306 resultados para hyperbolic fourth-R quadratic equation


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Spatial data analysis has become more and more important in the studies of ecology and economics during the last decade. One focus of spatial data analysis is how to select predictors, variance functions and correlation functions. However, in general, the true covariance function is unknown and the working covariance structure is often misspecified. In this paper, our target is to find a good strategy to identify the best model from the candidate set using model selection criteria. This paper is to evaluate the ability of some information criteria (corrected Akaike information criterion, Bayesian information criterion (BIC) and residual information criterion (RIC)) for choosing the optimal model when the working correlation function, the working variance function and the working mean function are correct or misspecified. Simulations are carried out for small to moderate sample sizes. Four candidate covariance functions (exponential, Gaussian, Matern and rational quadratic) are used in simulation studies. With the summary in simulation results, we find that the misspecified working correlation structure can still capture some spatial correlation information in model fitting. When the sample size is large enough, BIC and RIC perform well even if the the working covariance is misspecified. Moreover, the performance of these information criteria is related to the average level of model fitting which can be indicated by the average adjusted R square ( [GRAPHICS] ), and overall RIC performs well.

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Previous studies have shown that the external growth records of the posterior adductor muscle scar (PAMS) of the bivalve Pinna nobilis are incomplete and do not produce accurate age estimations. We have developed a new methodology to study age and growth using the inner record of the PAMS, which avoids the necessity of costly in situ shell measurements or isotopic studies. Using the inner record we identified the positions of PAMS previously obscured by nacre and estimated the number of missing records in adult specimens with strong abrasion of the calcite layer in the anterior portion of the shell. The study of the PAMS and inner record of two shells that were 6 years old when collected showed that only 2 and 3 PAMS were observed, while 6 inner records could be counted, thus confirming our working methodology. Growth parameters of a P. nobilis population located in Moraira, Spain (western Mediterranean) were estimated with the new methodology and compared to those obtained using PAMS data and in situ measurements. For the comparisons, we applied different models considering the data alternatively as length-at-age (LA) and tag-recapture (TR). Among every method we tested to fit the Von Bertalanffy growth model, we observed that LA data from inner record fitted to the model using non-linear mixed effects and the estimation of missing records using the calcite width was the most appropriate. The equation obtained with this method, L = 573*(1 - e(-0.16(t-0.02))), is very similar to that calculated previously from in situ measurements for the same population.

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Serum immunoreactive cationic trypsinogen levels were determined in 99 control subjects and 381 cystic fibrosis (CF) patients. To evaluate the status of the exocrine pancreas all CF patients had previously undergone fecal fat balance studies and/or pancreatic stimulation tests. Three hundred fourteen CF patients had fat malabsorption and/or had inadequate pancreatic enzyme secretion (pancreatic insufficiency) requiring oral pancreatic enzyme supplements with meals. Sixty-seven CF patients did not have fat malabsorption and/or had adequate enzyme secretion (pancreatic sufficiency) and were not receiving pancreatic enzyme supplements with meals. Mean serum trypsinogen in 99 control subjects was 31.4 ± 14.8 /µg/hter (± 2 SD) and levels did not vary with age or sex. In CF infants (< 2 yr) with pancreatic insufficiency, mean serum trypsinogen was significantly above the non-CF values (p < 0.001). Ninety-one percent of the CF infants had elevated levels. Serum trypsinogen values in the pancreatic insuffi ient group declined steeply up to 5 years, reaching subnormal values by age 6. An equation was developed which described these age-related changes very accurately. Only six CF patients with pancreatic insufficiency had serum trypsinogen levels above the 95% confidence limits of this equation. In contrast, there was no age related decline in serum trypsinogen among the CF group with pancreatic sufficiency. Under 7 yr, serum trypsinogen failed to distinguish the two groups. In those over 7 yr of age, however, serum trypsinogen was significantly higher than the CF group with pancreatic insufficiency (p < 0.001), and 93% had values within or above the control range. In conclusion, serum trypsinogen appears to be a useful screening test for CF in infancy. Between 2 and 7 yr of age this test is of little diagnostic value. After 7 yr of age, serum trypsinogen can reliably distinguish between CF patients with and without pancreatic insufficiency.

