Mathematics Teacher Leadership Preparation, Mentorship, and Service: Communities of Practice Through Online Modalities

This article is a preface to a special issue of the Journal of Mathematics and Science: Collaborative Explorations which features articles that describe (a) online components of mathematics specialist preparation and mentoring programs, (b) the mentoring and support of teachers preparing to serve as mathematics teacher leaders, and (c) the subsequent service of mathematics specialists in leadership roles. This preface describes the context within which the described online activities took place, provides a common glossary of terms that will be used consistently across all the articles, and briefly introduces each of the fourteen papers that constitute the special issue

Level and Change in Alcohol Consumption, Depression and Dysfunctional Attitudes among Females Treated for Alcohol Addiction

Aims: To examine whether individual changes in alcohol consumption among female alcoholics under treatment are predicted by level of and changes in depression and dysfunctional attitudes. Method: A total of 120 women who were treated for alcohol addiction at the Karolinska Hospital in Stockholm (Sweden) were assessed twice over a 2-year period using the Depression scale from the Symptom Checklist-90, the Alcohol Use Inventory and the Dysfunctional Attitude Scale (DAS). Latent growth curve analysis was used. Results: Decrease in alcohol consumption, depression and dysfunctional attitude variables were found at group level. The results also showed significant individual variation in change. Changes in alcohol consumption were predicted by baseline alcohol drinking, as well as by level and changes in depression. Stronger reduction in depression was related to higher level of depression at baseline, and with reduction in dysfunctional attitudes. Different DAS sub-scales resulted in different magnitude of the model relations. Good treatment compliance was related to lower baseline level in depression, but also with higher baseline level in dysfunctional attitudes, and predicted stronger reduction in alcohol consumption. Conclusion: This paper shows the importance of incorporating both individual level and change in depression as predictors of change in alcohol consumption among subjects treated for alcohol addiction. Also, dysfunctional attitudes are both indirectly and directly related to treatment outcome. By incorporating alcohol consumption, depression and dysfunctional attitudes as targets of intervention, treatment compliance and outcome may be enhanced

Karyotype, C-and fluorescence banding patterns, NOR location and FISH in the grasshopper Xestotrachelus robustus (Romaleidae).

Different techniques involving fluorochrome staining, C-banding, NOR location and FISH were used in order to characterize the karyotype and to determine the characteristics of the constitutive heterochromatin in the genome of grasshopper Xestotrachelus robustus. This species presents uniform karyotype in terms of chromosome number (2n=23, XO in males) but deffered in the morphology of some chromosomes of the complement. Fluorescence in situ hybridization (FISH) was applied to the location of 45S genes. The results of FISH are compared with those coming from classical cytogenetics (C, AgNO3 and CMA3) banding procedures

Household-level risk factors for water contamination and antimicrobial resistance in drinking water among households with children under 5 in rural San Marcos, Cajamarca, Peru

Household water contamination at point of use depends on human, animal and environmental factors embodying all aspects of a One Health approach. This study investigated the association between household factors, the presence of thermotolerant coliform, and the presence of antibiotic resistant bacteria in drinking water among 314 households with children under 5 in Cajamarca, Peru. This study analysed data from a baseline sampling of a randomized controlled trial, including household surveys covering household water management and factors such as household animals, as well as microbiological data from samples collected from drinking water. Data were analysed using generalized linear models. Drinking water samples collected from narrow-mouthed containers were less likely to be contaminated than samples collected from the faucet (OR = 0.55, p = 0.030) or wide mouthed containers. The presence of thermotolerant coliform was associated with owning farm birds, which increased the proportion of contamination from 42.2% to 59.1% (OR = 1.98, p = 0.017) and with animal waste observed in the kitchen area, which increased the prevalence of contamination from 51.4% to 65.6% (OR = 1.80, p = 0.024). Resistance to any antibiotic was higher among pig owners at 60%, relative to non-pig owners at 36.4% (OR = 1.97, p = 0.012) as well as households with free-roaming animals in the kitchen area at 59.6% compared to households without free-roaming animals at 39.7% (OR = 2.24, p = 0.035). Recent child antibiotic use increased the prevalence of trimethoprim-sulfamethoxazole resistance among E. coli isolates to 22.3% relative to 16.7% (OR = 3.00, p = 0.037). Overall, these findings suggest that water storage in a secure container to protect from in-home contamination is likely to be important in providing safe drinking water at point of use. In addition, transmission of thermotolerant coliform and AMR between domestic animals and human drinking water supplies is likely. Further research should explore transmission pathways and methods to support safe drinking water access in multi-species households

Truncation of the series expressions in the advanced ENZ-theory of diffraction integrals

