The eigenspectra of Indian musical drums

In a family of drums used in the Indian subcontinent, the circular drum head is made of material of non-uniform density. Remarkably, and in contrast to a circular membrane of uniform density, the low eigenmodes of the non-uniform membrane are harmonic. In this work we model the drum head by a non-uniform membrane whose density varies smoothly between two prescribed values. Using a Fourier-Chebyshev spectral collocation method we obtain the eigenmodes and eigenvalues of the drum head. For a suitable choice of parameters, which we find by optimising a cost function, the eigenspectra obtained from our model are in excellent agreement with experimental values. Our model and the numerical method should find application in numerical sound synthesis

Multicentric validation of proteomic biomarkers in urine specific for diabetic nephropathy

Background: Urine proteome analysis is rapidly emerging as a tool for diagnosis and prognosis in disease states. For diagnosis of diabetic nephropathy (DN), urinary proteome analysis was successfully applied in a pilot study. The validity of the previously established proteomic biomarkers with respect to the diagnostic and prognostic potential was assessed on a separate set of patients recruited at three different European centers. In this case-control study of 148 Caucasian patients with diabetes mellitus type 2 and duration >= 5 years, cases of DN were defined as albuminuria >300 mg/d and diabetic retinopathy (n = 66). Controls were matched for gender and diabetes duration (n = 82). Methodology/Principal Findings: Proteome analysis was performed blinded using high-resolution capillary electrophoresis coupled with mass spectrometry (CE-MS). Data were evaluated employing the previously developed model for DN. Upon unblinding, the model for DN showed 93.8% sensitivity and 91.4% specificity, with an AUC of 0.948 (95% CI 0.898-0.978). Of 65 previously identified peptides, 60 were significantly different between cases and controls of this study. In <10% of cases and controls classification by proteome analysis not entirely resulted in the expected clinical outcome. Analysis of patient's subsequent clinical course revealed later progression to DN in some of the false positive classified DN control patients. Conclusions: These data provide the first independent confirmation that profiling of the urinary proteome by CE-MS can adequately identify subjects with DN, supporting the generalizability of this approach. The data further establish urinary collagen fragments as biomarkers for diabetes-induced renal damage that may serve as earlier and more specific biomarkers than the currently used urinary albumin

Synchronization of Sound Sources

Sound generation and -interaction is highly complex, nonlinear and self-organized. Already 150 years ago Lord Rayleigh raised the following problem: Two nearby organ pipes of different fundamental frequencies sound together almost inaudibly with identical pitch. This effect is now understood qualitatively by modern synchronization theory (M. Abel et al., J. Acoust. Soc. Am., 119(4), 2006). For a detailed, quantitative investigation, we substituted one pipe by an electric speaker. We observe that even minute driving signals force the pipe to synchronization, thus yielding three decades of synchronization -- the largest range ever measured to our knowledge. Furthermore, a mutual silencing of the pipe is found, which can be explained by self-organized oscillations, of use for novel methods of noise abatement. Finally, we develop a specific nonlinear reconstruction method which yields a perfect quantitative match of experiment and theory.Comment: 5 pages, 4 figure