New Coordinates for the Amplitude Parameter Space of Continuous Gravitational Waves

The parameter space for continuous gravitational waves (GWs) can be divided into amplitude parameters (signal amplitude, inclination and polarization angles describing the orientation of the source, and an initial phase) and phase-evolution parameters. The division is useful in part because the Jaranowski-Krolak-Schutz (JKS) coordinates on the four-dimensional amplitude parameter space allow the GW signal to be written as a linear combination of four template waveforms with the JKS coordinates as coefficients. We define a new set of coordinates on the amplitude parameter space, with the same properties, which is more closely connected to the physical amplitude parameters. These naturally divide into two pairs of Cartesian-like coordinates on two-dimensional subspaces, one corresponding to left- and the other to right-circular polarization. We thus refer to these as CPF (circular polarization factored) coordinates. The corresponding two sets of polar coordinates (known as CPF-polar) can be related in a simple way to the physical parameters. We illustrate some simplifying applications for these various coordinate systems, such as: a calculation of Jacobians between various coordinate systems; an illustration of the signal coordinate singularities associated with left- and right-circular polarization, which correspond to the origins of the two two-dimensional subspaces; and an elucidation of the form of the log-likelihood ratio between hypotheses of Gaussian noise with and without a continuous GW signal. These are used to illustrate some of the prospects for approximate evaluation of a Bayesian detection statistic defined by marginalization over the physical parameter space. Additionally, in the presence of simplifying assumptions about the observing geometry, we are able to explicitly evaluate the integral for the Bayesian detection statistic, and compare it to the approximate results.Comment: REVTeX, 18 pages, 8 image files included in 7 figure

Reducing Decay Losses in Hardwood Forests and Farm Woodlots

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Fabrication of cantilever arrays with tips for parallel optical readout

We report on progress in the fabrication of cantilever arrays with tips. The process features only one lithographic step for the definition of both the tips and cantilevers. The tips have a uniform height distribution and are placed by selfalignment on the cantilever. The arrays are fabricated for an optical readout technique under development in which the cantilever arrays serve as diffraction gratings. This work describes our ongoing effort in array fabrication as well as preliminary results on optical readout of a previously fabricated batch of tipless cantilever arrays using Fraunhofer diffraction

Reliability of multi-parameter mapping (MPM) in the cervical cord: A multi-center multi-vendor quantitative MRI study

MRI based multicenter studies which target neurological pathologies affecting the spinal cord and brain – including spinal cord injury (SCI) – require standardized acquisition protocols and image processing methods. We have optimized and applied a multi-parameter mapping (MPM) protocol that simultaneously covers the brain and the cervical cord within a traveling heads study across six clinical centers (Leutritz et al., 2020). The MPM protocol includes quantitative maps (magnetization transfer saturation (MT), proton density (PD), longitudinal (R1), and effective transverse (R2*) relaxation rates) sensitive to myelination, water content, iron concentration, and morphometric measures, such as cross-sectional cord area. Previously, we assessed the repeatability and reproducibility of the brain MPM data acquired in the five healthy participants who underwent two scan-rescans (Leutritz et al., 2020). This study focuses on the cervical cord MPM data derived from the same acquisitions to determine its repeatability and reproducibility in the cervical cord. MPM matrices of the cervical cord were generated and processed using the hMRI and the spinal cord toolbox. To determine reliability of the cervical MPM data, the intra-site (i.e., scan-rescan) coefficient of variation (CoV), inter-site CoV, and bias within region of interests (C1, C2 and C3 levels) were determined. The range of the mean intra- and inter-site CoV of MT, R1 and PD was between 2.5% and 12%, and between 1.1% and 4.0% for the morphometric measures. In conclusion, the cervical MPM data showed a high repeatability and reproducibility for key imaging biomarkers and hence can be employed as a standardized tool in multi-center studies, including clinical trials

The Crustal Rigidity of a Neutron Star, and Implications for PSR 1828-11 and other Precession Candidates

We calculate the crustal rigidity parameter, b, of a neutron star (NS), and show that b is a factor 40 smaller than the standard estimate due to Baym & Pines (1971). For a NS with a relaxed crust, the NS's free-precession frequency is directly proportional to b. We apply our result for b to PSR 1828-11, a 2.5 Hz pulsar that appears to be precessing with period 511 d. Assuming this 511-d period is set by crustal rigidity, we show that this NS's crust is not relaxed, and that its reference spin (roughly, the spin for which the crust is most relaxed) is 40 Hz, and that the average spindown strain in the crust is 5 \times 10^{-5}. We also briefly describe the implications of our b calculation for other well-known precession candidates.Comment: 44 pages, 10 figures, submitted to Ap