Homogeneous (α, k) -polynomial solutions of the fractional riesz system in hyperbolic space

In this paper we study the fractional analogous of the Laplace-Beltrami equation and the Riesz system studied previously by H. Leutwiler , in \BR^3. In both cases we replace the integer derivatives by Caputo fractional derivatives of order $0 <\alpha <1$. We characterize the space of solutions of the fractional Laplace-Beltrami equation, and we calculate its dimension. We establish relations between the solutions of the fractional Laplace-Beltrami equation and the solutions of the fractional Riesz system. Some examples of the polynomial solutions will be presented. Moreover, the behaviour of the obtained results when $\alpha=1$ is presented, and a final remark about the consideration of Riemann-Liouville fractional derivatives instead of Caputo fractional derivatives is made

Prediction of uncomplicated pregnancies in obese women: a prospective multicentre study.

BACKGROUND: All obese pregnant women are considered at equal high risk with respect to complications in pregnancy and birth, and are commonly managed through resource-intensive care pathways. However, the identification of maternal characteristics associated with normal pregnancy outcomes could assist in the management of these pregnancies. The present study aims to identify the factors associated with uncomplicated pregnancy and birth in obese women, and to assess their predictive performance. METHODS: Data form obese women (BMI ≥ 30 kg/m2) with singleton pregnancies included in the UPBEAT trial were used in this analysis. Multivariable logistic regression was used to identify sociodemographic, clinical and biochemical factors at 15+0 to 18+6 weeks' gestation associated with uncomplicated pregnancy and birth, defined as delivery of a term live-born infant without antenatal or labour complications. Predictive performance was assessed using area under the receiver operating characteristic curve (AUROC). Internal validation and calibration were also performed. Women were divided into fifths of risk and pregnancy outcomes were compared between groups. Sensitivity, specificity, and positive and negative predictive values were calculated using the upper fifth as the positive screening group. RESULTS: Amongst 1409 participants (BMI 36.4, SD 4.8 kg/m2), the prevalence of uncomplicated pregnancy and birth was 36% (505/1409). Multiparity and increased plasma adiponectin, maternal age, systolic blood pressure and HbA1c were independently associated with uncomplicated pregnancy and birth. These factors achieved an AUROC of 0.72 (0.68-0.76) and the model was well calibrated. Prevalence of gestational diabetes, preeclampsia and other hypertensive disorders, preterm birth, and postpartum haemorrhage decreased whereas spontaneous vaginal delivery increased across the fifths of increasing predicted risk of uncomplicated pregnancy and birth. Sensitivity, specificity, and positive and negative predictive values were 38%, 89%, 63% and 74%, respectively. A simpler model including clinical factors only (no biomarkers) achieved an AUROC of 0.68 (0.65-0.71), with sensitivity, specificity, and positive and negative predictive values of 31%, 86%, 56% and 69%, respectively. CONCLUSION: Clinical factors and biomarkers can be used to help stratify pregnancy and delivery risk amongst obese pregnant women. Further studies are needed to explore alternative pathways of care for obese women demonstrating different risk profiles for uncomplicated pregnancy and birth

Early Antenatal Prediction of Gestational Diabetes in Obese Women: Development of Prediction Tools for Targeted Intervention.

All obese women are categorised as being of equally high risk of gestational diabetes (GDM) whereas the majority do not develop the disorder. Lifestyle and pharmacological interventions in unselected obese pregnant women have been unsuccessful in preventing GDM. Our aim was to develop a prediction tool for early identification of obese women at high risk of GDM to facilitate targeted interventions in those most likely to benefit. Clinical and anthropometric data and non-fasting blood samples were obtained at 15+0-18+6 weeks' gestation in 1303 obese pregnant women from UPBEAT, a randomised controlled trial of a behavioural intervention. Twenty one candidate biomarkers associated with insulin resistance, and a targeted nuclear magnetic resonance (NMR) metabolome were measured. Prediction models were constructed using stepwise logistic regression. Twenty six percent of women (n = 337) developed GDM (International Association of Diabetes and Pregnancy Study Groups criteria). A model based on clinical and anthropometric variables (age, previous GDM, family history of type 2 diabetes, systolic blood pressure, sum of skinfold thicknesses, waist:height and neck:thigh ratios) provided an area under the curve of 0.71 (95%CI 0.68-0.74). This increased to 0.77 (95%CI 0.73-0.80) with addition of candidate biomarkers (random glucose, haemoglobin A1c (HbA1c), fructosamine, adiponectin, sex hormone binding globulin, triglycerides), but was not improved by addition of NMR metabolites (0.77; 95%CI 0.74-0.81). Clinically translatable models for GDM prediction including readily measurable variables e.g. mid-arm circumference, age, systolic blood pressure, HbA1c and adiponectin are described. Using a ≥35% risk threshold, all models identified a group of high risk obese women of whom approximately 50% (positive predictive value) later developed GDM, with a negative predictive value of 80%. Tools for early pregnancy identification of obese women at risk of GDM are described which could enable targeted interventions for GDM prevention in women who will benefit the most

Polymorphism analysis of the CTLA-4 gene in paracoccidioidomycosis patients

The CTLA-4 protein is expressed in activated T cells and plays an essential role in the immune response through its regulatory effect on T cell activation. Polymorphisms of the CTLA-4 gene have been correlated with autoimmune, neoplastic and infectious illnesses. This work aimed to verify possible associations between single nucleotide polymorphisms (SNPs) in CTLA-4, -318C/T in the promoter and +49A/G in exon 1 and paracoccidioidomycosis (PCM) caused by Paracoccidioides brasiliensis. For this purpose, 66 chronic form PCM patients and 76 healthy controls had their allele, genotype and haplotype frequencies determined. The genetic admixture structure of the patients and controls was evaluated to eliminate ancestral bias. The comparison of frequencies indicated no significant differences between patients and controls that could link the SNPs to PCM. Groups were admixture matched with no difference observed in population ancestry inference, indicating that the absence of association between CTLA-4 polymorphisms and PCM could not be attributed to ancestral bias. This study showed that there was no association between the CTLA-4 SNPs -318 and +49 and the resistance or susceptibility to PCM.22022