Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis

Effect of 4 years of growth hormone therapy in children with Noonan syndrome in the American Norditropin Studies: Web-Enabled Research (ANSWER) Program® registry.

BACKGROUND: Noonan syndrome (NS) is a genetic disorder characterized by phenotypic features, including facial dysmorphology, cardiovascular anomalies, and short stature. Growth hormone (GH) has been approved by the United States Food and Drug Administration for short stature in children with NS. The objective of this analysis was to assess the height standard deviation score (HSDS) and change in HSDS (ΔHSDS) for up to 4 years (Y4) of GH therapy in children with NS. METHODS: The American Norditropin Studies: Web-Enabled Research (ANSWER) Program®, a US-based registry, collects long-term efficacy and safety information on patients treated with Norditropin® (somatropin rDNA origin, Novo Nordisk A/S) at the discretion of participating physicians. A total of 120 children (90 boys, 30 girls) with NS, naïve to previous GH treatment, were included in this analysis. RESULTS: The mean (SD) baseline age of subjects (n = 120) was 9.2 (3.8) years. Mean (SD) HSDS increased from -2.65 (0.73) at baseline to -1.32 (1.11) at Y4 (n = 17). Subjects showed continued increase in HSDS from baseline to Y4 without significant differences between genders at Y1 or Y2. The mean (SD) GH dose was 47 (11) mcg/kg/day at baseline and 59 (16) mcg/kg/day at Y4. There was a negative correlation between baseline age and ΔHSDS at Y1 (R = -0.3156; P = 0.0055) and Y2 (R = -0.3394; P = 0.017). ΔHSDS at Y1 was significantly correlated with ΔHSDS at Y2 (n = 37; R = 0.8527, P \u3c 0.0001) and Y3 (n = 20; R = 0.5145; P = 0.0203), but not Y4 (n = 12; R = 0.4066, P = 0.1896). CONCLUSIONS: GH treatment-naïve patients with NS showed continued increases in HSDS during 4 years of treatment with GH with no significant differences between genders up to 2 years. Baseline age was negatively correlated with ΔHSDS at Y1 and Y2. Whether long-term therapy in NS results in continued increase in HSDS to adult height remains to be investigated. TRIAL REGISTRATION: ClinicalTrials.gov NCT01009905

Game-theoretic versions of strong law of large numbers for unbounded variables

We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality's moves are unbounded. Our game-theoretic versions of SLLN largely correspond to standard measure-theoretic results. However game-theoretic proofs are different from measure-theoretic ones in the explicit consideration of various hedges. In measure-theoretic proofs existence of moments are assumed, whereas in our game-theoretic proofs we assume availability of various hedges to Skeptic for finite prices

DNA methylation profiling of the human major histocompatibility complex: A pilot study for the Human Epigenome Project

The Human Epigenome Project aims to identify, catalogue, and interpret genome-wide DNA methylation phenomena. Occurring naturally on cytosine bases at cytosine-guanine dinucleotides, DNA methylation is intimately involved in diverse biological processes and the aetiology of many diseases. Differentially methylated cytosines give rise to distinct profiles, thought to be specific for gene activity, tissue type, and disease state. The identification of such methylation variable positions will significantly improve our understanding of genome biology and our ability to diagnose disease. Here, we report the results of the pilot study for the Human Epigenome Project entailing the methylation analysis of the human major histocompatibility complex. This study involved the development of an integrated pipeline for high-throughput methylation analysis using bisulphite DNA sequencing, discovery of methylation variable positions, epigenotyping by matrix-assisted laser desorption/ionisation mass spectrometry, and development of an integrated public database available at http://www.epigenome.org. Our analysis of DNA methylation levels within the major histocompatibility complex, including regulatory exonic and intronic regions associated with 90 genes in multiple tissues and individuals, reveals a bimodal distribution of methylation profiles (i.e., the vast majority of the analysed regions were either hypo- or hypermethylated), tissue specificity, inter-individual variation, and correlation with independent gene expression data

A Bose-Einstein Approach to the Random Partitioning of an Integer

Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of connected components. Questions such as the evaluation of the probability of random covering and parking configurations, number and length of the gaps are addressed. They are the discrete versions of similar problems raised in the continuum. For each value of k, asymptotic results are presented when n,N both go to infinity according to two different regimes. This model may equivalently be viewed as a random partitioning problem of N items into n recipients. A grand-canonical balls in boxes approach is also supplied, giving some insight into the multiplicities of the box filling amounts or spacings. The latter model is a k-nearest neighbor random graph with N vertices and kn edges. We shall also briefly consider the covering problem in the context of a random graph model with N vertices and n (out-degree 1) edges whose endpoints are no more bound to be neighbors

