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We present a method to deterministically obtain broad bandwidth frequency combs in microresonators. These broadband frequency combs correspond to cnoidal waves in the limit when they can be considered soliton crystals or single solitons. The method relies on moving adiabatically through the (frequency detuning)×(pump amplitude) parameter space, while avoiding the chaotic regime. We consider in detail Si₃N₄microresonators with small or intermediate dimensions and an SiO₂microresonator with large dimensions, corresponding to prior experimental work. We also discuss the impact of thermal effects on the stable regions for the cnoidal waves. Their principal effect is to increase the detuning for all the stable regions, but they also skew the stable regions, since higher pump power corresponds to higher power and hence increased temperature and detuning. The change in the detuning is smaller for single solitons than it is for soliton crystals. Without temperature effects, the stable regions for single solitons and soliton crystals almost completely overlap. When thermal effects are included, the stable region for single solitons separates from the stable regions for the soliton crystals, explaining in part the effectiveness of backwards-detuning to obtaining single solitons.

 

This paper studies the security aspect of gossip-based decentralized optimization algorithms for multi agent systems against data injection attacks. Our contributions are two-fold. First, we show that the popular distributed projected gradient method (by Nedi´c et al.) can be attacked by coordinated insider attacks, in which the attackers are able to steer the final state to a point of their choosing. Second, we propose a metric that can be computed locally by the trustworthy agents processing their own iterates and those of their neighboring agents. This metric can be used by the trustworthy agents to detect and localize the attackers. We conclude the paper by supporting our findings with numerical experiments.