Geodesics on Lie groups: Euler equations and totally geodesic subgroup

The geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler-Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given. The setting works both in the classical nite dimensional case, and in the category of in nite dimensional Fr echet Lie groups, in which di eomorphism groups are included. Using the framework we give new examples of both nite and in nite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving di eomorphisms is totally geodesic. The paper also gives a general framework for the representation of Euler-Arnold equations in arbitrary choice of dual pairing

Electromagnetic backscattering by plates and disks

With the recent development of diffraction coefficients for imperfectly conducting half-planes, it has become possible to analyze a wide variety of problems for which the impedance surface boundary condition applies. This impedance boundary condition, while approximate, was utilized to extend the usefulness of the Uniform Geometrical Theory of Diffraction (UTD) beyond the perfectly conducting geometries. These half-plane diffraction coefficients are used to analyze patterns of an antenna in the presence of an imperfectly conducting flat polygonal plate. The Geometrical Theory of Diffraction (GTD) techniques were also used to investigate the backscattering from perfectly conducting plates. To further improve the soft polarization results for wide angles, a model for the creeping wave or circulating current on the edge of the disk was obtained and used to find an additional component of the backscattered field. The backscattering from a square plate was then analyzed using GTD. Backscattering in both the principal and off-principal planes was examined

A Multi-signal Variant for the GPU-based Parallelization of Growing Self-Organizing Networks

Among the many possible approaches for the parallelization of self-organizing networks, and in particular of growing self-organizing networks, perhaps the most common one is producing an optimized, parallel implementation of the standard sequential algorithms reported in the literature. In this paper we explore an alternative approach, based on a new algorithm variant specifically designed to match the features of the large-scale, fine-grained parallelism of GPUs, in which multiple input signals are processed at once. Comparative tests have been performed, using both parallel and sequential implementations of the new algorithm variant, in particular for a growing self-organizing network that reconstructs surfaces from point clouds. The experimental results show that this approach allows harnessing in a more effective way the intrinsic parallelism that the self-organizing networks algorithms seem intuitively to suggest, obtaining better performances even with networks of smaller size.Comment: 17 page

A Noninvasive Optical Probe for Detecting Electrical Signals in Silicon IC’s

We report using a 1.3µm(silicon-sub-bandgap) optical probing system to detect electrical signals in silicon integrated circuits. Free carriers within integrated active devices perturb the index of refraction of the material, and we have used a Nomarski interferometer to sense this perturbation. Typical charge-density modulation in active devices produces a substantial index perturbation, and because of this, we have used an InGaAsP semiconductor laser to experimentally observe real-time 0.8V digital signals applied to a bipolar transistor. These signals were detected with a signal-to-noise ratio of 20dB in a system detection bandwidth of over 200MHz. Since the free-carrier-induced refractive-index perturbation is present in all semiconductor materials, in the future, we expect to be able to detect signals in integrated circuits fabricated in GaAs or any other material, and by taking advantage of the high spatial and temporal resolution of this system, we should be able to observe free-carrier dynamics within most active devices

Plasma arginine vasopressin concentrations in epileptics under monotherapy

Plasma arginine vasopressin concentrations were determined by radio-immunoassay in 112 adult epileptics who were taking carbamazepine, phenytoin, primidone, or sodium valproate in long-term monotherapy, and in 19 controls. No significant difference was found between the groups, but some epileptics taking carbamazepine and primidone showed low values. Serum concentrations of carbamazepine did not correlate with the concentrations of plasma arginine vasopressin. In conclusion, there was no evidence of a stimulating effect of chronic carbamazepine medication or a special inhibiting effect of phenytoin on the release of vasopressin arginine from the posterior pituitary

An assessment of the statistical distribution of Random Telegraph Noise Time Constants

As transistor sizes are downscaled, a single trapped charge has a larger impact on smaller devices and the Random Telegraph Noise (RTN) becomes increasingly important. To optimize circuit design, one needs assessing the impact of RTN on the circuit and this can only be accomplished if there is an accurate statistical model of RTN. The dynamic Monte Carlo modelling requires the statistical distribution functions of both the amplitude and the capture/emission time (CET) of traps. Early works were focused on the amplitude distribution and the experimental data of CETs were typically too limited to establish their statistical distribution reliably. In particular, the time window used has been often small, e.g. 10 sec or less, so that there are few data on slow traps. It is not known whether the CET distribution extracted from such a limited time window can be used to predict the RTN beyond the test time window. The objectives of this work are three fold: to provide the long term RTN data and use them to test the CET distributions proposed by early works; to propose a methodology for characterizing the CET distribution for a fabrication process efficiently; and, for the first time, to verify the long term prediction capability of a CET distribution beyond the time window used for its extraction