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- Background This study examined relationships between adiposity, physical functioning and physical activity. - Methods Obese (N=107) and healthy-weight (N=132) children aged 10-13 years underwent assessments of percent body fat (%BF, dual energy X-ray absorptiometry), knee extensor strength (KE, isokinetic dynamometry), cardiorespiratory fitness (CRF, peak oxygen uptake by cycle ergometry), physical health-related quality of life (HRQOL), worst pain intensity and walking capacity [six-minute walk (6MWT)]. Structural equation modelling was used to assess relationships between variables. - Results Moderate relationships were observed between %BF and 6MWT, KE strength corrected for mass and CRF relative to mass (r -.36 to -.69, P≤.007). Weak relationships were found between: %BF and physical HRQOL (r -.27, P=.008); CRF relative to mass and physical HRQOL (r -.24, P=.003); physical activity and 6MWT (r .17, P=.004). Squared multiple correlations showed that 29.6% variance in physical HRQOL was explained by %BF, pain and CRF relative to mass, while 28% variance in 6MWT was explained by %BF and physical activity. - Conclusions It appears that children with a higher body fat percentage have poorer KE strength, CRF and overall physical functioning. Reducing percent fat appears to be the best target to improve functioning. However, a combined approach to intervention, targeting reductions in body fat percentage, pain and improvements in physical activity and CRF may assist physical functioning.

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In the opening pages of Selling Sex we are introduced to 'Joy', a statue of a young female sex worker which stood in East Sydney for eighteen months during 1995- 1997. Following complaints by local residents, the statue was removed from public view and returned to its owner. Evidently, Joy was considered a reminder of the community's 'bad old days', when it was better known for prostitution than restaurants. In a nation in which almost every sizable community has proudly erected monuments to military men, the removal of Joy reveals much about labour and gender relations in Australia. For Frances, the removal of Joy is symbolic, our historical treatment of sex workers having parallels with our treatment of the convicts. This work sets out to give these women (male prostitutes do not figure in this history) a voice and break with the stereotypes of 'abandoned whores' or 'sad victims'. It also sets out to place the sex industry in the broader national and international context in which it has historically operated...

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The ratio of the lengths of an individual's second to fourth digit (2D:4D) is commonly used as a noninvasive retrospective biomarker for prenatal androgen exposure. In order to identify the genetic determinants of 2D:4D, we applied a genome-wide association approach to 1507 11-year-old children from the Avon Longitudinal Study of Parents and Children (ALSPAC) in whom 2D:4D ratio had been measured, as well as a sample of 1382 12- to 16-year-olds from the Brisbane Adolescent Twin Study. A meta-analysis of the two scans identified a single variant in the LIN28B gene that was strongly associated with 2D:4D (rs314277: p = 4.1 x 10(-8)) and was subsequently independently replicated in an additional 3659 children from the ALSPAC cohort (p = 1.53 x 10(-6)). The minor allele of the rs314277 variant has previously been linked to increased height and delayed age at menarche, but in our study it was associated with increased 2D:4D in the direction opposite to that of previous reports on the correlation between 2D:4D and age at menarche. Our findings call into question the validity of 2D:4D as a simplistic retrospective biomarker for prenatal testosterone exposure.

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Most common human traits and diseases have a polygenic pattern of inheritance: DNA sequence variants at many genetic loci influence the phenotype. Genome-wide association (GWA) studies have identified more than 600 variants associated with human traits, but these typically explain small fractions of phenotypic variation, raising questions about the use of further studies. Here, using 183,727 individuals, we show that hundreds of genetic variants, in at least 180 loci, influence adult height, a highly heritable and classic polygenic trait. The large number of loci reveals patterns with important implications for genetic studies of common human diseases and traits. First, the 180 loci are not random, but instead are enriched for genes that are connected in biological pathways (P = 0.016) and that underlie skeletal growth defects (P < 0.001). Second, the likely causal gene is often located near the most strongly associated variant: in 13 of 21 loci containing a known skeletal growth gene, that gene was closest to the associated variant. Third, at least 19 loci have multiple independently associated variants, suggesting that allelic heterogeneity is a frequent feature of polygenic traits, that comprehensive explorations of already-discovered loci should discover additional variants and that an appreciable fraction of associated loci may have been identified. Fourth, associated variants are enriched for likely functional effects on genes, being over-represented among variants that alter amino-acid structure of proteins and expression levels of nearby genes. Our data explain approximately 10% of the phenotypic variation in height, and we estimate that unidentified common variants of similar effect sizes would increase this figure to approximately 16% of phenotypic variation (approximately 20% of heritable variation). Although additional approaches are needed to dissect the genetic architecture of polygenic human traits fully, our findings indicate that GWA studies can identify large numbers of loci that implicate biologically relevant genes and pathways.

