Timely-automatic procedure for estimating the endocardial limits of the left ventricle assessed echocardiographically in clinical practice

In this paper, we propose an analytical rapid method to estimate the endocardial borders of the left ventricular walls on echocardiographic images for prospective clinical integration. The procedure was created as a diagnostic support tool for the clinician and it is based on the use of the anisotropic generalized Hough transform. Its application is guided by a Gabor-like filtering for the approximate delimitation of the region of interest without the need for computing further anatomical characteristics. The algorithm is applying directly a deformable template on the predetermined filtered region and therefore it is responsive and straightforward implementable. For accuracy considerations, we have employed a support vector machine classifier to determine the confidence level of the automated marking. The clinical tests were performed at the Cardiology Clinic of the County Emergency Hospital Timisoara and they improved the physicians perception in more than 50% of the cases. The report is concluded with medical discussions.European Union (UE)Ministerio de Economía y Competitividad (MINECO). Españ

A method to generate first integrals from infinitesimal symmetries

We propose a method to construct first integrals of a dynamical system, starting with a given set of independent infinitesimal symmetries. In the case of two infinitesimal symmetries, a rank two Poisson structure on the ambient space it is found, such that the vector field that generates the dynamical system, becomes a Poisson vector field. Moreover, the symplectic leaves and the Casimir functions of the associated Poisson manifold are characterized. Explicit conditions that guarantee Hamilton-Poisson realizations of the dynamical system are also given.Comment: 14 page

On a unified formulation of completely integrable systems

The purpose of this article is to show that a $\mathcal{C}^1$ differential system on $\R^n$ which admits a set of $n-1$ independent $\mathcal{C}^2$ conservation laws defined on an open subset $\Omega\subseteq \R^n$, is essentially $\mathcal{C}^1$ equivalent on an open and dense subset of $\Omega$, with the linear differential system $u^\prime_1=u_1, \ u^\prime_2=u_2,..., \ u^\prime_n=u_n$. The main results are illustrated in the case of two concrete dynamical systems, namely the three dimensional Lotka-Volterra system, and respectively the Euler equations from the free rigid body dynamics.Comment: 11 page

Asymptotic Stability for a Class of Metriplectic Systems

Using the framework of metriplectic systems on $\R^n$ we will describe a constructive geometric method to add a dissipation term to a Hamilton-Poisson system such that any solution starting in a neighborhood of a nonlinear stable equilibrium converges towards a certain invariant set. The dissipation term depends only on the Hamiltonian function and the Casimir functions