Aspects of elementary number theory illustrated in the spreadsheet environment

Number theory has in recent decades assumed a great practical importance, due primarily to its application to cryptography. This chapter discusses how elementary concepts of number theory may be illuminated and made accessible to upper secondary school students via appropriate spreadsheet models. In such environments, students can observe patterns, gain structural insight, form and test conjectures, and solve problems. The chapter begins by reviewing literature on the use of spreadsheets in general and the use of spreadsheets in number theory in particular. Two sample applications are then discussed. The first, factoring factorials, is presented and instructions are given to construct a model in Excel 2007. The second application, the RSA cryptosystem, is included because of its importance to Science, Technology, Engineering, and Mathematics (STEM) students. Number theoretic concepts relevant to RSA are discussed, and an outline of RSA. is given, with example. The chapter ends with instructions on how to construct a simple spreadsheet illustrating RSA.

JK1 (FAM134B) gene and colorectal cancer : a pilot study on the gene copy number alterations and correlations with clinicopathological parameters

AIMS The aims of the study are to characterize changes in JK-1 (FAM134B) at the DNA level in colorectal adenocarcinoma and adenoma and exploring the possible correlations with clinical and pathological features. METHOD JK-1 gene DNA copy number changes were studied in 211 colorectal carcinomas, 32 colorectal adenoma and 20 colorectal non-cancer colorectal tissue samples by real-time quantitative polymerase chain reaction. The results were correlated with clinical and pathological parameters. RESULTS Colorectal adenomas were more likely to be amplified than deleted with regard to JK-1 (FAM134B) DNA copy number change. The copy number level of JK-1 (FAM134B) DNA in colorectal adenocarcinomas was significantly lower in comparison to colorectal adenomas. Changes in JK-1 (FAM134B) DNA copy number were associated with histological subtypes, and cancer stage. Lower copy numbers were associated with higher tumor stage, lymph node stage and overall pathological stage of cancer. Conversely, higher DNA copy numbers were detected more often in the mucinous adenocarcinoma. CONCLUSIONS This is the first study showing significant correlations of the JK-1 (FAM134B) gene copy number alterations with clinical and pathological features in a large cohort of pre-invasive and invasive colorectal malignancies. The changes in DNA copy number associated with progression of colorectal malignancies reflect that JK-1 (FAM134B) gene could play a role in controlling some steps in development of the invasive phenotypes.

Particle number emissions from a large fleet of diesel and CNG buses

Exhaust emissions were monitored in real-time at the kerb of a busy busway used by a mix of diesel and CNG-powered transport buses. Particle number concentration in the size range 3 nm to 3 µm was measured with a TSI condensation particle counter (CPC 3025). Particle mass (PM2.5) was measured with a TSI Dustrak 8520. The CO2 emissions were measured with a fast response CO2 analyser (Sable CA-10A). All emission concentrations were recorded in real time at 1 sec resolution, together with the precise passage times of buses. The instantaneous ratio of particle number (or mass) to CO2 concentration, denoted Z, was used as a measure of the particle number (or mass) emission factor of each passing bus.

Nano and ultrafine particle number concentrations in different environments : application towards air quality regulations

Particle number concentrations vary significantly with environment and, in this study, we attempt to assess the significance of these differences. Towards this aim, we reviewed 85 papers that have reported particle number concentrations levels at 126 sites covering different environments. We grouped the results into eight categories according to measurement location including: road tunnel, on-road, road-side, street canyon, urban, urban background, rural, and clean background. From these reports, the overall median number concentration for each of the eight site categories was calculated. The eight location categories may be classified into four distinct groups. The mean median particle number locations for these four types were found to be statistically different from each other. Rural and clean background sites had the lowest concentrations of about 3x103 cm-3. Urban and urban background sites showed concentrations that were three times higher (9x103 cm-3). The mean concentration for the street canyon, roadside and on-road measurement sites was 4.6x104 cm-3, while the highest concentrations were observed in the road tunnels (8.6x104 cm-3). This variation is important when assessing human exposure-response for which there is very little data available, making it difficult to develop health guidelines, a basis for national regulations. Our analyses shows that the current levels in environments affected by vehicle emissions are 3 to 28 times higher than in the natural environments. At present, there is no threshold level in response to exposure to ultrafine particles. Therefore, future control and management strategies should target a decrease of these particles in urban environments by more than one order of magnitude to bring them down to the natural background. At present there is a long way to go to achieve this.

Comparison of particle number concentrations between different environments

Particle number concentrations vary significantly with environment and, in this study, we attempt to assess the significance of these differences. Towards this aim, we reviewed 85 papers that have reported particle number concentrations levels at 126 sites covering different environments. We grouped the results into eight categories according to measurement location including: road tunnel, on-road, road-side, street canyon, urban, urban background, rural, and clean background. Median values were calculated for each category. This review was restricted to papers that presented concentrations numerically. The majority of the reports were based on either CPC or SMPS measurements, with a limited number of papers reporting results from both instruments at the same site. Hence there were several overlaps between the number of CPC and SMPS measuring sites. Most of the studies reported multiple measurements at a given study site, while some studies included results from more than one site. From these reports, the overall median value for each location category was calculated...

Jump into Number

The DVD, Jump into Number, was a joint project between Independent Schools Queensland, Queensland University of Technology and Catholic Education (Diocese of Cairns) aimed at improving mathematical practice in the early years. Independent Schools Queensland Executive Director Dr John Roulston said the invaluable teaching resource features a series of unscripted lessons which demonstrate the possibilities of learning among young Indigenous students. “Currently there is a lack of teaching resources for numeracy in younger students, especially from pre Prep to Year 3 which is such an important stage of a child’s early education. Jump into Number is a benchmark for all teachers to learn more about the mathematical development of younger students,” Dr Roulston said.

