This paper reports on an unmodeled, all-sky search for gravitational waves from merging intermediate mass black hole binaries (IMBHB). The search was performed on data from the second joint science run of the LIGO and Virgo detectors (July 2009 - October 2010) and was sensitive to IMBHBs with a range up to $\sim 200$ Mpc, averaged over the possible sky positions and inclinations of the binaries with respect to the line of sight. No significant candidate was found. Upper limits on the coalescence-rate density of nonspinning IMBHBs with total masses between 100 and $450 \ \mbox{M}_{\odot}$ and mass ratios between $0.25$ and $1\,$ were placed by combining this analysis with an analogous search performed on data from the first LIGO-Virgo joint science run (November 2005 - October 2007). The most stringent limit was set for systems consisting of two $88 \ \mbox{M}_{\odot}$ black holes and is equal to $0.12 \ \mbox{Mpc}^{-3} \ \mbox{Myr}^{-1}$ at the $90\%$ confidence level. This paper also presents the first estimate, for the case of an unmodeled analysis, of the impact on the search range of IMBHB spin configurations: the visible volume for IMBHBs with nonspinning components is roughly doubled for a population of IMBHBs with spins aligned with the binary's orbital angular momentum and uniformly distributed in the dimensionless spin parameter up to 0.8, whereas an analogous population with antialigned spins decreases the visible volume by $\sim 20\%\,$.

In this paper we report on a search for short-duration gravitational wave bursts in the frequency range $64$\,Hz--$1792$\,Hz associated with gamma-ray bursts (GRBs), using data from GEO\,600 and one of the LIGO or Virgo detectors. We introduce the method of a linear search grid to analyse GRB events with large sky localisation uncertainties, for example the localisations provided by the \emph{Fermi} Gamma-ray Burst Monitor (GBM). Coherent searches for gravitational waves (GWs) can be computationally intensive when the GRB sky position is not well-localised, due to the corrections required for the difference in arrival time between detectors. Using a linear search grid we are able to reduce the computational cost of the analysis by a factor of $\mathcal{O}$(10) for GBM events. Furthermore, we demonstrate that our analysis pipeline can improve upon the sky localisation of GRBs detected by the GBM, if a high-frequency GW signal is observed in coincidence. We use the method of the linear grid in a search for GWs associated with 129 GRBs observed satellite-based gamma-ray experiments between 2006 and 2011. The GRBs in our sample had not been previously analysed for GW counterparts. A fraction of our GRB events are analysed using data from GEO\,600 while the detector was using squeezed-light states to improve its sensitivity; this is the first search for GWs using data from a squeezed-light interferometric observatory. We find no evidence for GW signals, either with any individual GRB in this sample or with the population as a whole.For each GRB we place lower bounds on the distance to the progenitor, under an assumption of a fixed GW emission energy of $10^{-2}\,\mathrm{M_{\odot}c^{2}}$, with a median exclusion distance of 0.8 Mpc for emission at 500\,Hz and 0.3 Mpc at 1\,kHz. The reduced computational cost associated with a linear search grid will enable rapid searches for GWs associated with \emph{Fermi} GBM events once the Advanced LIGO and Virgo detectors begin operation.

Cosmic strings can give rise to a large variety of interesting astrophysical phenomena. Among them, powerful bursts of gravitational waves (GWs) produced by cusps are a promising observational signature. In this Letter we present a search for GWs from cosmic string cusps in data collected by the LIGO and Virgo gravitational wave detectors between 2005 and 2010, with over 625 days of live time. We find no evidence of GW signals from cosmic strings. From this result, we derive new constraints on cosmic string parameters, which complement and improve existing limits from previous searches for a stochastic background of GWs from cosmic microwave background measurements and pulsar timing data. In particular, if the size of loops is given by the gravitational backreaction scale, we place upper limits on the string tension $G\mu$ below $10^{-8}$ in some regions of the cosmic string parameter space.

We present the results of a search for gravitational waves associated with 223 gamma-ray bursts (GRBs) detected by the InterPlanetary Network (IPN) in 2005-2010 during LIGO's fifth and sixth science runs and Virgo's first, second and third science runs. The IPN satellites provide accurate times of the bursts and sky localizations that vary significantly from degree scale to hundreds of square degrees. We search for both a well-modeled binary coalescence signal, the favored progenitor model for short GRBs, and for generic, unmodeled gravitational wave bursts. Both searches use the event time and sky localization to improve the gravitational-wave search sensitivity as compared to corresponding all-time, all-sky searches. We find no evidence of a gravitational-wave signal associated with any of the IPN GRBs in the sample, nor do we find evidence for a population of weak gravitational-wave signals associated with the GRBs. For all IPN-detected GRBs, for which a sufficient duration of quality gravitational-wave data is available, we place lower bounds on the distance to the source in accordance with an optimistic assumption of gravitational-wave emission energy of $10^{-2}M_{\odot}c^2$ at 150 Hz, and find a median of 13 Mpc. For the 27 short-hard GRBs we place 90\% confidence exclusion distances to two source models: a binary neutron star coalescence, with a median distance of 12Mpc, or the coalescence of a neutron star and black hole, with a median distance of 22 Mpc. Finally, we combine this search with previously published results to provide a population statement for GRB searches in first-generation LIGO and Virgo gravitational-wave detectors, and a resulting examination of prospects for the advanced gravitational-wave detectors.

