The distance function from the boundary in a Minkowski space

Let the space $\mathbb{R}^n$ be endowed with a Minkowski structure $M$ (that is $M\colon \mathbb{R}^n \to [0,+\infty)$ is the gauge function of a compact convex set having the origin as an interior point, and with boundary of class $C^2$), and let $d^M(x,y)$ be the (asymmetric) distance associated to $M$. Given an open domain $\Omega\subset\mathbb{R}^n$ of class $C^2$, let $d_{\Omega}(x) := \inf\{d^M(x,y); y\in\partial\Omega\}$ be the Minkowski distance of a point $x\in\Omega$ from the boundary of $\Omega$. We prove that a suitable extension of $d_{\Omega}$ to $\mathbb{R}^n$ (which plays the r\"ole of a signed Minkowski distance to $\partial \Omega$) is of class $C^2$ in a tubular neighborhood of $\partial \Omega$, and that $d_{\Omega}$ is of class $C^2$ outside the cut locus of $\partial\Omega$ (that is the closure of the set of points of non--differentiability of $d_{\Omega}$ in $\Omega$). In addition, we prove that the cut locus of $\partial \Omega$ has Lebesgue measure zero, and that $\Omega$ can be decomposed, up to this set of vanishing measure, into geodesics starting from $\partial\Omega$ and going into $\Omega$ along the normal direction (with respect to the Minkowski distance). We compute explicitly the Jacobian determinant of the change of variables that associates to every point $x\in \Omega$ outside the cut locus the pair $(p(x), d_{\Omega}(x))$, where $p(x)$ denotes the (unique) projection of $x$ on $\partial\Omega$, and we apply these techniques to the analysis of PDEs of Monge-Kantorovich type arising from problems in optimal transportation theory and shape optimization.Comment: 34 page

On the Finsler metrics obtained as limits of chessboard structures

We study the geodesics in a planar chessboard structure with two values 1 and $\beta>1$. The results for a fixed structure allow us to infer the properties of the Finsler metrics obtained, with an homogenization procedure, as limit of oscillating chessboard structures.Comment: 31 pages, 15 figure

A variational approach to the macroscopic electrodynamics of anisotropic hard superconductors

We consider the Bean's critical state model for anisotropic superconductors. A variational problem solved by the quasi--static evolution of the internal magnetic field is obtained as the $\Gamma$-limit of functionals arising from the Maxwell's equations combined with a power law for the dissipation. Moreover, the quasi--static approximation of the internal electric field is recovered, using a first order necessary condition. If the sample is a long cylinder subjected to an axial uniform external field, the macroscopic electrodynamics is explicitly determined.Comment: 24 pages, 15 figure

Azathioprine Biotransformation in Young Patients with Inflammatory Bowel Disease: Contribution of Glutathione-S Transferase M1 and A1 Variants

The contribution of candidate genetic variants involved in azathioprine biotransformation on azathioprine efficacy and pharmacokinetics in 111 young patients with inflammatory bowel disease was evaluated. Azathioprine doses, metabolites thioguanine-nucleotides (TGN) and methylmercaptopurine-nucleotides (MMPN) and clinical effects were assessed after at least 3 months of therapy. Clinical efficacy was defined as disease activity score below 10. Candidate genetic variants (TPMT rs1142345, rs1800460, rs1800462, GSTA1 rs3957357, GSTM1, and GSTT1 deletion) were determined by polymerase chain reaction (PCR) assays and pyrosequencing. Statistical analysis was performed using linear mixed effects models for the association between the candidate variants and the pharmacological variables (azathioprine doses and metabolites). Azathioprine metabolites were measured in 257 samples (median 2 per patient, inter-quartile range IQR 1-3). Clinical efficacy at the first evaluation available resulted better in ulcerative colitis than in Crohn's disease patients (88.0% versus 52.5% responders, p = 0.0003, linear mixed effect model, LME). TGN concentration and the ratio TGN/dose at the first evaluation were significantly higher in responder. TPMT rs1142345 variant (4.8% of patients) was associated with increased TGN (LME p = 0.0042), TGN/dose ratio (LME p < 0.0001), decreased azathioprine dose (LME p = 0.0087), and MMPN (LME p = 0.0011). GSTM1 deletion (58.1% of patients) was associated with a 18.5% decrease in TGN/dose ratio and 30% decrease in clinical efficacy. GSTA1 variant (12.8% of patients) showed a trend (p = 0.049, LME) for an association with decreased clinical efficacy; however, no significant effect on azathioprine pharmacokinetics could be detected. In conclusion, GSTs variants are associated with azathioprine efficacy and pharmacokinetics

