Targeting large phosp(III)azane macrocyles [{P(mu-NR)}(2)(LL)](n) (n> or = 2)

The condensation reactions of the dimer [ClP(micro-NR)](2) with organic diacids [LL(H)(2)], possessing linear orientations of their organic groups, result in the formation of phospha(III)zane macrocyles of the type [{P(mu-NR)}(2)(LL)](n) of various sizes. The series of macrocycles [{P(mu-N(t)Bu)}(2){1,5-(NH)(2)C(10)H(6)}](3), [{P(mu-NCy)}(2)(1,5-O(2)C(10)H(6))](n) [n = 3; n = 4], [{P(mu-N(t)Bu)}(2){1,4-(NH)(2)C(6)H(4)}](4), [{P(mu-N(t)Bu)}(2)(1,4-O(2)C(6)H(4))], [{P(mu-NCy)}(2)(1,4-O(2)C(6)H(4))](3) and [{P(mu-N(t)Bu)}(2){(NH)C(6)H(4)OC(6)H(4)(NH)}](2) can be related to classical organic frameworks, like calixarenes.     

How does imposing a step-by-step solution method impact students’ approach to mathematical word problem solving?

This paper presents the second phase of a larger research program with the purpose of exploring the possible consequences of a gap between what is done in the classroom regarding mathematical word problem solving and what research shows to be effective in this particular field of study. Data from the first phase of our study on teachers’ self-proclaimed practices showed that one-third of elementary teachers from the region of Quebec require their students to follow a specific sequential problem-solving method, known as the ‘what I know, what I look for’ method. These results led us to hypothesize that the observed gap may have an impact on students’ comprehension of mathematical word problems. The use of this particular method was the foundation for us to study, in the second phase, the effect of the imposition of this sequential method on students’ literal and inferential understanding of word problems. A total of 278 fourth graders (9–10 years old) solved mathematical word problems followed by a test to assess their understanding of the word problems they had just solved. The results suggest that the use of this problem solving method does not seem to improve or impair students’ understanding. From a more fundamental point of view, our study led us to the conclusion that the way word problem solving is addressed in the mathematics classroom, through sequential and inflexible methods, does not help students develop their word problem solving competence.     

An integrated mass spectrometry imaging and digital pathology workflow for objective detection of colorectal tumours by unique atomic signatures

Tumours are abnormal growths of cells that reproduce by redirecting essential nutrients and resources from surrounding tissue. Changes to cell metabolism that trigger the growth of tumours are reflected in subtle differences between the chemical composition of healthy and malignant cells. We used LA-ICP-MS imaging to investigate whether these chemical differences can be used to spatially identify tumours and support detection of primary colorectal tumours in anatomical pathology. First, we generated quantitative LA-ICP-MS images of three colorectal surgical resections with case-matched normal intestinal wall tissue and used this data in a Monte Carlo optimisation experiment to develop an algorithm that can classify pixels as tumour positive or negative. Blinded testing and interrogation of LA-ICP-MS images with micrographs of haematoxylin and eosin stained and Ki67 immunolabelled sections revealed Monte Carlo optimisation accurately identified primary tumour cells, as well as returning false positive pixels in areas of high cell proliferation. We analysed an additional 11 surgical resections of primary colorectal tumours and re-developed our image processing method to include a random forest regression machine learning model to correctly identify heterogenous tumours and exclude false positive pixels in images of non-malignant tissue. Our final model used over 1.6 billion calculations to correctly discern healthy cells from various types and stages of invasive colorectal tumours. The imaging mass spectrometry and data analysis methods described, developed in partnership with clinical cancer researchers, have the potential to further support cancer detection as part of a comprehensive digital pathology approach to cancer care through validation of a new chemical biomarker of tumour cells.

Digital pathology and laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) imaging reveals a unique elemental signature of colorectal cancer.     

Quaternionic theta constants

We investigate the six quaternionic theta constants introduced by Freitag and Hermann. More precisely we investigate their restrictions to the Hermitian resp. Siegel half-space of degree 2. It turns out that these theta constants generate the graded ring of symmetric Hermitian modular forms for the principal congruence subgroup of level 1 + i over the Gaussian number field resp. of Siegel modular forms for the principal congruence subgroup of level 2 and even weight. As an application we obtain a simple construction of Igusa’s Siegel modular form of degree 2 and weight 30 with respect to the non-trivial character.     

Orientability of the Minor Director of Homeotropically Aligned Smectic‐A Elastomers in External Mechanical Fields

We present studies on bulk smectic‐A copolymer networks with end‐on attached homeotropically oriented mesogens that show spontaneous optical biaxiality at room temperature. Orthoscopic and conoscopic investigations under uniaxial extension in the layer planes give first evidence of the orientability of the minor director in mechanical fields yielding biaxial monodomains with 3‐d orientational long‐range order of all three principle axes. This is an important step towards the synthesis of permanently oriented biaxial monodomain elastomers for which highly interesting mechanical and optical properties are expected.     

A Finite Deformation Microsphere Model for Magneto-Visco-Elastic Response in Magnetorheological Elastomers

In this work we present a novel approach to the modeling of magnetorheological elastomers (MREs) for finite deformations. Keeping in mind the composite nature at the microscale, we employ the microsphere model as an effective tool to capture the constitutive response of the material. The microsphere model has been successfully applied to the modelling of rubber-like materials. Here, we extend this approach by taking into account the effect of the magnetic dipole-dipole interactions on the orientation of the polymer chains. Thus, the presented microsphere model is directly motivated by considering the underlying phenomena at the microscale level. Finally the material model is embedded in a finite element framework and the results of a boundary value problems is presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of and numerical schemes for a mouse population model in Hantavirus epidemics

This paper considers a non-linear system of ordinary differential equations, which arises in the study of hantavirus epidemics. The system has the property that the total population obeys the logistic equation. For this system, we use linearization and the dynamical properties of the logistic equation to analyze the dynamics of the subpopulation system. In view of the usual numerical instabilities associated with standard finite difference methods used for simulating such systems, we construct non-standard finite difference (NSFD) schemes, which preserve the dynamic properties of the system, and may therefore be used for its simulation.     

Stability properties of a nonstandard finite difference scheme for a hantavirus epidemic model

This paper studies the stability properties of a nonstandard finite difference (NSFD) scheme used to simulate the dynamics of a mouse population model in hantavirus epidemics. It is shown that this difference scheme and the underlying system of differential equations have the same dynamics. The proof uses the fact that the total population obeys the logistic equation, as well as techniques from calculus, graphical analysis, and dynamical systems.