Michele's wiki/blog

Authors: Thierry Dauxois, Michel Peyrard, Stefano Ruffo

Date: Mon, 31 Jan 2005

Abstract: The Fermi-Pasta-Ulam (FPU) pioneering numerical experiment played a major role in the history of computer simulation because it introduced this concept for the first time. Moreover, it raised a puzzling question which was answered more than 10 years later. After an introduction to this problem, we briefly review its history and then suggest some simple numerical experiments, with a provided Matlab code, to study various aspects of the ‘FPU’ problem.

abs pdf

Authors: S. Deser

Date: Thu, 24 Feb 2005

Abstract: We show that the empirical signs of the fundamental {\it static} Coulomb/Newton forces are dictated by the seemingly unrelated requirement that the photons/gravitons in the respective underlying Maxwell/Einstein physics be stable. This linkage, which is imposed by special relativity, is manifested upon decomposing the corresponding fields and sources in a gauge-invariant way, and without appeal to static limits. The signs of these free field excitation energies determine those of the instantaneous forces between sources; opposite Coulomb/Newton signs are direct consequences of the Maxwell/Einstein free excitations' odd/even spins.

abs pdf

Authors: Linqing Wen, Jonathan R Gair

Date: Thu, 24 Feb 2005

Abstract: The inspirals of stellar-mass compact objects into supermassive black holes are some of the most important sources for LISA. Detection techniques based on fully coherent matched filtering have been shown to be computationally intractable. We describe an efficient and robust detection method that utilizes the time-frequency evolution of such systems. We show that a typical extreme mass ratio inspiral (EMRI) source could possibly be detected at distances of up to ~2 Gpc, which would mean ~10s of EMRI sources can be detected per year using this technique. We discuss the feasibility of using this method as a first step in a hierarchical search.

abs pdf

Authors: Fabrice Beauville, Damir Buskulic, Raffaele Flaminio, Frédérique Marion, Louis Massonet, Benoit Mours, Julien Ramonet, Edwige Tournefier, Didier Verkindt, Olivier Veziant and Michel Yvert

Ref: Class. Quantum Grav. 20 S789-S801

Abstract: The generation of a grid of templates and their placement in the parameter space is one of the problems that has to be addressed in the search for binary system coalescences detectable in interferometric gravitational wave detectors. We present a technique that computes the closed contour of equal match values around a point in parameter space and a first test of a template placement algorithm using these contours. This algorithm could be used to pave the parameter space. First results about the algorithm's covering efficiency are also presented.

Notes: Good analysis and procedure in the 2-D case, based on minimal-steepness contour reconstruction and a "guiding ellipse" principle for placement. A bit weak on references.

link

Authors: Mark Miller

Date: Mon, 21 Feb 2005

Abstract: I discuss the accuracy requirements on numerical relativity calculations of inspiraling compact object binaries whose extracted gravitational waveforms are to be used as templates for matched filtering signal extraction and physical parameter estimation in modern interferometric gravitational wave detectors. Using a post-Newtonian point particle model for the pre-merger phase of the binary inspiral, I calculate the maximum allowable errors for the mass and relative velocity and positions of the binary during numerical simulations of the binary inspiral. These maximum allowable errors are compared to the errors of state-of-the-art numerical simulations of multiple-orbit binary neutron star calculations in full general relativity, and are found to be smaller by several orders of magnitude. A post-Newtonian model for the error of these numerical simulations suggests that adaptive mesh refinement coupled with second order accurate finite difference codes will not be able to robustly obtain the accuracy required for reliable gravitational wave extraction on Terabyte-scale computers. I conclude that higher order methods (higher order finite difference methods and/or spectral methods) combined with adaptive mesh refinement and/or multipatch technology will be needed for robustly accurate gravitational wave extraction from numerical relativity calculations of binary coalescence scenarios.

Notes: while in this paper Miller uses a questionable definition of allowable template error [first given by Flanagan and Hughes, PRD 57, 4566 (1998)], he avoids claiming effects on detection efficiency, and he makes an interesting attempt to estimate the errors caused by truncation error and close boundaries, drawing conclusions on the computational power required for accurate simulations.

abs pdf

- Time-frequency data analysis

- Template bank economization

- Cumulative distribution of ML detection statistic

- Stochastic-resonance based detectors [see also work by Gammaitoni, Frank Moss, John Sidorowich]

- Binary stars (with large eccentricity)

- Signum coded data analysis [!]

