Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

R&D investment in green building initiatives in Western Australia

This paper reports on a current case study of green building initiatives implemented by the Western Australian government in the past decade. The intent is to provide a qualitative understanding of past R&D investments in the Australian built environment. The case method was selected to illustrate three sector-based investments, one of which is reported on here. The conceptual framework underpinning interview design and data analysis uses dynamic capability, absorptive capacity and open innovation theories to better understand the organisational environment in which these initiatives were implemented. Data has been thematically coded to criteria identified from the literature to illustrate organisational characteristics which may have contributed to dissemination and impact. The results will be combined with two further case studies (construction safety and digital modelling), to inform this research. This industry supported project will conclude by developing policy guidelines for future R&D investment in the built environment.

The effect of Tenofovir on vitamin D metabolism in HIV-infected adults is dependent on sex and ethnicity

Background: Tenofovir has been associated with renal phosphate wasting, reduced bone mineral density, and higher parathyroid hormone levels. The aim of this study was to carry out a detailed comparison of the effects of tenofovir versus non-tenofovir use on calcium, phosphate and, vitamin D, parathyroid hormone (PTH), and bone mineral density. Methods: A cohort study of 56 HIV-1 infected adults at a single centre in the UK on stable antiretroviral regimes comparing biochemical and bone mineral density parameters between patients receiving either tenofovir or another nucleoside reverse transcriptase inhibitor. Principal Findings: In the unadjusted analysis, there was no significant difference between the two groups in PTH levels (tenofovir mean 5.9 pmol/L, 95% confidence intervals 5.0 to 6.8, versus non-tenofovir; 5.9, 4.9 to 6.9; p = 0.98). Patients on tenofovir had significantly reduced urinary calcium excretion (median 3.01 mmol/24 hours) compared to non-tenofovir users (4.56; p,0.0001). Stratification of the analysis by age and ethnicity revealed that non-white men but not women, on tenofovir had higher PTH levels than non-white men not on tenofovir (mean difference 3.1 pmol/L, 95% CI 5.3 to 0.9; p = 0.007). Those patients with optimal 25-hydroxyvitamin D (.75 nmol/L) on tenofovir had higher 1,25-dihydroxyvitamin D [1,25(OH)2D] (median 48 pg/mL versus 31; p = 0.012), fractional excretion of phosphate (median 26.1%, versus 14.6;p = 0.025) and lower serum phosphate (median 0.79 mmol/L versus 1.02; p = 0.040) than those not taking tenofovir. Conclusions: The effects of tenofovir on PTH levels were modified by sex and ethnicity in this cohort. Vitamin D status also modified the effects of tenofovir on serum concentrations of 1,25(OH)2D and phosphate.

Vitamin D intake, sun exposure and 25-hydroxy vitamin D status in Peritoneal dialysis (PD) and Haemodialysis (HD) patients

Inadequate vitamin D levels have been linked to bone disease but more recently have been associated with wider health implications. Limited studies suggest a high prevalence of Vitamin D deficiency in dialysis patients, although evidence is lacking on whether this is due to dietary restrictions, limited mobility and time outdoors or a combination of these. The aim of this study was to assess the contributions of diet, supplements and sunlight exposure to serum Vitamin D (25(OH)D) levels in dialysis patients. Cross-sectional data were obtained from 30 PD (Mean±SD age 56.9±16.2 y; n=13 male) and 22 HD (Mean±SD age 65.4±14.0 y; n=18 male) patients between 2009 and 2010. Serum 25(OH)D was measured and oral vitamin D intake estimated through a food-frequency-questionnaire and quantifying inactive supplementation. Sunlight exposure was assessed using a validated questionnaire. Prevalence of inadequate/insufficient vitamin D differed between dialysis modality (31% and 43% insufficient (<50nmol/L); 4% and 34% deficient (<25nmol/L) in HD and PD patients respectively (p=0.002)). In HD patients, there was a significant correlation between diet plus supplemental vitamin D intake and 25(OH)D (ρ=0.84, p<0.001). Results suggest a higher frequency of 25(OH)D inadequacy/deficiency in PD compared to HD patients. No other relationships between intake, sun exposure and 25(OH)D were seen. This could reflect limitations of the study design or the importance of other factors such as age, ethnicity and sun protection as interactions in the analysis. Understanding these factors is important given Vitamin D’s emerging status as a biomarker of systemic ill health.

Collective dynamics and control of a 3-D small-world network with time delays

The paper presents a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network. The trivial equilibrium of the model is first investigated, showing that the uncontrolled model exhibits complicated unbounded behavior. Then three control strategies, namely a position feedback control, a velocity feedback control, and a hybrid control combined velocity with acceleration feedback, are then introduced to stabilize this unstable system. It is shown in these three control schemes that only the hybrid control can easily stabilize the 3-D network system. And with properly chosen delay and gain in the delayed feedback path, the hybrid controlled model may have stable equilibrium, or periodic solutions resulting from the Hopf bifurcation, or complex stranger attractor from the period-doubling bifurcation. Moreover, the direction of Hopf bifurcation and stability of the bifurcation periodic solutions are analyzed. The results are further extended to any "d" dimensional network. It shows that to stabilize a "d" dimensional delayed small-world network, at least a "d – 1" order completed differential feedback is needed. This work provides a constructive suggestion for the high dimensional delayed systems.

Comparison of robust criteria for D-optimal design

This study compared the performance of a local and three robust optimality criteria in terms of the standard error for a one-parameter and a two-parameter nonlinear model with uncertainty in the parameter values. The designs were also compared in conditions where there was misspecification in the prior parameter distribution. The impact of different correlation between parameters on the optimal design was examined in the two-parameter model. The designs and standard errors were solved analytically whenever possible and numerically otherwise.

Prenatal Vitamin D deficiency induces an early and more severe experimental autoimmune encephalomyelitis in the second generation

In a previous study, we demonstrated that mouse adult F(1) offspring, exposed to a vitamin d deficiency during pregnancy, developed a less severe and delayed Experimental Autoimmune Encephalomyelitis (EAE), when compared with control offspring. We then wondered whether a similar response was observed in the subsequent generation. To answer this question, we assessed F(2) females whose F(1) parents (males or females) were vitamin d-deprived when developing in the uterus of F(0) females. Unexpectedly, we observed that the vitamin d deficiency affecting the F(0) pregnant mice induced a precocious and more severe EAE in the F(2) generation. This paradoxical finding led us to assess its implications for the epidemiology of Multiple Sclerosis (MS) in humans. Using the REFGENSEP database for MS trios (the patient and his/her parents), we collected the parents' dates of birth and assessed a potential season of birth effect that could potentially be indicative of the vitamin d status of the pregnant grandmothers. A trend for a reduced number of births in the Fall for the parents of MS patients was observed but statistical significance was not reached. Further well powered studies are warranted to validate the latter finding.