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Future time perspective - the way individuals perceive their remaining time in life - importantly influences socio-emotional goals and motivational outcomes. Recently, researchers have called for studies that investigate relationships between personality and future time perspective. Using a cross-lagged panel design, this study investigated effects of chronic regulatory focus dimensions (promotion and prevention orientation) on future time perspective dimensions (focus on opportunities and limitations). Survey data were collected two times, separated by a 3. month time lag, from 85 participants. Results of structural equation modeling showed that promotion orientation had a positive lagged effect on focus on opportunities, and prevention orientation had a positive lagged effect on focus on limitations.

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Aims We combine measurements of weak gravitational lensing from the CFHTLS-Wide survey, supernovae Ia from CFHT SNLS and CMB anisotropies from WMAP5 to obtain joint constraints on cosmological parameters, in particular, the dark-energy equation-of-state parameter w. We assess the influence of systematics in the data on the results and look for possible correlations with cosmological parameters. Methods We implemented an MCMC algorithm to sample the parameter space of a flat CDM model with a dark-energy component of constant w. Systematics in the data are parametrised and included in the analysis. We determine the influence of photometric calibration of SNIa data on cosmological results by calculating the response of the distance modulus to photometric zero-point variations. The weak lensing data set is tested for anomalous field-to-field variations and a systematic shape measurement bias for high-redshift galaxies. Results Ignoring photometric uncertainties for SNLS biases cosmological parameters by at most 20% of the statistical errors, using supernovae alone; the parameter uncertainties are underestimated by 10%. The weak-lensing field-to-field variance between 1 deg2-MegaCam pointings is 5-15% higher than predicted from N-body simulations. We find no bias in the lensing signal at high redshift, within the framework of a simple model, and marginalising over cosmological parameters. Assuming a systematic underestimation of the lensing signal, the normalisation increases by up to 8%. Combining all three probes we obtain -0.10 < 1 + w < 0.06 at 68% confidence ( -0.18 < 1 + w < 0.12 at 95%), including systematic errors. Our results are therefore consistent with the cosmological constant . Systematics in the data increase the error bars by up to 35%; the best-fit values change by less than 0.15.

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We develop a conceptual model, based on person-environment fit theory, which explains how employee age affects occupational strain and well-being. We begin by explaining how age directly affects different dimensions of objective and subjective P-E fit. Next, we illustrate how age can moderate the relationship between objective P-E fit and subjective P-E fit. Third, we discuss how age can moderate the relationships between P-E fit, on one hand, and occupational strain and well-being on the other. Fourth, we explain how age can impact occupational strain and well-being directly independent of P-E fit. The chapter concludes with implications for future research and practice.

