Two of G. Matheron’s seminal contributions have been his development of size distributions (else called ‘granulometries’) and his kernel representation theory. The first deals with semigroups of multiscale openings and closings of binary images (shapes) by compact convex sets, a basic ingredient of which are the multiscale Minkowski dilations and erosions. The second deals with representing inc...

We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup defined in Quantum Probability via quantum stochastic differential equations. Given a homogeneous Markov chain in continuous time in a finite state space E, we introduce a second system, an environment, and a deterministic invertible time-homogeneous global evolution of the system E with this environme...

We consider characterisations of unitary dilations and approximations irreversible classical dynamical systems on a Hilbert space. In the commutative case, building work in [9], one can express well known approximants (e.g. Hille- Yosida-approximants) via expectations over certain stochastic processes. Using this, our first result characterises simultaneous regular dilatability commuting famili...

The magnitude of task-evoked pupillary dilations during mental activity has previously been shown to index the cognitive capacity utilized in the performance of the mental task. To determine the relation between "intelligence" and capacity demands during mental activity, task-evoked pupillary dilations were measured while two groups of university students differing in their scores on the Schola...

Background and Purpose—Endothelium-derived hyperpolarizing factor (EDHF)–mediated dilations are potentiated after several pathologies, including ischemia/reperfusion (I/R). However, no study to date has addressed the mechanism by which this potentiation occurs. This study tested the hypothesis that potentiated EDHF-mediated dilations are due to altered endothelial Ca handling after I/R. Methods...

BACKGROUND AND PURPOSE Endothelium-derived hyperpolarizing factor (EDHF)-mediated dilations are potentiated after several pathologies, including ischemia/reperfusion (I/R). However, no study to date has addressed the mechanism by which this potentiation occurs. This study tested the hypothesis that potentiated EDHF-mediated dilations are due to altered endothelial Ca2+ handling after I/R. MET...

The effects of the synthetic 28-amino-acid alpha-human atrial natriuretic peptide (ANP) on the proximal coronary arteries and coronary blood flow were evaluated in 17 patients. Proximal coronary dimension was quantitated by digital angiography, and coronary flow was quantitated with 3F Doppler flow catheters. ANP, when given as a 2.5-micrograms/kg bolus in the left ventricle, caused sustained s...

BACKGROUND Experience of balloon dilation of peripheral pulmonary stenosis (PPS) in Williams syndrome (WS) is limited. METHODS AND RESULTS Catheterizations in all patients with WS undergoing therapy for PPS from 1984 to 1999 were reviewed. Criteria for successful dilation included an increase >50% in predilation diameter and a decrease >20% in ratio of right ventricular (RV) to aortic (Ao) sy...