Network Synchronization in a Noisy Environment with Time Delays: Fundamental Limits and Trade-Offs

We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in an arbitrary network. Using the known exact threshold value from the theory of differential equations with delays, we provide the synchronizability threshold for an arbitrary network. Further, by constructing the scaling theory of the underlying fluctuations, we establish the absolute limit of synchronization efficiency in a noisy environment with uniform time delays, i.e., the minimum attainable value of the width of the synchronization landscape. Our results have also strong implications for optimization and trade-offs in network synchronization with delays.Comment: 3 figure

Building Damage-Resilient Dominating Sets in Complex Networks against Random and Targeted Attacks

We study the vulnerability of dominating sets against random and targeted node removals in complex networks. While small, cost-efficient dominating sets play a significant role in controllability and observability of these networks, a fixed and intact network structure is always implicitly assumed. We find that cost-efficiency of dominating sets optimized for small size alone comes at a price of being vulnerable to damage; domination in the remaining network can be severely disrupted, even if a small fraction of dominator nodes are lost. We develop two new methods for finding flexible dominating sets, allowing either adjustable overall resilience, or dominating set size, while maximizing the dominated fraction of the remaining network after the attack. We analyze the efficiency of each method on synthetic scale-free networks, as well as real complex networks

Large 2D Coulomb crystals in a radio frequency surface ion trap

We designed and operated a surface ion trap, with an ion-substrate distance of 500\mum, realized with standard printed-circuit-board techniques. The trap has been loaded with up to a few thousand Sr+ ions in the Coulomb-crystal regime. An analytical model of the pseudo-potential allowed us to determine the parameters that drive the trap into anisotropic regimes in which we obtain large (N>150) purely 2D ion Coulomb crystals. These crystals may open a simple and reliable way to experiments on quantum simulations of large 2D systems.Comment: 4 pages, 4 figure