6,147 research outputs found

    Set Systems Containing Many Maximal Chains

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    The purpose of this short problem paper is to raise an extremal question on set systems which seems to be natural and appealing. Our question is: which set systems of a given size maximise the number of (n+1)(n+1)-element chains in the power set P({1,2,…,n})\mathcal{P}(\{1,2,\dots,n\})? We will show that for each fixed α>0\alpha>0 there is a family of α2n\alpha 2^n sets containing (α+o(1))n!(\alpha+o(1))n! such chains, and that this is asymptotically best possible. For smaller set systems we are unable to answer the question. We conjecture that a `tower of cubes' construction is extremal. We finish by mentioning briefly a connection to an extremal problem on posets and a variant of our question for the grid graph.Comment: 5 page

    The Long-term Health Effects of Mass Political Violence: Evidence From China’s Cultural Revolution

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    There is much interest in the causes of several adverse health outcomes in middle and old age. In searching for new explanations for adverse health outcomes later in life, researchers have started to look beyond behavioural risk factors to examine the effect of shocks to health in utero and in childhood on health in old age. In this paper we extend this literature to examine the long-term health effects of mass political violence experienced in utero and in childhood using China’s Cultural Revolution as a natural experiment. We find that individuals who were in utero in the Cultural Revolution have reduced lung capacity later in life, but we find no evidence that being in utero has adverse effects on other health indicators later in life. We find more evidence that being an adolescent in the Cultural Revolution has an adverse effect on health later in life. Specifically, we find that individuals who were adolescents in the Cultural Revolution have higher blood pressure and reduced ability to engage in activities of daily living later in life. We also find that males who were adolescents in the Cultural Revolution have reduced cognitive skills later in life, while females who were adolescents in the Cultural Revolution have reduced lung capacity in middle and old age. specific recommendations for the Canadian context.Health, Idiosyncratic Shocks, Cultural Revolution, Long-term effects

    Vapour-liquid equilibrium studies at atmospheric to moderate pressures

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    A study of vapour-liquid equilibria is presented together with current developments. The theory of vapour-liquid equilibria is discussed. Both experimental and prediction methods for obtaining vapour-liquid equilibria data are critically reviewed. The development of a new family of equilibrium stills to measure experimental VLE data from sub-atmosphere to 35 bar pressure is described. Existing experimental techniques are reviewed, to highlight the needs for these new apparati and their major attributes. Details are provided of how apparatus may be further improved and how computer control may be implemented. To provide a rigorous test of the apparatus the stills have been commissioned using acetic acid-water mixture at one atmosphere pressure. A Barker-type consistency test computer program, which allows for association in both phases has been applied to the data generated and clearly shows that the stills produce data of a very high quality. Two high quality data sets, for the mixture acetone-chloroform, have been generated at one atmosphere and 64.3oC. These data are used to investigate the ability of the new novel technique, based on molecular parameters, to predict VLE data for highly polar mixtures. Eight, vapour-liquid equilibrium data sets have been produced for the cyclohexane-ethanol mixture at one atmosphere, 2, 4, 6, 8 and 11 bar, 90.9oC and 132.8oC. These data sets have been tested for thermodynamic consistency using a Barker-type fitting package and shown to be of high quality. The data have been used to investigate the dependence of UNIQUAC parameters with temperature. The data have in addition been used to compare directly the performance of the predictive methods - Original UNIFAC, a modified version of UNIFAC, and the new novel technique, based on molecular parameters developed from generalised London's potential (GLP) theory

    Cross-adaptation and bitterness inhibition of L-Tryptophan, L-Phenylalanine and urea : further support for shared peripheral physiology

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    A previous study investigating individuals\u27 bitterness sensitivities found a close association among three compounds: L-tryptophan (L-trp), L-phenylalanine (L-phe) and urea (Delwiche et al., 2001, Percept. Psychophys. 63, 761-776). In the present experiment, psychophysical cross-adaptation and bitterness inhibition experiments were performed on these three compounds to determine whether the bitterness could be differentially affected by either technique. If the two experimental approaches failed to differentiate L-trp, L-phe and urea\u27s bitterness, then we may infer they share peripheral physiological mechanisms involved in bitter taste. All compounds were intensity matched in each of 13 subjects, so the judgments of adaptation or bitterness inhibition would be based on equal initial magnitudes and, therefore, directly comparable. In the first experiment, cross-adaptation of bitterness between the amino acids was high (&gt;80%) and reciprocal. Urea and quinine-HCl (control) did not cross-adapt with the amino acids symmetrically. In a second experiment, the sodium salts, NaCl and Na gluconate, did not differentially inhibit the bitterness of L-trp, L-phe and urea, but the control compound, MgSO4, was differentially affected. The bitter inhibition experiment supports the hypothesis that L-trp, L-phe and urea share peripheral bitter taste mechanisms, while the adaptation experiment revealed subtle differences between urea and the amino acids indicating that urea and the amino acids activate only partially overlapping bitter taste mechanisms.<br /
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