Dirichlet forms on metric measure spaces as Mosco limits of Korevaar-Schoen energies

This paper establishes sufficient general conditions for the existence of Mosco limits of Korevaar-Schoen $L^2$ energies, first in the context of Cheeger spaces and then in the context of fractal-like spaces with walk dimension greater than 2. Among the ingredients, a new Rellich-Kondrachov type theorem for Korevaar-Schoen-Sobolev spaces is of independent interest

Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates

With a view toward fractal spaces, by using a Korevaar-Schoen space approach, we introduce the class of bounded variation (BV) functions in a general framework of strongly local Dirichlet spaces with a heat kernel satisfying sub-Gaussian estimates. Under a weak Bakry-\'Emery curvature type condition, which is new in this setting, this BV class is identified with a heat semigroup based Besov class. As a consequence of this identification, properties of BV functions and associated BV measures are studied in detail. In particular, we prove co-area formulas, global $L^1$ Sobolev embeddings and isoperimetric inequalities. It is shown that for nested fractals or their direct products the BV class we define is dense in $L^1$. The examples of the unbounded Vicsek set, unbounded Sierpinski gasket and unbounded Sierpinski carpet are discussed.Comment: The notes arXiv:1806.03428 will be divided in a series of papers. This is the third paper. v2: Final versio

Correction of refraction induced distortion in optical coherence tomography corneal reconstructions for volume deformation measurements

In this project, the depth-resolved full-field deformation of the porcine cornea under changing intraocular pressure was investigated by performing digital volume correlation (DVC) on the reconstructed volume images generated through swept source optical coherence tomography (SS-OCT). Posterior inflation test of porcine cornea sample for two load steps were performed and the distribution patterns of displacement and strain fields were produced. The error sources for the measurements were analyzed. The refraction induced OCT image distortion is a main error source for the measurement results. Then, a methodology was developed to correct the OCT distortion based on the Fermat’s principle

Acceptability of generic versus innovator oral medicines: not only a matter of taste

Optimum use of generic products would require equivalence, not only in terms of quality, safety, and efficacy in clinical studies, but also patient acceptability to not jeopardize treatment success because of nonadherence which would de facto limit the potential cost saving anticipated by their use. Although acceptability is a requirement for the authorization of pediatric innovator products, our survey of European Union (EU) regulatory authorities showed that few have a formal process for assessing patient acceptability of generic products during the registration processes. The current International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (ICH) focus on unifying guidance for the development and scrutiny of generics but should include acceptability alongside the other factors being considered for harmonization