Schur Multipliers and Spherical Functions on Homogeneous Trees

Let X be a homogeneous tree of degree q+1 (for q between 2 and infinity) and let f be a complex function on X times X for which f(x,y) only depend on the distance between x and y in X. Our main result gives a necessary and sufficient condition for such a function to be a Schur multiplier on X times X. Moreover, we find a closed expression for the Schur norm of f. As applications, we obtain a closed expression for the completely bounded Fourier multiplier norm of the radial functions on the free (non-abelian) group on N generators (for N between 2 and infinity) and of the spherical functions on the p-adic group PGL_2(Q_q) for every prime number q.Comment: 51 page

Clinical Study Interferon Alpha Association with Neuromyelitis Optica

Interferon-alpha (IFN-) has immunoregulatory functions in autoimmune inflammatory diseases. The goal of this study was to determine occurrence and clinical consequences of IFN-in neuromyelitis optica (NMO) patients. Thirty-six NMO and 41 multiple sclerosis (MS) patients from a population-based retrospective case series were included. Expanded Disability Status Scale (EDSS) score and MRI findings determined disease activity. Linear regression was used to assess the effects of the level of IFN-on disability (EDSS). IFN-was determined by sensitive ELISA assays. IFN-was detectable in sera from 9/36 NMO patients, significantly more often than in the MS group (2/41) ( = 0.0197). A higher frequency of IFN-was observed in NMO patients with acute relapse compared to NMO patients in remission ( < 0.001) and compared to the MS patients with relapse ( = 0.010). In NMO patients, the levels of IFN-were significantly associated with EDSS ( = 0.0062). It may be concluded that IFN-was detectable in a subgroup of NMO patients. Association of IFN-levels with clinical disease activity and severity suggests a role for IFN-in disease perpetuation and may provide a plausible explanation for a negative effect of IFN-1 treatment in NMO patients

Association of leukocyte telomere length with mortality among adult participants in 3 longitudinal studies

Importance: Leukocyte telomere length (LTL) is a trait associated with risk of cardiovascular disease and cancer, the 2 major disease categories that largely define longevity in the United States. However, it remains unclear whether LTL is associated with the human life span. Objective: To examine whether LTL is associated with the life span of contemporary humans. Design, Setting, and Participants: This cohort study included 3259 adults of European ancestry from the Cardiovascular Health Study (CHS), Framingham Heart Study (FHS), and Women's Health Initiative (WHI). Leukocyte telomere length was measured in 1992 and 1997 in the CHS, from 1995 to 1998 in the FHS, and from 1993 to 1998 in the WHI. Data analysis was conducted from February 2017 to December 2019. Main Outcomes and Measures: Death and LTL, measured by Southern blots of the terminal restriction fragments, were the main outcomes. Cause of death was adjudicated by end point committees. Results: The analyzed sample included 3259 participants (2342 [71.9%] women), with a median (range) age of 69.0 (50.0-98.0) years at blood collection. The median (range) follow-up until death was 10.9 (0.2-23.0) years in CHS, 19.7 (3.4-23.0) years in FHS, and 16.6 (0.5-20.0) years in WHI. During follow-up, there were 1525 deaths (482 [31.6%] of cardiovascular disease; 373 [24.5%] of cancer, and 670 [43.9%] of other or unknown causes). Short LTL, expressed in residual LTL, was associated with increased mortality risk. Overall, the hazard ratio for all-cause mortality for a 1-kilobase decrease in LTL was 1.34 (95% CI, 1.21-1.47). This association was stronger for noncancer causes of death (cardiovascular death: hazard ratio, 1.28; 95% CI, 1.08-1.52; cancer: hazard ratio, 1.13; 95% CI, 0.93-1.36; and other causes: hazard ratio, 1.53; 95% CI, 1.32-1.77). Conclusions and Relevance: The results of this study indicate that LTL is associated with a natural life span limit in contemporary humans

Telomeres and the natural lifespan limit in humans

An ongoing debate in demography has focused on whether the human lifespan has a maximal natural limit. Taking a mechanistic perspective, and knowing that short telomeres are associated with diminished longevity, we examined whether telomere length dynamics during adult life could set a maximal natural lifespan limit. We define leukocyte telomere length of 5 kb as the 'telomeric brink', which denotes a high risk of imminent death. We show that a subset of adults may reach the telomeric brink within the current life expectancy and more so for a 100-year life expectancy. Thus secular trends in life expectancy should confront a biological limit due to crossing the telomeric brink

The telomere lengthening conundrum - artifact or biology?

Recent longitudinal studies of age-dependent leukocyte telomere length (LTL) attrition have reported that variable proportions of individuals experience LTL lengthening. Often, LTL lengthening has been taken at face value, and authors have speculated about the biological causation of this finding. Based on empirical data and theoretical considerations, we show that regardless of the method used to measure telomere length (Southern blot or quantitative polymerase chain reaction-based methods), measurement error of telomere length and duration of follow-up explain almost entirely the absence of age-dependent LTL attrition in longitudinal studies. We find that LTL lengthening is far less frequent in studies with long follow-up periods and those that used a high-precision Southern blot method (as compared with quantitative polymerase chain reaction determination, which is associated with larger laboratory error). We conclude that the LTL lengthening observed in longitudinal studies is predominantly, if not entirely, an artifact of measurement error, which is exacerbated by short follow-up periods. We offer specific suggestions for design of longitudinal studies of LTL attrition to diminish this artifact

Interferon Alpha Association with Neuromyelitis Optica

Interferon-alpha (IFN-α) has immunoregulatory functions in autoimmune inflammatory diseases. The goal of this study was to determine occurrence and clinical consequences of IFN-α in neuromyelitis optica (NMO) patients. Thirty-six NMO and 41 multiple sclerosis (MS) patients from a population-based retrospective case series were included. Expanded Disability Status Scale (EDSS) score and MRI findings determined disease activity. Linear regression was used to assess the effects of the level of IFN-α on disability (EDSS). IFN-α was determined by sensitive ELISA assays. IFN-α was detectable in sera from 9/36 NMO patients, significantly more often than in the MS group (2/41) (P=0.0197). A higher frequency of IFN-α was observed in NMO patients with acute relapse compared to NMO patients in remission (P<0.001) and compared to the MS patients with relapse (P=0.010). In NMO patients, the levels of IFN-α were significantly associated with EDSS (P=0.0062). It may be concluded that IFN-α was detectable in a subgroup of NMO patients. Association of IFN-α levels with clinical disease activity and severity suggests a role for IFN-α in disease perpetuation and may provide a plausible explanation for a negative effect of IFN-1 treatment in NMO patients