Quadrature formulas on the unit circle based on rational functions

AbstractQuadrature formulas on the unit circle were introduced by Jones in 1989. On the other hand, Bultheel also considered such quadratures by giving results concerning error and convergence. In other recent papers, a more general situation was studied by the authors involving orthogonal rational functions on the unit circle which generalize the well-known Szegő polynomials. In this paper, these quadratures are again analyzed and results about convergence given. Furthermore, an application to the Poisson integral is also made

Convergence of modified approximants associated with orthogonal rational functions

AbstractLet {αn} be a sequence in the unit disk D = {z ∈ C: ¦z¦ < 1} consisting of a finite number of points cyclically repeated, and let L be the linear space generated by the functions Bn(z) = Πk=0n − αk(z − αk)¦αk¦(1 − αkz). Let {ϕn(z)} be orthogonal rational functions obtained from the sequence {Bn(z)} (orthogonalization with respect to a given functional on L), and let {ψn(z)} be the corresponding functions of the second kind (with superstar transforms ϕn∗(z) and ψn∗(z) respectively). Interpolation and convergence properties of the modified approximants Rn(z, un, vn) = (unψn(z) − vnψn∗(z))(unϕn(z) + vnϕn∗(z)) that satisfy ¦un¦ = ¦vn¦ are discussed

Analyzing and Predicting Purchase Intent in E-commerce: Anonymous vs. Identified Customers

The popularity of e-commerce platforms continues to grow. Being able to understand, and predict customer behavior is essential for customizing the user experience through personalized result presentations, recommendations, and special offers. Previous work has considered a broad range of prediction models as well as features inferred from clickstream data to record session characteristics, and features inferred from user data to record customer characteristics. So far, most previous work in the area of purchase prediction has focused on known customers, largely ignoring anonymous sessions, i.e., sessions initiated by a non-logged-in or unrecognized customer. However, in the de-identified data from a large European e-commerce platform available to us, more than 50% of the sessions start as anonymous sessions. In this paper, we focus on purchase prediction for both anonymous and identified sessions on an e-commerce platform. We start with a descriptive analysis of purchase vs. non-purchase sessions. This analysis informs the definition of a feature-based model for purchase prediction for anonymous sessions and identified sessions; our models consider a range of session-based features for anonymous sessions, such as the channel type, the number of visited pages, and the device type. For identified user sessions, our analysis points to customer history data as a valuable discriminator between purchase and non-purchase sessions. Based on our analysis, we build two types of predictors: (1) a predictor for anonymous that beats a production-ready predictor by over 17.54% F1; and (2) a predictor for identified customers that uses session data as well as customer history and achieves an F1 of 96.20%. Finally, we discuss the broader practical implications of our findings.Comment: 10 pages, accepted at SIGIR eCommerce 202

An Unusual Triad in Pediatric Neurology:A Case Report on Cerebral Palsy, Epilepsy, and Duchenne Muscular Dystrophy

We present a case of an unusual triad in pediatric neurology: a currently 12-year-old boy with cerebral palsy and epilepsy who was later also diagnosed with Duchenne muscular dystrophy. We describe the clinical path that resulted in this exceptional diagnosis. This case report illustrates how different neurological disorders may overshadow each other. In addition, it demonstrates that every child with cerebral palsy and either an atypical clinical course or with inexplicable laboratory values-as well as every infant boy born to a theoretical Duchenne muscular dystrophy carrier-should be subjected to additional investigations.</p

Point-of-care measurement of blood lactate in children admitted with febrile illness to an African District Hospital.

BACKGROUND: Lactic acidosis is a consistent predictor of mortality owing to severe infectious disease, but its detection in low-income settings is limited to the clinical sign of "deep breathing" because of the lack of accessible technology for its measurement. We evaluated the use of a point-of-care (POC) diagnostic device for blood lactate measurement to assess the severity of illness in children admitted to a district hospital in Tanzania. METHODS: Children between the ages of 2 months and 13 years with a history of fever were enrolled in the study during a period of 1 year. A full clinical history and examination were undertaken, and blood was collected for culture, microscopy, complete blood cell count, and POC measurement of blood lactate and glucose. RESULTS: The study included 3248 children, of whom 164 (5.0%) died; 45 (27.4%) of these had raised levels of blood lactate (>5 mmol/L) but no deep breathing. Compared with mortality in children with lactate levels of ≤ 3 mmol/L, the unadjusted odds of dying were 1.6 (95% confidence interval [CI].8-3.0), 3.4 (95% CI, 1.5-7.5), and 8.9 (95% CI, 4.7-16.8) in children with blood lactate levels of 3.1-5.0, 5.1-8.0, or >8.0 mmol/L, respectively. The prevalence of raised lactate levels (>5 mmol/L) was greater in children with malaria than in children with nonmalarial febrile illness (P < .001) although the associated mortality was greater in slide-negative children. CONCLUSIONS: POC lactate measurement can contribute to the assessment of children admitted to hospital with febrile illness and can also create an opportunity for more hospitals in resource-poor settings to participate in clinical trials of interventions to reduce mortality associated with hyperlactatemia

The legacy of cover crops on the soil habitat and ecosystem services in a heavy clay, minimum tillage rotation

Abstract Cover crops are grown as potential ways to improve soil fertility, soil structure, and biodiversity, while reducing weed/pest burdens. Yet, increased costs (in both time and fuel), farmer knowledge requirements, and yield uncertainty (green bridge effect and variable crop establishment) have led to hesitation among farmers. This study was conducted at the field scale (covering an area of nearly 20 hectares) to determine whether different cover crop mixtures affected soil properties and ecosystem services on a heavy clay soil. Measurements of soil chemistry, physics, biology, weed abundance, and subsequent crop performance were taken within a minimum tillage management system, across three cover crop mixtures (commonly sold to UK farmers). The cover crop mixtures included oats (Avena sativa), radish (Raphanus sativus), phacelia (Phacelia tanacetifolia), vetch (Vicia sativa), legumes, buckwheat (Fagopyrum esculentum) and a bare stubble control followed by a spring oat crop. Soil physics (penetrometer and bulk density) and chemistry (N, P, K, Mg, Ca, and organic matter) varied little across treatments, although there was significantly lower Mg in the cover crop including legumes and an increase in NO3 within this treatment. Soil biology and botanical composition were also assessed, monitoring earthworm and mesofauna abundance; and sown and unsown (weed) biomass. Epigeic earthworms were found to have significantly larger abundance in cover crop mixtures with radish present, although other meso- and macrofauna did not differ. Significant weed suppression was found during both the cover crop growing period and as a legacy in the subsequent crop, leading to significant yield increases and economic benefits in some treatments. Our study confirms that cover crops are providing benefits, even on heavy clay soils, including improvements in nutrient leaching risk reduction, weed suppression, and crop yield, coupled with wider ecosystem benefits. We therefore consider cover crops to have a role in sustainable management of arable rotations