Teaching square roots: conceptual complexity in mathematics language

The article presents strategies for communicating the concept of square roots to limited English-proficient students. Instead of using mathematical terminology, mathematics teachers could communicate the concept of square roots by integrating the literal concept of square to the actual meaning of a square root. Such approach addresses the learning difficulty experienced by limited English proficient students who tend to associate square roots to geometric concepts. Several strategies for illustrating the concept of a square root using square figures are presented.

A soil-free plant growth system to facilitate analysis of plant pathogen interactions in roots

Analysis of the interaction of pathogens with plant roots is often complicated by the growth of plants in a soil substrate. A soil-free plant growth system (SPS) was developed that removes the need for a substrate while supporting the growth of seedlings in a nutrient rich, oxygenated environment. The model legume Lupinus angustifolius was used to compare the growth of seedlings within soil and the SPS. Seedlings grown under both conditions were similar in morphology, anatomy and health (measured by leaf chlorophyll abundance) and importantly there was little difference in root growth and development although straighter and fuller root systems were achieved in the SPS. The ease of access to the root system proved efficient for the analysis of root and pathogen interactions with no interference from soil or adhering particulate matter. Following inoculation of L. angustifolius roots with Phytophthora cinnamomi the host/pathogen interaction was easily observed and tissues sampled undamaged.

Heterotrimeric G protein γ subunits provide functional selectivity in Gβγ dimer signaling in arabidopsis

The Arabidopsis thaliana heterotrimeric G protein complex is encoded by single canonical Galpha and Gbeta subunit genes and two Ggamma subunit genes (AGG1 and AGG2), raising the possibility that the two potential G protein complexes mediate different cellular processes. Mutants with reduced expression of one or both Ggamma genes revealed specialized roles for each Ggamma subunit. AGG1-deficient mutants, but not AGG2-deficient mutants, showed impaired resistance against necrotrophic pathogens, reduced induction of the plant defensin gene PDF1.2, and decreased sensitivity to methyl jasmonate. By contrast, both AGG1- and AGG2-deficient mutants were hypersensitive to auxin-mediated induction of lateral roots, suggesting that Gbetagamma1 and Gbetagamma2 synergistically inhibit auxin-dependent lateral root initiation. However, the involvement of each Ggamma subunit in this root response differs, with Gbetagamma1 acting within the central cylinder, attenuating acropetally transported auxin signaling, while Gbetagamma2 affects the action of basipetal auxin and graviresponsiveness within the epidermis and/or cortex. This selectivity also operates in the hypocotyl. Selectivity in Gbetagamma signaling was also found in other known AGB1-mediated pathways. agg1 mutants were hypersensitive to glucose and the osmotic agent mannitol during seed germination, while agg2 mutants were only affected by glucose. We show that both Ggamma subunits form functional Gbetagamma dimers and that each provides functional selectivity to the plant heterotrimeric G proteins, revealing a mechanism underlying the complexity of G protein-mediated signaling in plants.

Why do Australians, New Zealanders and Americans travel to Fiji? Evidence from cointegration, unit roots and parameter stability tests

The aim of this study was to estimate the demand for Fiji’s tourism from its three main source markets—Australia, New Zealand, and the US—using the bounds testing approach to cointegration. Our main finding was that visitor arrivals to Fiji and its key determinants are cointegrated over the 1970–2000 period. We then used the autoregressive distributed lag model to estimate short-run and long-run elasticities and found that income in origin countries, transport costs, and prices were significant determinants of Fiji’s tourism demand. We also found that coups negatively impact visitor arrivals from all markets. In testing for parameter stability, we established that the series were integrated of order one in the presence of a structural break. We then used the Hansen test for parameter stability and found that the parameters of our long-run model are stable over time.

Structural breaks and unit roots in Australian macroeconomic time series

We examine the unit root properties of 16 Australian macroeconomic time series using monthly data spanning the period 1960–2004. In addition to the standard Augmented Dickey Fuller (ADF) test, we implement one- and two-break endogenous structural break ADF-type unit root tests as well as one- and two-break Lagrange multiplier (LM) unit root tests. While the ADF test provides relatively little evidence against the unit root null hypothesis, once we allow for structural breaks we are able to reject the unit root null for just under half of the variables at the 10% level or better.

