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# In this context our observation that the dominant predictor

In this context, our observation that the Tigecycline receptor predictor of positive QFN-CMV responses is background CMV seropositivity was not unexpected. Older age, despite well-known effects of CMV memory inflation did not appear to independently impact QFN-CMV responses in our study. The inter-play between reactivated CMV and stimulation of chronic CMV immunity may have been reflected in some patients converting from an initial negative QFN-CMV result to a positive result 2 months later. The fact that low grade asymptomatic CMV viraemia can both signify a compromise to CMV immunity, but also be a powerful stimulant to CMV immunity means that viral load per se cannot act as a static predictor of progression to CMV disease. This dynamic makes CMV viraemia in the absence of clinical disease and without concurrent assessment of CMV immunity difficult to interpret in practice, and often defaults to empirical CMV treatment as the safest course of action.
Although current CMV prevention strategies used in Western Australian solid organ transplant patients are effective at preventing CMV disease, this is not without its own costs and risks.4, 8, 10, 11 Although not specifically examined in our study, valganciclovir is known to cause side effects such as neutropenia in up to 15% of patients in other studies and promote drug resistant CMV disease. There is also the cost of antiviral drugs and laboratory costs of intensive CMV viral load monitoring to take into account.4, 8, 10, 11 Based on our testing of QFN-CMV responses, a large proportion of patients commenced on antiviral medication pre-emptively had preserved CMV cellular immune responses. Although we cannot determine what may have been the ultimate outcome of untreated viraemia in these individuals, natural control of viraemia was the rule in those with positive QFN-CMV responses not commenced on treatment, raising the possibility that immunological information may allow reduced use of pre-emptive treatment safely. Conversely, CMV disease did occur within this period of observation and was associated with a clear loss of CMV-specific T cell immunity. In practice it is likely that those patients who develop low level viral reactivation but have a positive QFN-CMV may not require antiviral therapy or such rigorous viral load monitoring, thereby avoiding the costs and side effects associated with more aggressive approaches. Conversely those patients without detectable immunity against CMV may require more aggressive and prolonged therapy and viral load monitoring. Overall, our data add to that of other studies suggesting that the QFN-CMV can be used to predict risk of CMV disease post-solid organ transplantation and guide clinical management.

Acknowledgements

Introduction and preliminaries
In physics, there is an interesting phenomenon called Anderson localization [1], which describes insulating behavior in the sense that quantum states are essentially localized in a suitable bounded region for all times, and which is named after the winner of the 1977 Nobel Prize in Physics, P. W. Anderson. In mathematics, Anderson localization often means that the corresponding operator has pure point spectrum with exponentially decaying eigenfunctions.
Recent developments in the theory of orthogonal polynomials on the unit circle (OPUC) have emphasized the importance of a class of unitary matrices called CMV matrices, a special class of unitary five-diagonal matrices. The corresponding unitary semi-infinite five-diagonal matrices were studied by Cantero, Moral and Velázquez [6], while in [11], Simon introduced the corresponding notion of unitary doubly infinite five-diagonal matrices and coined the term extended CMV matrices.
In this paper, we study the spectral theory of regular and extended CMV matrices. Since these matrices can be regarded as the unitary analogues of Schrödinger (or more generally Jacobi) matrices, one expects many analogies between the spectral theory of CMV matrices and that of discrete Schrödinger operators. This has been worked out in a variety of settings, many of them were already addressed in [12], including periodic and decaying coefficients. See also the recent paper [4] devoted to CMV matrices with random coefficients.