Visualization and reification of concepts in advanced mathematical thinking

A concept image is that collection of all images, pictures, symbols, definitions and properties associated with any given mathematical concept. One of the most important components in the mental representation of concepts in the concept image of advanced mathematical thinkers is visualization. This component, in turn, is indispensable in the intuition process which is essential to advanced mathematical thought. The visual aspect of intuitive reasoning in mathematics falls into three main categories - diagrammatic reasoning, which is predominantly though not exclusively graphical, analogic reasoning, relying heavily on non-mathematical experiences as models for abstract mathematical concepts, and the use of prototypes, the selection of one typical example as a representative of the concept. This study was designed to examine and describe the nature of visual images used by advanced mathematical thinkers, as prototypical, analogic or diagrammatic images. We also sought to identify hooks, which provide initial access to the concept image, we looked for links among them, and for image schemas, which provide the mental 'scaffolding' for the concept image. We sought evidence of progress in the construction process of concept images by looking for the interiorization and condensation stages, during which time the concept is internalized and all related information is condensed into a gestalt, and in particular, the reification stage, an event which produces a radical restructuring of the concept image. Nine case studies are presented and analyzed, in which advanced mathematics undergraduates, mathematics graduate students, and mathematics faculty were extensively interviewed, and their responses audiotaped and transcribed. The interviews were reflective in nature, comprised of a series of questions, which were asked regarding twenty-one different mathematical concepts. A detailed analysis of each individual, in light of the above questions, is presented, summarizing the individual nature of the concept image in advanced mathematical thought

Vasodilator factors in the systemic and local adaptations to pregnancy

We postulate that an orchestrated network composed of various vasodilatory systems participates in the systemic and local hemodynamic adaptations in pregnancy. The temporal patterns of increase in the circulating and urinary levels of five vasodilator factors/systems, prostacyclin, nitric oxide, kallikrein, angiotensin-(1–7) and VEGF, in normal pregnant women and animals, as well as the changes observed in preeclamptic pregnancies support their functional role in maintaining normotension by opposing the vasoconstrictor systems. In addition, the expression of these vasodilators in the different trophoblastic subtypes in various species supports their role in the transformation of the uterine arteries. Moreover, their expression in the fetal endothelium and in the syncytiotrophoblast in humans, rats and guinea-pigs, favour their participation in maintaining the uteroplacental circulation. The findings that sustain the functional associations of the various vasodilators, and their participation by endocrine, paracrine and autocrine regulation of the systemic and local vasoactive changes of pregnancy are abundant and compelling. However, further elucidation of the role of the various players is hampered by methodological problems. Among these difficulties is the complexity of the interactions between the different factors, the likelihood that experimental alterations induced in one system may be compensated by the other players of the network, and the possibility that data obtained by manipulating single factors in vitro or in animal studies may be difficult to translate to the human. In addition, the impossibility of sampling the uteroplacental interface along normal pregnancy precludes obtaining longitudinal profiles of the various players. Nevertheless, the possibility of improving maternal blood pressure regulation, trophoblast invasion and uteroplacental flow by enhancing vasodilation (e.g. L-arginine, NO donors, VEGF transfection) deserves unravelling the intricate association of vasoactive factors and the systemic and local adaptations to pregnancy

Decision support system for Potato cyst nematode management

Potato cyst nematodes (PCN) are in the Northern Netherlands and the Weser-Ems Region in Germany a major issue for farmers. The yearly average damage by PCN is about 100 Euros/hectare for farmers. Infestations of potato cyst nematodes can be controlled in a sustainable way by proper potato variety selection. Potato varieties vary in the degree of tolerance and resistance to PCN. However, this knowledge is used by only a small fraction of the farmers. The AGROBIOKON project, which is funded by the INTERREG EDR-region, the Landwirtschaftskammer Niedersachsen and the Dutch farmers association, have developed a decision support system for potato variety selection based upon population dynamic models for PCN: OPTIRas. The scientific principles and the model behind the decision support system will be presented. The model will be applied to PCN field experiments in the Weser-Ems region. Experience of using this decision support system in farmer study groups in the Netherlands and Germany will be shared

VEGF, a prosurvival factor, acts in concert with TGF-β1 to induce endothelial cell apoptosis

VEGF and TGF-β1 are potent angiogenesis inducers with opposing effects on endothelial cells. TGF-β1 induces apoptosis; VEGF protects endothelial cells from apoptosis. We found that TGF-β1 promotes endothelial cell expression of FGF-2, which up-regulates VEGF synthesis. Inhibition of VEGF signaling through VEGF receptor 2 (flk-1) abrogates TGF-β1-induced apoptosis and p38(MAPK) activation. Inhibition of p38(MAPK) blocks TGF-β1-induced apoptosis, showing that VEGF/flk-1-mediated activation of p38(MAPK) is required for TGF-β1 induction of apoptosis. In the absence of TGF-β1, VEGF activates p38(MAPK) and promotes endothelial cell survival. However, in context with TGF-β1, VEGF/flk-1-mediated activation of p38(MAPK) results in apoptosis. Thus, cross-talk between TGF-β1 and VEGF signaling converts VEGF/flk-1-activated p38(MAPK) into a proapoptotic signal. This finding illustrates an unexpected role of VEGF and indicates that VEGF can be pharmacologically converted into an apoptotic factor, a novel approach to antiangiogenesis therapy