Invariance of the white noise for KdV

We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space \hat{b}^s_{p, \infty}, sp <-1, contains the support of the white noise. Then, we prove local well-posedness in \hat{b}^s_{p, \infty} for p= 2+, s = -{1/2}+ such that sp <-1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical proof of the invariance of the white noise under the flow of KdV obtained in Quastel-Valko.Comment: 18 pages. To appear in Comm. Math. Phy

Random data wave equations

Nowadays we have many methods allowing to exploit the regularising properties of the linear part of a nonlinear dispersive equation (such as the KdV equation, the nonlinear wave or the nonlinear Schroedinger equations) in order to prove well-posedness in low regularity Sobolev spaces. By well-posedness in low regularity Sobolev spaces we mean that less regularity than the one imposed by the energy methods is required (the energy methods do not exploit the dispersive properties of the linear part of the equation). In many cases these methods to prove well-posedness in low regularity Sobolev spaces lead to optimal results in terms of the regularity of the initial data. By optimal we mean that if one requires slightly less regularity then the corresponding Cauchy problem becomes ill-posed in the Hadamard sense. We call the Sobolev spaces in which these ill-posedness results hold spaces of supercritical regularity. More recently, methods to prove probabilistic well-posedness in Sobolev spaces of supercritical regularity were developed. More precisely, by probabilistic well-posedness we mean that one endows the corresponding Sobolev space of supercritical regularity with a non degenerate probability measure and then one shows that almost surely with respect to this measure one can define a (unique) global flow. However, in most of the cases when the methods to prove probabilistic well-posedness apply, there is no information about the measure transported by the flow. Very recently, a method to prove that the transported measure is absolutely continuous with respect to the initial measure was developed. In such a situation, we have a measure which is quasi-invariant under the corresponding flow. The aim of these lectures is to present all of the above described developments in the context of the nonlinear wave equation.Comment: Lecture notes based on a course given at a CIME summer school in August 201

Neurotensin(8–13) analogs as dual NTS1 and NTS2 receptor ligands with enhanced effects on a mouse model of Parkinson's disease

: The modulatory interactions between neurotensin (NT) and the dopaminergic neurotransmitter system in the brain suggest that NT may be associated with the progression of Parkinson's disease (PD). NT exerts its neurophysiological effects by interactions with the human NT receptors type 1 (hNTS1) and 2 (hNTS2). Therefore, both receptor subtypes are promising targets for the development of novel NT-based analogs for the treatment of PD. In this study, we used a virtually guided molecular modeling approach to predict the activity of NT(8-13) analogs by investigating the docking models of ligands designed for binding to the human NTS1 and NTS2 receptors. The importance of the residues at positions 8 and/or 9 for hNTS1 and hNTS2 receptor binding affinity was experimentally confirmed by radioligand binding assays. Further in vitro ADME profiling and in vivo studies revealed that, compared to the parent peptide NT(8-13), compound 10 exhibited improved stability and BBB permeability combined with a significant enhancement of the motor function and memory in a mouse model of PD. The herein reported NTS1/NTS2 dual-specific NT(8-13) analogs represent an attractive tool for the development of therapeutic strategies against PD and potentially other CNS disorders

Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation

The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.Comment: 39 pages, 36 figures (high resolution figures at http://www.mis.mpg.de/preprints/index.html

On the ill-posedness result for the BBM equation

We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in Hs(R), s < 0 in the sense that the ow-map u0 7! u(t) that associates to initial data u0 the solution u cannot be continuous at the origin from Hs(R) to even D0(R) at any _xed t > 0 small enough. This result is sharp.Fundação para a Ciência e a Tecnologia (FCT

Impact of whole genome amplification on analysis of copy number variants

Large-scale copy number variants (CNVs) have recently been recognized to play a role in human genome variation and disease. Approaches for analysis of CNVs in small samples such as microdissected tissues can be confounded by limited amounts of material. To facilitate analyses of such samples, whole genome amplification (WGA) techniques were developed. In this study, we explored the impact of Phi29 multiple-strand displacement amplification on detection of CNVs using oligonucleotide arrays. We extracted DNA from fresh frozen lymph node samples and used this for amplification and analysis on the Affymetrix Mapping 500k SNP array platform. We demonstrated that the WGA procedure introduces hundreds of potentially confounding CNV artifacts that can obscure detection of bona fide variants. Our analysis indicates that many artifacts are reproducible, and may correlate with proximity to chromosome ends and GC content. Pair-wise comparison of amplified products considerably reduced the number of apparent artifacts and partially restored the ability to detect real CNVs. Our results suggest WGA material may be appropriate for copy number analysis when amplified samples are compared to similarly amplified samples and that only the CNVs with the greatest significance values detected by such comparisons are likely to be representative of the unamplified samples

