SLEPLET: Slepian Scale-Discretised Wavelets in Python

Wavelets are widely used in various disciplines to analyse signals both in space and scale. Whilst many fields measure data on manifolds (i.e., the sphere), often data are only observed on a partial region of the manifold. Wavelets are a typical approach to data of this form, but the wavelet coefficients that overlap with the boundary become contaminated and must be removed for accurate analysis. Another approach is to estimate the region of missing data and to use existing whole-manifold methods for analysis. However, both approaches introduce uncertainty into any analysis. Slepian wavelets enable one to work directly with only the data present, thus avoiding the problems discussed above. Applications of Slepian wavelets to areas of research measuring data on the partial sphere include gravitational/magnetic fields in geodesy, ground-based measurements in astronomy, measurements of whole-planet properties in planetary science, geomagnetism of the Earth, and cosmic microwave background analyses.Comment: 4 page

SLEPLET: Slepian Scale-Discretised Wavelets in Python

Wavelets are widely used in various disciplines to analyse signals both in space and scale. Whilst many fields measure data on manifolds (i.e., the sphere), often data are only observed on a partial region of the manifold. Wavelets are a typical approach to data of this form, but the wavelet coefficients that overlap with the boundary become contaminated and must be removed for accurate analysis. Another approach is to estimate the region of missing data and to use existing whole-manifold methods for analysis. However, both approaches introduce uncertainty into any analysis. Slepian wavelets enable one to work directly with only the data present, thus avoiding the problems discussed above. Applications of Slepian wavelets to areas of research measuring data on the partial sphere include gravitational/magnetic fields in geodesy, ground-based measurements in astronomy, measurements of whole-planet properties in planetary science, geomagnetism of the Earth, and cosmic microwave background analyses

Sifting Convolution on the Sphere

A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the adoption of an alternative translation operator on the sphere. This translation operator follows by analogy with the Euclidean translation when viewed in harmonic space. The sifting convolution satisfies a variety of desirable properties that are lacking in alternate definitions, namely: it supports directional kernels; it has an output which remains on the sphere; and is efficient to compute. An illustration of the sifting convolution on a topographic map of the Earth demonstrates that it supports directional kernels to perform anisotropic filtering, while its output remains on the sphere.Comment: 5 pages, 3 figure

Molecular Cloning and Characterization of a Human Mitochondrial Ceramidase

We have recently purified a rat brain membrane-bound nonlysosomal ceramidase (El Bawab, S., Bielawska, A., and Y. A. Hannun (1999) J. Biol. Chem. 274, 27948-27955). Using peptide sequences obtained from the purified rat brain enzyme, we report here the cloning of the human isoform. The deduced amino acid sequence of the protein did not show any similarity with proteins of known function but was homologous to three putative proteins from Arabidospis thaliana, Mycobacterium tuberculosis, and Dictyostelium discoideum. Several blocks of amino acids were highly conserved in all of these proteins. Analysis of the protein sequence revealed the presence at the N terminus of a signal peptide followed by a putative myristoylation site and a putative mitochondrial targeting sequence. The predicted molecular mass was 84 kDa, and the isoelectric point was 6.69, in agreement with rat brain purified enzyme. Northern blot analysis of multiple human tissues showed the presence of a major band corresponding to a size of 3.5 kilobase. Analysis of this major band on the blot indicated that the enzyme is ubiquitously expressed with higher levels in kidney, skeletal muscle, and heart. The enzyme was then overexpressed in HEK 293 and MCF7 cells using the pcDNA3. 1/His-ceramidase construct, and ceramidase activity (at pH 9.5) increased by 50- and 12-fold, respectively. Next, the enzyme was characterized using lysate of overexpressing cells. The results confirmed that the enzyme catalyzes the hydrolysis of ceramide in the neutral alkaline range and is independent of cations. Finally, a green fluorescent protein-ceramidase fusion protein was constructed to investigate the localization of this enzyme. The results showed that the green fluorescent protein-ceramidase fusion protein presented a mitochondrial localization pattern and colocalized with mitochondrial specific probes. These results demonstrate that this novel ceramidase is a mitochondrial enzyme, and they suggest the existence of a topologically restricted pathways of sphingolipid metabolism

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer's classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation

Upper limits on the strength of periodic gravitational waves from PSR J1939+2134

The first science run of the LIGO and GEO gravitational wave detectors presented the opportunity to test methods of searching for gravitational waves from known pulsars. Here we present new direct upper limits on the strength of waves from the pulsar PSR J1939+2134 using two independent analysis methods, one in the frequency domain using frequentist statistics and one in the time domain using Bayesian inference. Both methods show that the strain amplitude at Earth from this pulsar is less than a few times $10^{-22}$.Comment: 7 pages, 1 figure, to appear in the Proceedings of the 5th Edoardo Amaldi Conference on Gravitational Waves, Tirrenia, Pisa, Italy, 6-11 July 200

