Miao Zeng, Roberto Murcio, Camilo Vargas-Ruiz, Elsa Arcaute

Achieving universal health coverage, as set out in Sustainable Development Goal 3.8, requires closing persistent geographic and socioeconomic gaps in healthcare access, especially in under-resourced settings across Africa. Healthcare-access inequality is shaped not only by poor local access, but also by limited connectivity to city- and regional-level services and opportunities. Conventional accessibility analysis can identify where poor access occurs, but not whether poorly served places form structurally disconnected pockets across scales. This paper therefore builds on and extends the percolation divergence tree framework to develop a connectivity-based multiscale approach for examining healthcare-access inequality in Ghana. It combines street-level accessibility mapping with the hierarchical structure of the road network to identify the scales at which inequality coincides with connectivity breaks. The results first show substantial inequality: around one quarter of the population lives more than 5 km from the nearest healthcare facility. Multiscale analysis further reveals distinct structural forms of poor access. In relatively well-connected, monocentric regions, local poor-access pockets emerge around metropolitan fringes despite overall regional advantage. In less well-connected, polycentric regions, poor access extends across larger subsystems, with local pockets nested within broader poorly served areas. These findings show that healthcare-access inequality reflects both local conditions and the hierarchical connectivity of the wider spatial system, which may also constrain marginalised communities’ access to other key resources and services. The framework can inform targeted local interventions and policy coordination across local and regional scales.

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Pablo Villegas, Sandro Meloni

Group interactions are widespread, and higher-order extensions of familiar models display collective phenomena absent from their pairwise baselines, which are routinely offered as evidence of a distinct higher-order physics. We ask whether that claim survives the test that gives new a precise meaning in statistical physics: that of universality. Revisiting canonical higher-order models, we argue that what classifies collective behavior are the infrared ingredients that survive at long scales. Arity is not a universality label. Beyond universality, we examine two further questions: whether higher-order structure is a fact about the system or a choice of description, and what data can and cannot tell us about interaction order. Higher-order descriptions remain indispensable when they expose the organizing structure, provide a better mechanistic language, or improve prediction. We close with what should be measured before new phenomena can be claimed, and where higher-order structure already earns its place.

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Emerence and complexity describe how systems can exhibit behaviors, patterns, and outcomes that cannot be fully understood by examining individual parts in isolation. As interactions between components increase, systems often become less predictable, more adaptive, and more sensitive to relationships, context, and feedback. Complex systems may display nonlinearity, self-organization, adaptation, and unexpected emergent behaviors that arise from the interactions within the system as a whole. Understanding these dynamics is essential for systems thinking and systems engineering, particularly when working with large-scale, interconnected, or socio-technical systems.Emerence and complexity describe how systems can exhibit behaviors, patterns, and outcomes that cannot be fully understood by examining individual parts in isolation. As interactions between components increase, systems often become less predictable, more adaptive, and more sensitive to relationships, context, and feedback. Complex systems may display nonlinearity, self-organization, adaptation, and unexpected emergent behaviors that arise from the interactions within the system as a whole. Understanding these dynamics is essential for systems thinking and systems engineering, particularly when working with large-scale, interconnected, or socio-technical systems.

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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