Coronary MR angiography clinical applications and potential for imaging coronary artery disease.

Over the past decade, CMRA has emerged as a unique clinical imaging tool with applications in selected populations. Patients with suspected coronary artery anomalies and patients with Kawasaki disease and coronary aneurysms are among those for whom CMRA has demonstrated clinical usefulness. For assessment of patients with atherosclerotic CAD, CMRA is useful for detection of patency of bypass grafts. At centers with appropriate expertise and resources, CMRA also appears to be of value for exclusion of severe proximal multivessel CAD in selected patients. Data from multicenter trials will continue to define the clinical role of CMRA, particularly as it relates to assessment of CAD. Future developments and enhancements of CMRA promise better lumen and coronary artery wall imaging. This may become the new target in noninvasive evaluation of CAD.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

A sharp concentration inequality with applications

We present a new general concentration-of-measure inequality and illustrate its power by applications in random combinatorics. The results find direct applications in some problems of learning theory.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

Limitations of stimulated echo acquisition mode (STEAM) techniques in cardiac applications.

Stimulated echoes are widely used for imaging functional tissue parameters such as diffusion coefficient, perfusion, and flow rates. They are potentially interesting for the assessment of various cardiac functions. However, severe limitations of the stimulated echo acquisition mode occur, which are related to the special dynamic properties of the beating heart and flowing blood. To the well-known signal decay due to longitudinal relaxation and through-plane motion between the preparation and the read-out period of the stimulated echoes, additional signal loss is often observed. As the prepared magnetization is fixed with respect to the tissue, this signal loss is caused by the tissue deformation during the cardiac cycle, which leads to a modification of the modulation frequency of the magnetization. These effects are theoretically derived and corroborated by phantom and in vivo experiments.

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.