Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks

Synchronization is of central importance in power distribution, telecommunication, neuronal, and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these clusters or understand the conditions under which they form, except for in the simplest of networks. In this article, we shed light on the intimate connection between network symmetry and cluster synchronization. We introduce general techniques that use network symmetries to reveal the patterns of synchronized clusters and determine the conditions under which they persist. The connection between symmetry and cluster synchronization is experimentally explored using an electro-optic network. We experimentally observe and theoretically predict a surprising phenomenon in which some clusters lose synchrony while leaving others synchronized. The results could guide the design of new power grid systems or lead to new understanding of the dynamical behavior of networks ranging from neural to social

Complete Characterization of Stability of Cluster Synchronization in Complex Dynamical Networks

Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling. Many networks exhibit incomplete synchronization, where two or more clusters of synchronization persist, and computational group theory has recently proved to be valuable in discovering these cluster states based upon the topology of the network. In the important case of Laplacian coupling, additional synchronization patterns can exist that would not be predicted from the group theory analysis alone. The understanding of how and when clusters form, merge, and persist is essential for understanding collective dynamics, synchronization, and failure mechanisms of complex networks such as electric power grids, distributed control networks, and autonomous swarming vehicles. We describe here a method to find and analyze all of the possible cluster synchronization patterns in a Laplacian-coupled network, by applying methods of computational group theory to dynamically-equivalent networks. We present a general technique to evaluate the stability of each of the dynamically valid cluster synchronization patterns. Our results are validated in an electro-optic experiment on a 5 node network that confirms the synchronization patterns predicted by the theory.Comment: 6 figure

Quantifying Isoniazid Levels in Small Hair Samples: A Novel Method for Assessing Adherence during the Treatment of Latent and Active Tuberculosis.

BackgroundTuberculosis (TB) is the leading cause of death from an infectious pathogen worldwide and the most prevalent opportunistic infection in people living with HIV. Isoniazid preventive therapy (IPT) reduces the incidence of active TB and reduces morbidity and mortality in HIV-infected patients independently of antiretroviral therapy. However, treatment of latent or active TB is lengthy and inter-patient variability in pharmacokinetics and adherence common. Current methods of assessing adherence to TB treatment using drug levels in plasma or urine assess short-term exposure and pose logistical challenges. Drug concentrations in hair assess long-term exposure and have demonstrated pharmacodynamic relevance in HIV.MethodsA large hair sample from a patient with active TB was obtained for assay development. Methods to pulverize hair and extract isoniazid were optimized and then the drug detected by liquid chromatography/ tandem mass spectrometry (LC/MS-MS). The method was validated for specificity, accuracy, precision, recovery, linearity and stability to establish the assay's suitability for therapeutic drug monitoring (TDM). Hair samples from patients on directly-observe isoniazid-based latent or active TB therapy from the San Francisco Department of Public Health TB clinic were then tested.ResultsOur LC/MS-MS-based assay detected isoniazid in quantities as low as 0.02ng/mg using 10-25 strands hair. Concentrations in spiked samples demonstrated linearity from 0.05-50ng/mg. Assay precision and accuracy for spiked quality-control samples were high, with an overall recovery rate of 79.5%. In 18 patients with latent or active TB on treatment, isoniazid was detected across a wide linear dynamic range.ConclusionsAn LC-MS/MS-based assay to quantify isoniazid levels in hair with performance characteristics suitable for TDM was developed and validated. Hair concentrations of isoniazid assess long-term exposure and may be useful for monitoring adherence to latent or active TB treatment in the setting of HIV

Existence of matching priors on compact spaces

A matching prior at level $1-\alpha$ is a prior such that an associated $1-\alpha$ credible set is also a $1-\alpha$ confidence set. We study the existence of matching priors for general families of credible regions. Our main result gives topological conditions under which matching priors for specific families of credible sets exist. Informally: on compact parameter spaces, if the so-called rejection-probability map is jointly continuous under the Wasserstein metric on priors, a matching prior exists. In light of this general result, we observe that typical families of credible regions, such as credible balls, highest-posterior density regions, quantiles, etc., fail to meet this topological condition. We show how to design approximate posterior credible balls and highest-posterior-density regions that meet these topological conditions, yielding matching priors. The proof of our main theorem uses tools from nonstandard analysis and establishes new results about the nonstandard extension of the Wasserstein metric which may be of independent interest.Comment: 53 pages, 1 figur