- Sequential detection [!]

Slides at EGO meeting

A lot here…

link

Authors: R. P. Croce (1), Th. Demma (1), V. Galdi (1), V. Pierro (1), I. M. Pinto (1), F. Postiglione (2) ((1) Univ. del Sannio at Benevento IT, (2) D.I.I.I.E. Univ. di Salerno IT)

Date: Wed, 16 Jun 2004

Abstract: In (V. Galdi et al., Phys. Rev. E57, 6470, 1998) a thorough characterization in terms of receiver operating characteristics (ROCs) of stochastic-resonance (SR) detectors of weak harmonic signals of known frequency in additive gaussian noise was given. It was shown that strobed sign-counting based strategies can be used to achieve a nice trade-off between performance and cost, by comparison with non-coherent correlators. Here we discuss the more realistic case where besides the sought signal (whose frequency is assumed known) further unwanted spectrally nearby signals with comparable amplitude are present. Rejection properties are discussed in terms of suitably defined false-alarm and false-dismissal probabilities for various values of interfering signal(s) strength and spectral separation.

abs pdf

Authors: R P Croce, Th Demma, M Longo, S Marano, V Matta, V Pierro and I M Pinto

Ref: Class. Quantum Grav. 20 S803-S813 (2003)

Abstract: The cumulative distribution of the supremum of a set (bank) of correlators is investigated in the context of maximum likelihood detection of gravitational wave chirps from coalescing binaries with unknown parameters. Accurate (lower-bound) approximants are introduced based on a suitable generalization of previous results by Mohanty. Asymptotic properties (in the limit where the number of correlators goes to infinity) are highlighted. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a Gaussian correlation inequality.

Notes: ‘The simplest assumption of statistical independence among N squared noncoherent correlators yields the CDF [1 - exp(-x)]ˆN for their supremum. Extensive numerical evidence [Dhurandhar and Schutz, Phys. Rev. D 50, 2390 (1994); Mohanty and Dhurandhar, Phys. Rev. D 54, 7108 (1996)] shows that this formula can be made fairly accurate provided N is reduced by a suitable factor epsilon, which can be loosely understood by assuming that all correlators in a covariance neighbourhood are counted as one [Jaranowski et al., Phys. Rev. D 58, 063001 (1998)]. An elegant argument whereby an approximate formula for epsilon could be obtained has been proposed by Mohanty [Phys. Rev. D 57, 630 (1998)], under the assumptions that (i) at most two (squared, noncoherent) correlators z, z' can simultaneously exceed a given threshold x, and (ii) these can only be nearest (largest absolute covariance) neighbours. Accurate (lower-bound) approximants are introduced based on a suitable generalization of previous results by Mohanty.’

link

Authors: R. P. Croce, Th. Demma, M. Longo, S. Marano, V. Matta, V. Pierro, I. M. Pinto

Date: Sat, 24 Apr 2004

Ref: Class. Quant. Grav. 21, 4955 (2004)

Abstract: In a recent paper dealing with maximum likelihood detection of gravitational wave chirps from coalescing binaries with unknown parameters we introduced an accurate representation of the no-signal cumulative distribution of the supremum of the whole correlator bank. This result can be used to derive a refined estimate of the number of templates yielding the best tradeoff between detector's performance (in terms of lost signals among those potentially detectable) and computational burden.

Notes: ``On the basis of the above findings, the following conclusions can be drawn: […] increasing the number of templates beyond a critical value corresponding to the knee-point in the curve of [MM vs. number of templates] does not produce a sensible increase in the detectable fraction of potentially observable sources, at the expense of a marked growth of computational load. On the other hand, using the presently most accurate available representation of the no-signal cumulative distribution of the (whole-bank) detection statistic to compute the threshold results in a sizeable increase (~ 5%) in the detectable fraction of potentially observable sources over the naive MMˆ3 estimate. Both findings above support the current trend toward the use of hierarchical search strategies for best tradeoff between detector’s performance and computational burden.''