We present an implementation of the $\mathcal{F}$-statistic to carry out the first search in data from the Virgo laser interferometric gravitational wave detector for periodic gravitational waves from {\em a priori} unknown, isolated rotating neutron stars. We searched a frequency $f_0$ range from 100\,Hz to 1\,kHz and the frequency dependent spindown $f_1$ range from $-1.6\,(f_0/100\,{\rm Hz}) \times 10^{-9}\,$\,Hz/s to zero. A large part of this frequency - spindown space was unexplored by any of the all-sky searches published so far. Our method consisted of a coherent search over two-day periods using the $\mathcal{F}$-statistic, followed by a search for coincidences among the candidates from the two-day segments. We have introduced a number of novel techniques and algorithms that allow the use of the Fast Fourier Transform (FFT) algorithm in the coherent part of the search resulting in a fifty-fold speed-up in computation of the $\mathcal{F}$-statistic with respect to the algorithm used in the other pipelines. No significant gravitational wave signal was found. The sensitivity of the search was estimated by injecting signals into the data. In the most sensitive parts of the detector band more than 90\% of signals would have been detected with dimensionless gravitational-wave amplitude greater than $5 \times 10^{-24}$.

We present an accurate and efficient numerical method for solving the Black–Scholes equation. The method uses an adaptive grid technique which is based on a far-field boundary position and the Peclet condition. We present the algorithm for the automatic adaptive grid generation: First, we determine a priori suitable far-field boundary location using the mathematical model parameters. Second, generate the uniform fine grid around the non-smooth point of the payoff and a non-uniform grid in the remaining regions. Numerical tests are presented to demonstrate the accuracy and efficiency of the proposed method. The results show that the computational time is reduced substantially with the accuracy being maintained.

We present the first results of an all-sky search for continuous gravitational waves from unknown spinning neutron stars in binary systems using LIGO and Virgo data. Using a specially developed analysis program, the TwoSpect algorithm, the search was carried out on data from the sixth LIGO Science Run and the second and third Virgo Science Runs. The search covers a range of frequencies from 20~Hz to 520~Hz, a range of orbital periods from 2 to $\sim$2,254~h and a frequency- and period-dependent range of frequency modulation depths from 0.277 to 100~mHz. This corresponds to a range of projected semi-major axes of the orbit from $\sim$$0.6\times10^{-3}$~ls to $\sim$6,500~ls assuming the orbit of the binary is circular. While no plausible candidate gravitational wave events survive the pipeline, upper limits are set on the analyzed data. The most sensitive 95\% confidence upper limit obtained on gravitational wave strain is $2.3\times10^{-24}$ at 217~Hz, assuming the source waves are circularly polarized. Although this search has been optimized for circular binary orbits, the upper limits obtained remain valid for orbital eccentricities as large as 0.9. In addition, upper limits are placed on continuous gravitational wave emission from the low-mass x-ray binary Scorpius X-1 between 20~Hz and 57.25~Hz.

We report the results of a multimessenger search for coincident signals from the LIGO and Virgo gravitational-wave observatories and the partially completed IceCube high-energy neutrino detector, including periods of joint operation between 2007-2010. These include parts of the 2005-2007 run and the 2009-2010 run for LIGO-Virgo, and IceCube's observation periods with 22, 59 and 79 strings. We find no significant coincident events, and use the search results to derive upper limits on the rate of joint sources for a range of source emission parameters. For the optimistic assumption of gravitational-wave emission energy of $10^{-2}$\,M$_\odot$c$^2$ at $\sim 150$\,Hz with $\sim 60$\,ms duration, and high-energy neutrino emission of $10^{51}$\,erg comparable to the isotropic gamma-ray energy of gamma-ray bursts, we limit the source rate below $1.6 \times 10^{-2}$\,Mpc$^{-3}$yr$^{-1}$. We also examine how combining information from gravitational waves and neutrinos will aid discovery in the advanced gravitational-wave detector era.

Gravitational waves from a variety of sources are predicted to superpose to create a stochastic background. This background is expected to contain unique information from throughout the history of the universe that is unavailable through standard electromagnetic observations, making its study of fundamental importance to understanding the evolution of the universe. We carry out a search for the stochastic background with the latest data from LIGO and Virgo. Consistent with predictions from most stochastic gravitational-wave background models, the data display no evidence of a stochastic gravitational-wave signal. Assuming a gravitational-wave spectrum of ${\Omega}_{\rm GW}(f)={\Omega}_{\alpha}\left({f/f_{\rm{ref}}}\right)^{\alpha}$, we place 95\% confidence level upper limits on the energy density of the background in each of four frequency bands spanning 41.5--1726~Hz. In the frequency band of 41.5--169.25~Hz for a spectral index of $\alpha=0$, we constrain the energy density of the stochastic background to be $\Omega_{\rm GW}(f)<5.6\times10^{-6}$. For the 600--1000~Hz band, $\Omega_{\rm GW}(f)<0.14(f/900~{\rm Hz})^3$, a factor of 2.5 lower than the best previously reported upper limits. We find $\Omega_{\rm GW}(f)<1.8\times10^{-4}$ using a spectral index of zero for 170--600~Hz and $\Omega_{\rm GW}(f)<1.0(f/1300~{\rm Hz})^3$ for 1000--1726~Hz, bands in which no previous direct limits have been placed. The limits in these four bands are the lowest direct measurements to date on the stochastic background. We discuss the implications of these results in light of the recent claim by the BICEP2 experiment of the possible evidence for inflationary gravitational waves.

For the coupled stochastic dynamical system, we study the functional relation between noisy fluctuation and node degree. We extend the approaches for obtaining functional relation in Wang et al. (2009) to the weighted network whose link weight is dependent on the node degree. For the network with strong heterogeneity in degree distribution, we find that the theoretical result derived from the approaches in Wang et al. (2009) shows disagreement with numerical results. Here, we propose novel approaches using the average of higher order moments and improve the accuracy of functional relation between noisy fluctuation and node degree. Also, we investigate the functional relation of noisy fluctuation versus node input strength.