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1
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85038340580
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These are the GEO Project [K. Danzmann, in First Edoardo Amaldi Conference on Gravitational Wave Experiments, edited by E. Coccia et al. (World Scientific, Singapore, 1995)];
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These are the GEO Project [K. Danzmann, in First Edoardo Amaldi Conference on Gravitational Wave Experiments, edited by E. Coccia et al. (World Scientific, Singapore, 1995)];
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2
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0011490655
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the TAMA Project [K. Tsubono, in First Edoardo Amaldi Conference on Gravitational Wave Experiments [1];
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the LIGO Project [A. Abramovici et al., Science 256, 325 (1992)];the TAMA Project [K. Tsubono, in First Edoardo Amaldi Conference on Gravitational Wave Experiments [1];
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(1992)
Science
, vol.256
, pp. 325
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Abramovici, A.1
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4
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85038323865
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K. S. Thorne, in 300 Years of Gravitation, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1987), pp. 330–458.
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K. S. Thorne, in 300 Years of Gravitation, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1987), pp. 330–458.
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8
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3843131083
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For neutron star–neutron star coalescences, J.A. Faber and F.A. Rasio, Phys. Rev. D 62, 064012 (2000);
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(2000)
Phys. Rev. D
, vol.62
, pp. 64012
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Faber, J.A.1
Rasio, F.A.2
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11
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0000606498
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É.É. Flanagan and S.A. Hughes, Phys. Rev. D 57, 4535 (1998).
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(1998)
Phys. Rev. D
, vol.57
, pp. 4535
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Hughes, S.A.1
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12
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0001143928
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É.É. Flanagan and S.A. Hughes, Phys. Rev. D 57, 4566 (1998).
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(1998)
Phys. Rev. D
, vol.57
, pp. 4566
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Hughes, S.A.1
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15
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85038327007
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An arbitrary random process can always be reduced to a set of uncorrelated coefficients (“whitened”) by the Karhunen-Loève expansion. Signals are affected by the whitening; however, the only place where this could have an adverse effect here is if the whitening were reducing the amount of clustering of astrophysical signals.
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An arbitrary random process can always be reduced to a set of uncorrelated coefficients (“whitened”) by the Karhunen-Loève expansion. Signals are affected by the whitening; however, the only place where this could have an adverse effect here is if the whitening were reducing the amount of clustering of astrophysical signals.
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16
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85038303354
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The Neyman-Pearson lemma shows that Eq. (3) is optimal when choosing between Eqs. (1) and (2); for the model (Formula presented) with (Formula presented) Eq. (3) is the most efficient estimator for A, in the sense of being unbiased and of achieving the minimum possible mean square error (from the Fisher information, this is (Formula presented): (Formula presented)
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The Neyman-Pearson lemma shows that Eq. (3) is optimal when choosing between Eqs. (1) and (2); for the model (Formula presented) with (Formula presented) Eq. (3) is the most efficient estimator for A, in the sense of being unbiased and of achieving the minimum possible mean square error (from the Fisher information, this is (Formula presented): (Formula presented)
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17
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85038320386
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E. L. Lehmann, Testing Statistical Hypothesis (Wiley, New York, 1986).
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E. L. Lehmann, Testing Statistical Hypothesis (Wiley, New York, 1986).
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18
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85038308333
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That is, the counterexample in B. W. Lindgren, Statistical Theory, 3rd ed. (Collier MacMillan, New York, 1976), p. 309.
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That is, the counterexample in B. W. Lindgren, Statistical Theory, 3rd ed. (Collier MacMillan, New York, 1976), p. 309.
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20
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0034395509
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W.G. Anderson, P.R. Brady, J.D.E. Creighton, and É.É. Flanagan, Int. J. Mod. Phys. D 9, 303 (2000);
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(2000)
Int. J. Mod. Phys. D
, vol.9
, pp. 303
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Anderson, W.G.1
Brady, P.R.2
Creighton, J.D.E.3
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21
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0035087661
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W.G. Anderson, P.R. Brady, J.D.E. Creighton, and É.É. Flanagan, Phys. Rev. D 63, 042003 (2001).
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(2001)
Phys. Rev. D
, vol.63
, pp. 42003
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Anderson, W.G.1
Brady, P.R.2
Creighton, J.D.E.3
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29
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85038293221
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Rules to use the Itô integral (Formula presented) are similar to those for normal integration, except that second order terms in the increment (Formula presented) are preserved, corresponding to the fact the these increments are (Formula presented) for a Wiener process. See Sec. II of 20 for a pedagogical introduction.
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Rules to use the Itô integral (Formula presented) are similar to those for normal integration, except that second order terms in the increment (Formula presented) are preserved, corresponding to the fact the these increments are (Formula presented) for a Wiener process. See Sec. II of 20 for a pedagogical introduction.
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32
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0027873602
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That is, the proof of Mallat’s heuristic, i.e., that wavelet bases are optimal for representing functions containing singularities, in D.L. Donoho, Appl. Comput. Harmon. Anal. 1, 100 (1993).
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(1993)
Appl. Comput. Harmon. Anal.
, vol.1
, pp. 100
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Donoho, D.L.1
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34
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85038317971
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Compare Eq. (3.11) with (Formula presented) in 6
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Compare Eq. (3.11) with (Formula presented) in 6.
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35
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85038286339
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That is, Eq. (B16) in 16
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That is, Eq. (B16) in 16.
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37
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21844485137
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An interesting fact about the distribution of sizes of connected clusters is the existence of a critical black pixel probability (Formula presented) such that an infinite (spanning) connected cluster occurs when (Formula presented) see A.R. Conway and A.J. Guttmann, J. Phys. A 28, 891 (1995).
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(1995)
J. Phys. A
, vol.28
, pp. 891
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Conway, A.R.1
Guttmann, A.J.2
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38
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85038343572
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The functions RAN2 and GASDEV in W. H. Press et al., Numerical Recipes in C (Cambridge University Press, Cambridge, England, 1992).
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The functions RAN2 and GASDEV in W. H. Press et al., Numerical Recipes in C (Cambridge University Press, Cambridge, England, 1992).
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39
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85038295777
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B. Allen et al., Numerical Algorithms Library Specification and Style Guide, LIGO technical note LIGO-T990030-E, 2001; See also http://www.lsc-group.phys.uwm.edu/lal/index.html
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B. Allen et al., Numerical Algorithms Library Specification and Style Guide, LIGO technical note LIGO-T990030-E, 2001; See also http://www.lsc-group.phys.uwm.edu/lal/index.html
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40
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0000679487
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[reprinted in A Selection of Early Statistical Papers on J. Neyman (University of California Press, Berkeley, CA, 1967), pp. 250–289].
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J. Neyman, Philos. Trans. R. Soc. London A236, 333 (1937);[reprinted in A Selection of Early Statistical Papers on J. Neyman (University of California Press, Berkeley, CA, 1967), pp. 250–289].
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(1937)
Philos. Trans. R. Soc. London
, vol.A236
, pp. 333
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Neyman, J.1
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41
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85038338422
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J. Sylvestre, Ph.D. thesis, Massachusetts Institute of Technology, 2002.
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J. Sylvestre, Ph.D. thesis, Massachusetts Institute of Technology, 2002.
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