Interactive 4-D Visualization of Stereographic Images From the Double Orthogonal Projection

The double orthogonal projection of the 4-space onto two mutually perpendicular 3-spaces is a method of visualization of four-dimensional objects in a three-dimensional space. We present an interactive animation of the stereographic projection of a hyperspherical hexahedron on a 3-sphere embedded in the 4-space. Described are synthetic constructions of stereographic images of a point, hyperspherical tetrahedron, and 2-sphere on a 3-sphere from their double orthogonal projections. Consequently, the double-orthogonal projection of a freehand curve on a 3-sphere is created inversely from its stereographic image. Furthermore, we show an application to a synthetic construction of a spherical inversion and visualizations of double orthogonal projections and stereographic images of Hopf tori on a 3-sphere generated from Clelia curves on a 2-sphere.Comment: ICGG 2020 submissio

Effects of external nutrient sources and extreme weather events on the nutrient budget of a Southern European coastal lagoon

The seasonal and annual nitrogen (N), phosphorus (P), and carbon (C) budgets of the mesotidal Ria Formosa lagoon, southern Portugal, were estimated to reveal the main inputs and outputs, the seasonal patterns, and how they may influence the ecological functioning of the system. The effects of extreme weather events such as long-lasting strong winds causing upwelling and strong rainfall were assessed. External nutrient inputs were quantified; ocean exchange was assessed in 24-h sampling campaigns, and final calculations were made using a hydrodynamic model of the lagoon. Rain and stream inputs were the main freshwater sources to the lagoon. However, wastewater treatment plant and groundwater discharges dominated nutrient input, together accounting for 98, 96, and 88 % of total C, N, and P input, respectively. Organic matter and nutrients were continuously exported to the ocean. This pattern was reversed following extreme events, such as strong winds in early summer that caused upwelling and after a period of heavy rainfall in late autumn. A principal component analysis (PCA) revealed that ammonium and organic N and C exchange were positively associated with temperature as opposed to pH and nitrate. These variables reflected mostly the benthic lagoon metabolism, whereas particulate P exchange was correlated to Chl a, indicating that this was more related to phytoplankton dynamics. The increase of stochastic events, as expected in climate change scenarios, may have strong effects on the ecological functioning of coastal lagoons, altering the C and nutrient budgets.Portuguese Science and Technology Foundation (FCT) [POCI/MAR/58427/2004, PPCDT/MAR/58427/2004]; Portuguese Science and Technology Foundation (FCT

Age- and region-specific hepatitis B prevalence in Turkey estimated using generalized linear mixed models: a systematic review

Toy M, Önder FO, Wörmann T, et al. Age- and region-specific hepatitis B prevalence in Turkey estimated using generalized linear mixed models: a systematic review. BMC infectious diseases. 2011;11(1): 337.BACKGROUND: To provide a clear picture of the current hepatitis B situation, the authors performed a systematic review to estimate the age- and region-specific prevalence of chronic hepatitis B (CHB) in Turkey. METHODS: A total of 339 studies with original data on the prevalence of hepatitis B surface antigen (HBsAg) in Turkey and published between 1999 and 2009 were identified through a search of electronic databases, by reviewing citations, and by writing to authors. After a critical assessment, the authors included 129 studies, divided into categories: 'age-specific'; 'region-specific'; and 'specific population group'. To account for the differences among the studies, a generalized linear mixed model was used to estimate the overall prevalence across all age groups and regions. For specific population groups, the authors calculated the weighted mean prevalence. RESULTS: The estimated overall population prevalence was 4.57, 95% confidence interval (CI): 3.58, 5.76, and the estimated total number of CHB cases was about 3.3 million. The outcomes of the age-specific groups varied from 2.84, (95% CI: 2.60, 3.10) for the 0-14-year olds to 6.36 (95% CI: 5.83, 6.90) in the 25-34-year-old group. CONCLUSION: There are large age-group and regional differences in CHB prevalence in Turkey, where CHB remains a serious health problem

