A certain necessary condition of potential blow up for Navier-Stokes equations

We show that a necessary condition for $T$ to be a potential blow up time is $\lim\limits_{t\uparrow T}\|v(\cdot,t)\|_{L_3}=\infty$.Comment: 16 page

Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier-Stokes equations in the whole space, as well as for the case of periodic boundary conditions

Impaired skin wound healing in peroxisome proliferator–activated receptor (PPAR)α and PPARβ mutant mice

We show here that the α, β, and γ isotypes of peroxisome proliferator–activated receptor (PPAR) are expressed in the mouse epidermis during fetal development and that they disappear progressively from the interfollicular epithelium after birth. Interestingly, PPARα and β expression is reactivated in the adult epidermis after various stimuli, resulting in keratinocyte proliferation and differentiation such as tetradecanoylphorbol acetate topical application, hair plucking, or skin wound healing. Using PPARα, β, and γ mutant mice, we demonstrate that PPARα and β are important for the rapid epithelialization of a skin wound and that each of them plays a specific role in this process. PPARα is mainly involved in the early inflammation phase of the healing, whereas PPARβ is implicated in the control of keratinocyte proliferation. In addition and very interestingly, PPARβ mutant primary keratinocytes show impaired adhesion and migration properties. Thus, the findings presented here reveal unpredicted roles for PPARα and β in adult mouse epidermal repair

Variable exponent Besov-Morrey spaces

In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.publishe

Wavelet Helmholtz decomposition for weak lensing mass map reconstruction

To derive the convergence field from the gravitational shear (gamma) of the background galaxy images, the classical methods require a convolution of the shear to be performed over the entire sky, usually expressed thanks to the Fast Fourier transform (FFT). However, it is not optimal for an imperfect geometry survey. Furthermore, FFT implicitly uses periodic conditions that introduce errors to the reconstruction. A method has been proposed that relies on computation of an intermediate field u that combines the derivatives of gamma and on convolution with a Green kernel. In this paper, we study the wavelet Helmholtz decomposition as a new approach to reconstructing the dark matter mass map. We show that a link exists between the Helmholtz decomposition and the E/B mode separation. We introduce a new wavelet construction, that has a property that gives us more flexibility in handling the border problem, and we propose a new method of reconstructing the dark matter mass map in the wavelet space. A set of experiments based on noise-free images illustrates that this Wavelet Helmholtz decomposition reconstructs the borders better than all other existing methods.Comment: Accepted for publication in A&A (16 pages, 12 figures

PPARgamma activity in subcutaneous abdominal fat tissue and fat mass gain during short-term overfeeding

Objective: As the peroxisome proliferator-activated receptor (PPAR) plays a central role in fat mass regulation, we investigated whether initial subcutaneous PPAR activity is related to fat mass generation during overfeeding. Subjects: Fourteen healthy female subjects (age 254 years, BMI 22.12.3 kg/m2). Design and measurements: Subjects were overfed with a diet supplying 50% more energy than baseline energy requirements for 14 days. Fasting blood samples were analyzed for leptin, insulin and glucose. Fasting subcutaneous abdominal fat biopsies were obtained for analysis of PPAR1, PPAR2, aP2 and UCP2 mRNAs. Results: Initial PPAR1 and 2, aP2 and UCP2 mRNAs were not related to fat gain (P>0.12). However, PPAR1, PPAR2 and aP2 mRNA changes were positively related to changes in plasma leptin (

Dynamic regulation of mitochondrial network and oxidative functions during 3T3-L1 fat cell differentiation

Mitochondria have been shown to be impaired in insulin resistance-related diseases but have not been extensively studied during the first steps of adipose cell development. This study was designed to determine the sequence of changes of the mitochondrial network and function during the first days of adipogenesis. 3T3-L1 preadipocytes were differentiated into adipocytes without using glitazone compounds. At days 0, 3, 6, 9, and 12, mitochondrial network imaging, mitochondrial oxygen consumption, membrane potential, and oxidative phosphorylation efficiency were assessed in permeabilized cells. Gene and protein expressions related to fatty acid metabolism and mitochondrial network were also determined. Compared to preadipocytes (day 0), new adipocytes (days 6 and 9) displayed profound changes of their mitochondrial network that underwent fragmentation and redistribution around lipid droplets. Drp1 and mitofusin 2 displayed a progressive increase in their gene expression and protein content during the first 9 days of differentiation. In parallel with the mitochondrial network redistribution, mitochondria switched to uncoupled respiration with a tendency towards decreased membrane potential, with no variation of mtTFA and NRF1 gene expression. The expression of PGC1α and NRF2 genes and genes involved in lipid oxidation (UCP2, CD36, and CPT1) was increased. Reactive oxygen species (ROS) production displayed a nadir at day 6 with a concomitant increase in antioxidant enzyme gene expression. This 3T3-L1-based in vitro model of adipogenesis showed that mitochondria adapted to the increased number of lipid droplets by network redistribution and uncoupling respiration. The timing and regulation of lipid oxidation-associated ROS production appeared to play an important role in these changes