abs pdf

Authors: R.P. Croce, Th. Demma, M. Longo, S. Marano, V. Matta, V. Pierro, I.M. Pinto

Date: Wed, 5 May 2004

Abstract: The general problem of computing the false-alarm rate vs. detection-threshold relationship for a bank of correlators is addressed, in the context of maximum-likelihood detection of gravitational waves, with specific reference to chirps from coalescing binary systems. Accurate (lower-bound) approximants for the cumulative distribution of the whole-bank supremum are deduced from a class of Bonferroni-type inequalities. The asymptotic properties of the cumulative distribution are obtained, in the limit where the number of correlators goes to infinity. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a gaussian-correlation inequality. The result is used to estimate the optimum template density, yielding the best tradeoff between computational cost and detection efficiency, in terms of undetected potentially observable sources at a prescribed false-alarm level, for the simplest case of Newtonian chirps.

abs pdf

Authors: Nicolas Arnaud, Matteo Barsuglia, Marie-Anne Bizouard, Violette Brisson, Fabien Cavalier, Michel Davier, Patrice Hello, Stephane Kreckelbergh, Edward K. Porter

Date: Tue, 14 Jan 2003

Abstract: Searching for a signal depending on unknown parameters in a noisy background with matched filtering techniques always requires an analysis of the data with several templates in parallel in order to ensure a proper match between the filter and the real waveform. The key feature of such an implementation is the design of the filter bank which must be small to limit the computational cost while keeping the detection efficiency as high as possible. This paper presents a geometrical method which allows one to cover the corresponding physical parameter space by a set of ellipses, each of them being associated to a given template. After the description of the main characteristics of the algorithm, the method is applied in the field of gravitational wave (GW) data analysis, for the search of damped sine signals. Such waveforms are expected to be produced during the de-excitation phase of black holes -- the so-called 'ringdown' signals -- and are also encountered in some numerically computed supernova signals.

abs pdf

Authors: Anand S. Sengupta (1), Sanjeev V. Dhurandhar (1), Albert Lazzarini (2), Tom Prince (3) ((1) IUCAA, Pune, India (2) LIGO Laboratory, Caltech (3) Jet Propulsion Laboratory, Caltech)

Date: Thu, 27 Sep 2001

Abstract: Pattern matching techniques like matched filtering will be used for online extraction of gravitational wave signals buried inside detector noise. This involves cross correlating the detector output with hundreds of thousands of templates spanning a multi-dimensional parameter space, which is very expensive computationally. A faster implementation algorithm was devised by Mohanty and Dhurandhar [1996] using a hierarchy of templates over the mass parameters, which speeded up the procedure by about 25 to 30 times. We show that a further reduction in computational cost is possible if we extend the hierarchy paradigm to an extra parameter, namely, the time of arrival of the signal. In the first stage, the chirp waveform is cut-off at a relatively low frequency allowing the data to be coarsely sampled leading to cost saving in performing the FFTs. This is possible because most of the signal power is at low frequencies, and therefore the advantage due to hierarchy over masses is not compromised. Results are obtained for spin-less templates up to the second post-Newtonian (2PN) order for a single detector with LIGO I noise power spectral density. We estimate that the gain in computational cost over a flat search is about 100.

abs pdf

Authors: R.P. Croce, Th. Demma, V.Pierro, I.M. Pinto

Date: Tue, 26 Mar 2002

Abstract: A simple recipe is given for constructing a maximally sparse regular lattice of spin-free post-1PN gravitational wave chirp templates subject to a given minimal match constraint, using Tanaka-Tagoshi coordinates.

abs pdf

Authors: Yuri Levin (CITA), Alice S. P. Wu (University of Toronto), Edward W. Thommes (CITA)

