RESUMEN

Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable complex functions. Yet, understanding, and ultimately harnessing, the structure-function relationship in oscillator networks remains an outstanding challenge of modern science. Here, we address this challenge by presenting a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators' parameters. To quantify the behavioral synchrony between coupled oscillators, we introduce the notion of functional pattern, which encodes the pairwise relationships between the oscillators' phases. Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. These conditions provide an interpretable mapping between the structural constraints and their functional implications in oscillator networks. As a proof of concept, we apply the proposed method to replicate empirically recorded functional relationships from cortical oscillations in a human brain, and to redistribute the active power flow in different models of electrical grids.

Asunto(s)

Encéfalo , Encéfalo/fisiología , Humanos

RESUMEN

Our ability to manipulate the behavior of complex networks depends on the design of efficient control algorithms and, critically, on the availability of an accurate and tractable model of the network dynamics. While the design of control algorithms for network systems has seen notable advances in the past few years, knowledge of the network dynamics is a ubiquitous assumption that is difficult to satisfy in practice. In this paper we overcome this limitation, and develop a data-driven framework to control a complex network optimally and without any knowledge of the network dynamics. Our optimal controls are constructed using a finite set of data, where the unknown network is stimulated with arbitrary and possibly random inputs. Although our controls are provably correct for networks with linear dynamics, we also characterize their performance against noisy data and in the presence of nonlinear dynamics, as they arise in power grid and brain networks.

Asunto(s)

Encéfalo/fisiología , Biología Computacional/métodos , Encéfalo/diagnóstico por imagen , Conectoma , Suministros de Energía Eléctrica , Humanos , Imagen por Resonancia Magnética , Red Nerviosa , Redes Neurales de la Computación , New England , Dinámicas no Lineales

RESUMEN

In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media requires understanding of how they propagate and transform information in the face of noise. Here, we develop a framework that enables us to examine how network structure, noise, and interference between consecutive packets jointly determine transmission performance in complex networks governed by linear dynamics. Mathematically, normal networks, which can be decomposed into separate low-dimensional information channels, suffer greatly from readout noise. Most details of their wiring have no impact on transmission quality. Non-normal networks, however, can largely cancel the effect of noise by transiently amplifying select input dimensions while ignoring others, resulting in higher net information throughput. Our theory could inform the design of new communication networks, as well as the optimal use of existing ones.

RESUMEN

Reliable information processing is a hallmark of many physical and biological networked systems. In this paper, we propose a novel framework for modelling information transmission within a linear dynamical network. Information propagation is modelled by means of a digital communication protocol that takes into account the realistic phenomenon of inter-symbol interference. Building on this framework, we adopt Shannon information rate to quantify the amount of information that can be reliably sent over the network within a fixed time window. We investigate how the latter information metric is affected by the connectivity structure of the network. Here, we focus in particular on networks characterized by a normal adjacency matrix. We show that for such networks the maximum achievable information rate depends only on the spectrum of the adjacency matrix. We then provide numerical results suggesting that non-normal network architectures could benefit information transmission in our framework.