Seeing an exercise as a single mathematical object: using variation to structure sense-making

In this theoretical paper we take an exercise to be a collection of procedural questions or tasks. It can be useful to treat such an exercise as a single object, with individual questions seen as elements in a mathematically and pedagogically structured set. We use the notions of 'dimensions of possible variation' and 'range of permissible change', derived from Ference Marton, to discuss affordances and constraints of some sample exercises. This gives insight into the potential pedagogical role of exercises, and shows how exercise analysis and design might contribute to hypotheses about learning trajectories. We argue that learners' response to an exercise has something in common with modeling that we might call 'micro-modeling', but we resort to a more inclusive description of mathematical thinking to describe learners' possible responses to a well-planned exercise. Finally we indicate how dimensions of possible variation inform the design and use of an exercise

RGS2 expression predicts amyloid-β sensitivity, MCI and Alzheimer's disease: genome-wide transcriptomic profiling and bioinformatics data mining

Alzheimer's disease (AD) is the most frequent cause of dementia. Misfolded protein pathological hallmarks of AD are brain deposits of amyloid-β (Aβ) plaques and phosphorylated tau neurofibrillary tangles. However, doubts about the role of Aβ in AD pathology have been raised as Aβ is a common component of extracellular brain deposits found, also by in vivo imaging, in non-demented aged individuals. It has been suggested that some individuals are more prone to Aβ neurotoxicity and hence more likely to develop AD when aging brains start accumulating Aβ plaques. Here, we applied genome-wide transcriptomic profiling of lymphoblastoid cells lines (LCLs) from healthy individuals and AD patients for identifying genes that predict sensitivity to Aβ. Real-time PCR validation identified 3.78-fold lower expression of RGS2 (regulator of G-protein signaling 2; P=0.0085) in LCLs from healthy individuals exhibiting high vs low Aβ sensitivity. Furthermore, RGS2 showed 3.3-fold lower expression (P=0.0008) in AD LCLs compared with controls. Notably, RGS2 expression in AD LCLs correlated with the patients' cognitive function. Lower RGS2 expression levels were also discovered in published expression data sets from postmortem AD brain tissues as well as in mild cognitive impairment and AD blood samples compared with controls. In conclusion, Aβ sensitivity phenotyping followed by transcriptomic profiling and published patient data mining identified reduced peripheral and brain expression levels of RGS2, a key regulator of G-protein-coupled receptor signaling and neuronal plasticity. RGS2 is suggested as a novel AD biomarker (alongside other genes) toward early AD detection and future disease modifying therapeutics

Deception in context: coding nonverbal cues, situational variables and risk of detection

There are many situations in which deception may arise and understanding the behaviors associated with it are compounded by various contexts in which it may occur. This paper sets out a coding protocol for identifying cues to deception and reports on three studies, in which deception was studied in different contexts. The contexts involved manipulating risks (i.e., probability) of being detected and reconnaissance, both of which are related to terrorist activities. Two of the studies examined the impact of changing the risks of deception detection, whilst the third investigated increased cognitive demand of duplex deception tasks including reconnaissance and deception. In all three studies, cues to deception were analyzed in relation to observable body movements and subjective impressions given by participants. In general, the results indicate a pattern of hand movement reduction by deceivers, and suggest the notion that raising the risk of detection influences deceivers? behaviors. Participants in the higher risk condition displayed increased negative affect (found in deceivers) and tension (found in both deceivers and truth-tellers) than those in lower risk conditions

Human neural stem cells enhance structural plasticity and axonal transport in the ischaemic brain

