Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

Cork derived TiO2 biomorphic ecoceramics

Environmentally conscious biomorphic ceramics (Ecoceramics) are a new class of material manufactured from renewable resources and wastes. Sustainable cork wastes were pyrolysed, and this activated carbon template infiltrated with a sol-gel precursor (from aqueous green-chemistry) to form TiO2 on heating in air, with the honeycomb microstructure of cork. Physical and optical band gap properties were characterised by XRD, SEM and Raman and UV–vis spectroscopy, and differences between alkaline and acidic activation of the carbon template also studied. With activation by HCl, HNO3 or H2SO4, a mixture of anatase and rutile formed. NaOH activation resulted in pure anatase, but a large amount of Na was retained. At 1000 °C acid activated ecoceramics formed pure rutile, but the NaOH activated one formed Na2Ti6O13 (sodium hexatitanate) as the major phase, coexisting with anatase, brookite and rutile. This material is worth further investigation, as Na2Ti6O13 is reported as a photocatalyst in its own right

Usability and Feasibility of PIERS on the Move: An mHealth App for Pre-Eclampsia Triage.

BACKGROUND: Pre-eclampsia is one of the leading causes of maternal death and morbidity in low-resource countries due to delays in case identification and a shortage of health workers trained to manage the disorder. Pre-eclampsia Integrated Estimate of RiSk (PIERS) on the Move (PotM) is a low cost, easy-to-use, mobile health (mHealth) platform that has been created to aid health workers in making decisions around the management of hypertensive pregnant women. PotM combines two previously successful innovations into a mHealth app: the miniPIERS risk assessment model and the Phone Oximeter. OBJECTIVE: The aim of this study was to assess the usability of PotM (with mid-level health workers) for iteratively refining the system. METHODS: Development of the PotM user interface involved usability testing with target end-users in South Africa. Users were asked to complete clinical scenario tasks, speaking aloud to give feedback on the interface and then complete a questionnaire. The tool was then evaluated in a pilot clinical evaluation in Tygerberg Hospital, Cape Town. RESULTS: After ethical approval and informed consent, 37 nurses and midwives evaluated the tool. During Study 1, major issues in the functionality of the touch-screen keyboard and date scroll wheels were identified (total errors n=212); during Study 2 major improvements in navigation of the app were suggested (total errors n=144). Overall, users felt the app was usable using the Computer Systems Usability Questionnaire; median (range) values for Study 1 = 2 (1-6) and Study 2 = 1 (1-7). To demonstrate feasibility, PotM was used by one research nurse for the pilot clinical study. In total, more than 500 evaluations were performed on more than 200 patients. The median (interquartile range) time to complete an evaluation was 4 min 55 sec (3 min 25 sec to 6 min 56 sec). CONCLUSIONS: By including target end-users in the design and evaluation of PotM, we have developed an app that can be easily integrated into health care settings in low- and middle-income countries. Usability problems were often related to mobile phone features (eg, scroll wheels, touch screen use). Larger scale evaluation of the clinical impact of this tool is underway

The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P0500

How Gaussian competition leads to lumpy or uniform species distributions

A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is 'lumped' (or 'clumped'), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either uniform or lumped species distributions. Here we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity. In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model. We analyze the origin of this sensitivity and discuss it in the context of recent applications of the model.Comment: 11 pages, 3 figures, revised versio

Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure

A Cognitive Model of an Epistemic Community: Mapping the Dynamics of Shallow Lake Ecosystems

