Solution of differential equations by application of transformation groups

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations

Application of group and transformation theory to the solution of ordinary and partial differential equations Final report, 17 Jan. 1967 - 16 Jan. 1968

Application of transformation groups to solution of partial differential equation

Application of group and transformation theory to the solution of ordinary and partial differential equations Final report

Lie transformation group for solution of partial differential equation

Prospective Teachers\u27 Use of Representations in Solving Statistical Tasks with Dynamic Statistical Software

This study examined a random stratified sample (n=62) of prospective teachers\u27 work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis

Pathology and regulation for research in the UK: An overview [version 2; peer review: 3 approved]

The input of pathologists is essential for the conduct of many forms of research, including clinical trials. As the custodians of patient samples, pathology departments have a duty to ensure compliance with the relevant regulations, standards and guidelines to ensure the ethical and effective use for their intended investigational analysis, including when patients are participating in a research study. The results of research studies have impacts beyond the research study itself as they may inform changes in policy and practice or support the licensing of medicines and devices. Compliance with regulations and standards provides public assurance that the rights, safety and wellbeing of research participants are protected, that the data have been collected and processed to ensure their integrity and that the research will achieve its purpose. The requirements of the regulatory environment should not be seen as a barrier to research and should not significantly impact on the work of the laboratory once established and integrated into practice. This paper highlights important regulations, policy, standards and available guidance documents that apply to research involving NHS pathology departments and academic laboratories that are contributing to research involving human subjects

Pathology and regulation for research in the UK: An overview [version 2; peer review: 3 approved]

The input of pathologists is essential for the conduct of many forms of research, including clinical trials. As the custodians of patient samples, pathology departments have a duty to ensure compliance with the relevant regulations, standards and guidelines to ensure the ethical and effective use for their intended investigational analysis, including when patients are participating in a research study. The results of research studies have impacts beyond the research study itself as they may inform changes in policy and practice or support the licensing of medicines and devices. Compliance with regulations and standards provides public assurance that the rights, safety and wellbeing of research participants are protected, that the data have been collected and processed to ensure their integrity and that the research will achieve its purpose. The requirements of the regulatory environment should not be seen as a barrier to research and should not significantly impact on the work of the laboratory once established and integrated into practice. This paper highlights important regulations, policy, standards and available guidance documents that apply to research involving NHS pathology departments and academic laboratories that are contributing to research involving human subjects

The Quality of Mathematics Education Technology Literature

Background: The present study evaluated the quality of 1,165 scholarly literature papers about mathematics education technology literature.Purpose: The purpose of the present study was to determine the extent to which mathematics education technology literature reports the information needed to support the scientific basis of a study.Setting: N/AIntervention: N/AResearch Design: A systematic review was used to organize the data collection and analysis processes Data Collection and Analysis: A literature search was conducted to identify scholarly papers that addressed the use of technology in mathematics education. A coding process was developed to record descriptive information about each paper. The Quality Framework developed for this process provided a structure to identify key information across research types based on types of analyses conducted, assigning a certain number of possible points based on the type of research conducted.Findings: Dissertations accounted for a surprisingly high portion of the literature and research: 39.7% of the available literature and 57.0% of the research studies. The overall quality of the mathematics education technology literature was lower than we expected, averaging only 48.9% of the points possible. We noted that the quality of research papers, with respect to possible point values averaged 54.6% over four decades. For mathematics education technology researchers, manuscript reviewers, and editors, these results suggest that more attention is needed on the information being included and excluded from scholarly papers, especially with regard to connections to theoretical frameworks and research designs

Research in Mathematics Educational Technology: Current Trends and Future Demands

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, and/or trustworthiness

Inhibition of β-catenin signalling in dermal fibroblasts enhances hair follicle regeneration during wound healing.

New hair follicles (HFs) do not form in adult mammalian skin unless epidermal Wnt signalling is activated genetically or within large wounds. To understand the postnatal loss of hair forming ability we monitored HF formation at small circular (2 mm) wound sites. At P2, new HFs formed in back skin, but HF formation was markedly decreased by P21. Neonatal tail also formed wound-associated HFs, albeit in smaller numbers. Postnatal loss of HF neogenesis did not correlate with wound closure rate but with a reduction in Lrig1-positive papillary fibroblasts in wounds. Comparative gene expression profiling of back and tail dermis at P1 and dorsal fibroblasts at P2 and P50 showed a correlation between loss of HF formation and decreased expression of genes associated with proliferation and Wnt/β-catenin activity. Between P2 and P50, fibroblast density declined throughout the dermis and clones of fibroblasts became more dispersed. This correlated with a decline in fibroblasts expressing a TOPGFP reporter of Wnt activation. Surprisingly, between P2 and P50 there was no difference in fibroblast proliferation at the wound site but Wnt signalling was highly upregulated in healing dermis of P21 compared with P2 mice. Postnatal β-catenin ablation in fibroblasts promoted HF regeneration in neonatal and adult mouse wounds, whereas β-catenin activation reduced HF regeneration in neonatal wounds. Our data support a model whereby postnatal loss of hair forming ability in wounds reflects elevated dermal Wnt/β-catenin activation in the wound bed, increasing the abundance of fibroblasts that are unable to induce HF formation

Complex mosaic of sexual dichromatism and monochromatism in Pacific robins results from both gains and losses of elaborate coloration

Pacific robins exhibit one of the most complex range-wide mosaics of sexual dichromatism and monochromatism. The evolutionary origins of this geographic mosaic remain poorly understood despite long-standing interest from ornithologists, and its influential role in the development of Ernst Mayr’s theories on speciation and the 'Biological Species Concept'. One factor limiting our understanding of the evolution of sexual plumage variation in Pacific robins is a lack of well-resolved taxon boundaries and phylogenetic relationships in the group. Here, we use primarily historical museum specimens to obtain dense sampling of mtDNA, nuclear DNA, plumage color and morphometrics from all named taxa in the radiation in order to infer taxon boundaries and relationships. We use these data to test hypotheses about colonization history, plumage evolution and reduced island dichromatism. Our data show that the Pacific robin radiation comprises four distinct lineages, which warrant recognition as separate species – the previously recognized Norfolk robin P. multicolor and redcapped robin P. goodenovii, and two new species we propose to name: ‘Solomon robin’ P. polymorpha Mayr, 1934 for the populations on Solomon and Bougainville Islands, and ‘Mayr’s robin’ P. pusilla Peale, 1848 (in honor of Ernst Mayr’s detailed work on the southwest Pacific robins) for the populations on Vanuatu, Fiji and Samoa. Our data suggest that the common ancestor of the entire Pacific robin radiation was most likely sexually dichromatic and that the radiation-wide mosaic of sexual plumage color arose via repeated losses of elaborate plumage in males and gains of elaborate plumage in females on separate islands.Anna M. Kearns, Leo Joseph, Jeremy J. Austin, Amy C. Driskell and Kevin E. Omlan