Increased height standard deviation scores in response to growth hormone therapy to near-adult height in older children with delayed skeletal maturation: results from the ANSWER Program

BACKGROUND: A primary goal of recombinant human growth hormone therapy (GHT) in children is attaining normal adult height. In this study, children with growth hormone deficiency (GHD) (including isolated idiopathic growth hormone deficiency [IGHD] and multiple pituitary hormone deficiency [MPHD]), idiopathic short stature (ISS), and Turner syndrome (TS) were evaluated for near-adult height (NAH) and percent achieving NAH within the normal range after approximately 4 years of GHT. METHODS: Data from the American Norditropin® Studies: Web-Enabled Research (ANSWER) Program were analyzed for NAH from age at treatment start (ATS) (i.e., referral age as defined by age at enrollment in the study) to last clinic visit using one of the following two criteria: 1) age ≥18 years, or 2) if male: ≥16 years and height velocity (HV) <2 cm/year; if female: ≥15 years and HV <2 cm/year. All patients had a baseline height standard deviation score (HSDS) ≤ -2, and either GHD (n = 201), ISS (n = 19), or TS (n = 41). The main outcome measures included HSDS and corrected HSDS (HSDS-target HSDS) in response to GH treatment, and correlation of ATS with NAH HSDS. RESULTS: Mean (± SD) chronological and bone ages at baseline were 14.0 ± 2.1 years and 11.7 ± 2.0 years, respectively, and mean GHT duration was 4.0 ± 1.6 years. Mean HSDS (baseline to NAH; GHD: -2.7 to -1.0; ISS: -2.8 to -1.4; TS: -3.0 to -1.8) and mean corrected HSDS (baseline to NAH; GHD: -2.1 to -0.3; ISS: -2.1 to -0.6; TS: -1.8 to -0.6) increased across diagnostic indications. Percentages of patients reaching near-adult HSDS > -2 were GHD: 87.6%; ISS: 78.9%; TS: 65.8%. Significant negative correlations were found between ATS and NAH HSDS when analyzed by sex. CONCLUSIONS: Despite a relatively advanced childhood age, the majority of GH-treated patients attained mean near-adult HSDS within the normal range (HSDS > -2). Negative correlations of ATS with near-adult HSDS indicate that an earlier age at treatment start would likely have resulted in greater adult height achieved in both male and female patients

Non-newtonian flow and pressure drop of pineapple juice in a plate heat exchanger

The study of non-Newtonian flow in plate heat exchangers (PHEs) is of great importance for the food industry. The objective of this work was to study the pressure drop of pineapple juice in a PHE with 50º chevron plates. Density and flow properties of pineapple juice were determined and correlated with temperature (17.4 < T < 85.8ºC) and soluble solids content (11.0 < Xs < 52.4 ºBrix). The Ostwald-de Waele (power law) model described well the rheological behavior. The friction factor for non-isothermal flow of pineapple juice in the PHE was obtained for diagonal and parallel/side flow. Experimental results were well correlated with the generalized Reynolds number (20 < Re g < 1230) and were compared with predictions from equations from the literature. The mean absolute error for pressure drop prediction was 4% for the diagonal plate and 10% for the parallel plate.(FAPESP) São Paulo Research Foundatio

The formation of medical workers subjectity in the patient care institution environment from a position of the eco-psychological approach

The process of the medical worker's subjectity development as the realization of the ability to be a subject of the optional activity in the shape of professional performance in the patient care institution environment is analyse

Cut Points and Diffusions in Random Environment

In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in the discrete setting providing a decoupling effect in the process. This allows us to take advantage of an ergodic structure to derive a strong law of large numbers with possibly vanishing limiting velocity and a central limit theorem under the quenched measure.Comment: 44 pages; accepted for publication in "Journal of Theoretical Probability

A preferential attachment model with random initial degrees

In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$ edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on $G(t-1)$, the probability that a given edge is connected to vertex i is proportional to $d_i(t-1)+\delta$, where $d_i(t-1)$ is the degree of vertex $i$ at time $t-1$, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power law with exponent $\tau=\min\{\tau_{W}, \tau_{P}\}$, where $\tau_{W}$ is the power-law exponent of the initial degrees $(W_t)_{t\geq 1}$ and $\tau_{P}$ the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze, which is surveyed.Comment: In the published form of the paper, the proof of Proposition 2.1 is incomplete. This version contains the complete proo