Packing constants in graphs and connectivity

AbstractWe prove the following theorem: If G an r-connected graph and there are k vertices of G which have pairwise distance at least d, then G has at least k(r⌞(itd−1)/2⌟+1)+ ((1+(−1)d)/2)r vertices. This bound is sharp

The role of stimulus-driven versus goal-directed processes in fight and flight tendencies measured with motor evoked potentials induced by Transcranial Magnetic Stimulation

This study examines two contrasting explanations for early tendencies to fight and flee. According to a stimulus-driven explanation, goal-incompatible stimuli that are easy/difficult to control lead to the tendency to fight/flee. According to a goal-directed explanation, on the other hand, the tendency to fight/flee occurs when the expected utility of fighting/fleeing is the highest. Participants did a computer task in which they were confronted with goal-incompatible stimuli that were (a) easy to control and fighting had the highest expected utility, (b) easy to control and fleeing had the highest expected utility, and (c) difficult to control and fleeing and fighting had zero expected utility. After participants were trained to use one hand to fight and another hand to flee, they either had to choose a response or merely observe the stimuli. During the observation trials, single-pulse Transcranial Magnetic Stimulation (TMS) was applied to the primary motor cortex 450 ms post-stimulus onset and motor evoked potentials (MEPs) were measured from the hand muscles. Results showed that participants chose to fight/flee when the expected utility of fighting/fleeing was the highest, and that they responded late when the expected utility of both responses was low. They also showed larger MEPs for the right/left hand when the expected utility of fighting/fleeing was the highest. This result can be interpreted as support for the goal-directed account, but only if it is assumed that we were unable to override the presumed natural mapping between hand (right/left) and response (fight/flight)

Erdős distance problems in normed spaces

AbstractWe study the problems of the maximum numbers of unit distances, largest distances and smallest distances among n points in a two-dimensional normed space. We determine the exact maximum numbers of smallest and largest distances for each normed space, the maximum number of unit distances for each normed space in which the unit sphere is not strictly convex, and show that the best known upper bound for the euclidean case applies also for each normed space with strictly convex unit sphere, thereby partially answering a question of Erdős and Ulam. The results on smallest distances give also the exact maximum number of touching pairs among n translates of a convex set in the plane, thereby generalizing the results on the translative kissing number by Hadwiger and Grünbaum

Quality learning of physics : Conceptions held by high school and university teachers

This paper reports an exploration of the conceptions of quality learning held by two samples of physics teachers - final year, high school physics teachers and academics teaching first year university physics. We begin by outlining our view of quality learning, that is a view of learning in which learners take control of their own learning and engage with active construction and reconstruction of their own meanings for concepts and phenomena. This view of quality learning recognises the crucial role of the affective dimension of learning on the extent to which students engage with and maintain such constructivist and metacognitive approaches to learning. The study explored the qualitatively different ways in which individuals conceptualise quality learning in physics, using semi structured interviews that explored aspects of learning that the respondents regarded as worth fostering in their classrooms. The interview approach was a modification of the Interview-About-Instances approach that allowed the possibility of interviewees suggesting instances of particular relevance to their view of quality learning. This process resulted in a considerable quantity of rich and complex data related to a large range of aspects of physics learning. These data are summarised here, and the qualitatively different conceptions of the respondents with respect to four significant aspects of physics learning are discussed. These aspects are: doing experimental work; linking physics to the real world; students taking responsibility for their own learning and being confident/feeling proud of what you can do. © 2003 Kluwer Academic Publishers.C

Thrombin responses in human endothelial cells. Contributions from receptors other than PAR1 include the transactivation of PAR2 by thrombin-cleaved PAR1.

The recent identification of two new thrombin receptors, PAR3 and PAR4, led us to re-examine the basis for endothelial cell responses to thrombin. Human umbilical vein endothelial cells (HUVEC) are known to express PAR1 and the trypsin/tryptase receptor, PAR2. Northern blots detected both of those receptors and, to a lesser extent, PAR3, but PAR4 message was undetectable and there was no response to PAR4 agonist peptides. To determine whether PAR3 or any other receptor contributes to thrombin signaling in HUVEC, PAR1 cleavage was blocked with two selective antibodies and PAR1 activation was inhibited with the antagonist, BMS200261. The antibodies completely inhibited HUVEC responses to thrombin, but BMS200261 was only partly effective, even though separate studies established that the antagonist completely inhibits PAR1 signaling at the concentrations used. Since peptides mimicking the PAR1 tethered ligand domain can also activate PAR2, we asked whether the remaining thrombin response in the presence of the antagonist could be due in part to the intermolecular transactivation of PAR2 by cleaved PAR1. Evidence that transactivation can occur was obtained in COS-7 cells co-expressing PAR2 and a variant of PAR1 that can be cleaved, but not signal. There was a substantial response to thrombin only in cells expressing both receptors. Conversely, in HUVEC, complete blockade of the thrombin response by the PAR1 antagonist occurred only when signaling through PAR2 was also blocked. From these observations we conclude that 1) PAR1 is the predominant thrombin receptor expressed in HUVEC and cleavage of PAR1 is required for endothelial cell responses to thrombin; 2) although PAR3 may be expressed, there is still no evidence that it mediates thrombin responses; 3) PAR4 is not expressed on HUVEC; and 4) transactivation of PAR2 by cleaved PAR1 can contribute to endothelial cell responses to thrombin, particularly when signaling through PAR1 is blocked. Such transactivation may limit the effectiveness of PAR1 antagonists, which compete with the tethered ligand domain rather than preventing PAR1 cleavage