Body appreciation around the world: Measurement invariance of the Body Appreciation Scale-2 (BAS-2) across 65 nations, 40 languages, gender identities, and age

Abstract The Body Appreciation Scale-2 (BAS-2) is a widely used measure of a core facet of the positive body image construct. However, extant research concerning measurement invariance of the BAS-2 across a large number of nations remains limited. Here, we utilised the Body Image in Nature (BINS) dataset – with data collected between 2020 and 2022 – to assess measurement invariance of the BAS-2 across 65 nations, 40 languages, gender identities, and age groups. Multi-group confirmatory factor analysis indicated that full scalar invariance was upheld across all nations, languages, gender identities, and age groups, suggesting that the unidimensional BAS-2 model has widespread applicability. There were large differences across nations and languages in latent body appreciation, while differences across gender identities and age groups were negligible-to-small. Additionally, greater body appreciation was significantly associated with higher life satisfaction, being single (versus being married or in a committed relationship), and greater rurality (versus urbanicity). Across a subset of nations where nation-level data were available, greater body appreciation was also significantly associated with greater cultural distance from the United States and greater relative income inequality. These findings suggest that the BAS-2 likely captures a near-universal conceptualisation of the body appreciation construct, which should facilitate further cross-cultural research

Changes to the Fossil Record of Insects through Fifteen Years of Discovery

The first and last occurrences of hexapod families in the fossil record are compiled from publications up to end-2009. The major features of these data are compared with those of previous datasets (1993 and 1994). About a third of families (>400) are new to the fossil record since 1994, over half of the earlier, existing families have experienced changes in their known stratigraphic range and only about ten percent have unchanged ranges. Despite these significant additions to knowledge, the broad pattern of described richness through time remains similar, with described richness increasing steadily through geological history and a shift in dominant taxa, from Palaeoptera and Polyneoptera to Paraneoptera and Holometabola, after the Palaeozoic. However, after detrending, described richness is not well correlated with the earlier datasets, indicating significant changes in shorter-term patterns. There is reduced Palaeozoic richness, peaking at a different time, and a less pronounced Permian decline. A pronounced Triassic peak and decline is shown, and the plateau from the mid Early Cretaceous to the end of the period remains, albeit at substantially higher richness compared to earlier datasets. Origination and extinction rates are broadly similar to before, with a broad decline in both through time but episodic peaks, including end-Permian turnover. Origination more consistently exceeds extinction compared to previous datasets and exceptions are mainly in the Palaeozoic. These changes suggest that some inferences about causal mechanisms in insect macroevolution are likely to differ as well

Numerical study of the asymptotics of the second Painlevé equation by a functional fitting method

The Painlevé equations arise as reductions of the soliton equations such as the Korteweg-de Vries equation, the nonlinear Schrödinger equation and so on. In this study, we are concerned with numerical approximation of the asymptotics of solutions of the second Painlevé equation on pole-free intervals along the real axis. Classical integrators such as high order Runge-Kutta schemes might be expensive to simulate oscillation, decay and blow-up behaviours depending on initial conditions. However, a lower order functional fitting method catches all kinds of solutions even for relatively large step sizes. © 2013 John Wiley & Sons, Ltd

An efficient numerical treatment for the asymptotic behaviour of the nonlinear Airy-type problems

This study focuses on symplectic integrators for numerical evaluation of the asymptotic solutions of the nonlinear Airy-type equations obtained by reducing the nonlinear dispersive equations. Since the nature of Airy-type equations has both highly oscillatory slow decay and exponential fast decay, most of classical integrators are not able to correctly exhibit challenging physical behaviour. We use specially designed symplectic integrators combining splitting methods with Magnus integrators to catch asymptotic behaviour of nonlinear Airy-type equations efficiently, even for large step sizes. Efficiency of the proposed methods for given problems is discussed. Moreover, numerical results obtained by the proposed methods are compared with the existing results in the literature. © 2020 Elsevier B.V