Intended Treatments of Arithmetic Average in U.S. and Asian School Mathematics Textbooks

This study examined how selected U.S. and Asian mathematics curricula are designed to facilitate students' understanding of the arithmetic average. There is a consistency regarding the learning goals among these curriculum series, but the focuses are different between the Asian series and the U.S. reform series. The Asian series and the U.S. commercial series focus the arithmetic average more on conceptual and procedural understanding of the concept as a computational algorithm than on understanding the concept as a representative of a data set; however, the two U.S. reform series focus the concept more on the latter. Because of the different focuses, the Asian and the U.S. curriculum series treat the concept differently. In the Asian series, the concept is first introduced in the context of “equal‐sharing” or “per‐unit‐quantity,” and the averaging formula is formally introduced at a very early stage. In the U.S. reform series, the concept is discussed as a measure of central tendency, and after students have some intuitive ideas of the statistical aspect of the concept, the averaging algorithm is briefly introduced.     

Connecting Mathematics and Science in Undergraduate Teacher Education Programs: Faculty Voices from the Maryland Collaborative for Teacher Preparation

The study reported in this paper investigated perceptions concerning connections between mathematics and science held by university/college instructors who participated in the Maryland Collaborative for Teacher Preparation (MCTP), an NSF-funded program aimed at developing special middle-level mathematics and science teachers. Specifically, we asked (a) “What are the perceptions of MCTP instructors about the ‘other’ discipline?” (b) “What are the perceptions of MCTP instructors about the connections between mathematics and science?” and (c) “What are some barriers perceived by MCTP instructors in implementing mathematics and science courses that emphasize connections?” The findings suggest that the benefits of emphasizing mathematics and science connections perceived by MCTP instructors were similar to the benefits reported by school teachers. The barriers reported were also similar. The participation in the project appeared to have encouraged MCTP instructors to grapple with some fundamental questions, like “What should be the nature of mathematics and science connections?” and “What is the nature of mathematics/science in relationship to the other discipline?”     

Multicomponent Peptide Stapling as a Diversity‐Driven Tool for the Development of Inhibitors of Protein–Protein Interactions

Stapled peptides are chemical entities in‐between biologics and small molecules, which have proven to be the solution to high affinity protein–protein interaction antagonism, while keeping control over pharmacological performance such as stability and membrane penetration. We demonstrate that the multicomponent reaction‐based stapling is an effective strategy for the development of α‐helical peptides with highly potent dual antagonistic action of MDM2 and MDMX binding p53. Such a potent inhibitory activity of p53‐MDM2/X interactions was assessed by fluorescence polarization, microscale thermophoresis, and 2D NMR, while several cocrystal structures with MDM2 were obtained. This MCR stapling protocol proved efficient and versatile in terms of diversity generation at the staple, as evidenced by the incorporation of both exo‐ and endo‐cyclic hydrophobic moieties at the side chain cross‐linkers. The interaction of the Ugi‐staple fragments with the target protein was demonstrated by crystallography.     

Experimental implementation of an adiabatic quantum optimization algorithm

We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to solve hard problems. This experiment uses a particularly well-suited three quantum bit molecule and was made possible by introducing a technique that encodes general instances of the given optimization problem into an easily applicable Hamiltonian. Our results indicate an optimal run time of the adiabatic algorithm that agrees well with the prediction of a simple decoherence model.     

The structure-based design of Mdm2/Mdmx-p53 inhibitors gets serious

The p53 protein is the cell's principal bastion of defense against tumor-associated DNA damage. Commonly referred as a "guardian of the genome", p53 is responsible for determining the fate of the cell when the integrity of its genome is damaged. The development of tumors requires breaching this defense line. All known tumor cells either mutate the p53 gene, or in a similar number of cases, use internal cell p53 modulators, Mdm2 and Mdmx proteins, to disable its function. The release of functional p53 from the inhibition by Mdm2 and Mdmx should in principle provide an efficient, nongenotoxic means of cancer therapy. In recent years substantial progress has been made in developing novel p53-activating molecules thanks to several reported crystal structures of Mdm2/x in complex with p53-mimicking peptides and nonpeptidic drug candidates. Understanding the structural attributes of ligand binding holds the key to developing novel, highly effective, and selective drug candidates. Two low-molecular-weight compounds have just recently progressed into early clinical studies.     

Communities of practice: Performance and evolution

We present a detailed model of collaboration in communities of practice and we examine its dynamic consequences for the group as a whole. We establish the existence of a novel mechanism that allows the community to naturally adapt to growth, specialization, or changes in the environment without the need for central controls. This mechanism relies on the appearance of a dynamic instability that initiates an exploration of novel interactions, eventually leading to higher performance for the community as a whole.     

Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay

In this paper, we study travelling front solutions of a vector disease model incorporating time delays and diffusion. Special attention is paid to the modelling of the time delays to incorporate the associated non-local spatial terms which account for the drift of individuals to their present positions from their possible positions at previous times. We shall show that such fronts exist for the weak generic delay kernel and sufficiently small delays by using geometric singular perturbation theory. Then, for the discrete-delay case, following Canosa’s asymptotic analysis method, we give some information on travelling front solutions.