Learning about multiplication by comparing algorithms: “One times one,but actually they are ten times ten”

Multiplication algorithms in primary school are still frequently introduced with little attention to meaning. We present a case study focusing on a third grade class that engaged in comparing two algorithms and discussing “why they both work”. The objectives of the didactical intervention were to foster students' development of mathematical meanings concerning multiplication algorithms, and their development of an attitude to judge and compare the value and efficiency of different algorithms. Underlying hypotheses were that it is possible to promote the simultaneous unfolding of the semiotic potential of two algorithms, considered as cultural artifacts, with respect to the objectives of the didactical intervention, and to establish a fruitful synergy between the two algorithms. As results, this study sheds light onto the new theoretical construct of “bridging sign”, illuminating students’ meaning-making processes involving more than one artifact; and it provides important insight into the actual unfolding of the hypothesized potential of the algorithms.     

Consequences of the formation of 3,4-dimethyl-5-phenyl-1,3-oxazolidine on the analysis of ephedrines in urine by gas chromatography and a new method for confirmation as N-trifluoroacetyl-O-t-butyldimethylsilyl ether derivatives

The compound 3,4-dimethyl-5-phenyl-1,3-oxazolidine can appear as an artifact during the gas chromatographic analysis of ephedrines. Its presence is a risk for doping control and forensic analyses. An evaluation about the consequences of its formation showed the possibility of a false positive for ephedrine, a false negative for pseudophedrine and increased uncertainty in the quantitative approach. Misinterpretations can be avoided with the observation of fragments m/z 56 and 71 in the ephedrine mass spectrum during GC-MS analysis and also by the formation of N-TFA-O-TBDMS derivatives prior to GC analysis. These N-TFA-O-TBDMS derivatives lead to an increase in the number and mass of diagnostic ions, meet the identification criteria, and provide an improvement in chromatographic resolution, allowing the separation of the ephedrines.     

Efficient sign based normalized adaptive filtering techniques for cancelation of artifacts in ECG signals: Application to wireless biotelemetry

In this paper, several simple and efficient sign based normalized adaptive filters, which are computationally superior having multiplier free weight update loops are used for cancelation of noise in electrocardiographic (ECG) signals. The proposed implementation is suitable for applications such as biotelemetry, where large signal to noise ratios with less computational complexity are required. These schemes mostly employ simple addition, shift operations and achieve considerable speed up over the other least mean square (LMS) based realizations. Simulation studies shows that the proposed realization gives better performance compared to existing realizations in terms of signal to noise ratio and computational complexity.     

Production of artifact methylmercury during the analysis of certified reference sediments: use of ionic exchange in the sample treatment step to minimise the problem

Production of artifact methylmercury (MeHg⁺) during the analysis of two certified reference sediments, CRM-580 and IAEA-405, was investigated. Leaching of the analyte from the solid sample was achieved by ultrasound assisted acidic extraction. The aqueous leachate was either ethylated (NaBEt₄) or phenylated (NaBPh₄) using acetic/acetate or citric/citrate to buffer the solution. Preconcentration of the volatile compounds was carried out by extraction with an organic solvent (n-hexane) or solid phase microextraction (SPME). MeHg⁺ was finally separated and detected by gas chromatography with atomic emission or mass spectrometry detection (GC-MIP-AED or GC-MS). In all the cases the concentrations obtained for MeHg⁺ in the CRM-580 were significantly higher than the certified value. For the IAEA-405, however, the MeHg⁺ concentration found was always statistically indistinguishable from the certified value. Experiments were also conducted with synthetic samples, such as aqueous mixtures of MeHg⁺ and inorganic mercury (Hg²⁺) or silica-gel spiked with both compounds. The methylation rates found (defined as the percentage of Hg²⁺ present in the sample which methylates to give artifact MeHg⁺) ranged from not observable (in certain synthetic aqueous mixtures) to 0.57% (analysis of CRM-580 under certain conditions). As the amount of Hg²⁺ available in the sample seems to be the main factor controlling the magnitude of the artifact, several experiments were conducted using an ionic exchange resin (Dowex M-41) in order to minimise the concentration of this chemical in the reaction medium. First, a hydrochloric leachate of the sample was passed through a microcolumn packed with the exchanger. Second, the resin was mixed with the sample prior to extraction with HCl. In both cases, the predominant Hg²⁺ species, HgCl₄²⁻, was adsorbed on the resin, whereas MeHg⁺, mainly as MeHgCl, remained in solution. Following the second option, a new method to analyse MeHg⁺ in conflictive matrices like certain sediments was proposed. This approach produced better results for the CRM-580, but a MeHg⁺ concentration slightly, but statistically significant, higher than the reference value was still obtained.     