We used fuzzy cognitive mapping (FCM) to develop a generic shallow lake ecosystem model by augmenting the individual cognitive maps drawn by 8 scientists working in the area of shallow lake ecology. We calculated graph theoretical indices of the individual cognitive maps and the collective cognitive map produced by augmentation. The graph theoretical indices revealed internal cycles showing non-linear dynamics in the shallow lake ecosystem. The ecological processes were organized democratically without a top-down hierarchical structure. The steady state condition of the generic model was a characteristic turbid shallow lake ecosystem since there were no dynamic environmental changes that could cause shifts between a turbid and a clearwater state, and the generic model indicated that only a dynamic disturbance regime could maintain the clearwater state. The model developed herein captured the empirical behavior of shallow lakes, and contained the basic model of the Alternative Stable States Theory. In addition, our model expanded the basic model by quantifying the relative effects of connections and by extending it. In our expanded model we ran 4 simulations: harvesting submerged plants, nutrient reduction, fish removal without nutrient reduction, and biomanipulation. Only biomanipulation, which included fish removal and nutrient reduction, had the potential to shift the turbid state into clearwater state. The structure and relationships in the generic model as well as the outcomes of the management simulations were supported by actual field studies in shallow lake ecosystems. Thus, fuzzy cognitive mapping methodology enabled us to understand the complex structure of shallow lake ecosystems as a whole and obtain a valid generic model based on tacit knowledge of experts in the field.Comment: 24 pages, 5 Figure

Dietary polyunsaturated fat intake is associated with low-density lipoprotein size, but not with susceptibility to oxidation in subjects with impaired glucose metabolism and type II diabetes: the Hoorn study

OBJECTIVE: A high monounsaturated fatty acid (MUFA) and polyunsaturated fatty acid (PUFA) intake is associated with lower plasma low-density lipoprotein (LDL)-cholesterol. However, PUFA may increase the susceptibility of LDL to undergo oxidative modifications. The aim of this study was to analyze the association of habitual dietary fat intake with LDL size and oxidizability. DESIGN: Cross-sectional. SETTING: Cohort study. SUBJECTS: Seven hundred and fifty-eight subjects with normal, impaired glucose metabolism and type II diabetes. INTERVENTIONS: Mean LDL size was measured by high-performance gel-filtration chromatography. In vitro oxidizability of LDL was determined by measuring lag time, reflecting the resistance of LDL to copper-induced oxidation. Information about dietary fat intake was obtained by a validated food frequency questionnaire. RESULTS: PUFA intake (energy percent) was significantly and negatively associated with LDL size in subjects with type II diabetes (standardized beta (95% confidence interval) -0.17 (-0.28;-0.06)) and impaired glucose metabolism - although not statistically significant - (-0.09 (-0.24;0.05)), but not in subjects with normal glucose metabolism (0.01 (-0.10;0.12)) (P-value for interaction=0.02). No significant associations were observed for total, saturated fat and MUFA intake with LDL size. Intake of fat was associated with lag time; however, the small magnitude of the associations suggested that the composition of dietary fat is not a major factor affecting lag time. The same association with lag time was observed in all three glucose metabolism categories. CONCLUSIONS: In individuals with abnormal glucose metabolism, higher PUFA intake is associated with smaller LDL particle size, but does not alter the susceptibility of LDL to in vitro oxidation. SPONSORSHIP: Dutch Diabetes Research Foundation, and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)

Early multidrug resistance, defined by changes in intracellular doxorubicin distribution, independent of P-glycoprotein.

Resistance to multiple antitumour drugs, mostly antibiotics or alkaloids, has been associated with a cellular plasma membrane P-glycoprotein (Pgp), causing energy-dependent transport of drugs out of cells. However, in many common chemotherapy resistant human cancers there is no overexpression of Pgp, which could explain drug resistance. In order to characterise early steps in multidrug resistance we have derived a series of P-glycoprotein-positive (Pgp/+) and P-glycoprotein-negative (Pgp/-) multidrug resistant cell lines, from a human non-small cell lung cancer cell line, SW-1573, by stepwise selection with increasing concentrations of doxorubicin. These cells were exposed to doxorubicin and its fluorescence in nucleus (N) and cytoplasm (C) was quantified with laserscan microscopy and image analysis. The fluorescence N/C ratio in parent cells was 3.8 and decreased both in Pgp/+ and Pgp/- cells with increasing selection pressure to 1.2-2.6 for cells with a resistance factor of 7-17. N/C ratios could be restored partly with verapamil only in Pgp/+ cells. N/C ratio measurements may define a general Pgp-independent type of defense of mammalian cells against certain anticancer agents which may precede Pgp expression in early doxorubicin resistance