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

Analysis of sequence variability and transcriptional profile of cannabinoid synthase genes in cannabis sativa l. Chemotypes with a focus on cannabichromenic acid synthase

Cannabis sativa L. has been long cultivated for its narcotic potential due to the accumulation of tetrahydrocannabinolic acid (THCA) in female inflorescences, but nowadays its production for fiber, seeds, edible oil and bioactive compounds has spread throughout the world. However, some hemp varieties still accumulate traces of residual THCA close to the 0.20% limit set by European Union, despite the functional gene encoding for THCA synthase (THCAS) is lacking. Even if some hypotheses have been produced, studies are often in disagreement especially on the role of the cannabichromenic acid synthase (CBCAS). In this work a set of European Cannabis genotypes, representative of all chemotypes, were investigated from a chemical and molecular point of view. Highly specific primer pairs were developed to allow an accurate distinction of different cannabinoid synthases genes. In addition to their use as markers to detect the presence of CBCAS at genomic level, they allowed the analysis of transcriptional profiles in hemp or marijuana plants. While the high level of transcription of THCAS and cannabidiolic acid synthase (CBDAS) clearly reflects the chemical phenotype of the plants, the low but stable transcriptional level of CBCAS in all genotypes suggests that these genes are active and might contribute to the final amount of cannabinoids

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

Clinical features, anger management and anxiety: a possible correlation in migraine children

Background: Psychological factors can increase severity and intensity of headaches. While great attention has been placed on the presence of anxiety and/or depression as a correlate to a high frequency of migraine attacks, very few studies have analyzed the management of frustration in children with headache. Aim of this study was to analyze the possible correlation between pediatric migraine severity (frequency and intensity of attacks) and the psychological profile, with particular attention to the anger management style. Methods: We studied 62 migraineurs (mean age 11.2 +/- 2.1 years; 29 M and 33 F). Patients were divided into four groups according to the attack frequency (low, intermediate, high frequency, and chronic migraine). Pain intensity was rated on a 3-levels graduate scale (mild, moderate and severe pain). Psychological profile was assessed by Picture Frustration Study test for anger management and SAFA-A scale for anxiety. Results: We found a relationship between IA/OD index (tendency to inhibit anger expression) and both attack frequency (r = 0.328, p = 0.041) and intensity (r = 0.413, p = 0.010). When we analyzed the relationship between anxiety and the headache features, a negative and significant correlation emerged between separation anxiety (SAFA-A Se) and the frequency of attacks (r = -0.409, p = 0.006). In our patients, the tendency to express and emphasize the presence of the frustrating obstacle (EA/OD index) showed a positive correlation with anxiety level ("Total anxiety" scale: r = 0.345; p = 0.033). Conclusions: Our results suggest that children suffering from severe migraine tend to inhibit their angry feelings. On the contrary, children with low migraine attack frequency express their anger and suffer from separation anxiety

BV functions and sets of finite perimeters in sub-Riemannian manifolds

We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms are given. When we consider sub-Riemannian manifolds, our definition coincides with the one given in the more general context of metric measure spaces which are doubling and support a Poincaré inequality. We focus on finite perimeter sets, i.e., sets whose characteristic function is BV, in sub-Riemannian manifolds. Under an assumption on the nilpotent approximation, we prove a blowup theorem, generalizing the one obtained for step-2 Carnot groups

Potential theory results for a class of PDOs admitting a global fundamental solution

We outline several results of Potential Theory for a class of linear par-tial differential operators L of the second order in divergence form. Under essentially the sole assumption of hypoellipticity, we present a non-invariant homogeneous Harnack inequality for L; under different geometrical assumptions on L (mainly, under global doubling/Poincar\ue9 assumptions), it is described how to obtainan invariant, non-homogeneous Harnack inequality. When L is equipped with a global fundamental solution \u393, further Potential Theory results are available (such as the Strong Maximum Principle). We present some assumptions on L ensuring that such a \u393 exists

Complete Genome Sequence of Mycoplasma suis and Insights into Its Biology and Adaption to an Erythrocyte Niche

Mycoplasma suis, the causative agent of porcine infectious anemia, has never been cultured in vitro and mechanisms by which it causes disease are poorly understood. Thus, the objective herein was to use whole genome sequencing and analysis of M. suis to define pathogenicity mechanisms and biochemical pathways. M. suis was harvested from the blood of an experimentally infected pig. Following DNA extraction and construction of a paired end library, whole-genome sequencing was performed using GS-FLX (454) and Titanium chemistry. Reads on paired-end constructs were assembled using GS De Novo Assembler and gaps closed by primer walking; assembly was validated by PFGE. Glimmer and Manatee Annotation Engine were used to predict and annotate protein-coding sequences (CDS). The M. suis genome consists of a single, 742,431 bp chromosome with low G+C content of 31.1%. A total of 844 CDS, 3 single copies, unlinked rRNA genes and 32 tRNAs were identified. Gene homologies and GC skew graph show that M. suis has a typical Mollicutes oriC. The predicted metabolic pathway is concise, showing evidence of adaptation to blood environment. M. suis is a glycolytic species, obtaining energy through sugars fermentation and ATP-synthase. The pentose-phosphate pathway, metabolism of cofactors and vitamins, pyruvate dehydrogenase and NAD+ kinase are missing. Thus, ribose, NADH, NADPH and coenzyme A are possibly essential for its growth. M. suis can generate purines from hypoxanthine, which is secreted by RBCs, and cytidine nucleotides from uracil. Toxins orthologs were not identified. We suggest that M. suis may cause disease by scavenging and competing for host' nutrients, leading to decreased life-span of RBCs. In summary, genome analysis shows that M. suis is dependent on host cell metabolism and this characteristic is likely to be linked to its pathogenicity. The prediction of essential nutrients will aid the development of in vitro cultivation systems