Colourings of lattices and coincidence site lattices

The relationship between the coincidence indices of a lattice $\Gamma_1$ and a sublattice $\Gamma_2$ of $\Gamma_1$ is examined via the colouring of $\Gamma_1$ that is obtained by assigning a unique colour to each coset of $\Gamma_2$. In addition, the idea of colour symmetry, originally defined for symmetries of lattices, is extended to coincidence isometries of lattices. An example involving the Ammann-Beenker tiling is provided to illustrate the results in the quasicrystal setting.Comment: 9 pages, 6 figure

Multiple CSLs for the body centered cubic lattice

Ordinary Coincidence Site Lattices (CSLs) are defined as the intersection of a lattice $\Gamma$ with a rotated copy $R\Gamma$ of itself. They are useful for classifying grain boundaries and have been studied extensively since the mid sixties. Recently the interests turned to so-called multiple CSLs, i.e. intersections of $n$ rotated copies of a given lattice $\Gamma$, in particular in connection with lattice quantizers. Here we consider multiple CSLs for the 3-dimensional body centered cubic lattice. We discuss the spectrum of coincidence indices and their multiplicity, in particular we show that the latter is a multiplicative function and give an explicit expression of it for some special cases.Comment: 4 pages, SSPCM (31 August - 7 September 2005, Myczkowce, Poland

Small Engine Component Technology (SECT)

A study of small gas turbine engines was conducted to identify high payoff technologies for year-2000 engines and to define companion technology plans. The study addressed engines in the 186 to 746 KW (250 to 1000 shp) or equivalent thrust range for rotorcraft, commuter (turboprop), cruise missile (turbojet), and APU applications. The results show that aggressive advancement of high payoff technologies can produce significant benefits, including reduced SFC, weight, and cost for year-2000 engines. Mission studies for these engines show potential fuel burn reductions of 22 to 71 percent. These engine benefits translate into reductions in rotorcraft and commuter aircraft direct operating costs (DOC) of 7 to 11 percent, and in APU-related DOCs of 37 to 47 percent. The study further shows that cruise missile range can be increased by as much as 200 percent (320 percent with slurry fuels) for a year-2000 missile-turbojet system compared to a current rocket-powered system. The high payoff technologies were identified and the benefits quantified. Based on this, technology plans were defined for each of the four engine applications as recommended guidelines for further NASA research and technology efforts to establish technological readiness for the year 2000

Coincidences in 4 dimensions

The coincidence site lattices (CSLs) of prominent 4-dimensional lattices are considered. CSLs in 3 dimensions have been used for decades to describe grain boundaries in crystals. Quasicrystals suggest to also look at CSLs in dimensions $d>3$. Here, we discuss the CSLs of the root lattice $A_4$ and the hypercubic lattices, which are of particular interest both from the mathematical and the crystallographic viewpoint. Quaternion algebras are used to derive their coincidence rotations and the CSLs. We make use of the fact that the CSLs can be linked to certain ideals and compute their indices, their multiplicities and encapsulate all this in generating functions in terms of Dirichlet series. In addition, we sketch how these results can be generalised for 4--dimensional $\Z$--modules by discussing the icosian ring.Comment: 6 pages, conference "Quasicrystals - The Silver Jubilee

Generalized Riemann sums

The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and elementary, thus available to the "common mathematician in the streets." However one may still see here interesting inter-connection and cohesiveness in mathematics

Coincidence isometries of a shifted square lattice

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by identifying the square lattice with the ring of Gaussian integers. To illustrate them, we calculate the set of coincidence isometries, as well as generating functions for the number of coincidence site lattices and coincidence isometries, for specific examples.Comment: 10 pages, 1 figure; paper presented at Aperiodic 2009 (Liverpool

Effects of sample handling and analytical procedures on thyroid hormone concentrations in pregnant women's plasma

Background: Maternal thyroid function is a critical mediator of fetal brain development. Pregnancy-related physiologic changes and handling conditions of blood samples may influence thyroid hormone biomarkers. We investigated the reliability of thyroid hormone biomarkers in plasma of pregnant women under various handling conditions. Methods: We enrolled 17 pregnant women; collected serum and plasma were immediately frozen. Additional plasma aliquots were subjected to different handling conditions before the analysis of thyroid biomarkers: storage at room temperature for 24 or 48 hours before freezing and an extra freeze-Thaw cycle. We estimated free thyroid hormone indices in plasma based on T3 uptake. Results: High correlations between plasma and serum (>0.94) and intraclass correlation coefficients for plasma handling conditions (0.96 to 1.00) indicated excellent reliability for all thyroid hormone biomarkers. Conclusion: Delayed freezing and freeze-Thaw cycles did not affect reliability of biomarkers of thyroid function in plasma during pregnancy. See video abstract at, http://links.lww.com/EDE/B180

Prenatal exposure to perfluoroalkyl substances and associations with symptoms of attention-deficit/hyperactivity disorder and cognitive functions in preschool children

