Integrating Hamiltonian systems defined on the Lie groups SO(4) and SO(1,3)

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E³, the spheres S³ and the hyperboloids H³ with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions is illustrated.

Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

The consumption of milk and dairy foods and the incidence of vascular disease and diabetes: An overview of the evidence

The health effects of milk and dairy food consumption would best be determined in randomised controlled trials. No adequately powered trial has been reported and none is likely because of the numbers required. The best evidence comes, therefore, from prospective cohort studies with disease events and death as outcomes. Medline was searched for prospective studies of dairy food consumption and incident vascular disease and Type 2 diabetes, based on representative population samples. Reports in which evaluation was in incident disease or death were selected. Meta-analyses of the adjusted estimates of relative risk for disease outcomes in these reports were conducted. Relevant case–control retrospective studies were also identified and the results are summarised in this article. Meta-analyses suggest a reduction in risk in the subjects with the highest dairy consumption relative to those with the lowest intake: 0.87 (0.77, 0.98) for all-cause deaths, 0.92 (0.80, 0.99) for ischaemic heart disease, 0.79 (0.68, 0.91) for stroke and 0.85 (0.75, 0.96) for incident diabetes. The number of cohort studies which give evidence on individual dairy food items is very small, but, again, there is no convincing evidence of harm from consumption of the separate food items. In conclusion, there appears to be an enormous mis-match between the evidence from long-term prospective studies and perceptions of harm from the consumption of dairy food items.

The effects of maternal postnatal depression and child sex on academic performance at age 16 years: a developmental approach

Background: Postnatal depression (PND) is associated with poor cognitive functioning in infancy and the early school years; long-term effects on academic outcome are not known. Method: Children of postnatally depressed (N = 50) and non-depressed mothers (N = 39), studied from infancy, were followed up at 16 years. We examined the effects on General Certificate of Secondary Education (GCSE) exam performance of maternal depression (postnatal and subsequent) and IQ, child sex and earlier cognitive development, and mother–child interactions, using structural equation modelling (SEM). Results: Boys, but not girls, of PND mothers had poorer GCSE results than control children. This was principally accounted for by effects on early child cognitive functioning, which showed strong continuity from infancy. PND had continuing negative effects on maternal interactions through childhood, and these also contributed to poorer GCSE performance. Neither chronic, nor recent, exposure to maternal depression had significant effects. Conclusions: The adverse effects of PND on male infants’ cognitive functioning may persist through development. Continuing difficulties in mother–child interactions are also important, suggesting that both early intervention and continuing monitoring of mothers with PND may be warranted.

Acute effects of elevated NEFA on vascular function: a comparison of SFA and MUFA

There is emerging evidence to show that high levels of NEFA contribute to endothelial dysfunction and impaired insulin sensitivity. However, the impact of NEFA composition remains unclear. A total of ten healthy men consumed test drinks containing 50 g of palm stearin (rich in SFA) or high-oleic sunflower oil (rich in MUFA) on separate occasions; a third day included no fat as a control. The fats were emulsified into chocolate drinks and given as a bolus (approximately 10 g fat) at baseline followed by smaller amounts (approximately 3 g fat) every 30 min throughout the 6 h study day. An intravenous heparin infusion was initiated 2 h after the bolus, which resulted in a three- to fourfold increase in circulating NEFA level from baseline. Mean arterial stiffness as measured by digital volume pulse was higher during the consumption of SFA (P,0·001) but not MUFA (P¼0·089) compared with the control. Overall insulin and gastric inhibitory peptide response was greater during the consumption of both fats compared with the control (P,0·001); there was a second insulin peak in response to MUFA unlike SFA. Consumption of SFA resulted in higher levels of soluble intercellular adhesion molecule-1 (sI-CAM) at 330 min than that of MUFA or control (P#0·048). There was no effect of the test drinks on glucose, total nitrite, plasminogen activator inhibitor-1 or endothelin-1 concentrations. The present study indicates a potential negative impact of elevated NEFA derived from the consumption of SFA on arterial stiffness and sI-CAM levels. More studies are needed to fully investigate the impact of NEFA composition on risk factors for CVD.

