Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

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

Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields

We consider a family of vector fields and we assume a horizontal regularity on their derivatives. We discuss the notion of commutator showing that different definitions agree. We apply our results to the proof of a ball-box theorem and Poincar\'e inequality for nonsmooth H\"ormander vector fields.Comment: arXiv admin note: material from arXiv:1106.2410v1, now three separate articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.520

A novel phytocannabinoid isolated from Cannabis sativa L. with an in vivo cannabimimetic activity higher than \u3949-tetrahydrocannabinol: \u3949-Tetrahydrocannabiphorol

(-)-Trans-Delta(9)-tetrahydrocannabinol (Delta(9)-THC) is the main compound responsible for the intoxicant activity of Cannabis sativa L. The length of the side alkyl chain influences the biological activity of this cannabinoid. In particular, synthetic analogues of Delta(9)-THC with a longer side chain have shown cannabimimetic properties far higher than Delta(9)-THC itself. In the attempt to define the phytocannabinoids profile that characterizes a medicinal cannabis variety, a new phytocannabinoid with the same structure of Delta(9)-THC but with a seven-term alkyl side chain was identified. The natural compound was isolated and fully characterized and its stereochemical configuration was assigned by match with the same compound obtained by a stereoselective synthesis. This new phytocannabinoid has been called (-)-trans-Delta(9)-tetrahydrocannabiphorol (Delta(9)-THCP). Along with Delta(9)-THCP, the corresponding cannabidiol (CBD) homolog with seven-term side alkyl chain (CBDP) was also isolated and unambiguously identified by match with its synthetic counterpart. The binding activity of Delta(9)-THCP against human CB1 receptor in vitro (K-i = 1.2 nM) resulted similar to that of CP55940 (K-i = 0.9 nM), a potent full CB1 agonist. In the cannabinoid tetrad pharmacological test, Delta(9)-THCP induced hypomotility, analgesia, catalepsy and decreased rectal temperature indicating a THC-like cannabimimetic activity. The presence of this new phytocannabinoid could account for the pharmacological properties of some cannabis varieties difficult to explain by the presence of the sole Delta(9)-THC

The role of fundamental solution in Potential and Regularity Theory for subelliptic PDE

In this survey we consider a general Hormander type operator, represented as a sum of squares of vector fields plus a drift and we outline the central role of the fundamental solution in developing Potential and Regularity Theory for solutions of related PDEs. After recalling the Gaussian behavior at infinity of the kernel, we show some mean value formulas on the level sets of the fundamental solution, which are the starting point to obtain a comprehensive parallel of the classical Potential Theory. Then we show that a precise knowledge of the fundamental solution leads to global regularity results, namely estimates at the boundary or on the whole space. Finally in the problem of regularity of non linear differential equations we need an ad hoc modification of the parametrix method, based on the properties of the fundamental solution of an approximating problem

First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-hermitian manifolds

We calculate the first and the second variation formula for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that can move the singular set of a C^2 surface and non-singular variation for C_H^2 surfaces. These formulas enable us to construct a stability operator for non-singular C^2 surfaces and another one for C2 (eventually singular) surfaces. Then we can obtain a necessary condition for the stability of a non-singular surface in a pseudo-hermitian 3-manifold in term of the pseudo-hermitian torsion and the Webster scalar curvature. Finally we classify complete stable surfaces in the roto-traslation group RT .Comment: 36 pages. Misprints corrected. Statement of Proposition 9.8 slightly changed and Remark 9.9 adde

Genome-Scale Analysis of Mycoplasma agalactiae Loci Involved in Interaction with Host Cells

Mycoplasma agalactiae is an important pathogen of small ruminants, in which it causes contagious agalactia. It belongs to a large group of “minimal bacteria” with a small genome and reduced metabolic capacities that are dependent on their host for nutrients. Mycoplasma survival thus relies on intimate contact with host cells, but little is known about the factors involved in these interactions or in the more general infectious process. To address this issue, an assay based on goat epithelial and fibroblastic cells was used to screen a M. agalactiae knockout mutant library. Mutants with reduced growth capacities in cell culture were selected and 62 genomic loci were identified as contributing to this phenotype. As expected for minimal bacteria, “transport and metabolism” was the functional category most commonly implicated in this phenotype, but 50% of the selected mutants were disrupted in coding sequences (CDSs) with unknown functions, with surface lipoproteins being most commonly represented in this category. Since mycoplasmas lack a cell wall, lipoproteins are likely to be important in interactions with the host. A few intergenic regions were also identified that may act as regulatory sequences under co-culture conditions. Interestingly, some mutants mapped to gene clusters that are highly conserved across mycoplasma species but located in different positions. One of these clusters was found in a transcriptionally active region of the M. agalactiae chromosome, downstream of a cryptic promoter. A possible scenario for the evolution of these loci is discussed. Finally, several CDSs identified here are conserved in other important pathogenic mycoplasmas, and some were involved in horizontal gene transfer with phylogenetically distant species. These results provide a basis for further deciphering functions mediating mycoplasma-host interactions

A novel substitution matrix fitted to the compositional bias in Mollicutes improves the prediction of homologous relationships

<p>Abstract</p> <p>Background</p> <p>Substitution matrices are key parameters for the alignment of two protein sequences, and consequently for most comparative genomics studies. The composition of biological sequences can vary importantly between species and groups of species, and classical matrices such as those in the BLOSUM series fail to accurately estimate alignment scores and statistical significance with sequences sharing marked compositional biases.</p> <p>Results</p> <p>We present a general and simple methodology to build matrices that are especially fitted to the compositional bias of proteins. Our approach is inspired from the one used to build the BLOSUM matrices and is based on learning substitution and amino acid frequencies on real sequences with the corresponding compositional bias. We applied it to the large scale comparison of Mollicute AT-rich genomes. The new matrix, MOLLI60, was used to predict pairwise orthology relationships, as well as homolog families among 24 Mollicute genomes. We show that this new matrix enables to better discriminate between true and false orthologs and improves the clustering of homologous proteins, with respect to the use of the classical matrix BLOSUM62.</p> <p>Conclusions</p> <p>We show in this paper that well-fitted matrices can improve the predictions of orthologous and homologous relationships among proteins with a similar compositional bias. With the ever-increasing number of sequenced genomes, our approach could prove valuable in numerous comparative studies focusing on atypical genomes.</p