H\"older regularity for weak solutions of H\"ormander type operators

Motivated by recent results on the (possibly conditional) regularity for time-dependent hypoelliptic equations, we prove a parabolic version of the Poincar\'e inequality, and as a consequence, we deduce a version of the classical Moser iteration technique using in a crucial way the geometry of the equation. The point of this contribution is to emphasize that one can use the {\sl elliptic} version of the Moser argument at the price of the lack of uniformity, even in the {\sl parabolic } setting. This is nevertheless enough to deduce H\"older regularity of weak solutions. The proof is elementary and unifies in a natural way several results in the literature on Kolmogorov equations, subelliptic ones and some of their variations

Submanifolds of Fixed Degree in Graded Manifolds for Perceptual Completion

We extend to a Engel type structure a cortically inspired model of perceptual completion initially proposed in the Lie group of positions and orientations with a sub-Riemannian metric. According to this model, a given image is lifted in the group and completed by a minimal surface. The main obstacle in extending the model to a higher dimensional group, which can code also curvatures, is the lack of a good definition of codimension 2 minimal surface. We present here this notion, and describe an application to image completion

Levi umbilical surfaces in complex space

We define a complex connection on a real hypersurface of \C^{n+1} which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in \C^{n+1}, $n\ge 2$, which are Levi umbilical and have non zero constant Levi curvature. It turns out that such surfaces are contained either in a sphere or in the boundary of a complex tube domain with spherical section.Comment: 18 page

Group analysis of a class of nonlinear Kolmogorov equations

A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group classification is achieved using a gauging of arbitrary elements (i.e. via reducing the number of variable coefficients) with the application of equivalence transformations. Two possible gaugings are discussed in detail in order to show how equivalence groups serve in making the optimal choice.Comment: 12 pages, 4 table

Sub-Riemannian Fast Marching in SE(2)

We propose a Fast Marching based implementation for computing sub-Riemanninan (SR) geodesics in the roto-translation group SE(2), with a metric depending on a cost induced by the image data. The key ingredient is a Riemannian approximation of the SR-metric. Then, a state of the art Fast Marching solver that is able to deal with extreme anisotropies is used to compute a SR-distance map as the solution of a corresponding eikonal equation. Subsequent backtracking on the distance map gives the geodesics. To validate the method, we consider the uniform cost case in which exact formulas for SR-geodesics are known and we show remarkable accuracy of the numerically computed SR-spheres. We also show a dramatic decrease in computational time with respect to a previous PDE-based iterative approach. Regarding image analysis applications, we show the potential of considering these data adaptive geodesics for a fully automated retinal vessel tree segmentation.Comment: CIARP 201

Kratom: The analytical challenge of an emerging herbal drug

Mitragyna speciosa or kratom is emerging worldwide as a “legal” herbal drug of abuse. An increasing number of papers is appearing in the scientific literature regarding its pharmacological profile and the analysis of its chemical constituents, mainly represented by alkaloids. However, its detection and identification are not straightforward as the plant material is not particularly distinctive. Hyphenated techniques are generally preferred for the identification and quantification of these compounds, especially the main purported psychoactive substances, mitragynine (MG) and 7-hydroxymitragynine (7-OH-MG), in raw and commercial products. Considering the vast popularity of this recreational drug and the growing concern about its safety, the analysis of alkaloids in biological specimens is also of great importance for forensic and toxicological laboratories. The review addresses the analytical aspects of kratom spanning the extraction techniques used to isolate the alkaloids, the qualitative and quantitative analytical methods and the strategies for the distinction of the naturally occurring isomers

Study on the Effect of Preheating Temperatures on Melt Pool Stability in Inconel 718 Components Processed by Laser Powder Bed Fusion

