Marginalizing the likelihood function for modeled gravitational wave searches

Matched filtering is a commonly used technique in gravitational wave searches for signals from compact binary systems and from rapidly rotating neutron stars. A common issue in these searches is dealing with four extrinsic parameters which do not affect the phase evolution of the system: the overall amplitude, initial phase, and two angles determining the overall orientation of the system. The F-statistic maximizes the likelihood function analytically over these parameters, while the B-statistic marginalizes over them. The B-statistic, while potentially more powerful and capable of incorporating astrophysical priors, is not as widely used because of the computational difficulty of performing the marginalization. In this paper we address this difficulty and show how the marginalization can be done analytically by combining the four parameters into a set of complex amplitudes. The results of this paper are applicable to both transient non-precessing binary coalescence events, and to long lived signals from rapidly rotating neutron stars.Comment: 26 page

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

Towards the graviton from spinfoams: higher order corrections in the 3d toy model

We consider the recent calculation gr-qc/0508124 of the graviton propagator in the spinfoam formalism. Within the 3d toy model introduced in gr-qc/0512102, we test how the spinfoam formalism can be used to construct the perturbative expansion of graviton amplitudes. Although the 3d graviton is a pure gauge, one can choose to work in a gauge where it is not zero and thus reproduce the structure of the 4d perturbative calculations. We compute explicitly the next to leading and next to next to leading orders, corresponding to one-loop and two-loop corrections. We show that while the first arises entirely from the expansion of the Regge action around the flat background, the latter receives contributions from the microscopic, non Regge-like, quantum geometry. Surprisingly, this new contribution reduces the magnitude of the next to next to leading order. It thus appears that the spinfoam formalism is likely to substantially modify the conventional perturbative expansion at higher orders. This result supports the interest in this approach. We then address a number of open issues in the rest of the paper. First, we discuss the boundary state ansatz, which is a key ingredient in the whole construction. We propose a way to enhance the ansatz in order to make the edge lengths and dihedral angles conjugate variables in a mathematically well-defined way. Second, we show that the leading order is stable against different choices of the face weights of the spinfoam model; the next to leading order, on the other hand, is changed in a simple way, and we show that the topological face weight minimizes it. Finally, we extend the leading order result to the case of a regular, but not equilateral, tetrahedron.Comment: 24 pages, many figure

The PyCBC search for gravitational waves from compact binary coalescence

We describe the PyCBC search for gravitational waves from compact-object binary coalescences in advanced gravitational-wave detector data. The search was used in the first Advanced LIGO observing run and unambiguously identified two black hole binary mergers, GW150914 and GW151226. At its core, the PyCBC search performs a matched-filter search for binary merger signals using a bank of gravitational-wave template waveforms. We provide a complete description of the search pipeline including the steps used to mitigate the effects of noise transients in the data, identify candidate events and measure their statistical significance. The analysis is able to measure false-alarm rates as low as one per million years, required for confident detection of signals. Using data from initial LIGO's sixth science run, we show that the new analysis reduces the background noise in the search, giving a 30% increase in sensitive volume for binary neutron star systems over previous searches.Comment: 29 pages, 7 figures, accepted by Classical and Quantum Gravit

The TcEG1 beetle (Tribolium castaneum) cellulase produced in transgenic switchgrass is active at alkaline pH and auto-hydrolyzes biomass for increased cellobiose release

Background Genetically engineered biofuel crops, such as switchgrass (Panicum virgatum L.), that produce their own cell wall-digesting cellulase enzymes would reduce costs of cellulosic biofuel production. To date, non-bioenergy plant models have been used in nearly all studies assessing the synthesis and activity of plant-produced fungal and bacterial cellulases. One potential source for cellulolytic enzyme genes is herbivorous insects adapted to digest plant cell walls. Here we examine the potential of transgenic switchgrass-produced TcEG1 cellulase from Tribolium castaneum (red flour beetle). This enzyme, when overproduced in Escherichia coliand Saccharomyces cerevisiae, efficiently digests cellulose at optima of 50 °C and pH 12.0. Results TcEG1 that was produced in green transgenic switchgrass tissue had a range of endoglucanase activity of 0.16–0.05 units (µM glucose release/min/mg) at 50 °C and pH 12.0. TcEG1 activity from air-dried leaves was unchanged from that from green tissue, but when tissue was dried in a desiccant oven (46 °C), specific enzyme activity decreased by 60%. When transgenic biomass was “dropped-in” into an alkaline buffer (pH 12.0) and allowed to incubate at 50 °C, cellobiose release was increased up to 77% over non-transgenic biomass. Saccharification was increased in one transgenic event by 28%, which had a concurrent decrease in lignin content of 9%. Histological analysis revealed an increase in cell wall thickness with no change to cell area or perimeter. Transgenic plants produced more, albeit narrower, tillers with equivalent dry biomass as the control. Conclusions This work describes the first study in which an insect cellulase has been produced in transgenic plants; in this case, the dedicated bioenergy crop switchgrass. Switchgrass overexpressing the TcEG1 gene appeared to be morphologically similar to its non-transgenic control and produced equivalent dry biomass. Therefore, we propose TcEG1 transgenics could be bred with other transgenic germplasm (e.g., low-lignin lines) to yield new switchgrass with synergistically reduced recalcitrance to biofuel production. In addition, transgenes for other cell wall degrading enzymes may be stacked with TcEG1 in switchgrass to yield complementary cell wall digestion features and complete auto-hydrolysis

Acceleration of generalized hypergeometric functions through precise remainder asymptotics

We express the asymptotics of the remainders of the partial sums {s_n} of the generalized hypergeometric function q+1_F_q through an inverse power series z^n n^l \sum_k c_k/n^k, where the exponent l and the asymptotic coefficients {c_k} may be recursively computed to any desired order from the hypergeometric parameters and argument. From this we derive a new series acceleration technique that can be applied to any such function, even with complex parameters and at the branch point z=1. For moderate parameters (up to approximately ten) a C implementation at fixed precision is very effective at computing these functions; for larger parameters an implementation in higher than machine precision would be needed. Even for larger parameters, however, our C implementation is able to correctly determine whether or not it has converged; and when it converges, its estimate of its error is accurate.Comment: 36 pages, 6 figures, LaTeX2e. Fixed sign error in Eq. (2.28), added several references, added comparison to other methods, and added discussion of recursion stabilit