Noninvasive deep brain stimulation using focused energy sources

A non-invasive methodological possibility for brain stimulation through the simultaneous use of an external energy beam and an existing brain imaging system such as functional magnetic resonance imaging (fMRI) is herein proposed; the main advantage is to confine the stimulation into a single brain area, avoiding unintentional stimulation of adjoining brain regions, thus, allowing for deep brain stimulation. The methodological possibility is to be used for research, treatment and diagnosis of neurological, cognitive and neurophysiologic disorders. The method includes the simultaneous steps of applying focused thermal energy stimulation within a living brain, and monitoring such stimulation using MRI thermometry images; in addition, it includes the detection of stimulated neuronal impulses by its potentially effects in the blood oxygenation level (BOLD) fMRI response signal

The H=xp model revisited and the Riemann zeros

Berry and Keating conjectured that the classical Hamiltonian H = xp is related to the Riemann zeros. A regularization of this model yields semiclassical energies that behave, in average, as the non trivial zeros of the Riemann zeta function. However, the classical trajectories are not closed, rendering the model incomplete. In this paper, we show that the Hamiltonian H = x (p + l_p^2/p) contains closed periodic orbits, and that its spectrum coincides with the average Riemann zeros. This result is generalized to Dirichlet L-functions using different self-adjoint extensions of H. We discuss the relation of our work to Polya's fake zeta function and suggest an experimental realization in terms of the Landau model.Comment: 5 pages, 3 figure

Surfaces containing a family of plane curves not forming a fibration

We complete the classification of smooth surfaces swept out by a 1-dimensional family of plane curves that do not form a fibration. As a consequence, we characterize manifolds swept out by a 1-dimensional family of hypersurfaces that do not form a fibration.Comment: Author's post-print, final version published online in Collect. Mat