On the regularity of p-harmonic functions in the Heisenberg group

In this thesis we first implement iteration methods for fractional difference quotients of weak solutions to the p-Laplace equation in the Heisenberg group. We obtain that $Tu in L^p_{loc} (Omega )$ for $1<p<4$, where $u$ is a p-harmonic function.Then we give detailed proofs for $HW^{2,2}$-regularity for $p$ in the range $2 leq p <4$ and $HW^{2,p}$-regularity in the case $frac{sqrt{17}-1}{2} leq p leq 2$ for $ep$-approximate p-harmonic functions in the Heisenberg group. These last estimates however are not uniform in $ep$. The method to prove uniform estimates is based on Cordes type estimates for subellipticlinear partial differential operators in non-divergence form with measurable coefficients in the Heisenberg group. In this way we establish interior $HW^{2,2}$-regularity for p-harmonic functions in the Heisenberg group ${mathbb H}^n$ for $p$ in an interval containing $2$. We will also show that the $C^{1,alpha}$ regularity is true for $p$ in a neighborhood of $2$. In the last chapter we extend our results to the more general case of Carnot groups

Development and In-Depth Characterization of Bacteria Repellent and Bacteria Adhesive Antibody-Coated Surfaces Using Optical Waveguide Biosensing

Bacteria repellent surfaces and antibody-based coatings for bacterial assays have shown a growing demand in the field of biosensors, and have crucial importance in the design of biomedical devices. However, in-depth investigations and comparisons of possible solutions are still missing. The optical waveguide lightmode spectroscopy (OWLS) technique offers label-free, non-invasive, in situ characterization of protein and bacterial adsorption. Moreover, it has excellent flexibility for testing various surface coatings. Here, we describe an OWLS-based method supporting the development of bacteria repellent surfaces and characterize the layer structures and affinities of different antibody-based coatings for bacterial assays. In order to test nonspecific binding blocking agents against bacteria, OWLS chips were coated with bovine serum albumin (BSA), I-block, PAcrAM-g-(PMOXA, NH(2), Si), (PAcrAM-P) and PLL-g-PEG (PP) (with different coating temperatures), and subsequent Escherichia coli adhesion was monitored. We found that the best performing blocking agents could inhibit bacterial adhesion from samples with bacteria concentrations of up to 10(7) cells/mL. Various immobilization methods were applied to graft a wide range of selected antibodies onto the biosensor’s surface. Simple physisorption, Mix&Go (AnteoBind) (MG) films, covalently immobilized protein A and avidin–biotin based surface chemistries were all fabricated and tested. The surface adsorbed mass densities of deposited antibodies were determined, and the biosensor;s kinetic data were evaluated to divine the possible orientations of the bacteria-capturing antibodies and determine the rate constants and footprints of the binding events. The development of affinity layers was supported by enzyme-linked immunosorbent assay (ELISA) measurements in order to test the bacteria binding capabilities of the antibodies. The best performance in the biosensor measurements was achieved by employing a polyclonal antibody in combination with protein A-based immobilization and PAcrAM-P blocking of nonspecific binding. Using this setting, a surface sensitivity of 70 cells/mm(2) was demonstrated

Weighted function spaces of fractional derivatives for vector fields

We introduce and study weighted function spaces for vector fields from the point of view of the regularity theory for quasilinear subelliptic PDEs

Cyclodextrins: Assessing the Impact of Cavity Size, Occupancy, and Substitutions on Cytotoxicity and Cholesterol Homeostasis

Cyclodextrins (CDs) are cyclic oligosaccharides; the most common CDs contain six, seven, or eight glucose units called α-CDs, β-CDs, and γ-CDs, respectively. The use of CDs in biomedical research is increasing due to their ability to interact with membrane lipids as well as a wide variety of poorly water-soluble molecules. We assessed the impact of CD cavity size, occupancy, and substitutions on cytotoxicity and cholesterol homeostasis. The potency of CD-mediated cytotoxicity was in the order of β-CDs, α-CDs, and γ-CDs. Substitutions with hydroxypropyl or carboxymethyl group attenuated cytotoxicity compared with the native CDs, whereas CDs substituted with methyl groups exhibited cytotoxicity that was similar to that of the native CDs. The lipid components in blood exerted remarkable hemolysis-alleviating effects in methyl-β-CD-induced hemolysis. Occupancy of the CD cavity with cholesterol or a structurally related lipid molecule abrogated the cytotoxic capacity of the CDs. Interestingly, hydroxypropyl-γ-CD (HPγCD) was able to reduce intracellular cholesterol accumulation in Niemann⁻Pick disease type C (NPC) patient-derived fibroblasts as efficiently as HPβCD. Proteomic study indicated that HPβCD and HPγCD treatments altered the expression pattern of cellular proteins, suggesting that some of the CD-induced cellular proteins may play an important function in modulating intracellular cholesterol homeostasis

