Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a n...

We propose a Fast Marching based implementation for computing sub-Riemanninan (SR) geodesics in the roto-translation group SE(2), with a metric depending on a cost induced by the image data. The key ingredient is a Riemannian approximation of the SR-metric. Then, a state of the art Fast Marching solver that is able to deal with extreme anisotropies is used to compute a SR-distance map as the so...

We focus on our experiences on translating ontologies between two ontology languages, FLogic and Ontolingua, in the framework of Methontology and ODE. Rather than building "ad hoc" translators between languages or using KIF, our option consists of translating through ODE intermediate representations. So, we have built direct translators from ODE intermediate representations to Ontolingua and FL...

Ordinary differential equations (ODE) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last 2 decades, ODEs have also emerged as a prevailing tool in various biomedical research fields, especially in infectious disease modeling. In practice, it is important and necessary to determine unknown parameters in ODE models based on e...

We associate certain probability measures on R to geodesics in the space H L of postively curved metrics on a line bundle L, and to geodesics in the finite dimensional symmetric space of hermitian norms on H 0 (X, kL). We prove that the measures associated to the finite dimensional spaces converge weakly to the measures related to geodesics in H L as k goes to infinity. The convergence of secon...

Geodesics on the infinite dimensional symmetric space H of Kähler metrics in a fixed Kähler class on a projective Kähler manifold X are solutions of a homogeneous complex Monge-Ampère equation in X×A, where A ⊂ C is an annulus. They are analogues of 1PS (one-parameter subgroups) on symmetric spaces GC/G. Donaldson, Arezzo-Tian and Phong-Sturm raised the question whether Monge-Ampère geodesics c...

We characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the Jacobi field along the geodesics, and the equations for a certain flow constrained in a fam...

A component-based methodology to derive parallel stiff Ordinary Differential Equation (ODE) solvers for multicomputers is presented. The methodology allows the exploitation of the multilevel parallelism of this kind of numerical algorithms and the particular structure of ODE systems by using parallel linear algebra modules. The approach furthers the reusability of the design specifications and ...

In re ent years there has been an in reasing trend toward the in orporation of omputers into a variety of devi es where the amount of memory available is limited. This makes it desirable to try to redu e the size of appli ations where possible. This arti le explores the use of ompiler te hniques to a omplish ode ompa tion to yield smaller exe utables. The main ontribution of this arti le is to ...

OBJECTIVE To assess optical coherence tomography in differentiating optic disc edema (ODE) due to papilledema and other optic neuropathies from optic nerve head drusen (ONHD). METHODS Optical coherence tomographic images from 60 subjects (20 with ODE, 20 with ONHD, and 20 control subjects) were assessed qualitatively and quantitatively. Qualitative criteria for ODE included an elevated optic ...