Background: Perfluoroalkyl substances (PFASs) are persistent organic pollutants that are suspected to be neurodevelopmental toxicants, but epidemiological evidence on neurodevelopmental effects of PFAS exposure is inconsistent. We investigated the associations between prenatal exposure to PFASs and symptoms of attention-deficit/hyperactivity disorder (ADHD) and cognitive functioning (language skills, estimated IQ and working memory) in preschool children, as well as effect modification by child sex. Material and methods: This study included 944 mother-child pairs enrolled in a longitudinal prospective study of ADHD symptoms (the ADHD Study), with participants recruited from The Norwegian Mother, Father and Child Cohort Study (MoBa). Boys and girls aged three and a half years, participated in extensive clinical assessments using well-validated tools; The Preschool Age Psychiatric Assessment interview, Child Development Inventory and Stanford-Binet (5th revision). Prenatal levels of 19 PFASs were measured in maternal blood at week 17 of gestation. Multivariable adjusted regression models were used to examine exposure-outcome associations with two principal components extracted from the seven detected PFASs. Based on these results, we performed regression analyses of individual PFASs categorized into quintiles. Results: PFAS component 1 was mainly explained by perfluoroheptane sulfonate (PFHpS), perfluorooctane sulfonate (PFOS), perfluorohexane sulfonate (PFHxS) and perfluorooctanoic acid (PFOA). PFAS component 2 was mainly explained by perfluorodecanoic acid (PFDA), perfluoroundecanoic acid (PFUnDA) and perfluorononanoic acid (PFNA). Regression models showed a negative association between PFAS component 1 and nonverbal working memory [β = -0.08 (CI: -0.12, -0.03)] and a positive association between PFAS component 2 and verbal working memory [β = 0.07 (CI: 0.01, 0.12)]. There were no associations with ADHD symptoms, language skills or IQ. For verbal working memory and PFAS component 2, we found evidence for effect modification by child sex, with associations only for boys. The results of quintile models with individual PFASs, showed the same pattern for working memory as the results in the component regression analyses. There were negative associations between nonverbal working memory and quintiles of PFOA, PFNA, PFHxS, PFHpS and PFOS and positive associations between verbal working memory and quintiles of PFOA, PFNA, PFDA and PFUnDA, with significant relationships mainly in the highest concentration groups. Conclusions: Based on our results, we did not find consistent evidence to conclude that prenatal exposure to PFASs are associated with ADHD symptoms or cognitive dysfunctions in preschool children aged three and a half years, which is in line with the majority of studies in this area. Our results showed some associations between PFASs and working memory, particularly negative relationships with nonverbal working memory, but also positive relationships with verbal working memory. The relationships were weak, as well as both positive and negative, which suggest no clear association – and need for replication

Maternal Thyroid Function during Pregnancy or Neonatal Thyroid Function and Attention Deficit Hyperactivity Disorder: A Systematic Review

Background: Attention deficit hyperactivity disorder (ADHD) is the most common neurobehavioral disorder in children, yet its etiology is poorly understood. Early thyroid hormone disruption may contribute to the development of ADHD. Disrupted maternal thyroid hormone function has been associated with adverse neurodevelopmental outcomes in children. Among newborns, early-treated congenital hypothyroidism has been consistently associated with later cognitive deficits. Methods: We systematically reviewed literature on the association between maternal or neonatal thyroid hormones and ADHD diagnosis or symptoms. We searched Embase, Pubmed, Cinahl, PsycInfo, ERIC, Medline, Scopus, and Web of Science for articles published or available ahead of print as of April 2018. Results: We identified 28 eligible articles: 16 studies of maternal thyroid hormones, seven studies of early-treated congenital hypothyroidism, and five studies of neonatal thyroid hormones. The studies provide moderate evidence for an association between maternal thyroid hormone levels and offspring ADHD, some evidence for an association between early-treated congenital hypothyroidism and ADHD, and little evidence for an association between neonatal thyroid hormone levels and later ADHD. Conclusions: The reviewed articles suggest an association between maternal thyroid function and ADHD, and possibly between early-treated congenital hypothyroidism and ADHD. Study limitations, however, weaken the conclusions in our systematic review, underlining the need for more research. Importantly, there was much variation in the measurement of thyroid hormone function and of ADHD symptoms. Recommendations for future research include using population-based designs, attending to measurement issues for thyroid hormones and ADHD, considering biologically relevant covariates (e.g., iodine intake), and assessing nonlinear dose-responses

Gestational thyroid hormone concentrations and risk of attention-deficit hyperactivity disorder in the Norwegian Mother, Father and Child Cohort Study

Background: Maternal thyroid function plays an important role in foetal brain development; however, little consensus exists regarding the relationship between normal variability in thyroid hormones and common neurodevelopmental disorders, such as attention-deficit hyperactivity disorder (ADHD). Objective: We sought to examine the association between mid-pregnancy maternal thyroid function and risk of clinically diagnosed ADHD in offspring. Methods: We conducted a nested case–control study in the Norwegian Mother, Father and Child Cohort Study. Among children born 2003 or later, we randomly sampled singleton ADHD cases obtained through linkage with the Norwegian Patient Registry (n = 298) and 554 controls. Concentrations of maternal triiodothyronine (T3), thyroxine (T4), T3-Uptake, thyroid-stimulating hormone (TSH) and thyroid peroxidase antibody (TPO-Ab) were measured in maternal plasma, collected at approximately 17 weeks' gestation. Indices of free T4 (FT4i) and free T3 (FT3i) were calculated. We used multivariable adjusted logistic regression to calculate odds ratios and accounted for missing covariate data using multiple imputation. We used restricted cubic splines to assess non-linear trends and provide flexible representations. We examined effect measure modification by dietary iodine and selenium intake. In sensitivity analyses, we excluded women with clinically significant thyroid disorders (n = 73). Results: High maternal T3 was associated with increased risk of ADHD (5th vs 1st quintile odds ratio 2.27, 95% confidence interval 1.21, 4.26). For FT4i, both the lowest and highest quintiles were associated with an approximate 1.6-fold increase in risk of ADHD, with similar trends found for T4. The FT4i association was modified by dietary iodine intake such that the highest risk strata were confined to the low intake group. Conclusions: Both high and low concentrations of maternal thyroid hormones, although within population reference ranges, increase the risk of ADHD in offspring. Increased susceptibility may be found among women with low dietary intake of iodine and selenium