Stem cell transplantation promises new hope for the treatment of stroke although significant questions remain about how the grafted cells elicit their effects. One hypothesis is that transplanted stem cells enhance endogenous repair mechanisms activated after cerebral ischaemia. Recognizing that bilateral reorganization of surviving circuits is associated with recovery after stroke, we investigated the ability of transplanted human neural progenitor cells to enhance this structural plasticity. Our results show the first evidence that human neural progenitor cell treatment can significantly increase dendritic plasticity in both the ipsi- and contralesional cortex and this coincides with stem cell-induced functional recovery. Moreover, stem cell-grafted rats demonstrated increased corticocortical, corticostriatal, corticothalamic and corticospinal axonal rewiring from the contralesional side; with the transcallosal and corticospinal axonal sprouting correlating with functional recovery. Furthermore, we demonstrate that axonal transport, which is critical for both proper axonal function and axonal sprouting, is inhibited by stroke and that this is rescued by the stem cell treatment, thus identifying another novel potential mechanism of action of transplanted cells. Finally, we established in vitro co-culture assays in which these stem cells mimicked the effects observed in vivo. Through immunodepletion studies, we identified vascular endothelial growth factor, thrombospondins 1 and 2, and slit as mediators partially responsible for stem cell-induced effects on dendritic sprouting, axonal plasticity and axonal transport in vitro. Thus, we postulate that human neural progenitor cells aid recovery after stroke through secretion of factors that enhance brain repair and plasticity

Who's been framed? Framing effects are reduced in financial gambles made for others

Background: Decisions made on behalf of other people are sometimes more rational than those made for oneself. In this study we used a monetary gambling task to ask if the framing effect in decision-making is reduced in surrogate decision-making. Methods: Participants made a series of choices between a predetermined sure option and a risky gambling option of winning a proportion of an initial stake. Trials were presented as either a gain or a loss relative to that initial stake. In half of the trials participants made choices to earn money for themselves and in the other half they earned money for another participant. Framing effects were measured as risk seeking in loss frames and risk aversion in gain frames. Results: Significant framing effects were observed both in trials in which participants earned money for themselves and those in which they earned money for another person; however, these framing effects were significantly reduced when making decisions for another person. It appears that the reduced emotional involvement when the decision-maker is not affected by the outcome of the decision thus lessens the framing effect without eradicating it altogether. Conclusions: This suggests that the deviation from rational choices in decision-making can be significantly reduced when the emotional impact on the decision maker is lessened. These results are discussed in relation to Somatic Distortion Theory

Endoscopic sinus surgery for maxillary sinus mucoceles

BACKGROUND: Maxillary sinus mucoceles are relatively rare among all paranasal sinus mucoceles. With the introduction of endoscopic sinus surgical techniques, rhinologic surgeons prefer transnasal endoscopic management of sinus mucoceles. The aim of this study is to describe the clinical presentation of maxillary sinus mucoceles and to establish the efficacy of endoscopic management of sinus mucoceles. METHODS: Between 2003 and 2005, 14 patients underwent endoscopic sinus surgery for maxillary sinus mucocele. The presenting sign and symptoms, radiological findings, surgical management and need for revision surgery were reviewed. RESULTS: There were eight males and six females with an age range of 14 to 65. Ten patients complained of nasal obstruction, five of nasal drainage, five of cheek pressure or pain and one of proptosis of the eye and cheek swelling. The maxillary sinus and ipsilateral ethmoid sinus involvement on computed tomographic studies was seen in 4 patients. Four patients had history of endoscopic ethmoidectomy surgery for ethmoid sinusitis and one had Caldwell-Luc operation in the past. Ethmoidectomy with middle meatal antrostomy and marsupialization of the mucocele was performed in all patients. Postoperative follow-up ranged between 8 to 48 months. All patients had a patent middle meatal antrostomy and healthy maxillary sinus mucosa. No patients need revision surgery. CONCLUSION: The most common causes of mucoceles are chronic infection, allergic sinonasal disease, trauma and previous surgery. In 64% of the patients of our study cause remains uncertain. Endoscopic sinus surgery is an effective treatment for maxillary sinus mucoceles with a favorable long-term outcome

Self-force: Computational Strategies

Building on substantial foundational progress in understanding the effect of a small body's self-field on its own motion, the past 15 years has seen the emergence of several strategies for explicitly computing self-field corrections to the equations of motion of a small, point-like charge. These approaches broadly fall into three categories: (i) mode-sum regularization, (ii) effective source approaches and (iii) worldline convolution methods. This paper reviews the various approaches and gives details of how each one is implemented in practice, highlighting some of the key features in each case.Comment: Synchronized with final published version. Review to appear in "Equations of Motion in Relativistic Gravity", published as part of the Springer "Fundamental Theories of Physics" series. D. Puetzfeld et al. (eds.), Equations of Motion in Relativistic Gravity, Fundamental Theories of Physics 179, Springer, 201