Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. Here we introduce an exact controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions. The framework reproduces the structural controllability of directed networks characterized by structural matrices. We explore the controllability of a large number of real and model networks, finding that dense networks with identical weights are difficult to be controlled. An efficient and accurate tool is offered to assess the controllability of large sparse and dense networks. The exact controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems.

Despite the long history of modelling human mobility, we continue to lack a highly accurate approach with low data requirements for predicting mobility patterns in cities. Here, we present a population-weighted opportunities model without any adjustable parameters to capture the underlying driving force accounting for human mobility patterns at the city scale. We use various mobility data collected from a number of cities with different characteristics to demonstrate the predictive power of our model. We find that insofar as the spatial distribution of population is available, our model offers universal prediction of mobility patterns in good agreement with real observations, including distance distribution, destination travel constraints and flux. By contrast, the models that succeed in modelling mobility patterns in countries are not applicable in cities, which suggests that there is a diversity of human mobility at different spatial scales. Our model has potential applications in many fields relevant to mobility behaviour in cities, without relying on previous mobility measurements.

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We develop a general framework to analyze the controllability of multiplex networks using multiple-relation networks and multiple-layer networks with interlayer couplings as two classes of prototypical systems. In the former, networks associated with different physical variables share the same set of nodes and in the latter, diffusion processes take place. We find that, for a multiplerelation network, a layer exists that dominantly determines the controllability of the whole network and, for a multiple-layer network, a small fraction of the interconnections can enhance the controllability remarkably. Our theory is generally applicable to other types of multiplex networks as well, leading to significant insights into the control of complex network systems with diverse structures and interacting patterns.

We present a scanning transmission x-ray microscopy setup combined with a novel microwave synchronization scheme for studying high frequency magnetization dynamics at synchrotron light sources. The sensitivity necessary to detect small changes in the magnetization on short time scales and nanometer spatial dimensions is achieved by combining the excitation mechanism with single photon counting electronics that is locked to the synchrotron operation frequency. Our instrument is capable of creating direct images of dynamical phenomena in the 5-10 GHz range, with high spatial resolution. When used together with circularly polarized x-rays, the above capabilities can be combined to study magnetic phenomena at microwave frequencies, such as ferromagnetic resonance (FMR) and spin waves. We demonstrate the capabilities of our technique by presenting phase resolved images of a ∼6 GHz nanoscale spin wave generated by a spin torque oscillator, as well as the uniform ferromagnetic precession with ∼0.1° amplitude at ∼9 GHz in a micrometer-sized cobalt strip.