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There has been much controversy over the Trans-Pacific Partnership (TPP) – a plurilateral trade agreement involving a dozen nations from throughout the Pacific Rim – and its impact upon the environment, biodiversity, and climate change. The secretive treaty negotiations involve Australia and New Zealand; countries from South East Asia such as Brunei Darussalam, Malaysia, Singapore, Vietnam, and Japan; the South American nations of Peru and Chile; and the members of the 1994 North American Free Trade Agreement (NAFTA), Canada, Mexico and the United States. There was an agreement reached between the parties in October 2015. The participants asserted: ‘We expect this historic agreement to promote economic growth, support higher-paying jobs; enhance innovation, productivity and competitiveness; raise living standards; reduce poverty in our countries; and to promote transparency, good governance, and strong labor and environmental protections.’ The final texts of the agreement were published in November 2015. There has been discussion as to whether other countries – such as Indonesia, the Philippines, and South Korea – will join the deal. There has been much debate about the impact of this proposed treaty upon intellectual property, the environment, biodiversity and climate change. There have been similar concerns about the Trans-Atlantic Trade and Investment Partnership (TTIP) – a proposed trade agreement between the United States and the European Union. In 2011, the United States Trade Representative developed a Green Paper on trade, conservation, and the environment in the context of the TPP. In its rhetoric, the United States Trade Representative has maintained that it has been pushing for strong, enforceable environmental standards in the TPP. In a key statement in 2014, the United States Trade Representative Mike Froman insisted: ‘The United States’ position on the environment in the Trans-Pacific Partnership negotiations is this: environmental stewardship is a core American value, and we will insist on a robust, fully enforceable environment chapter in the TPP or we will not come to agreement.’ The United States Trade Representative maintained: ‘Our proposals in the TPP are centered around the enforcement of environmental laws, including those implementing multilateral environmental agreements (MEAs) in TPP partner countries, and also around trailblazing, first-ever conservation proposals that will raise standards across the region’. Moreover, the United States Trade Representative asserted: ‘Furthermore, our proposals would enhance international cooperation and create new opportunities for public participation in environmental governance and enforcement.’ The United States Trade Representative has provided this public outline of the Environment Chapter of the TPP: A meaningful outcome on environment will ensure that the agreement appropriately addresses important trade and environment challenges and enhances the mutual supportiveness of trade and environment. The Trans-Pacific Partnership countries share the view that the environment text should include effective provisions on trade-related issues that would help to reinforce environmental protection and are discussing an effective institutional arrangement to oversee implementation and a specific cooperation framework for addressing capacity building needs. They also are discussing proposals on new issues, such as marine fisheries and other conservation issues, biodiversity, invasive alien species, climate change, and environmental goods and services. Mark Linscott, an assistant Trade Representative testified: ‘An environment chapter in the TPP should strengthen country commitments to enforce their environmental laws and regulations, including in areas related to ocean and fisheries governance, through the effective enforcement obligation subject to dispute settlement.’ Inside US Trade has commented: ‘While not initially expected to be among the most difficult areas, the environment chapter has emerged as a formidable challenge, partly due to disagreement over the United States proposal to make environmental obligations binding under the TPP dispute settlement mechanism’. Joshua Meltzer from the Brookings Institute contended that the trade agreement could be a boon for the protection of the environment in the Pacific Rim: Whether it is depleting fisheries, declining biodiversity or reduced space in the atmosphere for Greenhouse Gas emissions, the underlying issue is resource scarcity. And in a world where an additional 3 billion people are expected to enter the middle class over the next 15 years, countries need to find new and creative ways to cooperate in order to satisfy the legitimate needs of their population for growth and opportunity while using resources in a manner that is sustainable for current and future generations. The TPP parties already represent a diverse range of developed and developing countries. Should the TPP become a free trade agreement of the Asia-Pacific region, it will include the main developed and developing countries and will be a strong basis for building a global consensus on these trade and environmental issues. The TPP has been promoted by its proponents as a boon to the environment. The United States Trade Representative has maintained that the TPP will protect the environment: ‘The United States’ position on the environment in the TPP negotiations is this: environmental stewardship is a core American value, and we will insist on a robust, fully enforceable environment chapter in the TPP or we will not come to agreement.’ The United States Trade Representative discussed ‘Trade for a Greener World’ on World Environment Day. Andrew Robb, at the time the Australian Trade and Investment Minister, vowed that the TPP will contain safeguards for the protection of the environment. In November 2015, after the release of the TPP text, Rohan Patel, the Special Assistant to the President and Deputy Director of Intergovernmental Affairs, sought to defend the environmental credentials of the TPP. He contended that the deal had been supported by the Nature Conservancy, the International Fund for Animal Welfare, the Joint Ocean Commission Initiative, the World Wildlife Fund, and World Animal Protection. The United States Congress, though, has been conflicted by the United States Trade Representative’s arguments about the TPP and the environment. In 2012, members of the United States Congress - including Senator Ron Wyden (D-OR), Olympia Snowe (R-ME), and John Kerry (D-MA) – wrote a letter, arguing that the trade agreement needs to provide strong protection for the environment: ‘We believe that a '21st century agreement' must have an environment chapter that guarantees ongoing sustainable trade and creates jobs, and this is what American businesses and consumers want and expect also.’ The group stressed that ‘A binding and enforceable TPP environment chapter that stands up for American interests is critical to our support of the TPP’. The Congressional leaders maintained: ‘We believe the 2007 bipartisan congressional consensus on environmental provisions included in recent trade agreements should serve as the framework for the environment chapter of the TPP.’ In 2013, senior members of the Democratic leadership expressed their opposition to granting President Barack Obama a fast-track authority in respect of the TPP House of Representatives Minority Leader Nancy Pelosi said: ‘No on fast-track – Camp-Baucus – out of the question.’ Senator Majority leader Harry Reid commented: ‘I’m against Fast-Track: Everyone would be well-advised to push this right now.’ Senator Elizabeth Warren has been particularly critical of the process and the substance of the negotiations in the TPP: From what I hear, Wall Street, pharmaceuticals, telecom, big polluters and outsourcers are all salivating at the chance to rig the deal in the upcoming trade talks. So the question is, Why are the trade talks secret? You’ll love this answer. Boy, the things you learn on Capitol Hill. I actually have had supporters of the deal say to me ‘They have to be secret, because if the American people knew what was actually in them, they would be opposed. Think about that. Real people, people whose jobs are at stake, small-business owners who don’t want to compete with overseas companies that dump their waste in rivers and hire workers for a dollar a day—those people, people without an army of lobbyists—they would be opposed. I believe if people across this country would be opposed to a particular trade agreement, then maybe that trade agreement should not happen. The Finance Committee in the United States Congress deliberated over the Trans-Pacific Partnership negotiations in 2014. The new chair Ron Wyden has argued that there needs to be greater transparency in trade. Nonetheless, he has mooted the possibility of a ‘smart-track’ to reconcile the competing demands of the Obama Administration, and United States Congress. Wyden insisted: ‘The new breed of trade challenges spawned over the last generation must be addressed in imaginative new policies and locked into enforceable, ambitious, job-generating trade agreements.’ He emphasized that such agreements ‘must reflect the need for a free and open Internet, strong labor rights and environmental protections.’ Elder Democrat Sander Levin warned that the TPP failed to provide proper protection for the environment: The TPP parties are considering a different structure to protect the environment than the one adopted in the May 10 Agreement, which directly incorporated seven multilateral environmental agreements into the text of past trade agreements. While the form is less important than the substance, the TPP must provide an overall level of environmental protection that upholds and builds upon the May 10 standard, including fully enforceable obligations. But many of our trading partners are actively seeking to weaken the text to the point of falling short of that standard, including on key issues like conservation. Nonetheless, 2015, President Barack Obama was able to secure the overall support of the United States Congress for his ‘fast-track’ authority. This was made possible by the Republicans and dissident Democrats. Notably, Oregon Senator Ron Wyden switched sides, and was transformed from a critic of the TPP to an apologist for the TPP. For their part, green political parties and civil society organisations have been concerned about the secretive nature of the negotiations; and the substantive implications of the treaty for the environment. Environmental groups and climate advocates have been sceptical of the environmental claims made by the White House for the TPP. The Green Party of Aotearoa New Zealand, the Australian Greens and the Green Party of Canada have released a joint declaration on the TPP observing: ‘More than just another trade agreement, the TPP provisions could hinder access to safe, affordable medicines, weaken local content rules for media, stifle high-tech innovation, and even restrict the ability of future governments to legislate for the good of public health and the environment’. In the United States, civil society groups such as the Sierra Club, Public Citizen, WWF, the Friends of the Earth, the Rainforest Action Network and 350.org have raised concerns about the TPP and the environment. Allison Chin, President of the Sierra Club, complained about the lack of transparency, due process, and public participation in the TPP talks: ‘This is a stealth affront to the principles of our democracy.’ Maude Barlow’s The Council of Canadians has also been concerned about the TPP and environmental justice. New Zealand Sustainability Council executive director Simon Terry said the agreement showed ‘minimal real gains for nature’. A number of organisations have joined a grand coalition of civil society organisations, which are opposed to the grant of a fast-track. On the 15th January 2013, WikiLeaks released the draft Environment Chapter of the TPP - along with a report by the Chairs of the Environmental Working Group. Julian Assange, WikiLeaks' publisher, stated: ‘Today's WikiLeaks release shows that the public sweetener in the TPP is just media sugar water.’ He observed: ‘The fabled TPP environmental chapter turns out to be a toothless public relations exercise with no enforcement mechanism.’ This article provides a critical examination of the draft Environment Chapter of the TPP. The overall argument of the article is that the Environment Chapter of the TPP is an exercise in greenwashing – it is a public relations exercise by the United States Trade Representative, rather than a substantive regime for the protection of the environment in the Pacific Rim. Greenwashing has long been a problem in commerce, in which companies making misleading and deceptive claims about the environment. In his 2012 book, Greenwash: Big Brands and Carbon Scams, Guy Pearse considers the rise of green marketing and greenwashing. Government greenwashing is also a significant issue. In his book Storms of My Grandchildren, the climate scientist James Hansen raises his concerns about government greenwashing. Such a problem is apparent with the TPP – in which there was a gap between the assertions of the United States Government, and the reality of the agreement. This article contends that the TPP fails to meet the expectations created by President Barack Obama, the White House, and the United States Trade Representative about the environmental value of the agreement. First, this piece considers the relationship of the TPP to multilateral environmental treaties. Second, it explores whether the provisions in respect of the environment are enforceable. Third, this article examines the treatment of trade and biodiversity in the TPP. Fourth, this study considers the question of marine capture fisheries. Fifth, there is an evaluation of the cursory text in the TPP on conservation. Sixth, the article considers trade in environmental services under the TPP. Seventh, this article highlights the tensions between the TPP and substantive international climate action. It is submitted that the TPP undermines effective and meaningful government action and regulation in respect of climate change. The conclusion also highlights that a number of other chapters of the TPP will impact upon the protection of the environment – including the Investment Chapter, the Intellectual Property Chapter, the Technical Barriers to Trade Chapter, and the text on public procurement.

