Observation of localized magnetic plasmon skyrmions

Optical skyrmions have recently been constructed by tailoring vectorial near-field distributions through the interference of multiple surface plasmon polaritons, offering promising features for advanced information processing, transport and storage. Here, we provide experimental demonstration of electromagnetic skyrmions based on magnetic localized spoof plasmons (LSP) showing large topological robustness against continuous deformations, without stringent external interference conditions. By directly measuring the spatial profile of all three vectorial magnetic fields, we reveal multiple π-twist target skyrmion configurations mapped to multi-resonant near-equidistant LSP eigenmodes. The real-space skyrmion topology is robust against deformations of the meta-structure, demonstrating flexible skyrmionic textures for arbitrary shapes. The observed magnetic LSP skyrmions pave the way to ultra-compact and robust plasmonic devices, such as flexible sensors, wearable electronics and ultra-compact antennas.

Graph Metrics for Network Robustness—A Survey

Research on the robustness of networks, and in particular the Internet, has gained critical importance in recent decades because more and more individuals, societies and firms rely on this global network infrastructure for communication, knowledge transfer, business processes and e-commerce. In particular, modeling the structure of the Internet has inspired several novel graph metrics for assessing important topological robustness features of large complex networks. This survey provides a comparative overview of these metrics, presents their strengths and limitations for analyzing the robustness of the Internet topology, and outlines a conceptual tool set in order to facilitate their future adoption by Internet research and practice but also other areas of network science.

Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths

Topological on-chip photonics based on tailored photonic crystals (PhCs) that emulate quantum valley-Hall effects has recently gained widespread interest owing to its promise of robust unidirectional transport of classical and quantum information. We present a direct quantitative evaluation of topological photonic edge eigenstates and their transport properties in the telecom wavelength range using phase-resolved near-field optical microscopy. Experimentally visualizing the detailed sub-wavelength structure of these modes propagating along the interface between two topologically non-trivial mirror-symmetric lattices allows us to map their dispersion relation and differentiate between the contributions of several higher-order Bloch harmonics. Selective probing of forward- and backward-propagating modes as defined by their phase velocities enables direct quantification of topological robustness. Studying near-field propagation in controlled defects allows us to extract upper limits of topological protection in on-chip photonic systems in comparison with conventional PhC waveguides. We find that protected edge states are two orders of magnitude more robust than modes of conventional PhC waveguides. This direct experimental quantification of topological robustness comprises a crucial step toward the application of topologically protected guiding in integrated photonics, allowing for unprecedented error-free photonic quantum networks.

Degree difference: a simple measure to characterize structural heterogeneity in complex networks

Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we analyze a simple, elegant yet underexplored measure, ‘degree difference’ (DD) between vertices of an edge, to understand the local network geometry. We describe the connection between DD and global assortativity of the network from both formal and conceptual perspective, and show that DD can reveal structural properties that are not obtained from other such measures in network science. Typically, edges with different DD play different structural roles and the DD distribution is an important network signature. Notably, DD is the basic unit of assortativity. We provide an explanation as to why DD can characterize structural heterogeneity in mixing patterns unlike global assortativity and local node assortativity. By analyzing synthetic and real networks, we show that DD distribution can be used to distinguish between different types of networks including those networks that cannot be easily distinguished using degree sequence and global assortativity. Moreover, we show DD to be an indicator for topological robustness of scale-free networks. Overall, DD is a local measure that is simple to define, easy to evaluate, and that reveals structural properties of networks not readily seen from other measures.

MODULARITY, ROBUSTNESS, AND CHANGE PROPAGATION: A MULTIFACETED RELATION

Increased system robustness is one of the promises of modularity. However, research on the topic has provided conflicting findings. By generating more than 2000 system architectures, this paper shows that the relation between modularity and robustness is multifaceted: Modularity decreases topological robustness, increases robustness to change propagation, and provides economic benefits. Results here confirm the importance of modularity, enable reconciliation of opposing findings from prior research, and guides researchers and practitioners in the selection of appropriate robustness measures.

Testing how antagonistic interactions impact the robustness of plant-pollinator networks

Given ongoing pollinator declines, it is important to understand the dynamics of linked extinctions of plants driven by pollinator extinctions. Topological robustness models focused on this question suggest relatively high robustness of plant species to pollinator species extinctions. Still, existing robustness models typically assume that all interactions in plant-pollinator networks are positive, which is clearly not always the case. For example, many pollinators remove floral resources without transferring pollen, or even damage floral structures in the case of nectar robbing. Here we introduce antagonistic interactions into plant-pollinator networks and assess the resilience of plant communities to pollinator species losses. Incorporating antagonistic interactions leads to lower network robustness, i.e. an increased rate of plant species loss (as compared to networks with only mutualistic interactions) in empirical plant-pollinator networks. In conjunction with extinction order, the addition of increasingly antagonistic interactions was idiosyncratic in that it did not always magnify the effects of extinction order across the three networks. These results underscore the importance of considering the full spectrum of interaction outcomes when assessing robustness to coextinctions in plant-pollinator networks, as well as other ecological systems.