Splitting method for elliptic equations with line sources

In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain $\Omega$ when the right-hand side is a (1D) line source $\Lambda$. The analysis and approximation of such problems is known to be non-standard as the line source causes the solution to be singular. Our main result is a splitting theorem for the solution; we show that the solution admits a split into an explicit, low regularity term capturing the singularity, and a high-regularity correction term $w$ being the solution of a suitable elliptic equation. The splitting theorem states the mathematical structure of the solution; in particular, we find that the solution has anisotropic regularity. More precisely, the solution fails to belong to $H^1$ in the neighbourhood of $\Lambda$, but exhibits piecewise $H^2$-regularity parallel to $\Lambda$. The splitting theorem can further be used to formulate a numerical method in which the solution is approximated via its correction function $w$. This approach has several benefits. Firstly, it recasts the problem as a 3D elliptic problem with a 3D right-hand side belonging to $L^2$, a problem for which the discretizations and solvers are readily available. Secondly, it makes the numerical approximation independent of the discretization of $\Lambda$; thirdly, it improves the approximation properties of the numerical method. We consider here the Galerkin finite element method, and show that the singularity subtraction then recovers optimal convergence rates on uniform meshes, i.e., without needing to refine the mesh around each line segment. The numerical method presented in this paper is therefore well-suited for applications involving a large number of line segments. We illustrate this by treating a dataset (consisting of $\sim 3000$ line segments) describing the vascular system of the brain

Effect of polyvinylpyrrolidone and activated charcoal on formation of microcallus from grapevine protoplasts (Vitis sp.)

The effect of the addition of polyvinylpyrrolidone (PVP-40) to grapevine protoplast cultures (Vitis sp. cv. Vidal blanc) at different stages of development (day 0, 7 and 14 of cultivation) and the influence of activated charcoal (AC) in several concentrations (0, 0.1, 0.5 and 1.0 %) on protoplast growth were studied. Both additives were investigated using different modified culture media (CPW-13, V/KM, MS-P). The application of 0.5% PVP could not prevent browning of the culture media but reduced it to a low level. Although the effect of PVP on plating efficiency was not clear, the formation of microcalli from grapevine protoplasts was remarkably improved when adding PVP at ''day 0'' or ''day 7'' of cultivation. AC could prevent browning of the media in all concentrations tested but at the same time inhibited plating efficiency. Conversely, formation of microalli occurred only with 0.5 and 1.0% AC, but at very low frequencies. A superior suitability of one of the culture media tested for grapevine protoplasts culture could not been found

Smoking among inpatients in treatment for substance use disorders: prevalence and effect on mental health and quality of life

Background - Smoking is still prevalent among people with substance use disorders. The objective of this study was to investigate the prevalence of smoking among patients in treatment for substance use disorders and to analyze the effect of smoking both at baseline and follow-up on drop-out, mental health and quality of life. Methods - One hundred and twenty-eight inpatients (26% female), mainly with alcohol use disorder, staying at three different rehabilitation clinics in Eastern Norway, were interviewed at admission, and at 6 weeks and 6 months follow-up. The interview contained mental health-related problems, trauma, questions on alcohol and other substances and quality of life. Non-parametric tests were used to test group differences and unadjusted and adjusted linear regression to test the associations between smoking and the main outcome variables, while logistic regression was used to test the association between smoking and drop-out. Results - At admission, 75% were daily smokers. Compared to non-smokers at baseline, the smokers had higher drop-out rates (37% vs. 13%), more mental distress, and lower quality of life from baseline up to 6 months follow-up. Those quitting smoking while admitted improved in mental distress and quality of life at the same rate as non-smokers. Alcohol-related factors did not differ between smokers and non-smokers. Conclusions - Smoking was associated with mental distress, quality of life and treatment drop-out among patients in primary alcohol use disorder treatment. The results indicate that smoking cessation should be recommended as an integral part of alcohol use treatment both before and during inpatient treatment to reduce drop-out

ADHD symptoms as risk factor for PTSD in inpatients treated for alcohol use disorder

Attention deficit hyperactivity disorder (ADHD) and post-traumatic stress disorder (PTSD) are more common in alcohol use disorder (AUD) patients than in the general population. Still, there is a lack of knowledge about the relationship between the two conditions in these patients. The main objective of this study was to examine the prevalence of ADHD symptoms, and the relationship between ADHD symptoms and PTSD in AUD inpatients in treatment. Data from 85 AUD patients were collected. The Adult ADHD Self-Report Scale (ASRS) was used to measure ADHD symptoms in all patients. Differences between groups split by PTSD diagnosis and by ASRS clinical cut-off were described, and the relationship between ADHD symptom level and PTSD was tested in a multiple regression model. Almost half the patients scored above ASRS cut-off and 14% had PTSD. Of the patients whose score was above cut-off on the ASRS 23% had PTSD, versus 7% among those below cut-off. Higher ASRS score was associated with PTSD even when age, sex and trauma were adjusted for. This study confirms the high level of ADHD symptoms in AUD patients in treatment. Diagnostic evaluation of PTSD is recommended in patients with ADHD attending inpatient treatment programs for AUD

Computational Screening of Tip and Stalk Cell Behavior Proposes a Role for Apelin Signaling in Sprout Progression

Angiogenesis involves the formation of new blood vessels by sprouting or splitting of existing blood vessels. During sprouting, a highly motile type of endothelial cell, called the tip cell, migrates from the blood vessels followed by stalk cells, an endothelial cell type that forms the body of the sprout. To get more insight into how tip cells contribute to angiogenesis, we extended an existing computational model of vascular network formation based on the cellular Potts model with tip and stalk differentiation, without making a priori assumptions about the differences between tip cells and stalk cells. To predict potential differences, we looked for parameter values that make tip cells (a) move to the sprout tip, and (b) change the morphology of the angiogenic networks. The screening predicted that if tip cells respond less effectively to an endothelial chemoattractant than stalk cells, they move to the tips of the sprouts, which impacts the morphology of the networks. A comparison of this model prediction with genes expressed differentially in tip and stalk cells revealed that the endothelial chemoattractant Apelin and its receptor APJ may match the model prediction. To test the model prediction we inhibited Apelin signaling in our model and in an \emph{in vitro} model of angiogenic sprouting, and found that in both cases inhibition of Apelin or of its receptor APJ reduces sprouting. Based on the prediction of the computational model, we propose that the differential expression of Apelin and APJ yields a "self-generated" gradient mechanisms that accelerates the extension of the sprout.Comment: 48 pages, 10 figures, 8 supplementary figures. Accepted for publication in PLoS ON

New Developments in Biotechnology and IPR in Aquaculture – Are They Sustainable?

The objective of this chapter is to give an overview and analysis of the current trends and developments in biotechnology in aquaculture research and management. The technological developments along with structural changes in the aquaculture sector may affect access and intellectual property rights (IPR) regimes. These issues will be discussed in a wide perspective involving both short and long-term biological effects, ethical and other social aspects (economic, legal and political issues), including their partly inherent contradictions needing compromising for sustainable development. The chapter will focus on current biological challenges within aquaculture as a growing food production sector, with less emphasis on external effects such as environmental effects. Cases from farmed salmon and cod in Norway in addition to shrimp and tilapia in Asia will be highlighted