A chemogenomic screening identifies CK2 as a target for pro-senescence therapy in PTEN-deficient tumours

Enhancement of cellular senescence in tumours triggers a stable cell growth arrest and activation of an antitumour immune response that can be exploited for cancer therapy. Currently, there are only a limited number of targeted therapies that act by increasing senescence in cancers, but the majority of them are not selective and also target healthy cells. Here we developed a chemogenomic screening to identify compounds that enhance senescence in PTEN-deficient cells without affecting normal cells. By using this approach, we identified casein kinase 2 (CK2) as a pro-senescent target. Mechanistically, we show that Pten loss increases CK2 levels by activating STAT3. CK2 upregulation in Pten null tumours affects the stability of Pml, an essential regulator of senescence. However, CK2 inhibition stabilizes Pml levels enhancing senescence in Pten null tumours. Taken together, our screening strategy has identified a novel STAT3-CK2-PML network that can be targeted for pro-senescence therapy for cancer

Production of a potential liquid plant bio-stimulant by immobilized Piriformospora indica in repeated-batch fermentation process

Piriformospora indica, a mycorrhizal-like fungus able to establish associations with roots of a wide range of plants, supporting plant nutrition and increasing plant resistance and tolerance to stress, was shown to solubilise phosphate applied in the form of animal bone char (HABO) in fermentation systems. The process of P solubilisation was caused most likely by proton extrusion and medium pH lowering. The fungal mycelium was successfully immobilized/retained in a polyurethane foam carrier. Further employment of the immobilized mycelium in repeated-batch fermentation process resulted in at least 5 cycles of P solubilization. The concentration of soluble P increased during the experiment with 1.0 and 3.0 g HABO l−1 and at the end of the 5th batch cycle reached 40.8 and 120 mg l−1, respectively. The resulting final liquid product, without or with solubilized phosphate, was found to significantly increase plant growth and P plant uptake. It can be used as a biostimulant containing microbial plant growth-promoting substances and soluble P derived from renewable sources (HABO) thus supporting the development of sustainable agro-ecosystems.This work was supported by Project CTM2014-53186-R, Ministerio de Economia y Competitividad-ES/EC FEDER Fund and the sabbatical Grant PRX16/00277 to NV

Enhancing phosphorus and zinc acquisition efficiency in rice: a critical review of root traits and their potential utility in rice breeding

Background: Rice is the world's most important cereal crop and phosphorus (P) and zinc (Zn) deficiency are major constraints to its production. Where fertilizer is applied to overcome these nutritional constraints it comes at substantial cost to farmers and the efficiency of fertilizer use is low. Breeding crops that are efficient at acquiring P and Zn from native soil reserves or fertilizer sources has been advocated as a cost-effective solution, but would benefit from knowledge of genes and mechanisms that confer enhanced uptake of these nutrients by roots. Scope: This review discusses root traits that have been linked to P and Zn uptake in rice, including traits that increase mobilization of P/Zn from soils, increase the volume of soil explored by roots or root surface area to recapture solubilized nutrients, enhance the rate of P/Zn uptake across the root membrane, and whole-plant traits that affect root growth and nutrient capture. In particular, this review focuses on the potential for these traits to be exploited through breeding programmes to produce nutrient-efficient crop cultivars. Conclusions: Few root traits have so far been used successfully in plant breeding for enhanced P and Zn uptake in rice or any other crop. Insufficient genotypic variation for traits or the failure to enhance nutrient uptake under realistic field conditions are likely reasons for the limited success. More emphasis is needed on field studies in mapping populations or association panels to identify those traits and underlying genes that are able to enhance nutrient acquisition beyond the level already present in most cultivars.T. J. Rose, S. M. Impa, M. T. Rose, J. Pariasca-Tanaka, A. Mori, S. Heuer, S. E. Johnson-Beebout and M. Wissuw