Enhancing transport properties in interconnected systems without altering their structure

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.

20 pages, 7 figures, To appear in Physical Review Research

References in corpus (10)

• The structure and dynamics of multilayer networks
• Diffusion dynamics on multiplex networks
• Layer aggregation and reducibility of multilayer interconnected networks
• Emergence of network features from multiplexity
• Navigability of Complex Networks
• Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems
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Cited by in corpus (11)

• Diversity of information pathways drives scaling and sparsity in real-world networks
• Statistical physics of complex information dynamics
• Multilayer Network Science: from Cells to Societies
• Unraveling the effects of multiscale network entanglement on disintegration of empirical systems
• Diffusion geometry of multiplex and interdependent systems
• Abrupt transition due to non-local cascade propagation in multiplex systems
• Generalized network density matrices for analysis of multiscale functional diversity
• Threshold-free estimation of entropy from a Pearson matrix
• Reconstruction of multiplex networks via graph embeddings
• Asymptotic entropy of the Gibbs state of complex networks
• Non-equilibrium random walks on multiplex networks