Topological Symmetry Groups of K_{4r+3}

We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the topological symmetry group of an embedding of the complete graph K_{4r+3} in S^3

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

The geometry of antisymplectic involutions, I

We study fixed loci of antisymplectic involutions on projective hyperkahler manifolds of K3([n])-type. When the involution is induced by an ample class of square 2 in the Beauville-Bogomolov-Fujiki lattice, we show that the number of connected components of the fixed locus is equal to the divisibility of the class, which is either 1 or 2

A tile model of circuit topology for self-entangled biopolymers

Building on the theory of circuit topology for intra-chain contacts in entangled proteins, we introduce tiles as a way to rigorously model local entanglements which are held in place by molecular forces. We develop operations that combine tiles so that entangled chains can be represented by algebraic expressions. Then we use our model to show that the only knot types that such entangled chains can have are 3(1), 4(1), 5(1), 5(2), 6(1), 6(2), 6(3), 7(7), 8(12) and connected sums of these knots. This includes all proteins knots that have thus far been identified.Pharmacolog

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

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