217 research outputs found
Groups with context-free co-word problem
The class of co-context-free groups is studied. A co-context-free group is defined as one whose coword
problem (the complement of its word problem) is context-free. This class is larger than the
subclass of context-free groups, being closed under the taking of finite direct products, restricted
standard wreath products with context-free top groups, and passing to finitely generated subgroups
and finite index overgroups. No other examples of co-context-free groups are known. It is proved
that the only examples amongst polycyclic groups or the BaumslagâSolitar groups are virtually
abelian. This is done by proving that languages with certain purely arithmetical properties cannot
be context-free; this result may be of independent interest
Random template placement and prior information
In signal detection problems, one is usually faced with the task of searching
a parameter space for peaks in the likelihood function which indicate the
presence of a signal. Random searches have proven to be very efficient as well
as easy to implement, compared e.g. to searches along regular grids in
parameter space. Knowledge of the parameterised shape of the signal searched
for adds structure to the parameter space, i.e., there are usually regions
requiring to be densely searched while in other regions a coarser search is
sufficient. On the other hand, prior information identifies the regions in
which a search will actually be promising or may likely be in vain. Defining
specific figures of merit allows one to combine both template metric and prior
distribution and devise optimal sampling schemes over the parameter space. We
show an example related to the gravitational wave signal from a binary inspiral
event. Here the template metric and prior information are particularly
contradictory, since signals from low-mass systems tolerate the least mismatch
in parameter space while high-mass systems are far more likely, as they imply a
greater signal-to-noise ratio (SNR) and hence are detectable to greater
distances. The derived sampling strategy is implemented in a Markov chain Monte
Carlo (MCMC) algorithm where it improves convergence.Comment: Proceedings of the 8th Edoardo Amaldi Conference on Gravitational
Waves. 7 pages, 4 figure
Localizing gravitational wave sources with optical telescopes and combining electromagnetic and gravitational wave data
Neutron star binaries, which are among the most promising sources for the
direct detection of gravitational waves (GW) by ground based detectors, are
also potential electromagnetic (EM) emitters. Gravitational waves will provide
a new window to observe these events and hopefully give us glimpses of new
astrophysics. In this paper, we discuss how EM information of these events can
considerably improve GW parameter estimation both in terms of accuracy and
computational power requirement. And then in return how GW sky localization can
help EM astronomers in follow-up studies of sources which did not yield any
prompt emission. We discuss how both EM source information and GW source
localization can be used in a framework of multi-messenger astronomy. We
illustrate how the large error regions in GW sky localizations can be handled
in conducting optical astronomy in the advance detector era. We show some
preliminary results in the context of an array of optical telescopes called
BlackGEM, dedicated for optical follow-up of GW triggers, that is being
constructed in La Silla, Chile and is expected to operate concurrent to the
advanced GW detectors.Comment: 8 pages, 8 figures, Proceeding for Sant Cugat Forum for Astrophysic
Gravitational-Wave Astronomy with Inspiral Signals of Spinning Compact-Object Binaries
Inspiral signals from binary compact objects (black holes and neutron stars)
are primary targets of the ongoing searches by ground-based gravitational-wave
interferometers (LIGO, Virgo, GEO-600 and TAMA-300). We present
parameter-estimation simulations for inspirals of black-hole--neutron-star
binaries using Markov-chain Monte-Carlo methods. For the first time, we have
both estimated the parameters of a binary inspiral source with a spinning
component and determined the accuracy of the parameter estimation, for
simulated observations with ground-based gravitational-wave detectors. We
demonstrate that we can obtain the distance, sky position, and binary
orientation at a higher accuracy than previously suggested in the literature.
