BACKGROUND Mitral annulus is a complex structure of poorly understood physiology. Full-volume real-time 3-dimensional transesophageal echocardiography offers a unique opportunity to completely image and quantify mitral annulus size and motion. METHODS AND RESULTS Real-time 3-dimensional transesophageal echocardiography of the mitral valve was acquired in 32 patients with myxomatous valve dise...

We study bifurcations from a singular heteroclinic cycle in R 3. This heteroclinic cycle contains a hyperbolic singularity and a saddle-node. At the saddle-node, the linearized vector eld has two complex conjugate eigenvalues in addition to an eigenvalue 0. This implies the existence of a cascade of inclination-ip homoclinic bifurcations to the heteroclinic bifurcation.

We solve saddle point problems by accelerated versions of the classical Cimmino’s method. For that, saddle point problems are reviewed and reformulated as best approximation problems. In that setting, low-cost optimization techniques are used for accelerating Cimmino’s method. Encouraging numerical results coming from KKT systems, Stokes problems and domain decomposition problems are presented....

The presence of a saddle-focus separatrix — a homoclinic curve in Poincaré’s terminology — plays a fundamental role in the onset and existence of chaos in dynamical systems. To observe chaotic behavior of trajectories, for instance, it is sufficient to have two conditions: the existence of a separatrix loop and Shil’nikov’s saddle-focus condition [1]. Consider a three-dimensional dynamical syst...

Background: Saddle nose deformities mostly result from trauma. Most reports of saddle nose correction after trauma relate to isolated fractures, but in this article the experience of the authors is presented in relation to bone grafting for the correction of the saddle nose in multiple facial fracture patients. Objectives: The current study aimed to report the results of a protocol for choosing...

REASONS FOR PERFORMING STUDY The exact relationship between the saddle pressure pattern during one stride cycle and the movements of horse and rider at the walk are poorly understood and have never been investigated in detail. HYPOTHESIS The movements of rider and horse account for the force distribution pattern under the saddle. METHOD Vertical ground reaction forces (GRF), kinematics of h...

A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. The simi...

In this research we present new results on discrete Lagrangian methods (DLM) and extend our previous (incomplete and highly simpli ed) theory on the method. Our proposed method forms a strong mathematical foundation for solving general nonlinear discrete optimization problems. Speci cally, we show for continuous Lagrangian methods the relationship among local minimal solutions satisfying constr...

For inviscid, rotational accretion flows driven by a general pseudoNewtonian potential on to a Schwarzschild black hole, the only possible fixed points are saddle points and centre-type points. For the specific choice of the Newtonian potential, the flow has only two critical points, of which the outer one is a saddle point while the inner one is a centre-type point. A restrictive upper bound i...

EON is a software package that uses distributed computing, systematic coarse graining and bookkeeping of minima and first order saddle points too speed up adaptive kinetic Monte Carlo simulations. It can be used to optimize continuously differentiable functions of a large number of variables. The approach is based on finding minima of the cost function by traversing low-lying, first-order saddl...