Abstract
Units of complex systems -- such as neurons in the brain or individuals in societies -- must communicate efficiently to function properly: e.g., allowing electrochemical signals to travel quickly among functionally connected neuronal areas in the human brain, or allowing for fast navigation of humans and goods in complex transportation landscapes. The coexistence of different types of relationships among the units, entailing a multilayer represention in which types are considered as networks encoded by layers, plays an important role in the quality of information exchange among them. While altering the structure of such systems -- e.g., by physically adding (or removing) units, connections or layers -- might be costly, coupling the dynamics of subset(s) of layers in a way that reduces the number of redundant diffusion pathways across the multilayer system, can potentially accelerate the overall information flow. To this aim, we introduce a framework for functional reducibility which allow us to enhance transport phenomena in multilayer systems by coupling layers together with respect to dynamics rather than structure. Mathematically, the optimal configuration is obtained by maximizing the deviation of system's entropy from the limit of free and non-interacting layers. Our results provide a transparent procedure to reduce diffusion time and optimize non-compact search processes in empirical multilayer systems, without the cost of altering the underlying structure.
Highlights
A wide variety of social, natural and artificial systems are inherently complex [1]
Complex systems are characterized by a wide variety of physical attributes and dynamics, making difficult to analyze them within a unified framework
This study provides a transparent framework to better understand the interplay between complex topologies and noncompact search dynamics [49], allowing one to exploit the multifaceted interactions among constituents of complex systems—usually encoded by multilayer networks—to enhance transport phenomena without altering the underlying structure
Summary
A wide variety of social, natural and artificial systems are inherently complex [1]. For instance, societies exhibit rich microscopic dynamics, at the level of single individuals, that might lead to emergent collective phenomena at larger scales [2]—e.g., financial collapses or revolutions—which are usually difficult to predict [3]. We show that a fundamentally different perspective must be considered instead of structural redundancy: by using random walk dynamics as a proxy for information flow, transport phenomena are enhanced when subsets of layers are functionally grouped together in such a way that the corresponding diffusion pathways are maximally different. By exploiting the relation between the flow distribution in a multiplex network and the spectral diversity of its layers, our framework can provide a broad spectrum of applications—from more optimal supply strategy that combine transportation of goods to more efficient navigability of urban areas by allowing for multimodal trips with the same ticket—that can be achieved by devising tailored policies targeting the dynamics of systems, without the cost of changing their structure
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