Spatial Graphs with Local Knots

It is shown that for any locally knotted edge of a 3-connected graph in $S^3$, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in $S^3$.Comment: 20 pages, 3 figures; in v. 2 the proof of Theorem 1 has been clarified, and other minor revisions have been mad

Inductive Construction of 2-Connected Graphs for Calculating the Virial Coefficients

In this paper we give a method for constructing systematically all simple 2-connected graphs with n vertices from the set of simple 2-connected graphs with n-1 vertices, by means of two operations: subdivision of an edge and addition of a vertex. The motivation of our study comes from the theory of non-ideal gases and, more specifically, from the virial equation of state. It is a known result of Statistical Mechanics that the coefficients in the virial equation of state are sums over labelled 2-connected graphs. These graphs correspond to clusters of particles. Thus, theoretically, the virial coefficients of any order can be calculated by means of 2-connected graphs used in the virial coefficient of the previous order. Our main result gives a method for constructing inductively all simple 2-connected graphs, by induction on the number of vertices. Moreover, the two operations we are using maintain the correspondence between graphs and clusters of particles.Comment: 23 pages, 5 figures, 3 table

Effect of ω-3 fatty acid supplementation on endothelial function, endogenous fibrinolysis and platelet activation in patients with a previous myocardial infarction:a randomised controlled trial

OBJECTIVE: The mechanisms through which ω-3 fatty acids reduce adverse cardiac events remain uncertain. We aimed to investigate the effect of ω-3 fatty acid supplementation on endothelial vasomotor function, endogenous fibrinolysis, and platelet and monocyte activation in patients with coronary heart disease. DESIGN: Randomised, double-blind, placebo-controlled, cross-over trial. SETTING: Academic cardiac centre. PARTICIPANTS: 20 male patients with a previous myocardial infarction. INTERVENTION: ω-3 Fatty acid supplementation (2 g/day for 6 weeks) versus olive oil placebo. OUTCOME MEASURES: Peripheral blood was taken for analysis of platelet and monocyte activation, and forearm blood flow (FBF) was assessed in a subset of 12 patients during intrabrachial infusions of acetylcholine, substance P and sodium nitroprusside. Stimulated plasma tissue plasminogen activator (t-PA) concentrations were measured during substance P infusion. RESULTS: All vasodilators caused dose-dependent increases in FBF (p<0.0001). ω-3 Fatty acid supplementation did not affect endothelium-dependent vasodilation with acetylcholine and substance P compared with placebo (p=0.5 and 0.9). Substance P caused a dose-dependent increase in plasma t-PA concentrations (p<0.0001), which was not affected by ω-3 fatty acid supplementation (p=0.9). ω-3 Fatty acids did not affect platelet–monocyte aggregation, platelet P-selectin or CD40L, or monocyte CD40. CONCLUSIONS: We have demonstrated that dietary supplementation with ω-3 fatty acids does not affect endothelial vasomotor function, endothelial t-PA release, or platelet and monocyte activation in patients with coronary heart disease. Cardiac benefits conferred by ω-3 fatty acids in coronary heart disease are unlikely to be mediated through effects on these systems

Predicting sudden death in patients with mild to moderate chronic heart failure

Objectives: To explore the relation between non-invasive measures of cardiac function and sudden cardiac death, as well as the development and utility of an index integrating these variables to identify patients at increased risk of this mode of death. Design: UK-HEART (United Kingdom-heart failure evaluation and assessment of risk trial) was a prospective study conducted between December 1993 and April 2000. The study was specifically designed to identify non-invasive markers of death and mode of death among patients with chronic heart failure. Setting: 8 UK general hospitals. Main outcome measures: Death and mode of death. Results: 553 patients aged a mean (SD) of 63 (10) years, in New York Heart Association functional class 2.3 (0.02), recruited prospectively. After 2365 patient-years’ follow up, 201 patients had died (67 suddenly). Predictors of sudden death were greater cardiothoracic ratio, QRS dispersion, QT dispersion corrected for rate (QTc) across leads V1–V6 on the 12 lead ECG, and the presence of non-sustained ventricular tachycardia. The hazard ratio and 95% confidence intervals (CI) of sudden death for a 10% increase in cardiothoracic ratio was 1.43 (95% CI 1.20 to 1.71), for a 10% increase in QRS dispersion 1.11 (95% CI 1.04 to 1.19), for the presence of non-sustained ventricular tachycardia 2.03 (95% CI 1.27 to 3.25), and for a 10% increase in QTc dispersion across leads V1–V6 1.03 (95% CI 1.00 to 1.07) (all p < 0.04). An index derived from these four factors performed well in identifying patients specifically at increased risk of sudden death. Conclusions: Results show that an index derived from three widely available non-invasive investigations has the potential to identify ambulant patients with chronic heart failure at increased risk of sudden death. This predictive tool could be used to target more sophisticated investigations or interventions aimed at preventing sudden death

