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

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

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 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

Loss of lag-response curvilinearity of indices of heart rate variability in congestive heart failure

BACKGROUND: Heart rate variability (HRV) is known to be impaired in patients with congestive heart failure (CHF). Time-domain analysis of ECG signals traditionally relies heavily on linear indices of an essentially non-linear phenomenon. Poincaré plots are commonly used to study non-linear behavior of physiologic signals. Lagged Poincaré plots incorporate autocovariance information and analysis of Poincaré plots for various lags can provide interesting insights into the autonomic control of the heart. METHODS: Using Poincaré plot analysis, we assessed whether the relation of the lag between heart beats and HRV is altered in CHF. We studied the influence of lag on estimates of Poincaré plot indices for various lengths of beat sequence in a public domain data set (PhysioNet) of 29 subjects with CHF and 54 subjects with normal sinus rhythm. RESULTS: A curvilinear association was observed between lag and Poincaré plot indices (SD1, SD2, SDLD and SD1/SD2 ratio) in normal subjects even for a small sequence of 50 beats (p value for quadratic term 3 × 10(-5), 0.002, 3.5 × 10(-5 )and 0.0003, respectively). This curvilinearity was lost in patients with CHF even after exploring sequences up to 50,000 beats (p values for quadratic term > 0.5). CONCLUSION: Since lagged Poincaré plots incorporate autocovariance information, these analyses provide insights into the autonomic control of heart rate that is influenced by the non-linearity of the signal. The differences in lag-response in CHF patients and normal subjects exist even in the face of the treatment received by the CHF patients

Effect of wood smoke exposure on vascular function and thrombus formation in healthy fire fighters

Background: Myocardial infarction is the leading cause of death in fire fighters and has been linked with exposure to air pollution and fire suppression duties. We therefore investigated the effects of wood smoke exposure on vascular vasomotor and fibrinolytic function, and thrombus formation in healthy fire fighters. Methods: In a double-blind randomized cross-over study, 16 healthy male fire fighters were exposed to wood smoke (~1 mg/m3 particulate matter concentration) or filtered air for one hour during intermittent exercise. Arterial pressure and stiffness were measured before and immediately after exposure, and forearm blood flow was measured during intra-brachial infusion of endothelium-dependent and -independent vasodilators 4–6 hours after exposure. Thrombus formation was assessed using the ex vivo Badimon chamber at 2 hours, and platelet activation was measured using flow cytometry for up to 24 hours after the exposure. Results: Compared to filtered air, exposure to wood smoke increased blood carboxyhaemoglobin concentrations (1.3% versus 0.8%; P &lt; 0.001), but had no effect on arterial pressure, augmentation index or pulse wave velocity (P &gt; 0.05 for all). Whilst there was a dose-dependent increase in forearm blood flow with each vasodilator (P &lt; 0.01 for all), there were no differences in blood flow responses to acetylcholine, sodium nitroprusside or verapamil between exposures (P &gt; 0.05 for all). Following exposure to wood smoke, vasodilatation to bradykinin increased (P = 0.003), but there was no effect on bradykinin-induced tissue-plasminogen activator release, thrombus area or markers of platelet activation (P &gt; 0.05 for all). Conclusions: Wood smoke exposure does not impair vascular vasomotor or fibrinolytic function, or increase thrombus formation in fire fighters. Acute cardiovascular events following fire suppression may be precipitated by exposure to other air pollutants or through other mechanisms, such as strenuous physical exertion and dehydration.Originally included in thesis in manuscript form.</p