Assessment and application of clustering techniques to atmospheric particle number size distribution for the purpose of source apportionment

Long-term measurements of particle number size distribution (PNSD) produce a very large number of observations and their analysis requires an efficient approach in order to produce results in the least possible time and with maximum accuracy. Clustering techniques are a family of sophisticated methods which have been recently employed to analyse PNSD data, however, very little information is available comparing the performance of different clustering techniques on PNSD data. This study aims to apply several clustering techniques (i.e. K-means, PAM, CLARA and SOM) to PNSD data, in order to identify and apply the optimum technique to PNSD data measured at 25 sites across Brisbane, Australia. A new method, based on the Generalised Additive Model (GAM) with a basis of penalised B-splines, was proposed to parameterise the PNSD data and the temporal weight of each cluster was also estimated using the GAM. In addition, each cluster was associated with its possible source based on the results of this parameterisation, together with the characteristics of each cluster. The performances of four clustering techniques were compared using the Dunn index and Silhouette width validation values and the K-means technique was found to have the highest performance, with five clusters being the optimum. Therefore, five clusters were found within the data using the K-means technique. The diurnal occurrence of each cluster was used together with other air quality parameters, temporal trends and the physical properties of each cluster, in order to attribute each cluster to its source and origin. The five clusters were attributed to three major sources and origins, including regional background particles, photochemically induced nucleated particles and vehicle generated particles. Overall, clustering was found to be an effective technique for attributing each particle size spectra to its source and the GAM was suitable to parameterise the PNSD data. These two techniques can help researchers immensely in analysing PNSD data for characterisation and source apportionment purposes.

Suppression of cluster ions during rapidly increasing particle number concentration events in the environment

We show that the cluster ion concentration (CIC) in the atmosphere is significantly suppressed during events that involve rapid increases in particle number concentration (PNC). Using a neutral cluster and air ion spectrometer, we investigated changes in CIC during three types of particle enhancement processes – new particle formation, a bushfire episode and an intense pyrotechnic display. In all three cases, the total CIC decreased with increasing PNC, with the rate of decrease being greater for negative CIC than positive. We attribute this to the greater mobility, and hence the higher attachment coefficient, of negative ions over positive ions in the air. During the pyrotechnic display, the rapid increase in PNC was sufficient to reduce the CIC of both polarities to zero. At the height of the display, the negative CIC stayed at zero for a full 10 min. Although the PNCs were not significantly different, the CIC during new particle formation did not decrease as much as during the bushfire episode and the pyrotechnic display. We suggest that the rate of increase of PNC, together with particle size, also play important roles in suppressing CIC in the atmosphere.

Amygdala-dependent learning increases the number of spinophilin-immunoreactive dendritic spines in the lateral amygdala

During Pavlovian auditory fear conditioning a previously neutral auditory stimulus (CS) gains emotional significance through pairing with a noxious unconditioned stimulus (US). These associations are believed to be formed by way of plasticity at auditory input synapses on principal neurons in the lateral nucleus of the amygdala (LA). One proposed form of cellular plasticity involves structural changes in the number and morphology of dendritic spines...

Tailoring surface properties and structure of layered double hydroxides using silanes with different number of functional groups

Four silanes, trimethylchlorosilane (TMCS), dimethyldiethoxylsilane (DMDES), 3-aminopropyltriethoxysilane (APTES) and tetraethoxysilane (TEOS), were adopted to graft layered double hydroxides (LDH) via an induced hydrolysis silylation method (IHS). Fourier transform infrared spectra (FTIR) and 29Si MAS nuclear magnetic resonance spectra (29Si MAS NMR) indicated that APTES and TEOS can be grafted onto LDH surfaces via condensation with hydroxyl groups of LDH, while TMCS and DMDES could only be adsorbed on the LDH surface with a small quantity. A combination of X-ray diffraction patterns (XRD) and 29Si MAS NMR spectra showed that silanes were exclusively present in the external surface and had little influence on the long range order of LDH. The surfactant intercalation experiment indicated that the adsorbed and/or grafted silane could not fix the interlamellar spacing of the LDH. However, they will form crosslink between the particles and affect the further surfactant intercalation in the silylated samples. The replacement of water by ethanol in the tactoids and/or aggregations and the polysiloxane oligomers formed during silylation procedure can dramatically increase the value of BET surface area (SBET) and total pore volumes (Vp) of the products.

Impact of particle formation on atmospheric ions and particle number concentrations in an urban environment

A measurement campaign was conducted from 3 to 19 December 2012 at an urban site of Brisbane, Australia. Size distribution of ions and particle number concentrations were measured to investigate the influence of particle formation and biomass burning on atmospheric ion and particle concentrations. Overall ion and particle number concentrations during the measurement period were found to be (-1.2 x 103 cm-3 | +1.6 x 103 cm-3) and 4.4 x 103, respectively. The results of correlation analysis between concentrations of ions and nitrogen oxides indicated that positive and negative ions originated from similar sources, and that vehicle exhaust emissions had a more significant influence on intermediate/large ions, while cluster ions rapidly attached to larger particles once emitted into the atmosphere. Diurnal variations in ion concentration suggested the enrichment of intermediate and large ions on new particle formation event days, indicating that they were involved in the particle formation processes. Elevated total ions, particularly larger ions, and particle number concentrations were found during biomass burning episodes. This could be due to the attachment of cluster ions onto accumulation mode particles or production of charged particles from biomass burning, which were in turn transported to the measurement site. The results of this work enhance scientific understanding of the sources of atmospheric ions in an urban environment, as well as their interactions with particles during particle formation processes.