Plancherel Inversion as Unified Approach to Wavelet Transforms and Wigner functions

We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The wavelet transform of a signal is an $L^2$-function on an appropriately chosen group, while the Wigner function is defined on a coadjoint orbit of the group and serves as an alternative characterization of the signal, which is often used in practical applications. The Plancherel transform maps $L^2$-functions on a group unitarily to fields of Hilbert-Schmidt operators, indexed by unitary irreducible representations of the group. The wavelet transform can essentiallly be looked upon as restricted inverse Plancherel transform, while Wigner functions are modified Fourier transforms of inverse Plancherel transforms, usually restricted to a subset of the unitary dual of the group. Some known results both on Wigner functions and wavelet transforms, appearing in the literature from very different perspectives, are naturally unified within our approach. Explicit computations on a number of groups illustrate the theory.Comment: 41 page

Racial differences in systemic sclerosis disease presentation: a European Scleroderma Trials and Research group study

Objectives. Racial factors play a significant role in SSc. We evaluated differences in SSc presentations between white patients (WP), Asian patients (AP) and black patients (BP) and analysed the effects of geographical locations.Methods. SSc characteristics of patients from the EUSTAR cohort were cross-sectionally compared across racial groups using survival and multiple logistic regression analyses.Results. The study included 9162 WP, 341 AP and 181 BP. AP developed the first non-RP feature faster than WP but slower than BP. AP were less frequently anti-centromere (ACA; odds ratio (OR) = 0.4, P < 0.001) and more frequently anti-topoisomerase-I autoantibodies (ATA) positive (OR = 1.2, P = 0.068), while BP were less likely to be ACA and ATA positive than were WP [OR(ACA) = 0.3, P < 0.001; OR(ATA) = 0.5, P = 0.020]. AP had less often (OR = 0.7, P = 0.06) and BP more often (OR = 2.7, P < 0.001) diffuse skin involvement than had WP.AP and BP were more likely to have pulmonary hypertension [OR(AP) = 2.6, P < 0.001; OR(BP) = 2.7, P = 0.03 vs WP] and a reduced forced vital capacity [OR(AP) = 2.5, P < 0.001; OR(BP) = 2.4, P < 0.004] than were WP. AP more often had an impaired diffusing capacity of the lung than had BP and WP [OR(AP vs BP) = 1.9, P = 0.038; OR(AP vs WP) = 2.4, P < 0.001]. After RP onset, AP and BP had a higher hazard to die than had WP [hazard ratio (HR) (AP) = 1.6, P = 0.011; HR(BP) = 2.1, P < 0.001].Conclusion. Compared with WP, and mostly independent of geographical location, AP have a faster and earlier disease onset with high prevalences of ATA, pulmonary hypertension and forced vital capacity impairment and higher mortality. BP had the fastest disease onset, a high prevalence of diffuse skin involvement and nominally the highest mortality

P2RX7 Purinoceptor: A Therapeutic Target for Ameliorating the Symptoms of Duchenne Muscular Dystrophy

open access articleDuchenne muscular dystrophy (DMD) is the most common inherited muscle disease, leading to severe disability and death in young men. Death is caused by the progressive degeneration of striated muscles aggravated by sterile inflammation. The pleiotropic effects of the mutant gene also include cognitive and behavioral impairments and low bone density. Current interventions in DMD are palliative only as no treatment improves the long-term outcome. Therefore, approaches with a translational potential should be investigated, and key abnormalities downstream from the absence of the DMD product, dystrophin, appear to be strong therapeutic targets. We and others have demonstrated that DMD mutations alter ATP signaling and have identified P2RX7 purinoceptor up-regulation as being responsible for the death of muscles in the mdx mouse model of DMD and human DMD lymphoblasts. Moreover, the ATP–P2RX7 axis, being a crucial activator of innate immune responses, can contribute to DMD pathology by stimulating chronic inflammation. We investigated whether ablation of P2RX7 attenuates the DMD model mouse phenotype to assess receptor suitability as a therapeutic target