Convex polytopes and quantization of symplectic manifolds

Quantum mechanics associate to some symplectic manifolds M a quantum model Q(M), which is a Hilbert space. The space Q(M) is the quantum mechanical analogue of the classical phase space M. We discuss here relations between the volume of M and the dimension of the vector space Q(M). Analogues for convex polyhedra are considered.

Stable and efficient gene transfer into the retina using an HIV-based lentiviral vector

The development of methods for efficient gene transfer to terminally differentiated retinal cells is important to study the function of the retina as well as for gene therapy of retinal diseases. We have developed a lentiviral vector system based on the HIV that can transduce terminally differentiated neurons of the brain in vivo. In this study, we have evaluated the ability of HIV vectors to transfer genes into retinal cells. An HIV vector containing a gene encoding the green fluorescent protein (GFP) was injected into the subretinal space of rat eyes. The GFP gene under the control of the cytomegalovirus promoter was efficiently expressed in both photoreceptor cells and retinal pigment epithelium. However, the use of the rhodopsin promoter resulted in expression predominantly in photoreceptor cells. Most successfully transduced eyes showed that photoreceptor cells in >80% of the area of whole retina expressed the GFP. The GFP expression persisted for at least 12 weeks with no apparent decrease. The efficient gene transfer into photoreceptor cells by HIV vectors will be useful for gene therapy of retinal diseases such as retinitis pigmentosa.

Electrical microstimulation suggests two different forms of representation of head-centered space in the intraparietal sulcus of rhesus monkeys.

We examined the effects of eye position on saccades evoked by electrical stimulation of the intraparietal sulcus (IPS) of rhesus monkeys. Microstimulation evoked saccades from sites on the posterior bank, floor, and the medial bank of the IPS. The size and direction of the eye movements varied as a function of initial eye position before microstimulation. At many stimulation sites, eye position affected primarily the amplitude and not the direction of the evoked saccades. These "modified vector saccades" were characteristic of most stimulation-sensitive zones in the IPS, with the exception of a narrow strip located mainly on the floor of the sulcus. Stimulation in this "intercalated zone" evoked saccades that moved the eyes into a particular region in head-centered space, independent of the starting position of the eyes. This latter response is compatible with the stimulation site representing a goal zone in head-centered coordinates. On the other hand, the modified vector saccades observed outside the intercalated zone are indicative of a more distributed representation of head-centered space. A convergent projection from many modified vector sites onto each intercalated site may be a basis for a transition from a distributed to a more explicit representation of space in head-centered coordinates.