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  • br Next let s recall some

    2020-04-07


    Next, let\'s recall some definitions and notations from [14] which are necessary to obtain the proof of Theorem 1. Let denote the CMV matrix whose Verblunsky coefficients replaced by , that is The corresponding extended CMV matrix is Recall the definition of in the proof of Theorem 2, replace by , we get
    Application In this section, we explain how to get Anderson localization of half-line CMV matrices via the method developed in [3] where our formula can play an important role, the extended CMV matrices case can be carried out similarly. From now on, we consider a special class of Verblunsky coefficients which are generated by a analytic function , i.e. , where . Recall the Szegő cocycle map which is given by Since and the method in [3] only cares about the norm of n-step transfer matrix, so it\'s equivalent to study the following one and the corresponding n-step transfer matrix Define then the Lyapunov exponent is given by
    Acknowledgments
    Introduction Allogeneic hematopoietic stem cell transplantation (allo-HCT) is a potentially curative treatment for a broad spectrum of hematological malignancies. The current standard for a fully matched allo-HCT is transplant from a donor matched at HLA-A, HLA-B, HLA-C, and HLA-DRB1. HLA-DP mismatching is associated with higher rate of grade II-IV acute graft versus host disease (aGVHD) and lower relapse rate resulting in no impact on overall survival (OS) [1,2]. For this reason, many centers do not take matching for HLA-DP into consideration when selecting an unrelated donor. HLA-DP antigens are αβ heterodimers encoded by the genes of two loci: (1) DPA1 locus, which has limited polymorphism, and (2) DPB1 locus which is highly polymorphic, with 520 Poziotinib coding for 424 different proteins [3]. HLA-DPB1 is a low expression locus (LEL) with both constitutive and inducible expression. Its constitutive expression is restricted to only thymic epithelial cells, antigen-presenting cells such as dendritic cells and mononuclear phagocytes as well as activated T cells and B cells. HLA-DPB1 expression can be induced in other tissues after exposure to interferon gamma and other cytokines [4,5]. Stevanovi´c et al. have previously demonstrated a link between CMV reactivation and HLA-DPB1 directed aGVHD. Their study suggested that CMV reactivation induces HLA-DPB1 expression resulting in HLA-DPB1 directed GVHD after HLA-DPB1-mismatched CD4+ donor lymphocyte infusion (DLI) [4,6]. No study has so far tested whether the increased aGVHD risk in HLA-DPB1 mismatched allo-HCTs correlates with recipient CMV serostatus, or more importantly, CMV reactivation. In addition, CMV reactivation is associated with increased risk of aGVHD with an unknown mechanism [[6], [7], [8]]. No study has analyzed whether the increased risk of aGVHD in patients with CMV reactivations is restricted to HLA-DPB1 mismatched allo-HCTs. Here in this retrospective study, we demonstrate that increased risk of aGVHD in HLA-DPB1 mismatched allo-HCT is independent of CMV reactivation. We also demonstrate that CMV reactivation increases risk of aGVHD independently of HLA-DPB1 matching status.
    Materials and methods We retrospectively evaluated all adult patients with AML or MDS who received matched related or unrelated allo-HCT at MD Anderson Cancer Center (MDACC) from January 2005 to December 2011 (total: 613 patients; HLA-DPB1 matched: 363 [59%], and HLA-DPB1 mismatched: 250 [41%]). All patients were matched at HLA-A, HLA-B, HLA-C, HLA-DRB1, and HLA-DQB1 (HLA level matching of 10/10). HLA typing was based on allelic typing. Patients receiving umbilical cord or haploidentical stem cell transplants, patients who died within 30 days of allo-HCT, and those less than 18 years of age were excluded from the analysis. All patients underwent weekly surveillance by CMV pp65 antigen testing from the time of engraftment and at least until day 100 post allo-HCT. CMV reactivation was defined as presence of > 1pp65 Ag cells/million WBC’s. Preemptive therapy was initiated for patients with > 3 pp65 Ag cells/million WBC’s. Clinical outcomes of interest included OS as well as cumulative incidences (CI) of GVHD, non-relapse mortality (NRM) and relapse. Severity of aGVHD was defined according to Glucksberg criteria [9]. OS was estimated using the Kaplan-Meier method and the association between OS and HLA-DPB1 mismatching was determined using a Cox proportional hazards model. The CI of GVHD, NRM, and relapse were determined using the competing risks method (i.e., competing risks for GVHD: relapse and death; NRM: relapse and death) and associations with HLA-DPB1 mismatching were evaluated by proportional subdistribution hazards models [10]. Additional factors considered were age in years (>50 vs. ≤ 50), race (others vs. Caucasian), gender (male vs. female), HLA-DPB1 mismatching direction (host versus graft vs. graft versus host), CMV donor (D)/recipient (R) group (D+/R−, D-/R+, D+/R + vs. D−/R−), transplantation year (2005–2008 vs. 2009–2011), conditioning regimens (myeloablative vs. non-myeloablative), ATG use (yes vs. no), and disease status at transplant (no CR vs. CR). Since CMV reactivation (yes vs. no) occurred after transplantation, it was included in the hazards models as a time-dependent covariate. Statistically significant factors in univariate analyses that were associated with the outcome at P ≤ 0.05 were included in the final multivariable models. The effect of HLA-DPB1 mismatching on transplant outcomes was evaluated in the whole cohort. To analyze the effect of recipient CMV serostatus on HLA-DPB1 related aGVHD, we compared the CI of aGVHD in HLA-DPB1 mismatch/CMV seropositive recipient with HLA-DPB1 mismatch/CMV seronegative recipients. Additionally to analyze the effect of CMV reactivation on HLA-DPB1 mismatch related aGVHD, we compared the CI of aGVHD in HLA-DPB1 mismatch/CMV reactivated recipients with HLA-DPB1 mismatch/no CMV reactivated recipients. For all analysis CMV reactivation was defined as presence of > 1pp65 Ag cells/million WBC’s except for a single analysis testing if CMV reactivation increases the chance of aGVHD in which CMV reactivation was defined as positive when the first day of CMV antigenemia occurred before or up to 7 days after the first day of aGVHD. For the purpose of this analysis, of the 270 with CMV reactivation, 178 (66%) were considered not CMV reactivated because it was discovered more than 7 days after the first day of aGVHD. Lastly, a landmark analysis was produced at day 100 to compare differences in OS, relapse, and NRM between patients who experienced CMV reactivation before 100 days and those who did not. For OS, differences between groups were assessed using the log-rank test while differences between groups for relapse and NRM were assessed using Gray’s test [11]. All statistical analyses were performed using SAS 9.3 (SAS Institute Inc., Cary, NC) and StataCorp 2013 (College Station, TX: StataCorp LP).