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Injectivity and Stability for a Generic Class of Generalized Radon Transforms.

ABSTRACT: Let (M, g) be an analytic, compact, Riemannian manifold with boundary, of dimension n?2 . We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in M, satisfying the Bolker condition (in: Quinto, Proceedings of conference "Seventy-five Years of Radon Transforms", Hong Kong, 1994). Using analytic microlocal analysis, we prove a microlocal regularity theorem for generalized Radon transforms on analytic manifolds defined on an analytic family of hypersurfaces. We then show injectivity and stability for an open, dense subset of smooth generalized Radon transforms satisfying the Bolker condition, including the analytic ones.

SUBMITTER: Homan A

PROVIDER: S-EPMC6313362 | biostudies-other | 2017

REPOSITORIES: biostudies-other

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Injectivity and Stability for a Generic Class of Generalized Radon Transforms.

Homan Andrew A Zhou Hanming H

Journal of geometric analysis 20160630 2

Let (M, g) be an analytic, compact, Riemannian manifold with boundary, of dimension n ≥ 2 . We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in M, satisfying the Bolker condition (in: Quinto, Proceedings of conference "Seventy-five Years of Radon Transforms", Hong Kong, 1994). Using analytic microlocal analysis, we prove a microlocal regularity theorem for generalized Radon transforms on analytic manifolds defined on an a ...[more]

PMID: 30636856

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Project description:The extents of generic-reference and generic-generic average bioequivalence and intra-subject variation of on-market drug products have not been prospectively studied on a large scale.We assessed bioequivalence of 42 generic products of 14 immediate-release oral drugs with the highest number of generic products on the Saudi market. We conducted 14 four-sequence, randomized, crossover studies on the reference and three randomly-selected generic products of amlodipine, amoxicillin, atenolol, cephalexin, ciprofloxacin, clarithromycin, diclofenac, ibuprofen, fluconazole, metformin, metronidazole, paracetamol, omeprazole, and ranitidine. Geometric mean ratios of maximum concentration (Cmax) and area-under-the-concentration-time-curve, to last measured concentration (AUCT), extrapolated to infinity (AUCI), or truncated to Cmax time of reference product (AUCReftmax) were calculated using non-compartmental method and their 90% confidence intervals (CI) were compared to the 80.00%-125.00% bioequivalence range. Percentages of individual ratios falling outside the ±25% range were also determined.Mean (SD) age and body-mass-index of 700 healthy volunteers (28-80/study) were 32.2 (6.2) years and 24.4 (3.2) kg/m2, respectively. In 42 generic-reference comparisons, 100% of AUCT and AUCI CIs showed bioequivalence, 9.5% of Cmax CIs barely failed to show bioequivalence, and 66.7% of AUCReftmax CIs failed to show bioequivalence/showed bioinequivalence. Adjusting for 6 comparisons, 2.4% of AUCT and AUCI CIs and 21.4% of Cmax CIs failed to show bioequivalence. In 42 generic-generic comparisons, 2.4% of AUCT, AUCI, and Cmax CIs failed to show bioequivalence, and 66.7% of AUCReftmax CIs failed to show bioequivalence/showed bioinequivalence. Adjusting for 6 comparisons, 2.4% of AUCT and AUCI CIs and 14.3% of Cmax CIs failed to show bioequivalence. Average geometric mean ratio deviation from 100% was ?3.2 and ?5.4 percentage points for AUCI and Cmax, respectively, in both generic-reference and generic-generic comparisons. Individual generic/reference and generic/generic ratios, respectively, were within the ±25% range in >75% of individuals in 79% and 71% of the 14 drugs for AUCT and 36% and 29% for Cmax.On-market generic drug products continue to be reference-bioequivalent and are bioequivalent to each other based on AUCT, AUCI, and Cmax but not AUCReftmax. Average deviation of geometric mean ratios and intra-subject variations are similar between reference-generic and generic-generic comparisons.ClinicalTrials.gov identifier: NCT01344070 (registered April 3, 2011).

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Injectivity and Stability for a Generic Class of Generalized Radon Transforms.

Publications

Injectivity and Stability for a Generic Class of Generalized Radon Transforms.

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