Based on physiological knowledge, and on an analysis of signals related to its dynamics, we propose a model of the cardiovascular system. It consists of coupled oscillators. Each of them describes one of the subsystems involved in the regulation of one passage of blood through the circulatory system. The flow of blood through the system of closed tubes-the blood vessels-is described by wave equations.

By studying the Heegaard Floer homology of the preimage of a knot K S 3 inside its double branched cover, we develop simple obstructions to K having finite order in the classical smooth concordance group. As an application, we prove that all 2-bridge knots of crossing number at most 12 for which the smooth concordance order was previously unknown have infinite smooth concordance order.57R58, 57M25; 57M12, 57M27

Using the Heegaard Floer homology of Ozsváth and Szabó we investigate obstructions to definite intersection pairings bounded by rational homology spheres. As an application we obtain new lower bounds for the four-ball genus of Montesinos links.In this section we study the relationship between a smooth four-manifold X and its boundary Y . We will assume throughout that X is negative definite. The following is an extension of [3, Lemma 3].Lemma 2.1 Let Y be a rational homology sphere; denote by h the order of H 1 (Y ; Z). Suppose that Y bounds X and denote by s the absolute value of the determinant of the intersection pairing on H 2 (X, Z)/Tors. Then h = st 2 , where st is the order of the image of H 2 (X; Z) in H 2 (Y ; Z), and t is the order of the image of the torsion subgroup of H 2 (X; Z).Proof. Note that for b 2 (X) > 0, X has a non-degenerate integer intersection formwe denote the absolute value of the determinant of this pairing by s. If b 2 (X) = 0, then set s = 1. The long exact sequence of the pair (X, Y ) yields the following (with integer coefficients):

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Dedicated to José Maria Montesinos on the occasion of his 65th birthday.Abstract. Given a knot K in the three-sphere, we address the question: which Dehn surgeries on K bound negative-definite four-manifolds? We show that the answer depends on a number m(K), which is a smooth concordance invariant. We study the properties of this invariant, and compute it for torus knots.