Cyclodextrins: Assessing the Impact of Cavity Size, Occupancy, and Substitutions on Cytotoxicity and Cholesterol Homeostasis

Cyclodextrins (CDs) are cyclic oligosaccharides; the most common CDs contain six, seven, or eight glucose units called &alpha;-CDs, &beta;-CDs, and &gamma;-CDs, respectively. The use of CDs in biomedical research is increasing due to their ability to interact with membrane lipids as well as a wide variety of poorly water-soluble molecules. We assessed the impact of CD cavity size, occupancy, and substitutions on cytotoxicity and cholesterol homeostasis. The potency of CD-mediated cytotoxicity was in the order of &beta;-CDs, &alpha;-CDs, and &gamma;-CDs. Substitutions with hydroxypropyl or carboxymethyl group attenuated cytotoxicity compared with the native CDs, whereas CDs substituted with methyl groups exhibited cytotoxicity that was similar to that of the native CDs. The lipid components in blood exerted remarkable hemolysis-alleviating effects in methyl-&beta;-CD-induced hemolysis. Occupancy of the CD cavity with cholesterol or a structurally related lipid molecule abrogated the cytotoxic capacity of the CDs. Interestingly, hydroxypropyl-&gamma;-CD (HP&gamma;CD) was able to reduce intracellular cholesterol accumulation in Niemann&ndash;Pick disease type C (NPC) patient-derived fibroblasts as efficiently as HP&beta;CD. Proteomic study indicated that HP&beta;CD and HP&gamma;CD treatments altered the expression pattern of cellular proteins, suggesting that some of the CD-induced cellular proteins may play an important function in modulating intracellular cholesterol homeostasis

An ensemble-based collaborative framework to support customized user needs

Abstract—Collaborative platforms with advanced and customized visualization capabilities are getting growing interest regarding IT systems. We describe a system having novel capabilities for fusing the stored data to increase the accuracy of the decision derived from the system. We also present a visualization tool used for interpreting the content and details on decision in a way that is the most suitable for the user. Based on the experience we gained during developing the specific system, we explain how it could be extended to serve aims that are more general. These aims cover other application fields, like advanced visualization and user interaction, data privacy for wider collaboration, usercontrolled automated application generation, and robust navigation of the system. Moreover, since our approach highly relies on the combination of different user input to increase accuracy, we discuss on the computational environments that should be considered, and also possible collaborative framework solutions. I

Combined Methods for Diabetic Retinopathy Screening, Using Retina Photographs and Tear Fluid Proteomics Biomarkers

Background. It is estimated that 347 million people suffer from diabetes mellitus (DM), and almost 5 million are blind due to diabetic retinopathy (DR). The progression of DR can be slowed down with early diagnosis and treatment. Therefore our aim was to develop a novel automated method for DR screening. Methods. 52 patients with diabetes mellitus were enrolled into the project. Of all patients, 39 had signs of DR. Digital retina images and tear fluid samples were taken from each eye. The results from the tear fluid proteomics analysis and from digital microaneurysm (MA) detection on fundus images were used as the input of a machine learning system. Results. MA detection method alone resulted in 0.84 sensitivity and 0.81 specificity. Using the proteomics data for analysis 0.87 sensitivity and 0.68 specificity values were achieved. The combined data analysis integrated the features of the proteomics data along with the number of detected MAs in the associated image and achieved sensitivity/specificity values of 0.93/0.78. Conclusions. As the two different types of data represent independent and complementary information on the outcome, the combined model resulted in a reliable screening method that is comparable to the requirements of DR screening programs applied in clinical routine

Two-phase abrasion illustration.

<p>The 2D schematic shows two well-separated phases emerging spontaneously from Gaussian-curvature-driven abrasion: In Phase I edges abrade but axis ratios remain constant; in Phase II, axis ratios evolve towards the sphere. Accompanying perspective images are topographic laser scans that illustrate the two phases in 3D; they were performed for a separate experiment with a smaller cuboid having similar axis ratios.</p