Higher order corrections for anisotropic bootstrap percolation

We study the critical probability for the metastable phase transition of the two-dimensional anisotropic bootstrap percolation model with $(1,2)$-neighbourhood and threshold $r = 3$. The first order asymptotics for the critical probability were recently determined by the first and second authors. Here we determine the following sharp second and third order asymptotics: $$p_c\big( [L]^2,\mathcal{N}_{(1,2)},3 \big) \; = \; \frac{(\log \log L)^2}{12\log L} \, - \, \frac{\log \log L \, \log \log \log L}{ 3\log L} + \frac{\left(\log \frac{9}{2} + 1 \pm o(1) \right)\log \log L}{6\log L}.$$ We note that the second and third order terms are so large that the first order asymptotics fail to approximate $p_c$ even for lattices of size well beyond $10^{10^{1000}}$.Comment: 46 page

De kwaliteit van warme maaltijden in (zorg)instellingen

Dit onderzoek heeft tot doel een goed beeld te vormen van de voedingsstoffensamenstelling van gekoppeld en ontkoppeld bereide maaltijden zoals deze in Nederland in (zorg)instellingen worden bereid. De volgende vraag is onderzocht in deze studie: is er in (zorg)instellingen in Nederland een verschil in nutriëntenretentie tussen warme maaltijden die bereid zijn volgens het gekoppelde en volgens het ontkoppelde bereidingsproces

Validating fatty acid intake as estimated by an FFQ : how does the 24 h recall perform as reference method compared with the duplicate portion?

Objective: To compare the performance of the commonly used 24 h recall (24hR) with the more distinct duplicate portion (DP) as reference method for validation of fatty acid intake estimated with an FFQ. Design: Intakes of SFA, MUFA, n-3 fatty acids and linoleic acid (LA) were estimated by chemical analysis of two DP and by on average five 24hR and two FFQ. Plasma n-3 fatty acids and LA were used to objectively compare ranking of individuals based on DP and 24hR. Multivariate measurement error models were used to estimate validity coefficients and attenuation factors for the FFQ with the DP and 24hR as reference methods. Setting: Wageningen, the Netherlands. Subjects: Ninety-two men and 106 women (aged 20–70 years). Results: Validity coefficients for the fatty acid estimates by the FFQ tended to be lower when using the DP as reference method compared with the 24hR. Attenuation factors for the FFQ tended to be slightly higher based on the DP than those based on the 24hR as reference method. Furthermore, when using plasma fatty acids as reference, the DP showed comparable to slightly better ranking of participants according to their intake of n-3 fatty acids (0·33) and n-3:LA (0·34) than the 24hR (0·22 and 0·24, respectively). Conclusions: The 24hR gives only slightly different results compared with the distinctive but less feasible DP, therefore use of the 24hR seems appropriate as the reference method for FFQ validation of fatty acid intake.</p

Validity of absolute intake and nutrient density of protein, potassium, and sodium assessed by various dietary assessment methods:An exploratory study

It is suggested that nutrient densities are less affected by measurement errors than absolute intake estimates of dietary exposure. We compared the validity of absolute intakes and densities of protein (kJ from protein/total energy (kJ)), potassium, and sodium (potassium or sodium (in mg)/total energy (kJ)) assessed by different dietary assessment methods. For 69 Dutch subjects, two duplicate portions (DPs), five to fifteen 24-h dietary recalls (24 hRs, telephone-based and web-based) and two food frequency questionnaires (FFQs) were collected and compared to duplicate urinary biomarkers and one or two doubly labelled water measurements. Multivariate measurement error models were used to estimate validity coefficients (VCs) and attenuation factors (AFs). This research showed that group bias diminished for protein and sodium densities assessed by all methods as compared to the respective absolute intakes, but not for those of potassium. However, the VCs and AFs for the nutrient densities did not improve compared to absolute intakes for all four methods; except for the AF of sodium density (0.71) or the FFQ which was better than that of the absolute sodium intake (0.51). Thus, using nutrient densities rather than absolute intakes does not necessarily improve the performance of the DP, FFQ, or 24 hR.</p

A minimally invasive tool to study immune response and skin barrier in children with atopic dermatitis

Background: Atopic dermatitis (AD) affects children of all skin types. Most research has focused on light skin types. Studies investigating biomarkers in people with AD with dark skin types are lacking. Objectives: To explore skin barrier and immune response biomarkers in stratum corneum (SC) tape strips from children with AD with different skin types. Methods: Tape strips were collected from lesional and nonlesional forearm skin of 53 children with AD and 50 controls. We analysed 28 immunomodulatory mediators, and natural moisturizing factors (NMF) and corneocyte morphology. Results: Interleukin (IL)-1β, IL-18, C-X-C motif chemokine (CXCL) 8 (CXCL8), C-C motif chemokine ligand (CCL) 22 (CCL22), CCL17, CXCL10 and CCL2 were significantly higher (P < 0·05) in lesional AD skin compared with nonlesional AD skin; the opposite trend was seen for IL-1α. CXCL8, CCL2 and CCL17 showed an association with objective SCORing Atopic Dermatitis score. NMF levels showed a gradual decrease from healthy skin to nonlesional and lesional AD skin. This gradual decreasing pattern was observed in skin type II but not in skin type VI. Skin type VI showed higher NMF levels in both nonlesional and lesional AD skin than skin type II. Corneocyte morphology was significantly different in lesional AD skin compared with nonlesional AD and healthy skin. Conclusions: Minimally invasive tape-stripping is suitable for the determination of many inflammatory mediators and skin barrier biomarkers in children with AD. This study shows differences between children with AD with skin type II and skin type VI in NMF levels, suggesting that some aspects of pathophysiological mechanisms may differ in AD children with light versus dark skin types

Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections

In this note we analyze an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.Comment: Key words: Bootstrap percolation, anisotropy, finite-size effect