Insulin and GH Signaling in Human Skeletal Muscle In Vivo following Exogenous GH Exposure: Impact of an Oral Glucose Load

GH induces acute insulin resistance in skeletal muscle in vivo, which in rodent models has been attributed to crosstalk between GH and insulin signaling pathways. Our objective was to characterize time course changes in signaling pathways for GH and insulin in human skeletal muscle in vivo following GH exposure in the presence and absence of an oral glucose load.Eight young men were studied in a single-blinded randomized crossover design on 3 occasions: 1) after an intravenous GH bolus 2) after an intravenous GH bolus plus an oral glucose load (OGTT), and 3) after intravenous saline plus OGTT. Muscle biopsies were taken at t = 0, 30, 60, and 120. Blood was sampled at frequent intervals for assessment of GH, insulin, glucose, and free fatty acids (FFA).GH increased AUC(glucose) after an OGTT (p<0.05) without significant changes in serum insulin levels. GH induced phosphorylation of STAT5 independently of the OGTT. Conversely, the OGTT induced acute phosphorylation of the insulin signaling proteins Akt (ser(473) and thr(308)), and AS160.The combination of OGTT and GH suppressed Akt activation, whereas the downstream expression of AS160 was amplified by GH. WE CONCLUDED THE FOLLOWING: 1) A physiological GH bolus activates STAT5 signaling pathways in skeletal muscle irrespective of ambient glucose and insulin levels 2) Insulin resistance induced by GH occurs without a distinct suppression of insulin signaling proteins 3) The accentuation of the glucose-stimulated activation of AS 160 by GH does however indicate a potential crosstalk between insulin and GH.ClinicalTrials.gov NCT00477997

Effects of Inhibition of Interleukin-6 Signalling on Insulin Sensitivity and Lipoprotein (A) Levels in Human Subjects with Rheumatoid Diseases

Interleukin-6 (IL-6) is a pro-inflammatory cytokine that has been found to be increased in type 2 diabetic subjects. However, it still remains unclear if these elevated IL-6 levels are co-incidental or if this cytokine is causally related to the development of insulin resistance and type 2 diabetes in humans. Therefore, in the present study we examined insulin sensitivity, serum adipokine levels and lipid parameters in human subjects before and after treatment with the IL-6 receptor antibody Tocilizumab.11 non-diabetic patients with rheumatoid disease were included in the study. HOMA-IR was calculated and serum levels for leptin, adiponectin, triglycerides, LDL-cholesterol, HDL-cholesterol and lipoprotein (a) (Lp (a)) were measured before as well as one and three months after Tocilizumab treatment. The HOMA index for insulin resistance decreased significantly. While leptin concentrations were not altered by inhibition of IL-6 signalling, adiponectin concentrations significantly increased. Thus the leptin to adiponectin ratio, a novel marker for insulin resistance, exhibited a significant decrease. Serum triglycerides, LDL-cholesterol and HDL-cholesterol tended to be increased whereas Lp (a) levels significantly decreased.Inhibition of IL-6 signalling improves insulin sensitivity in humans with immunological disease suggesting that elevated IL-6 levels in type 2 diabetic subjects might be causally involved in the pathogenesis of insulin resistance. Furthermore, our data indicate that inhibition of IL-6 signalling decreases Lp (a) serum levels, which might reduce the cardiovascular risk of human subjects

Association between the Interleukin-6 Promoter Polymorphism −174G/C and Serum Lipoprotein(a) Concentrations in Humans

Background: Lipoprotein(a) [Lp(a)] is an independent risk factor for cardiovascular disease. The interleukin-6 (IL-6) receptor antagonist tocilizumab has been shown to lower serum Lp(a) concentrations. We investigated whether the IL-6 single nucleotide polymorphism 2174G/C is associated with baseline serum Lp(a) concentrations. Methodology/Principal Findings: We divided 2321 subjects from the Lipid Analytic Cologne (LIANCO) cohort into 2 groups, the ones with substantially elevated Lp(a), defined as concentrations $60 mg/dl (n = 510), and the ones with Lp(a),60 mg/ dl (n = 1811). The association with the genotypes GG (33.7%), GC (50.75%) and CC (15.55%) was investigated. The GC and the CC genotype were associated with a significantly increased odds ratio of having substantially elevated Lp(a) concentrations (OR = 1.3, 95 % CI 1.04 to 1.63, P = 0.02 and OR = 1.44, 95 % CI 1.06 to 1.93, P = 0.018). These associations remained significant after adjusting for age, sex, smoking behavior, body mass index, serum lipoproteins, hypertension and diabetes. Of these covariates, only LDL cholesterol was significantly and independently associated with elevated Lp(a) concentrations. Conclusions/Significance: The IL-6 single nucleotide polymorphism 2174G/C is associated with increased odds of having elevated Lp(a). Whether this association plays a role in the Lp(a)-lowering effects of IL-6 receptor antagonists remains to b