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Electronic pacemakers can treat electrical conduction disorders in hearts; however, they are invasive, bulky, and linked to increased incidence of infection at the tissue–device interface. Thus, researchers have looked to other more biocompatible methods for cardiac pacing or resynchronization, such as femtosecond infrared light pulsing, optogenetics, and polymer-based cardiac patches integrated with metal electrodes. Here we develop a biocompatible nongenetic approach for the optical modulation of cardiac cells and tissues. We demonstrate that a polymer–silicon nanowire composite mesh can be used to convert fast moving, low-radiance optical inputs into stimulatory signals in target cardiac cells. Our method allows for the stimulation of the cultured cardiomyocytes or ex vivo heart to beat at a higher target frequency.

We study a simple Markov chain, known as the Glauber dynamics, for generating a random k-coloring of an n-vertex graph with maximum degree ∆. We prove that, for every ǫ > 0, the dynamics converges to a random coloring within O(n log n) steps assuming k ≥ k 0 (ǫ) and either: (i) k/∆ > α * + ǫ where α * ≈ 1.763 and the girth g ≥ 5, or (ii) k/∆ > β * + ǫ where β * ≈ 1.489 and the girth g ≥ 7. Our work improves upon, and builds on, previous results which have similar restrictions on k/∆ and the minimum girth but also required ∆ = Ω(log n). The best known result for general graphs is O(n log n) mixing time when k/∆ > 2 and O(n 2 ) mixing time when k/∆ > 11/6. Related results of Goldberg et al apply when k/∆ > α * for all ∆ ≥ 3 on triangle-free "neighborhood-amenable" graphs.

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