The point-spread function (PSF) is used in optics for design and assessment of the imaging capabilities of an optical system. It is therefore of vital importance that this PSF can be calculated fast and accurately. In the past 12 years, the Extended Nijboer-Zernike (ENZ) approach has been developed for the purpose of semi-analytic evaluation of the PSF, for circularly symmetric optical systems, in the focal region. In the earliest ENZ-years, the Debye approximation of the diffraction integral, by which the PSF is given, was considered for the very basic situation of a low-NA optical system and relatively small defocus values, so that a scalar treatment was allowed with a focal factor comprising a quadratic function in the exponential. At present, the ENZ-method allows calculation of the PSF in low- and high-NA cases, in scalar form and for vector fields (including polarization), for large wave-front aberrations, including amplitude non-uniformities, using a quasi-spherical phase focal factor in a virtually unlimited focal range around the focal plane, and no limitations in the off-axis direction. Additionally, the application range of the method has been broadened and generalized to the calculation of aerial images of extended objects by including the finite distance of the object to the entrance pupil. Also imaging into a multi-layer is now possible by accounting for both forward and backward propagation in the layers.In the advanced ENZ-approach, the generalized, complex-valued pupil function is developed into a series of Zernike circle polynomials, with exponential azimuthal dependence (having cosine/sine azimuthal dependence as special cases). For each Zernike term, the diffraction integral reduces after azimuthal integration to an integral that can be expressed as an infinite double series involving spherical Bessel functions, accounting for the parameters of the optical system and the defocus value, and Jinc functions comprising the radial off-axis value. The contribution of the present paper is the formulation of truncation rules for these double series expressions, with a general rule valid for all circle polynomials at the same time, and a dedicated rule that takes into account the degree and the azimuthal order of the involved circle polynomials to significantly reduce computational cost in specific cases. The truncation rules are based on effective bounds and asymptotics (of the Debye type) for the mentioned spherical Bessel functions and Jinc functions, and show feasibility of computation of practically all diffraction integrals that one encounters in the ENZ-practice. Thus it can be said that the advanced ENZ-theory is more or less completed from the computational point of view by the achievements of the present paper

Advanced analytic treatment and efficient computation of the diffraction integrals in the extended Nijboer-Zernike theory

The computational methods for the diffraction integrals that occur in the Extended Nijboer-Zernike (ENZ-) approach to circular, aberrated, defocused optical systems are reviewed and updated. In the ENZ-approach, the Debye approximation of Rayleigh’s integral for the through-focus, complex, point-spread function is evaluated in semi-analytic form. To this end, the generalized pupil function, comprising phase aberrations as well as amplitude non-uniformities, is assumed to be expanded into a series of Zernike circle polynomials, and the contribution of each of these Zernike terms to the diffraction integral is expressed in the form of a rapidly converging series (containing power functions and/or Bessel functions of various kinds). The procedure of expressing the through-focus point-spread function in terms of Zernike expansion coefficients of the pupil function can be reversed and has led to the ENZ-method of retrieval of pupil functions from measured through-focus (intensity) point-spread functions. The review and update concern the computation for systems ranging from as basic as having low NA and small defocus parameter to high-NA systems, with vector fields and polarization, meant for imaging of extended objects into a multi-layered focal region.In the period 2002-2010, the evolution of the form of the diffraction integral (DI) was dictated by the agenda of the ENZ-team in which a next instance of the DI was handled by amending the computation scheme of the previous one. This has resulted into a variety of ad hoc measures, lack of transparency of the schemes, and sometimes prohibitively slow computer codes. It is the aim of the present paper to reconstruct the whole building of computation methods, using consistently more advanced mathematical tools. These tools areexplicit Zernike expansion of the focal factor in the DI,Clebsch-Gordan coefficients for the omnipresent problem of linearizing products ofZernike circle polynomials,recursions for Bessel functions, binomials and for the coefficients of algebraic functionsthat occur as pre-factors of the focal factor in the DI.This results in a series representation of the DI involving (spherical) Bessel functions and Clebsch-Gordon coefficients, in which the dependence of the DI on parameters of the optical configuration, on focal values, on spatial variables in the image planes, and on degree and azimuthal order of the circle polynomials are separated. This separation of dependencies, together with bounds on Clebsch-Gordon coefficients and spherical Besselfunctions, facilitate the error analysis for the truncation of series, showing that in the new scheme the DI can be computed virtually without loss-of-digits. Furthermore, this separation allows for a modular implementation of the computation scheme that offers speed and flexibility when varying the various parameters and variables. The resulting scheme is pre-eminently appropriate for use in advanced optical simulations, where large defocus values, high NA and Zernike terms of high order and degree occur

Quantitative proteomics and systems analysis of cultured H9C2 cardiomyoblasts during differentiation over time supports a ‘function follows form’ model of differentiation

The rat cardiomyoblast cell line H9C2 has emerged as a valuable tool for studying cardiac development, mechanisms of disease and toxicology. We present here a rigorous proteomic analysis that monitored the changes in protein expression during differentiation of H9C2 cells into cardiomyocyte-like cells over time. Quantitative mass spectrometry followed by gene ontology (GO) enrichment analysis revealed that early changes in H9C2 differentiation are related to protein pathways of cardiac muscle morphogenesis and sphingolipid synthesis. These changes in the proteome were followed later in the differentiation time-course by alterations in the expression of proteins involved in cation transport and beta-oxidation. Studying the temporal profile of the H9C2 proteome during differentiation in further detail revealed eight clusters of co-regulated proteins that can be associated with early, late, continuous and transient up- and downregulation. Subsequent reactome pathway analysis based on these eight clusters further corroborated and detailed the results of the GO analysis. Specifically, this analysis confirmed that proteins related to pathways in muscle contraction are upregulated early and transiently, and proteins relevant to extracellular matrix organization are downregulated early. In contrast, upregulation of proteins related to cardiac metabolism occurs at later time points. Finally, independent validation of the proteomics results by immunoblotting confirmed hereto unknown regulators of cardiac structure and ionic metabolism. Our results are consistent with a function follows form' model of differentiation, whereby early and transient alterations of structural proteins enable subsequent changes that are relevant to the characteristic physiology of cardiomyocytes