Isospectral Sets for Fourth-Order Ordinary Differential Operators

Let L(p)u = D4u - (p1u’)’ + p2u be a fourth-order differential operator acting on L2[0; 1] with p ≡ (p1; p2) belonging to L2ℝ[0, 1] x L2ℝ[0, 1] and boundary conditions u(0) = u\u27\u27(0) = u(1) = u\u27\u27(1) = 0. We study the isospectral set of L(p) when L(p) has simple spectrum. In particular we show that for such p, the isospectral manifold is a real-analytic submanifold of L2ℝ[0, 1] x L2ℝ[0, 1] which has infinite dimension and codimension. A crucial step in the proof is to show that the gradients of the eigenvalues of L(p) with respect to p are linearly independent: we study them as solutions of a non-self-ajdoint fifth-order system, the Borg system, among whose eigenvectors are the gradients

Satellite laser ranging work at the Goddard Space Flight Center

Laser ranging systems, their range and accuracy capabilities, and planned improvements for future systems are discussed, the systems include one fixed and two mobile lasers ranging systems. They have demonstrated better than 10 cm accuracy both on a carefully surveyed ground range and in regular satellite ranging operations. They are capable of ranging to all currently launched retroreflector equipped satellites with the exception of Timation III. A third mobile system is discussed which will be accurate to better than 5 cm and will be capable of ranging to distant satellites such as Timation III and LAGEOS

Choline: Exploring the Growing Science on Its Benefits for Moms and Babies

The importance of ensuring adequate choline intakes during pregnancy is increasingly recognized. Choline is critical for a number of physiological processes during the prenatal period with roles in membrane biosynthesis and tissue expansion, neurotransmission and brain development, and methyl group donation and gene expression. Studies in animals and humans have shown that supplementing the maternal diet with additional choline improves several pregnancy outcomes and protects against certain neural and metabolic insults. Most pregnant women in the U.S. are not achieving choline intake recommendations of 450 mg/day and would likely benefit from boosting their choline intakes through dietary and/or supplemental approaches

Comparative performance of some popular ANN algorithms on benchmark and function approximation problems

We report an inter-comparison of some popular algorithms within the artificial neural network domain (viz., Local search algorithms, global search algorithms, higher order algorithms and the hybrid algorithms) by applying them to the standard benchmarking problems like the IRIS data, XOR/N-Bit parity and Two Spiral. Apart from giving a brief description of these algorithms, the results obtained for the above benchmark problems are presented in the paper. The results suggest that while Levenberg-Marquardt algorithm yields the lowest RMS error for the N-bit Parity and the Two Spiral problems, Higher Order Neurons algorithm gives the best results for the IRIS data problem. The best results for the XOR problem are obtained with the Neuro Fuzzy algorithm. The above algorithms were also applied for solving several regression problems such as cos(x) and a few special functions like the Gamma function, the complimentary Error function and the upper tail cumulative $\chi^2$-distribution function. The results of these regression problems indicate that, among all the ANN algorithms used in the present study, Levenberg-Marquardt algorithm yields the best results. Keeping in view the highly non-linear behaviour and the wide dynamic range of these functions, it is suggested that these functions can be also considered as standard benchmark problems for function approximation using artificial neural networks.Comment: 18 pages 5 figures. Accepted in Pramana- Journal of Physic

Music-induced analgesia in chronic pain: efficacy and assessment through a primary-task paradigm

Research into music-induced analgesia, the ability of music to affect the perception of pain, has under-represented the non-acute, chronic pain population. This longitudinal study aimed to investigate the impact of music listening on chronic pain. To extend traditional questionnaire-based approaches to pain assessment, a computerised visual search task was used before and after music listening as an objective measure of pain-related cognitive processing difficulties. Twenty-three participants (chronic pain sufferers or age and gender matched controls) listened to music for 28 days. Questionnaire-based results indicated that music listening consistently reduced pain intensity, unpleasantness and anxiety levels in the short-term. However there were no long-term or cumulative changes in pain relief or anxiety, with participant ratings at baseline comparable to those at 28 days. Visual search task performance demonstrated that chronic pain sufferers showed pain-related cognitive processing inhibitions on the target deviations demanding the greatest processing capacity. This suggests that though music-induced analgesia was demonstrated through reduced pain ratings, chronic pain continued to interfere with cognitive processing. Durability of music-induced analgesia is therefore likely to be time-limited and hindered by pain-related attentional disruption, reduced engagement and low absorption levels. Explanations for these results and suggestions for alternative objective monitors of music listening interventions are offered