Improving the sensitivity to gravitational-wave sources by modifying the input-output optics of advanced interferometers

We study frequency dependent (FD) input-output schemes for signal-recycling interferometers, the baseline design of Advanced LIGO and the current configuration of GEO 600. Complementary to a recent proposal by Harms et al. to use FD input squeezing and ordinary homodyne detection, we explore a scheme which uses ordinary squeezed vacuum, but FD readout. Both schemes, which are sub-optimal among all possible input-output schemes, provide a global noise suppression by the power squeeze factor, while being realizable by using detuned Fabry-Perot cavities as input/output filters. At high frequencies, the two schemes are shown to be equivalent, while at low frequencies our scheme gives better performance than that of Harms et al., and is nearly fully optimal. We then study the sensitivity improvement achievable by these schemes in Advanced LIGO era (with 30-m filter cavities and current estimates of filter-mirror losses and thermal noise), for neutron star binary inspirals, and for narrowband GW sources such as low-mass X-ray binaries and known radio pulsars. Optical losses are shown to be a major obstacle for the actual implementation of these techniques in Advanced LIGO. On time scales of third-generation interferometers, like EURO/LIGO-III (~2012), with kilometer-scale filter cavities, a signal-recycling interferometer with the FD readout scheme explored in this paper can have performances comparable to existing proposals. [abridged]Comment: Figs. 9 and 12 corrected; Appendix added for narrowband data analysi

Search for gravitational wave bursts in LIGO's third science run

We report on a search for gravitational wave bursts in data from the three LIGO interferometric detectors during their third science run. The search targets subsecond bursts in the frequency range 100-1100 Hz for which no waveform model is assumed, and has a sensitivity in terms of the root-sum-square (rss) strain amplitude of hrss ~ 10^{-20} / sqrt(Hz). No gravitational wave signals were detected in the 8 days of analyzed data.Comment: 12 pages, 6 figures. Amaldi-6 conference proceedings to be published in Classical and Quantum Gravit

Searching for a Stochastic Background of Gravitational Waves with LIGO

The Laser Interferometer Gravitational-wave Observatory (LIGO) has performed the fourth science run, S4, with significantly improved interferometer sensitivities with respect to previous runs. Using data acquired during this science run, we place a limit on the amplitude of a stochastic background of gravitational waves. For a frequency independent spectrum, the new limit is $\Omega_{\rm GW} < 6.5 \times 10^{-5}$. This is currently the most sensitive result in the frequency range 51-150 Hz, with a factor of 13 improvement over the previous LIGO result. We discuss complementarity of the new result with other constraints on a stochastic background of gravitational waves, and we investigate implications of the new result for different models of this background.Comment: 37 pages, 16 figure

Investigating the effectiveness of oral ketamine on pain, mood and quality of life in treatment resistant chronic pain

IntroductionChronic pain is defined as pain lasting longer than 3 months. This often causes persistent emotional distress and functional disability that is refractory to conventional treatments. Emerging evidence suggests that oral Ketamine therapy may have a specific role in managing treatment-resistant chronic pain. This study aimed to assess the effectiveness of oral ketamine within a tertiary chronic pain management clinic.MethodsThis study was a clinic-based retrospective descriptive study of 79 patients with a broad range of chronic pain diagnoses and treated with oral ketamine over a period up to 12 years. Changes in pain, mood and quality of life (QoL) were assessed using a numerical pain severity score, the Brief Pain Inventory (BPI), the Public Health Questionnaire (PHQ-9) and American Chronic Pain Association Quality of Life (QoL) scale.Results73 patients were accessible for follow-up (mean daily dose and treatment duration were 193.84 mg and 22.6 months respectively). Pain scores decreased (p &lt; 0.0001) on both numerical scores (41.6% decrease) and BPI scoring (mean decrease 2.61). Mood improved (p &lt; 0.0001) across both PHQ-9 and BPI measurements. Patients also reported less difficulty with daily activities and improved QoL. The most common adverse reaction was drowsiness (21.9%), with 30.1% reporting no adverse reactions from Ketamine.DiscussionThis work adds to the growing body of evidence that under the supervision of a pain specialist, oral ketamine therapy may be a safe, tolerable and effective treatment for chronic pain conditions which have not responded to other management options. Further research is required to produce a more accurate understanding of its chronic use. Key messageThis real-world study shows that patients being treated with oral ketamine for chronic pain report decreased severity of pain, improved mood and increased quality of life across all conditions