Cerebral cortex : an MRI-based study of volume and variance with age and sex

The aim of the present study was to examine quantitative differences in lobar cerebral cortical volumes in a healthy adult population. Quantitative volumetric MRI of whole brain, cerebral and cerebellar volumes was performed in a cross-sectional analysis of 97 normal volunteers, with segmented frontal, temporal, parietal and occipital cortical volumes measured in a subgroup of 60 subjects, 30 male and 30 female, matched for age and sex. The right cerebral hemisphere was larger than the left across the study group with a small (<1%) but significant difference in symmetry (P < 0.001). No difference was found between volumes of right and left cerebellar hemispheres. Rightward cerebral cortical asymmetry (right larger than left) was found to be significant across all lobes except parietal. Males had greater cerebral, cerebellar and cerebral cortical lobar volumes than females. Larger male cerebral cortical volumes were seen in all lobes except for left parietal. Females had greater left parietal to left cerebral hemisphere and smaller left temporal to left cerebral hemisphere ratios. There was a mild reduction in cerebral volumes with age, more marked in males. This study confirms and augments past work indicating underlying structural asymmetries in the human brain, and provides further evidence that brain structures in humans are differentially sensitive to the effects of both age and sex.

Profiling secondary metabolites of plant roots inoculated with Phytophthora cinnamomi

The soil-borne pathogen, Phytophthora cinnamomi, continues to cause severe dieback in Australian native forest species and is of great international significance due to its global distribution. This research established a protocol to successfully identify phyto-chemicals associated with the defense response of plants challenged by the disease caused by Phytophthora cinnamomi.

Excitability at the motoneuron pool and motor cortex is specifically modulated in lengthening compared to isometric contractions

Excitability at the motoneuron pool and motor cortex is specifically modulated in lengthening compared to isometric contractions. J Neurophysiol 101: 2030–2040, 2009. First published January 28, 2008; doi:10.1152/jn.91104.2008. Neural control of muscle contraction seems to be unique during muscle lengthening. The present study aimed to determine the specific sites of modulatory control for lengthening compared with isometric contractions. We used stimulation of the motor cortex and corticospinal tract to observe changes at the spinal and cortical levels. Motor-evoked potentials (MEPs) and cervicomedullary MEPs (CMEPs) were evoked in biceps brachii and brachioradialis during maximal and submaximal lengthening and isometric contractions at the same elbow angle. Sizes of CMEPs and MEPs were lower in lengthening contractions for both muscles (by 28 and 16%, respectively; P 0.01), but MEP-to-CMEP ratios increased (by 21%; P 0.05). These results indicate reduced excitability at the spinal level but enhanced motor cortical excitability for lengthening compared with isometric muscle contractions.

Differential involvement of rat medial prefrontal cortex dopamine receptors in modulation of hypothalamic- pituitary-adrenal axis responses to different stressors

Recent investigations have implicated the medial prefrontal cortex (mPFC) in modulation of subcortical pathways that contribute to the generation of behavioural, autonomic and endocrine responses to stress. However, little is known of the mechanisms involved. One of the key neurotransmitters involved in mPFC function is dopamine, and we therefore aimed, in this investigation, to examine the role of mPFC dopamine in response to stress in Wistar rats. In this regard, we infused dopamine antagonists SCH23390 or sulpiride into the mPFC via retrodialysis. We then examined changes in numbers of cells expressing the c-fos immediate-early gene protein product, Fos, in subcortical neuronal populations associated with regulation of hypothalamic-pituitary-adrenal (HPA) axis stress responses in response to either of two stressors; systemic injection of interleukin-1β, or air puff. The D1 antagonist, SCH23390, and the D2 antagonist, sulpiride, both attenuated expression of Fos in the medial parvocellular hypothalamic paraventricular nucleus (mpPVN) corticotropin-releasing factor cells at the apex of the HPA axis, as well as in most extra-hypothalamic brain regions examined in response to interleukin-1β. By contrast, SCH23390 failed to affect Fos expression in response to air puff in any brain region examined, while sulpiride resulted in an attenuation of the air puff-induced response in only the mpPVN and the bed nucleus of the stria terminalis. These results indicate that the mPFC differentially processes the response to different stressors and that the two types of dopamine receptor may have different roles.