Teacher preparation for a problem-solving curriculum in Singapore

Problem solving is at the heart of the Singapore Mathematics curriculum. However, it remains a challenge for teachers to realise this curricular goal in practice. Here, we review the efforts of Singapore mathematics teacher educators in incorporating problem-solving (teaching) competency in teacher education and PD programmes. We discuss conceptual and practical issues, actions taken and changes made in building teachers?? capacity to enact a problem-solving curriculum in a school-based design experiment project. In the project, teachers learnt problem solving, observed and then carried out lessons, using the ??Mathematics Practical????akin to the science practical??as key to instruction and assessment.     

Discrete particle swarm optimization for the team orienteering problem

Orienteering problem is a well researched routing problem which is a generalization of the traveling salesman problem. Team orienteering problem (TOP) is the extended version of the orienteering problem with more than one member in the team. In this paper the first known discrete particle swarm optimization (DPSO) algorithm has been developed for 2, 3 and 4-member TOP. In the DPSO meta-heuristic novel methods have been introduced for the initial particle generation process. Reduced variable neighborhood search and 2-opt were applied as the local search tools. The efficacy of the algorithm was tested using seven commonly used benchmark problem sets ranging in size from 21 to 102 nodes. The results of the DPSO algorithm were compared against seven other heuristic algorithms that have been developed for TOP. It was concluded that the developed DPSO algorithm for the TOP is competitive and robust across the benchmark problem sets.     

Dark matter results from 100 live days of XENON100 data

We present results from the direct search for dark matter with the XENON100 detector, installed underground at the Laboratori Nazionali del Gran Sasso of INFN, Italy. XENON100 is a two-phase time-projection chamber with a 62 kg liquid xenon target. Interaction vertex reconstruction in three dimensions with millimeter precision allows the selection of only the innermost 48 kg as the ultralow background fiducial target. In 100.9 live days of data, acquired between January and June 2010, no evidence for dark matter is found. Three candidate events were observed in the signal region with an expected background of (1.8 ± 0.6) events. This leads to the most stringent limit on dark matter interactions today, excluding spin-independent elastic weakly interacting massive particle (WIMP) nucleon scattering cross sections above 7.0 × 10(-45) cm(2) for a WIMP mass of 50 GeV/c(2) at 90% confidence level.     

Monte Carlo simulation and theory of proton NMR transverse relaxation induced by aggregation of magnetic particles used as MRI contrast agents

Superparamagnetic particles are widely used in MRI as R2 contrast agents. In this last decade, different studies have focused on aggregation of superparamagnetic particles for important applications such as multimodal agents. A complete study--via simulations--of the influence of aggregation on the MR efficiency of these particles at high magnetic field is presented here. First, an empirical expression is proposed for R2 in the presence of uniformly distributed nanoparticles, taking into account two regimes at once (motional averaging and slow motion regimes). Three cluster shapes are simulated: Sphere, shell and line. An analytical model is proposed to understand water transverse relaxation induced by spherical and shell aggregates. Simulations lead to the conclusion that, in the motional averaging regime, the most efficient aggregate contrast agent is the densest sphere or shell.     

Molecular histology analysis by matrix-assisted laser desorption/ionization imaging mass spectrometry using gold nanoparticles as matrix

Gold nanoparticles (AuNPs) were applied and optimized as matrix for matrix-assisted laser desorption/ionization mass spectrometry analysis of animal tissues, and enabled histological analysis of animal tissues at molecular level by imaging mass spectrometry (IMS). AuNPs were coated on animal tissue in a solvent-free manner via argon ion sputtering. Metabolites, including neurotransmitters, fatty acids and nucleobases, were directly detected from mouse brain tissue. Based on region-specific chemical profiles, fine histological features of mouse brain tissue and heterogeneous regions of tumor tissue were both revealed.     

Octaarginine-modified chitosan as a nonviral gene delivery vector: properties and in vitro transfection efficiency

Protein transduction domains (PTD) have been identified to have the capacity to facilitate molecular cargo to translocate through cell membrane. This study aims to utilize the cell membrane penetrating ability of octaarginine oligopeptide, a simplified prototype of the PTD, to enhance the transfection efficiency of chitosan. Octaarginine-modified chitosan (R₈-CS) was synthesized as a gene transfer carrier by carbodiimide chemistry. The structure and composition of R₈-CSs were characterized using FTIR and ¹H NMR. Agarose gel electrophoresis assay showed that R₈-CS could efficiently condense the DNA. The particle size of R₈-CS/DNA complexes were determined to be around 100–200 nm. The nanoparticle complexes exhibited a spherical and compact morphology. R₈-CS demonstrated higher transfection activity and lower cytotoxicity as compared to the unmodified chitosan and also showed good serum resistance.     

Bidirectional passively mode-locked soliton fiber laser with a four-port circulator

We present an all-fiber bidirectional passively mode-locked soliton laser with what we believe is a novel cavity configuration. Using a four-port circulator, we incorporate two different semiconductor saturable absorber mirrors (SESAMs) into the laser cavity, which enables bidirectional mode locking. The laser allows the generation of two independent countercirculating mode-locked pulse trains, each with an individual fundamental repetition rate that can be adjusted by varying the SESAM pigtail length. Two countercirculating pulse trains with repetition rates of 21.3 and 15.2 MHz are obtained simultaneously. By controlling the intracavity loss imposed on these two pulse trains, either one of the two pulse trains can be switched on or off. The bidirectional operation with other repetition rates is also demonstrated.     

A Model for Evaluation of Transport Policies in Multimodal Networks with Road and Parking Capacity Constraints

This paper presents a model for evaluation of transport policies in multimodal networks with road and parking capacity constraints. The proposed model simultaneously considers choices of travelers on route, parking location and mode between auto and transit. In the proposed model, it is assumed that auto drivers make a simultaneous route and parking location choice in a user equilibrium manner, and the modal split between auto and transit follows a multinomial logit formulation. A mathematical programming model with capacity constraints on road link and parking facilities is proposed that generates optimality conditions equivalent to the requirements for multimodal network equilibrium. An augmented Lagrangian dual algorithm embedded by partial linearization approach is developed to solve the proposed model. Numerical results on two example networks are presented to illustrate the proposed methodology. The results show that the service level of transit, parking charges, road link and parking capacities, and addition of a new parking location may bring significant impacts on travelers’ behavior and network performance. In addition, transport policies may result in paradoxical phenomenon.