Sums of two squares and a power

We extend results of Jagy and Kaplansky and the present authors and show that for all $k\geq 3$ there are infinitely many positive integers $n$, which cannot be written as $x^2+y^2+z^k=n$ for positive integers $x,y,z$, where for $k\not\equiv 0 \bmod 4$ a congruence condition is imposed on $z$. These examples are of interest as there is no congruence obstruction itself for the representation of these $n$. This way we provide a new family of counterexamples to the Hasse principle or strong approximation.Comment: 6 pages, to appear in the memorial volume "From Arithmetic to Zeta-Functions - Number Theory in Memory of Wolfgang Schwarz

Searching for gravitational waves from known pulsars

We present upper limits on the amplitude of gravitational waves from 28 isolated pulsars using data from the second science run of LIGO. The results are also expressed as a constraint on the pulsars' equatorial ellipticities. We discuss a new way of presenting such ellipticity upper limits that takes account of the uncertainties of the pulsar moment of inertia. We also extend our previous method to search for known pulsars in binary systems, of which there are about 80 in the sensitive frequency range of LIGO and GEO 600.Comment: Accepted by CQG for the proceeding of GWDAW9, 7 pages, 2 figure

First upper limits from LIGO on gravitational wave bursts

We report on a search for gravitational wave bursts using data from the first science run of the LIGO detectors. Our search focuses on bursts with durations ranging from 4 ms to 100 ms, and with significant power in the LIGO sensitivity band of 150 to 3000 Hz. We bound the rate for such detected bursts at less than 1.6 events per day at 90% confidence level. This result is interpreted in terms of the detection efficiency for ad hoc waveforms (Gaussians and sine-Gaussians) as a function of their root-sum-square strain h_{rss}; typical sensitivities lie in the range h_{rss} ~ 10^{-19} - 10^{-17} strain/rtHz, depending on waveform. We discuss improvements in the search method that will be applied to future science data from LIGO and other gravitational wave detectors.Comment: 21 pages, 15 figures, accepted by Phys Rev D. Fixed a few small typos and updated a few reference

GHOSTM: A GPU-Accelerated Homology Search Tool for Metagenomics

A large number of sensitive homology searches are required for mapping DNA sequence fragments to known protein sequences in public and private databases during metagenomic analysis. BLAST is currently used for this purpose, but its calculation speed is insufficient, especially for analyzing the large quantities of sequence data obtained from a next-generation sequencer. However, faster search tools, such as BLAT, do not have sufficient search sensitivity for metagenomic analysis. Thus, a sensitive and efficient homology search tool is in high demand for this type of analysis.We developed a new, highly efficient homology search algorithm suitable for graphics processing unit (GPU) calculations that was implemented as a GPU system that we called GHOSTM. The system first searches for candidate alignment positions for a sequence from the database using pre-calculated indexes and then calculates local alignments around the candidate positions before calculating alignment scores. We implemented both of these processes on GPUs. The system achieved calculation speeds that were 130 and 407 times faster than BLAST with 1 GPU and 4 GPUs, respectively. The system also showed higher search sensitivity and had a calculation speed that was 4 and 15 times faster than BLAT with 1 GPU and 4 GPUs.We developed a GPU-optimized algorithm to perform sensitive sequence homology searches and implemented the system as GHOSTM. Currently, sequencing technology continues to improve, and sequencers are increasingly producing larger and larger quantities of data. This explosion of sequence data makes computational analysis with contemporary tools more difficult. We developed GHOSTM, which is a cost-efficient tool, and offer this tool as a potential solution to this problem

Applying refinement to the use of mice and rats in rheumatoid arthritis research

Rheumatoid arthritis (RA) is a painful, chronic disorder and there is currently an unmet need for effective therapies that will benefit a wide range of patients. The research and development process for therapies and treatments currently involves in vivo studies, which have the potential to cause discomfort, pain or distress. This Working Group report focuses on identifying causes of suffering within commonly used mouse and rat ‘models’ of RA, describing practical refinements to help reduce suffering and improve welfare without compromising the scientific objectives. The report also discusses other, relevant topics including identifying and minimising sources of variation within in vivo RA studies, the potential to provide pain relief including analgesia, welfare assessment, humane endpoints, reporting standards and the potential to replace animals in RA research

Setting upper limits on the strength of periodic gravitational waves from PSR J1939+2134 using the first science data from the GEO 600 and LIGO detectors

Data collected by the GEO 600 and LIGO interferometric gravitational wave detectors during their first observational science run were searched for continuous gravitational waves from the pulsar J1939+2134 at twice its rotation frequency. Two independent analysis methods were used and are demonstrated in this paper: a frequency domain method and a time domain method. Both achieve consistent null results, placing new upper limits on the strength of the pulsar's gravitational wave emission. A model emission mechanism is used to interpret the limits as a constraint on the pulsar's equatorial ellipticity

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

Analysis of LIGO data for gravitational waves from binary neutron stars

We report on a search for gravitational waves from coalescing compact binary systems in the Milky Way and the Magellanic Clouds. The analysis uses data taken by two of the three LIGO interferometers during the first LIGO science run and illustrates a method of setting upper limits on inspiral event rates using interferometer data. The analysis pipeline is described with particular attention to data selection and coincidence between the two interferometers. We establish an observational upper limit of $\mathcal{R}<$1.7 \times 10^{2}$per year per Milky Way Equivalent Galaxy (MWEG), with 90coalescence rate of binary systems in which each component has a mass in the range 1--3$M_\odot$.Comment: 17 pages, 9 figure

Expansion of the Protein Repertoire in Newly Explored Environments: Human Gut Microbiome Specific Protein Families

The microbes that inhabit particular environments must be able to perform molecular functions that provide them with a competitive advantage to thrive in those environments. As most molecular functions are performed by proteins and are conserved between related proteins, we can expect that organisms successful in a given environmental niche would contain protein families that are specific for functions that are important in that environment. For instance, the human gut is rich in polysaccharides from the diet or secreted by the host, and is dominated by Bacteroides, whose genomes contain highly expanded repertoire of protein families involved in carbohydrate metabolism. To identify other protein families that are specific to this environment, we investigated the distribution of protein families in the currently available human gut genomic and metagenomic data. Using an automated procedure, we identified a group of protein families strongly overrepresented in the human gut. These not only include many families described previously but also, interestingly, a large group of previously unrecognized protein families, which suggests that we still have much to discover about this environment. The identification and analysis of these families could provide us with new information about an environment critical to our health and well being