Alfred Ramani

Learn More
1 Abstract A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painlevé V equation. Its derivation is based on the similarity reduction on the two-dimensional lattice of integrable partial difference equations of KdV type. The new equation which is referred to as GDP(More)
A methodology is presented for extracting precise quantitative MT parameters using a magnetisation-prepared spoiled gradient echo sequence. This method, based on a new mathematical model, provides relaxation parameters for human brain in-vitro and in-vivo. The in-vivo parameters have been obtained from three different regions of normal white matter:(More)
Quantitative analysis of magnetization transfer images has the potential to allow a more thorough characterization of the protons, both bound and free, in a tissue by extracting a number of parameters relating to the NMR properties of the protons and their local environment. This work develops previously presented techniques to produce estimates of(More)
This study used a model for magnetization transfer (MT) to estimate two underlying parameters: the macromolecular proton fraction (f) and the bound pool T2 (T2b) in patients with multiple sclerosis (MS). Sixty patients with clinically definite MS and 27 healthy controls were imaged using: (1) a dual echo fast spin echo sequence, (2) a MT sequence (with ten(More)
We report on a new quantitative magnetization transfer (MT) technique that allows for the in vivo estimation of the macromolecular proton fraction (f) and the bound pool T2 relaxation time (T2b), whilst permitting whole brain coverage. In this pilot study, five subjects with multiple sclerosis (MS) and five healthy controls were studied. Both f and T2b were(More)
We confront two integrability criteria for rational mappings. The first is the singularity confinement based on the requirement that every singu-larity, spontaneously appearing during the iteration of a mapping, disappear after some steps. The second recently proposed is the algebraic entropy criterion associated to the growth of the degree of the iterates.(More)
We examine whether the Painlevé property is a necessary condition for the integra-bility of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we investigate whether the singularity confinement property is satisfied for the discrete analogues of the non-Painlevé(More)