Positive solutions for singular ϕ−\phi-Laplacian BVPs on the positive half-line

In this work, we are concerned with the existence of positive solutions for a $\phi$ Laplacian boundary value problem on the half-line. The results are proved using the fixed point index theory on cones of Banach spaces and the upper and lower solution technique. The nonlinearity may exhibit a singularity at the origin with respect to the solution. This singularity is treated by regularization and approximation together with compactness and sequential arguments

System of singular second-order differential equations with integral condition on the positive half-line

In this work, we are concerned with the existence and the multiplicity of nontrivial positive solutions for a boundary value problem of a system of second-order differential equations subject to an integral boundary condition and posed on the positive half-line. The positive nonlinearities depend on the solution and their derivatives and may have space singularities. New existence results of single and multiple solutions are obtained by means of the fixed point index theory on special cones in some weighted Banach space. Examples with numerical computations are included to illustrate the obtained existence theorems. This paper surveys and generalizes previous works

A class of second order BVPs on infinite intervals

In this work, we are concerned with a boundary value problem associated with a generalized Fisher-like equation. This equation involves an eigenvalue and a parameter which may be viewed as a wave speed. According to the behavior of the nonlinear source term, existence results of bounded solutions, positive solutions, classical as well as weak solutions are provided. We mainly use fixed point arguments

The Degasperis-Procesi equation as a non-metric Euler equation

In this paper we present a geometric interpretation of the periodic Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric linear connection on the diffeomorphism group of the circle. We also show that for any evolution in the family of $b$-equations there is neither gain nor loss of the spatial regularity of solutions. This in turn allows us to view the Degasperis-Procesi and the Camassa-Holm equation as an ODE on the Fr\'echet space of all smooth functions on the circle.Comment: 17 page

Cancer somatic mutations cluster in a subset of regulatory sites predicted from the ENCODE data

Background: Transcriptional regulation of gene expression is essential for cellular differentiation and function, and defects in the process are associated with cancer. The ENCODE project has mapped potential regulatory sites across the complete genome in many cell types, and these regions have been shown to harbour many of the somatic mutations that occur in cancer cells, suggesting that their effects may drive cancer initiation and development. The ENCODE data suggests a very large number of regulatory sites, and methods are needed to identify those that are most relevant and to connect them to the genes that they control. Methods: Predictive models of gene expression were developed by integrating the ENCODE data for regulation, including transcription factor binding and DNase1 hypersensitivity, with RNA-seq data for gene expression. A penalized regression method was used to identify the most predictive potential regulatory sites for each transcript. Known cancer somatic mutations from the COSMIC database were mapped to potential regulatory sites, and we examined differences in the mapping frequencies associated with sites chosen in regulatory models and other (rejected) sites. The effects of potential confounders, for example replication timing, were considered. Results: Cancer somatic mutations preferentially occupy those regulatory regions chosen in our models as most predictive of gene expression. Conclusion: Our methods have identified a significantly reduced set of regulatory sites that are enriched in cancer somatic mutations and are more predictive of gene expression. This has significance for the mechanistic interpretation of cancer mutations, and the understanding of genetic regulation

Methods to study splicing from high-throughput RNA Sequencing data

The development of novel high-throughput sequencing (HTS) methods for RNA (RNA-Seq) has provided a very powerful mean to study splicing under multiple conditions at unprecedented depth. However, the complexity of the information to be analyzed has turned this into a challenging task. In the last few years, a plethora of tools have been developed, allowing researchers to process RNA-Seq data to study the expression of isoforms and splicing events, and their relative changes under different conditions. We provide an overview of the methods available to study splicing from short RNA-Seq data. We group the methods according to the different questions they address: 1) Assignment of the sequencing reads to their likely gene of origin. This is addressed by methods that map reads to the genome and/or to the available gene annotations. 2) Recovering the sequence of splicing events and isoforms. This is addressed by transcript reconstruction and de novo assembly methods. 3) Quantification of events and isoforms. Either after reconstructing transcripts or using an annotation, many methods estimate the expression level or the relative usage of isoforms and/or events. 4) Providing an isoform or event view of differential splicing or expression. These include methods that compare relative event/isoform abundance or isoform expression across two or more conditions. 5) Visualizing splicing regulation. Various tools facilitate the visualization of the RNA-Seq data in the context of alternative splicing. In this review, we do not describe the specific mathematical models behind each method. Our aim is rather to provide an overview that could serve as an entry point for users who need to decide on a suitable tool for a specific analysis. We also attempt to propose a classification of the tools according to the operations they do, to facilitate the comparison and choice of methods.Comment: 31 pages, 1 figure, 9 tables. Small corrections adde

Hydro-thermo-viscoelastic Based Finite Element Modeling of Apple Convective Drying Process

In the present work we aim to simulate unsteady two-dimensional evolution of the moisture content, temperature and mechanical stress in a parallelepiped apple sample during convective drying. The model is based on the heat and mass transfer equations and the mechanical equilibrium equation under the assumptions of plane deformation, viscoelasticity and isotropic hydric shrinkage. The Finite Elements COMSOL Multiphysics solver is used to solve the developed model. The hydro-thermal model was validated on experimental data drawn in our laboratory for moisture and temperature internal profiles of the product. Excellent agreement has been obtained between numerical and measured data for different drying temperatures. The hydro-thermal model was, then, implemented in a Finite Element hydro-thermo-viscoelastic developed model. Results for mechanical stresses are found to be in good agreement with former observations. It was found, also, that the maximum stress arises at the beginning of drying and holds at the top external surface of the sample which is the surface facing the airflow. The phenomenon is augmented by temperature

Transcriptome characterization by RNA sequencing identifies a major molecular and clinical subdivision in chronic lymphocytic leukemia

Chronic lymphocytic leukemia (CLL) has heterogeneous clinical and biological behavior. Whole-genome and -exome sequencing has contributed to the characterization of the mutational spectrum of the disease, but the underlying transcriptional profile is still poorly understood. We have performed deep RNA sequencing in different subpopulations of normal B-lymphocytes and CLL cells from a cohort of 98 patients, and characterized the CLL transcriptional landscape with unprecedented resolution. We detected thousands of transcriptional elements differentially expressed between the CLL and normal B cells, including protein-coding genes, noncoding RNAs, and pseudogenes. Transposable elements are globally derepressed in CLL cells. In addition, two thousand genes-most of which are not differentially expressed-exhibit CLL-specific splicing patterns. Genes involved in metabolic pathways showed higher expression in CLL, while genes related to spliceosome, proteasome, and ribosome were among the most down-regulated in CLL. Clustering of the CLL samples according to RNA-seq derived gene expression levels unveiled two robust molecular subgroups, C1 and C2. C1/C2 subgroups and the mutational status of the immunoglobulin heavy variable (IGHV) region were the only independent variables in predicting time to treatment in a multivariate analysis with main clinico-biological features. This subdivision was validated in an independent cohort of patients monitored through DNA microarrays. Further analysis shows that B-cell receptor (BCR) activation in the microenvironment of the lymph node may be at the origin of the C1/C2 differences