Apple polyphenols in human and animal health*

Apples contain substantial amounts of polyphenols, and diverse phenolics mainly flavonoids and phenolic acids, have been identified in their flesh and skins. This work aimed to analyze the overall landscape of the research literature published to date on apple phenolic compounds in the context of human and animal health. The Web of Science Core Collection electronic database was queried with (apple* polyphenol*) AND (health* OR illness* OR disease* OR medic* OR pharma*) to identify relevant papers covering these words and their derivatives in the titles, abstracts, and keywords. The resulted 890 papers were bibliometrically analyzed. The VOSviewer software was utilized to produce term maps that illustrate how the frequent phrases fared in terms of publication and citation data. The apple polyphenol papers received global contributions, particularly from China, Italy, the United States, Spain, and Germany. Examples of frequently mentioned chemicals/chemical classes are quercetin, anthocyanin, catechin, epicatechin, and flavonol, while examples of frequently mentioned medical conditions are cardiovascular disease, atherosclerosis, diabetes, Alzheimers disease, and obesity. The potential health benefits of apple polyphenols on humans and animals are diverse and warrant further study.Authors acknowledge the support from The National Centre for Research and Development (NCBR) of Poland (project number POIR.01.01.01-00-0593/18).info:eu-repo/semantics/publishedVersio

No association of vitamin D metabolism-related polymorphisms and melanoma risk as well as melanoma prognosis: a case–control study

Melanoma is one of the most aggressive human cancers. The vitamin D system contributes to the pathogenesis and prognosis of malignancies including cutaneous melanoma. An expression of the vitamin D receptor (VDR) and an anti-proliferative effect of vitamin D in melanocytes and melanoma cells have been shown in vitro. Studies examining associations of polymorphisms in genes coding for vitamin D metabolism-related proteins (1α-hydroxylase [CYP27B1], 1,25(OH)2D-24hydroxylase [CYP24A1], vitamin D-binding protein [VDBP]) and cancer risk are scarce, especially with respect to melanoma. Mainly VDR polymorphisms regarding melanoma risk and prognosis were examined although other vitamin D metabolism-related genes may also be crucial. In our hospital-based case–control study including 305 melanoma patients and 370 healthy controls single nucleotide polymorphisms in the genes CYP27B1 (rs4646536), CYP24A1 (rs927650), VDBP (rs1155563, rs7041), and VDR (rs757343, rs731236, rs2107301, rs7975232) were analyzed for their association with melanoma risk and prognosis. Except VDR rs731236 and VDR rs2107301, the other six polymorphisms have not been analyzed regarding melanoma before. To further improve the prevention as well as the treatment of melanoma, it is important to identify further genetic markers for melanoma risk as well as prognosis in addition to the crude phenotypic, demographic, and environmental markers used in the clinic today. A panel of genetic risk markers could help to better identify individuals at risk for melanoma development or worse prognosis. We, however, found that none of the polymorphisms tested was associated with melanoma risk as well as prognosis in logistic and linear regression models in our study population

Pharmacogenetics: data, concepts and tools to improve drug discovery and drug treatment

Variation in the human genome is a most important cause of variable response to drugs and other xenobiotics. Susceptibility to almost all diseases is determined to some extent by genetic variation. Driven by the advances in molecular biology, pharmacogenetics has evolved within the past 40 years from a niche discipline to a major driving force of clinical pharmacology, and it is currently one of the most actively pursued disciplines in applied biomedical research in general. Nowadays we can assess more than 1,000,000 polymorphisms or the expression of more than 25,000 genes in each participant of a clinical study – at affordable costs. This has not yet significantly changed common therapeutic practices, but a number of physicians are starting to consider polymorphisms, such as those in CYP2C9, CYP2C19, CYP2D6, TPMT and VKORC1, in daily medical practice. More obviously, pharmacogenetics has changed the practices and requirements in preclinical and clinical drug research; large clinical trials without a pharmacogenomic add-on appear to have become the minority. This review is about how the discipline of pharmacogenetics has evolved from the analysis of single proteins to current approaches involving the broad analyses of the entire genome and of all mRNA species or all metabolites and other approaches aimed at trying to understand the entire biological system. Pharmacogenetics and genomics are becoming substantially integrated fields of the profession of clinical pharmacology, and education in the relevant methods, knowledge and concepts form an indispensable part of the clinical pharmacology curriculum and the professional life of pharmacologists from early drug discovery to pharmacovigilance

Disruption of Yarrowia lipolytica TPS1 Gene Encoding Trehalose-6-P Synthase Does Not Affect Growth in Glucose but Impairs Growth at High Temperature

We have cloned the Yarrowia lipolytica TPS1 gene encoding trehalose-6-P synthase by complementation of the lack of growth in glucose of a Saccharomyces cerevisiae tps1 mutant. Disruption of YlTPS1 could only be achieved with a cassette placed in the 3′half of its coding region due to the overlap of its sequence with the promoter of the essential gene YlTFC1. The Yltps1 mutant grew in glucose although the Y. lipolytica hexokinase is extremely sensitive to inhibition by trehalose-6-P. The presence of a glucokinase, insensitive to trehalose-6-P, that constitutes about 80% of the glucose phosphorylating capacity during growth in glucose may account for the growth phenotype. Trehalose content was below 1 nmol/mg dry weight in Y. lipolytica, but it increased in strains expressing YlTPS1 under the control of the YlTEF1promoter or with a disruption of YALI0D15598 encoding a putative trehalase. mRNA levels of YlTPS1 were low and did not respond to thermal stresses, but that of YlTPS2 (YALI0D14476) and YlTPS3 (YALI0E31086) increased 4 and 6 times, repectively, by heat treatment. Disruption of YlTPS1 drastically slowed growth at 35°C. Homozygous Yltps1 diploids showed a decreased sporulation frequency that was ascribed to the low level of YALI0D20966 mRNA an homolog of the S. cerevisiae MCK1 which encodes a protein kinase that activates early meiotic gene expression