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Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative protocols, which consist of multiple agents that are coupled together via an undirected state-dependent graph. We develop a representation of the system solution by decomposing the nonlinear system utilizing ideas from the Koopman operator theory and its spectral analysis. We use recent results on the extensions of the wellknown Hartman theorem for hyperbolic systems to establish a connection between the original nonlinear dynamics and the linearized dynamics in terms of Koopman spectral properties. The expected value of the output energy of the nonlinear protocol, which is related to the notions of coherence and robustness in dynamical networks, is evaluated and characterized in terms of Koopman eigenvalues, eigenfunctions, and modes. Spectral representation of the performance measure enables us to develop algorithmic methods to assess the performance of this class of nonlinear dynamical networks as a function of their graph topology. Finally, we propose a scalable computational method for approximation of the components of the Koopman mode decomposition, which is necessary to evaluate the systemic performance measure of the nonlinear dynamic network. [ABSTRACT FROM AUTHOR]

Background: Hepatitis C virus (HCV) is a blood born virus and the leading cause of advanced hepatitis disease. HCV genotype 3a is predominant among Iranian blood donors. The aim of this study was to evaluate the relationship between HCV genotype and HCV viral load. Methods: In this analytical cross-sectional study 106 anti-HCV positive and HCV RNA positive blood donors referred to Iranian blood centers across the county were entered. HCV viral loads were determined by an in-house one step Taq Man Real-Time RT-PCR assay. Penalized logistic regression was performed for data analysis. STATA software version 13 was used for statistical analysis. Results: The mean age was 37.94 ± 9.04 years ranged from 19 to 58 years. Male gender included 104 (98.1%) of subjects. 31, 10 and 65 subjects were infected with genotypes1a, 1b, and 3a, respectively. The mean viral load was 1.44 × 106 ± 4.5× 105 IU/ml. HCV viral load was not significantly different among subjects infected with HCV genotypes 1, 1.49 × 10 6 ± 4.57 × 10 6 IU/ml compare to genotype 3, 1.40 × 10 6 ± 5.58 4.58 × 106 IU/ml (p=0.93). Conclusion: Although not significant, the frequency of subjects with high viral load (> 800,000 IU/ml) was higher in subjects infected with genotype 3 than those of genotype 1. No associations were found between demographic characteristics and HCV genotype. Although the study was unable to find any association between HCV genotype and HCV viral load/ HCV viral load group, it highlighted the role of high viral load in the high circulation of HCV genotype 3a among Iranian blood donors., (© 2019 Iran University of Medical Sciences.)