Date: Mon, 7 Feb 2005

Abstract: Many young stars reside within the central half-parsec from SgrA*, the supermassive black hole in the Galactic Center. The origin of these stars remains a puzzle. Recently, Hansen and Milosavljevic (2003, HM) have argued that an Intermediate-Mass Black Hole (IMBH) could have delivered the young stars to the immediate vicinity of SgrA*. Here we focus on the final stages of the HM scenario. Namely, we integrate numerically the orbits of stars which are initially bound to the IMBH, but are stripped from it by the tidal field of SgrA*. Our numerical algorithm is a symplectic integrator designed specifically for the problem at hand; however, we have checked our results with SYMBA, a version of the widely available SWIFT code. We find that the distribution of the post-inspiral orbital parameters is sensitive to the eccentricity of the inspiraling IMBH. If the IMBH is on a circular orbit, then the inclinations of numerically computed orbits relative to the inspiral plane are almost always smaller than 10 degrees, and therefore (a) the simulations are in good agreement with the observed motions of stars in a clockwise-moving stellar disc, (b) the simulations never reproduce the orbits of stars outside this disc, which include those in the second thick ring of stars and the randomly oriented unrelaxed orbits of some of the S-stars. If the IMBH's orbital eccentricity is e=0.6, then approximately half of the stars end up with orbital inclinations below 10 degrees, and another half have inclinations anywhere between 0 and 180 degrees; this is somewhat closer to what's observed. We also show that if IRS13 cluster is bound by an IMBH, as has been argued by Maillard et. al. 2004, then the same IMBH could not have delivered all of the young stars to their present location.

abs pdf

Authors: Leor Barack, Curt Cutler

Date: Fri, 11 Feb 2005

Abstract: Captures of compact objects (COs) by massive black holes in galactic nuclei (aka ‘extreme-mass-ratio inspirals’) will be an important source for LISA. However, a large fraction of captures will not be individually resolvable, and so will constitute a source of ‘confusion noise,’ obscuring other types of sources. Here we estimate the shape and overall magnitude of the spectrum of confusion noise from CO captures. The overall magnitude depends on the capture rates, which are rather uncertain, so we present results for a plausible range of rates. We show that the impact of capture confusion noise on the total LISA noise curve ranges from insignificant to modest, depending on these rates. Capture rates at the high end of estimated ranges would raise LISA's overall (effective) noise level by at most a factor $\sim 2$. While this would somewhat decrease LISA's sensitivity to other classes of sources, it would be a pleasant problem for LISA to have, overall, as it would also imply that detection rates for CO captures were at nearly their maximum possible levels (given LISA's baseline design).

abs pdf

Authors: Hideaki Kudoh, Atsushi Taruya

Date: Tue, 8 Feb 2005

Abstract: We discuss the sensitivity to anisotropies of stochastic gravitational-wave backgrounds (GWBs) observed via space-based interferometer. In addition to the unresolved galactic binaries as the most promising GWB source of the planned Laser Interferometer Space Antenna (LISA), the extragalactic sources for GWBs might be detected in the future space missions. The anisotropies of the GWBs thus play a crucial role to discriminate various components of the GWBs. We study general features of antenna pattern sensitivity to the anisotropies of GWBs beyond the low-frequency approximation. We show that the sensitivity of space-based interferometer to GWBs is severely restricted by the data combinations and the symmetries of the detector configuration. The spherical harmonic analysis of the antenna pattern functions reveals that the angular power of the detector response increases with frequency and the detectable multipole moments with effective sensitivity h_{eff} \sim 10ˆ{-20} Hzˆ{-½} may reach $\ell \sim$ 8-10 at $f \sim f_*=10$ mHz in the case of the single LISA detector. However, the cross correlation of optimal interferometric variables is blind to the monopole (\ell=0) intensity anisotropy, and also to the dipole (\ell=1) in some case, irrespective of the frequency band. Besides, all the self-correlated signals are shown to be blind to the odd multipole moments (\ell=odd), independently of the frequency band.

abs pdf

Authors: S. Babak, H. Grote, M. Hewitson, H. L{\"u}ck, K.A. Strain

Date: Tue, 1 Feb 2005

Abstract: The matched filtering technique is used to search for gravitational wave signals of a known form in the data taken by ground-based detectors. However, the analyzed data contains a number of artifacts arising from various broad-band transients (glitches) of instrumental or environmental origin which can appear with high signal-to-noise ratio on the matched filtering output. This paper describes several techniques to discriminate genuine events from the false ones, based on our knowledge of the signals we look for. Starting with the $\chiˆ2$ discriminator, we show how it may be optimized for free parameters. We then introduce several alternative vetoing statistics and discuss their performance using data from the GEO600 detector.

abs pdf