Laser Powder Bed Fusion (L-PBF) is one of the most widespread, versatile, and promising metal Additive Manufacturing (AM) techniques. L-PBF allows for the manufacturing of geometrically complex parts with good surface characteristics. In this process, in order to minimize the heat loss in the first layers of printing, the building platform is preheated to a temperature ranging between 80 and 250 °C. This aspect turns out to be very critical, and further investigation is needed for situations where the part to be printed is only a few layers high, as is the case in sensor printing. This work aims to investigate the melt pool stability under a variation in the preheating temperatures. We investigate the distance from the building platform, considering the number of layers printed. This is where the melt pool reaches its stability in terms of depth and width. This aspect turns out to be of remarkable importance for ensuring the structural integrity of parts with a few layers of height that are processed through L-PBF, such as sensors, which are proliferating in different industries. Thus, two case studies were carried out on IN718 superalloys at 40 and 60 microns of layer thickness and a preheating temperature of 170 °C on the machine. The results obtained show that after 1.2 mm of distance from the building platform, the melt pool reached its stability in terms of width and depth dimensions and consequently for the melting regime

Proteomics Profiling of Heterozygous and Homozygous Patients with ABCA1 Gene Mutation: A Tangier Disease Molecular Map

Tangier Disease (TD) is a rare inherited disorder with approximately 100 worldwide identified cases. Alpha-lipoprotein deficiency is the main characteristic of this disease, associated with a virtual absence of High Density Lipoproteins (HDL) in blood. Additional symptoms are mild hypertriglyceridemia, neuropathy and enlarged, orange-colored tonsils. Genetically TD is caused by mutations in the ABCA1 gene, which prevent the release of cholesterol and phospholipids from cells, leading to the accumulation of lipids within cells and body tissues. In this work a TD patient and his parental heterozygous were examined from a proteomics point of view. Plasma as well as proteome and secretome of circulating monocytes were analyzed. Plasma proteins underlined in TD the imbalance of lipid trafficking and metabolism, associated with the stimulation of pro-inflammatory pathways. Proteome and secretome of monocytes highlighted an extensive down regulation of mitochondrial enzymes and vesicular trafficking agents along with a substantial cytoskeletal rearrangement, suggesting a reduced activation state of monocytes from TD homozygous patient. This work is the first proteomics profiling of heterozygous and homozygous TD phenotypes and it suggests a TD case as a model to understand general mechanisms of lipid transport and metabolism and their linkage to inflammatory processes

Involvement of basic fibroblast growth factor in suramin-induced inhibition of V79/AP4 fibroblast cell proliferation.

The V79/AP4 Chinese hamster fibroblasts were densely stained with the anti-basic fibroblast growth factor (bFGF) antibody demonstrating an endogenous production of the peptide. The in vitro proliferation of these cells was stimulated by exogenous bFGF and the maximum growth (259% increase in 3H-thymidine incorporation into DNA) was reached with bFGF 10 ng ml-1. Inhibition of bFGF-mediated mitogenic pathway was obtained with a 15-mer antisense oligodeoxynucleotide targeted against bFGF mRNA and with suramin, a drug which blocks the biological activity of heparin-binding growth factors. bFGF antisense oligomer reduced the synthesis of DNA by 79.5 and 89.5% at 20 and 60 microM, respectively; this effect was reversed by the addition of exogenous bFGF to the culture medium. A short-term exposure to suramin 300 micrograms ml-1 produced a modest reduction in 3H-thymidine incorporation but suppressed the mitogenic effect of bFGF on V79/AP4 cells. In cells treated with suramin 300 micrograms ml-1 the drug concentration increased linearly over 3 days, reaching 13.15 micrograms mg-1 of protein; cell proliferation was inhibited in a dose-related manner as evaluated by the colony formation assay (IC50: 344.22 micrograms ml-1) and by the number of mitoses observed in culture. Furthermore, the drug induced ultrastructural alterations, consisting of perinuclear cisternae swelling, chromatin condensation, nucleolar segregation and cytoplasmic vacuolations. These findings demonstrated that the endogenous production of bFGF plays an important role in V79/AP4 fibroblasts proliferation, and the inhibition of bFGF-mediated mitogenic signalling with bFGF antisense oligomer or suramin is an effective mean of reducing cell growth