Infant sensitivity to negative maternal emotional shifts: Effects of infant sex, maternal postnatal depression, and interactive style

This study examined the effects of infant sex, maternal postnatal depression, and maternal interactive style on infant sensitivity to maternal negative emotional shifts. Face-to-face interactions of 68 mother–infant dyads were analyzed at 8 and 18 weeks. Twenty-five (28%) mothers had postnatal depression. Interactions were analyzed in terms of overall maternal interactive style: “sensitive,” “anxious,” “intrusive,” and “sad.” Episodes of negative shifts in maternal emotional expression were recorded, along with expressions of infant sensitivity to these changes. Daughters of depressed mothers showed higher rates of sensitivity to maternal negative emotion whereas their sons showed lower rates, in comparison to both girl and boy infants of well mothers. While maternal interactive style had no effect on 8-week infant sensitivity to maternal negative emotional shifts, high rates of 18-week infant sensitivity were predicted by both an 8-week and a concurrent, “sad” maternal interactive style. The findings are discussed in relation to theories of emotional and interpersonal development.

Interpretation of infant facial expression in the context of maternal postnatal depression

Postnatal maternal depression is associated with difficulties in maternal responsiveness. As most signals arising from the infant come from facial expressions one possible explanation for these difficulties is that mothers with postnatal depression are differentially affected by particular infant facial expressions. Thus, this study investigates the effects of postnatal depression on mothers’ perceptions of infant facial expressions. Participants (15 controls, 15 depressed and 15 anxious mothers) were asked to rate a number of infant facial expressions, ranging from very positive to very negative. Each face was shown twice, for a short and for a longer period of time in random order. Results revealed that mothers used more extreme ratings when shown the infant faces (i.e. more negative or more positive) for a longer period of time. Mothers suffering from postnatal depression were more likely to rate negative infant faces shown for a longer period more negatively than controls. The differences were specific to depression rather than an effect of general postnatal psychopathology—as no differences were observed between anxious mothers and controls. There were no other significant differences in maternal ratings of infant faces showed for short periods or for positive or neutral valence faces of either length. The findings that mothers with postnatal depression rate negative infant faces more negatively indicate that appraisal bias might underlie some of the difficulties that these mothers have in responding to their own infants signals.

A randomised trial to investigate the effects of acute consumption of a blackcurrant juice drink on markers of vascular reactivity and bioavailability of anthocyanins in human subjects

Objective: To study the bioavailability of anthocyanins and the effects of a 20% blackcurrant juice drink on vascular reactivity, plasma antioxidant status and other CVD risk markers. Subjects/Methods: The study was a randomised, cross over, double blind, placebo controlled acute meal study. Twenty healthy volunteers (11 females 9 males) were recruited, and all subjects completed the study. Fasted volunteers consumed a 20% blackcurrant juice drink (250 ml) or a control drink following a low-flavonoid diet for the previous 72 hours. Vascular reactivity was assessed at baseline and 120 mins after juice consumption by Laser Doppler Imaging (LDI). Plasma and urine samples were collected periodically over an 8 hour period for analysis, with a final urine sample collected at 24h. The cross over was performed after a 4-week washout. Results: There were no significant effects of the 20% blackcurrant juice drink on acute measures of vascular reactivity, biomarkers of endothelial function or lipid risk factors. Consumption of the test juice caused increases in plasma vitamin C (P=0.006), and urinary anthocyanins (P<0.001). Delphinidin-3-rutinoside and cyanidin-3-rutinoside were the main anthocyanins excreted in urine with delphinidin-3-glucoside also detected. The yield of anthocyanins in urine was 0.021 ± 0.003% of the dietary intake of delphinidin glycosides and 0.009 ± 0.002 % of the dietary intake of cyanidin glycosides. Conclusions: The juice consumption did not have a significant effect on vascular reactivity. Anthocyanins were present at low concentrations in the urine, and microbial metabolites of flavonoids were detected in plasma after juice consumption.

Stakeholder-defined corporate responsibility for a pre-credit-crunch financial service company: lessons for how good reputations are won and lost

This paper presents a study that identifies a stakeholder-defined concept of Corporate Responsibility (CR) in the context of a UK financial service organisation in the immediate pre-credit crunch era. From qualitative analysis of interviews and focus groups with employees and customers, we identify, in a wide-ranging stakeholder-defined concept of CR, six themes that together imply two necessary conditions for a firm to be regarded as responsible— both corporate actions and character must be consonant with CR. This provides both empirical support for a notable, recent theoretical contribution by Godfrey (in Acad Manag Rev 30:777–798, 2005) and novel lessons for reputation management practice.