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Access to quality higher education is challenging for many Western Australians that live outside the metropolitan area. In 2010, the School of Education moved to flexible delivery of a fully online Bachelor of Education degree for their non -metropolitan students. The new model of delivery allows access for students from any location provided they have a computer and an internet connection. A number of academic staff had previously used an asynchronous environment to deliver learning modules housed within a learning management system (LMS) but had not used synchronous software with their students. To enhance the learning environment and to provide high quality learning experiences to students learning at a distance, the adoption of synchronous software (Elluminate Live) was introduced. This software is a real-time virtual classroom environment that allows for communication through Voice over Internet Protocol (VoIP) and videoconferencing, along with a large number of collaboration tools to engage learners. This research paper reports on the integration of a live e-learning solution into the current LMS environment. Qualitative data were collected from academic staff through informal interviews and participant observation. The findings discuss (i) perceived level of support; (ii) identification of strategies used to create an effective online teacher presence; (iii) the perceived impact on the students' learning outcomes; and (iv) guidelines for professional development to enhance pedagogy within the live e-learning environment.

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Microsatellite markers have demonstrated their value for performing paternity exclusion and hence exploring mating patterns in plants and animals. Methodology is well established for diploid species, and several software packages exist for elucidating paternity in diploids; however, these issues are not so readily addressed in polyploids due to the increased complexity of the exclusion problem and a lack of available software. We introduce polypatex, an r package for paternity exclusion analysis using microsatellite data in autopolyploid, monoecious or dioecious/bisexual species with a ploidy of 4n, 6n or 8n. Given marker data for a set of offspring, their mothers and a set of candidate fathers, polypatex uses allele matching to exclude candidates whose marker alleles are incompatible with the alleles in each offspring–mother pair. polypatex can analyse marker data sets in which allele copy numbers are known (genotype data) or unknown (allelic phenotype data) – for data sets in which allele copy numbers are unknown, comparisons are made taking into account all possible genotypes that could arise from the compared allele sets. polypatex is a software tool that provides population geneticists with the ability to investigate the mating patterns of autopolyploids using paternity exclusion analysis on data from codominant markers having multiple alleles per locus.

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Parent involvement is widely accepted as being associated with children’s improved educational outcomes. However, the role of early school-based parent involvement is still being established. This study investigated the mediating role of self-regulated learning behaviors in the relationship between early school-based parent involvement and children’s academic achievement, using data from the Longitudinal Study of Australian Children (N = 2616). Family socioeconomic position, Aboriginal and Torres Strait Islander status, language background, child gender and cognitive competence, were controlled, as well home and community based parent involvement activity in order to derive a more confident interpretation of the results. Structural equation modeling analyses showed that children’s self-regulated learning behaviors fully mediated the relationships between school-based parent involvement at Grade 1 and children’s reading achievement at Grade 3. Importantly, these relationships were evident for children across all socio-economic backgrounds. Although there was no direct relationship between parent involvement at Grade 1 and numeracy achievement at Grade 3, parent involvement was indirectly associated with higher children’s numeracy achievement through children’s self-regulation of learning behaviors, though this relationship was stronger for children from middle and higher socio-economic backgrounds. Implications for policy and practice are discussed, and further research recommended.

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PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.