not merely to be survived but actively used to promote growth. This scoping review synthesizes 18 emerging research studies focused on antifragility in human systems across disciplines, distinguishing antifragility from resilience and robustness and highlighting key empirical gaps, particularly in psychological research. During the screening process, articles were categorized as human or non-human systems. Non-human systems (n = 29; e.g., robotics, logistics, information systems, urban planning, artificial intelligence) were excluded from synthesis to align with the review’s focus on human domains (e.g., psychology, leadership, coaching, health). Drawing from biology, psychology, and organizational studies, the review summarizes applications in mental health, performance, and quality of life. Findings emphasize the proactive nature of antifragility, in which stressors are intentionally engaged to strengthen capabilities. Biological concepts like hormesis and psychological frameworks such as post-traumatic growth align with mechanisms relevant to growth through adversity. Yet empirical studies remain scarce, underscoring the need for robust measurement tools and longitudinal designs. Future directions include refining antifragility as a state, trait, or process, developing dose-specific models, and exploring biopsychosocial correlates. Embracing antifragility could transform how individuals and systems confront challenge, not by resisting breakdown, but by evolving beyond it.

Read the full article at: journals.sagepub.com

Xiangyi Meng, Benjamin Piazza, Csaba Both, Baruch Barzel & Albert-László Barabási 

Nature volume 649, pages 315–322 (2026)

The brain’s connectome1,2,3 and the vascular system4 are examples of physical networks whose tangible nature influences their structure, layout and, ultimately, their function. The material resources required to build and maintain these networks have inspired decades of research into wiring economy, offering testable predictions about their expected architecture and organization. Here we empirically explore the local branching geometry of a wide range of physical networks, uncovering systematic violations of the long-standing predictions of wiring minimization. This leads to the hypothesis that predicting the true material cost of physical networks requires us to account for their full three-dimensional geometry, resulting in a largely intractable optimization problem. We discover, however, an exact mapping of surface minimization onto high-dimensional Feynman diagrams in string theory5,6,7, predicting that, with increasing link thickness, a locally tree-like network undergoes a transition into configurations that can no longer be explained by length minimization. Specifically, surface minimization predicts the emergence of trifurcations and branching angles in excellent agreement with the local tree organization of physical networks across a wide range of application domains. Finally, we predict the existence of stable orthogonal sprouts, which are not only prevalent in real networks but also play a key functional role, improving synapse formation in the brain and nutrient access in plants and fungi.

Read the full article at: www.nature.com