For an observation of an inspiral with sufficient spin and two or three
detectors we find an accuracy in the determination of the sky position of
typically a few tens of square degrees.Comment: v2: major conceptual changes, 4 pages, 1 figure, 1 table, submitted
to ApJ
The effects of LIGO detector noise on a 15-dimensional Markov-chain Monte-Carlo analysis of gravitational-wave signals
Gravitational-wave signals from inspirals of binary compact objects (black
holes and neutron stars) are primary targets of the ongoing searches by
ground-based gravitational-wave (GW) interferometers (LIGO, Virgo, and
GEO-600). We present parameter-estimation results from our Markov-chain
Monte-Carlo code SPINspiral on signals from binaries with precessing spins. Two
data sets are created by injecting simulated GW signals into either synthetic
Gaussian noise or into LIGO detector data. We compute the 15-dimensional
probability-density functions (PDFs) for both data sets, as well as for a data
set containing LIGO data with a known, loud artefact ("glitch"). We show that
the analysis of the signal in detector noise yields accuracies similar to those
obtained using simulated Gaussian noise. We also find that while the Markov
chains from the glitch do not converge, the PDFs would look consistent with a
GW signal present in the data. While our parameter-estimation results are
encouraging, further investigations into how to differentiate an actual GW
signal from noise are necessary.Comment: 11 pages, 2 figures, NRDA09 proceeding
Bayesian parameter estimation in the second LISA Pathfinder Mock Data Challenge
A main scientific output of the LISA Pathfinder mission is to provide a noise
model that can be extended to the future gravitational wave observatory, LISA.
The success of the mission depends thus upon a deep understanding of the
instrument, especially the ability to correctly determine the parameters of the
underlying noise model. In this work we estimate the parameters of a simplified
model of the LISA Technology Package (LTP) instrument. We describe the LTP by
means of a closed-loop model that is used to generate the data, both injected
signals and noise. Then, parameters are estimated using a Bayesian framework
and it is shown that this method reaches the optimal attainable error, the
Cramer-Rao bound. We also address an important issue for the mission: how to
efficiently combine the results of different experiments to obtain a unique set
of parameters describing the instrument.Comment: 14 pages, 4 figures, submitted to PR
Parameter estimation of spinning binary inspirals using Markov-chain Monte Carlo
We present a Markov-chain Monte-Carlo (MCMC) technique to study the source
parameters of gravitational-wave signals from the inspirals of stellar-mass
compact binaries detected with ground-based gravitational-wave detectors such
as LIGO and Virgo, for the case where spin is present in the more massive
compact object in the binary. We discuss aspects of the MCMC algorithm that
allow us to sample the parameter space in an efficient way. We show sample runs
that illustrate the possibilities of our MCMC code and the difficulties that we
encounter.Comment: 10 pages, 2 figures, submitted to Classical and Quantum Gravit
Inference on inspiral signals using LISA MLDC data
In this paper we describe a Bayesian inference framework for analysis of data
obtained by LISA. We set up a model for binary inspiral signals as defined for
the Mock LISA Data Challenge 1.2 (MLDC), and implemented a Markov chain Monte
Carlo (MCMC) algorithm to facilitate exploration and integration of the
posterior distribution over the 9-dimensional parameter space. Here we present
intermediate results showing how, using this method, information about the 9
parameters can be extracted from the data.Comment: Accepted for publication in Classical and Quantum Gravity, GWDAW-11
special issu
Coherent Bayesian analysis of inspiral signals
We present in this paper a Bayesian parameter estimation method for the
analysis of interferometric gravitational wave observations of an inspiral of
binary compact objects using data recorded simultaneously by a network of
several interferometers at different sites. We consider neutron star or black
hole inspirals that are modeled to 3.5 post-Newtonian (PN) order in phase and
2.5 PN in amplitude. Inference is facilitated using Markov chain Monte Carlo
methods that are adapted in order to efficiently explore the particular
parameter space. Examples are shown to illustrate how and what information
about the different parameters can be derived from the data. This study uses
simulated signals and data with noise characteristics that are assumed to be
defined by the LIGO and Virgo detectors operating at their design
sensitivities. Nine parameters are estimated, including those associated with
the binary system, plus its location on the sky. We explain how this technique
will be part of a detection pipeline for binary systems of compact objects with
masses up to 20 \sunmass, including cases where the ratio of the individual
masses can be extreme.Comment: Accepted for publication in Classical and Quantum Gravity, Special
issue for GWDAW-1
- âŠ