Correction strategy for diffusion-weighted images corrupted with motion: application to the DTI evaluation of infants' white matter

Objective

Diffusion imaging techniques such as DTI and HARDI are difficult to implement in infants because of their sensitivity to subject motion. A short acquisition time is generally preferred, at the expense of spatial resolution and signal-to-noise ratio. Before estimating the local diffusion model, most pre-processing techniques only register diffusion-weighted volumes, without correcting for intra-slice artifacts due to motion or technical problems. Here, we propose a fully automated strategy, which takes advantage of a high orientation number and is based on spherical-harmonics decomposition of the diffusion signal.

Material and methods

The correction strategy is based on two successive steps: 1) automated detection and resampling of corrupted slices; 2) correction for eddy current distortions and realignment of misregistered volumes. It was tested on DTI data from adults and non-sedated healthy infants.

Results

The methodology was validated through simulated motions applied to an uncorrupted dataset and through comparisons with an unmoved reference. Second, we showed that the correction applied to an infant group enabled to improve DTI maps and to increase the reliability of DTI quantification in the immature cortico-spinal tract.

Conclusion

This automated strategy performed reliably on DTI datasets and can be applied to spherical single- and multiple-shell diffusion imaging.     

Cascaded z-filters for efficient single-scan suppression of zero-quantum coherence

A simple and robust method to suppress zero-quantum coherence (ZQC) in NMR experiments, in a single scan and with very high suppression ratio, is described. It is an appreciable improvement on a previous technique by Thrippleton and Keeler [Angew. Chem. Int. Ed. 42 (2003) 3938]. The method, called a z-filter cascade, preserves longitudinal, or z-magnetization, with high efficiency. Losses depend mostly on T1 relaxation but not T2 relaxation mechanisms. At the same time, suppression of ZQC can be essentially complete in a single scan. The time duration of the z-filter cascade scales inversely to representative chemical shift differences between the coupled spins, and is typically a few tens of milliseconds. The high efficiency of the zero-quantum suppression and excellent retention of the desired z-magnetization, in a single scan without resort to phase cycling or difference spectroscopy, makes the z-filter cascade a useful new pulse sequence building block for a whole range of NMR experiments. In cases where unwanted residual ZQC may have previously contributed to baseline " t1-noise" in two-dimensional NMR spectra, the z-filter cascade can deliver a noteworthy improvement in spectral quality.     

Synthesis of topsentolides A2 and C2, and non-enzymatic conversion of the former to the latter

The first total synthesis of the marine-derived cytotoxin topsentolide A₂, which eventually culminated in its stereochemical determination, was accomplished in 17 steps from a known chiral alcohol. An improved synthesis of its congener, topsentolide C₂, from a synthetic intermediate of topsentolide A₂ was also performed by utilizing the Yamaguchi lactonization to construct its nine-membered lactone ring. Treatment of epoxide ring-containing topsentolide A₂ with HCl/MeOH brought about its quantitative conversion into topsentolide C₂.     

Employing spatially constrained ICA and wavelet denoising, for automatic removal of artifacts from multichannel EEG data

Detecting artifacts produced in electroencephalographic (EEG) data by muscle activity, eye blinks and electrical noise, etc., is an important problem in EEG signal processing research. These artifacts must be corrected before further analysis because it renders subsequent analysis very error-prone. One solution is to reject the data segment if artifact is present during the observation interval, however, the rejected data segment could contain important information masked by the artifact. The independent component analysis (ICA) can be an effective and applicable method for EEG denoising. The goal of this paper is to propose a framework, based on ICA and wavelet denoising (WD), to improve the pre-processing of EEG signals. In particular we employ concept of the spatially constrained ICA (SCICA) to extract artifact-only independent components (ICs) from the given EEG data, use WD to remove any cerebral activity from the extracted-artifacts ICs, and finally project back the artifacts to be subtracted from EEG signals to get clean EEG data. The main advantage of the proposed approach is faster computation, as it is not necessary to identify all ICs. Computer experiments are carried out, which demonstrate effectiveness of the proposed approach in removing focal artifacts that can be well separated by SCICA.     

Mode dependent loop filter for intra prediction coding in H.264/AVC

In this paper, a high performance and low complexity loop filter is proposed for intra prediction coding. Although the deblocking loop filter (DLF) has achieved outstanding performance on suppressing quantization noise, it also induces details information loss because of the smoothing operation. To achieve better restoration performance, we propose a filter set named mode dependent loop filter (MDLF) which adaptively select the filter coefficients according to various local characteristics. In the homogeneous areas, the task of the filter emphasizes on smoothing the noise. In the heterogeneous areas, the proposed filter concentrates on preserving the details. Based on the spatial correlation assumption and statistical analysis, the intra mode combination is used to classify the training samples with different local characteristics. Then the classical least mean square error framework is employed to solve the coefficients for the proposed filter set. In this way, a more efficient adaptive loop filter scheme can be achieved for specific intra mode combination. Experiment results show that the proposed loop filter achieves superior coding gains compared to the H.264/AVC High Profile. Furthermore, relative to QALF+DLF, a comparable performance also can be achieved by the proposed MDLF with far less complexity increase.