Effect of moderate walnut consumption on lipid profile, arterial stiffness and platelet activation in humans

BACKGROUND/OBJECTIVES: A large intake of walnuts may improve lipid profile and endothelial function. The effect of moderate walnut consumption is not known. We investigated whether a moderate intake of walnuts would affect lipid profile, arterial stiffness and platelet activation in healthy volunteers. SUBJECTS/METHODS: Thirty healthy males were recruited into a single-blind randomised controlled crossover trial of 4 weeks dietary walnut supplementation (15 g/day) and 4 weeks control (no walnuts). Arterial stiffness was assessed using pulse waveform analysis to determine the augmentation index and augmented pressure. Platelet activation was determined using flow cytometry to measure circulating platelet-monocyte aggregates. RESULTS: There were no differences in lipid profile after 4 weeks of walnut supplementation compared with control. Dietary intake of alpha-linolenic acid was increased during the walnut diet (2.1±0.4 g/day versus 0.7±0.4 g/day, P<0.0001). There were no differences in augmentation index or augmented pressure during walnut supplementation. Walnut supplementation did not affect platelet-monocyte aggregation . CONCLUSIONS: Dietary intervention with a moderate intake of walnuts does not affect lipid profile, arterial stiffness or platelet activation in man. Our results suggest that the potentially beneficial cardiac effects of walnuts may not be apparent at lower and more practical levels of consumption

Vascular effects of apelin in vivo in man

ObjectivesThis study was designed to establish the direct vascular effects of apelin in vivo in man.BackgroundApelin is the endogenous ligand for the previously orphaned G-protein–coupled receptor, APJ. This novel pathway is widely expressed in the cardiovascular system and is emerging as an important mediator of cardiovascular homeostasis. In pre-clinical models, apelin causes venous and arterial vasodilation.MethodsVascular effects of apelin were assessed in 24 healthy volunteers. Dorsal hand vein diameter was measured by the Aellig technique during local intravenous infusions (0.1 to 3 nmol/min) of apelin-36, (Pyr1)apelin-13, and sodium nitroprusside (0.6 nmol/min). Forearm blood flow was measured by venous occlusion plethysmography during intrabrachial infusions of apelin-36 and (Pyr1)apelin-13 (0.1 to 30 nmol/min) and subsequently in the presence or absence of a “nitric oxide clamp” (nitric oxide synthase inhibitor, L-NG-monomethylarginine [8 μmol/min], coinfused with nitric oxide donor, sodium nitroprusside [90 to 900 ng/min]), or a single oral dose of aspirin (600 mg) or matched placebo.ResultsAlthough sodium nitroprusside caused venodilation (p < 0.0001), apelin-36 and (Pyr1)apelin-13 had no effect on dorsal hand vein diameter (p = 0.2). Both apelin isoforms caused reproducible vasodilation in forearm resistance vessels (p < 0.0001). (Pyr1)apelin-13–mediated vasodilation was attenuated by the nitric oxide clamp (p = 0.004) but unaffected by aspirin (p = 0.7).ConclusionsAlthough having no apparent effect on venous tone, apelin causes nitric oxide–dependent arterial vasodilation in vivo in man. The apelin-APJ system merits further clinical investigation to determine its role in cardiovascular homeostasis