Introducing students to geometric theorems: how the teacher can exploit the semiotic potential of a DGS

Since their appearance new technologies have raised many expectations about their potential for innovating teaching and learning practices; in particular any didactical software, such as a Dynamic Geometry System (DGS) or a Computer Algebra System (CAS), has been considered an innovative element suited to enhance mathematical learning and support teachers’ classroom practice. This paper shows how the teacher can exploit the potential of a DGS to overcome crucial difficulties in moving from an intuitive to a deductive approach to geometry. A specific intervention will be presented and discussed through examples drawn from a long-term teaching experiment carried out in the 9th and 10th grades of a scientific high school. Focusing on an episode through the lens of a semiotic analysis we will see how the teacher’s intervention develops, exploiting the semiotic potential offered by the DGS Cabri-Géomètre. The semiotic lens highlights specific patterns in the teacher’s action that make students’ personal meanings evolve towards the mathematical meanings that are the objective of the intervention.     

A divergent and stereoselective approach to phenolic 1,7-dihydroxy-bisabolane sesquiterpenes: asymmetric total synthesis of (+)-curcutetraol, (+)-sydonol, (+)-sydonic acid,and (+)-7-O-methylsydonic acid

The combined use of the Sharpless asymmetric epoxidation, a number of stereospecific chemical transformations, and the 3,5-hexadienoic acid benzannulation protocol allowed us to devise a new, divergent, and stereoselective approach to terpenes with a chiral tertiary hydroxyl group at the ortho-position of a phenol functional group. Accordingly, the natural occurring enantiomeric forms of the bisabolane sesquiterpenes (+)-curcutetraol, (+)-sydonol, (+)-sydonic acid, and (+)-7-O-methylsydonic acid were synthesized with high enantiomeric purity starting from geraniol. The latter two acids were prepared in enantioenriched form for the first time.     

Regularized Quadratic Penalty Methods for Shape from Shading

Shape from shading (SFS) denotes the problem of reconstructing a 3D surface, starting from a single shaded image which represents the surface itself. Minimization techniques are commonly used for solving the SFS problem, where the objective function is a weighted combination of the brightness error, plus one or more terms aiming to obtain a valid solution. We present a regularized quadratic penalty method where quadratic penalization is used to adaptively adjust the smoothing weights, and regularization improves the robustness and reliability of the procedure. A nonmonotone Barzilai–Borwein method is employed to efficiently solve the arising subproblems. Numerical results are provided showing the reliability of the proposed approach.     

An Assessment of the Utility of Tissue Smears in Rapid Cancer Profiling with Desorption Electrospray Ionization Mass Spectrometry (DESI-MS)

Mass spectrometry imaging with desorption electrospray ionization mass spectrometry (DESI-MS) is used to characterize cancer from ex vivo slices of tissues. The process is time-consuming. The use of tissue smears for DESI-MS analysis has been proposed as it eliminates the time required to snap-freeze and section the tissue. To assess the utility of tissue smears for rapid cancer characterization, principal component analysis (PCA) was performed to evaluate the concordance between DESI-MS profiles of breast cancer from tissue slices and smears prepared on various surfaces. PCA suggested no statistical discrimination between DESI-MS profiles of tissue sections and tissue smears prepared on glass, polytetrafluoroethylene (PTFE), and porous PTFE. However, the abundances of cancer biomarker ions varied between sections and smears, with DESI-MS analysis of tissue sections yielding higher ion abundances of cancer biomarkers compared with smears. Coefficient of variance (CV) analysis suggests DESI-MS profiles from tissue smears are as reproducible as the ones from tissue sections. The limit of detection with smear samples from single pixel analysis is comparable to tissue sections that average the signal from a tissue area of 0.01 mm². The smears prepared on the PTFE surface possessed a higher degree of homogeneity compared with the smears prepared on the glass surface. This allowed single MS scans (~1 s) from random positions across the surface of the smear to be used in rapid cancer typing with good reproducibility, providing pathologic information for cancer typing at speeds suitable for clinical utility.

Open image in new window

Graphical Abstract ?

     

Variable selection in high‐dimensional regression: a nonparametric procedure for business failure prediction

Business failure prediction models are important in providing warning for preventing financial distress and giving stakeholders time to react in a timely manner to a crisis. The empirical approach to corporate distress analysis and forecasting has recently attracted new attention from financial institutions, academics, and practitioners. In fact, this field is as interesting today as it was in the 1930s, and over the last 80 years, a remarkable body of both theoretical and empirical studies on this topic has been published. Nevertheless, some issues are still under investigation, such as the selection of financial ratios to define business failure and the identification of an optimal subset of predictors. For this purpose, there exist a large number of methods that can be used, although their drawbacks are usually neglected in this context. Moreover, most variable selection procedures are based on some very strict assumptions (linearity and additivity) that make their application difficult in business failure prediction. This paper proposes to overcome these limits by selecting relevant variables using a nonparametric method named Rodeo that is consistent even when the aforementioned assumptions are not satisfied. We also compare Rodeo with two other variable selection methods (Lasso and Adaptive Lasso), and the empirical results demonstrate that our proposed procedure outperforms the others in terms of positive/negative predictive value and is able to capture the nonlinear effects of the selected variables. Copyright © 2017 John Wiley & Sons, Ltd.