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At the larger values of r. especially when £ is near 0. the bootstrap procedure appears to be somewhat conservative. while the Poisson errors become more accurate. | At the larger values of $r$ , especially when $\xi$ is near 0, the bootstrap procedure appears to be somewhat conservative, while the Poisson errors become more accurate. |
We made some time measurements of various sections of the algorithm: the functions computingoO DD and OR took 1 minute and 13 minutes respectively. | We made some time measurements of various sections of the algorithm: the functions computing $DD$ and $DR$ took 1 minute and 13 minutes respectively. |
Here. NjFE.=200.000 and we did not use any sophisticated methods (such as tree-based algorithms) to speed up the computation. | Here, $N_R = 200,000$ and we did not use any sophisticated methods (such as tree-based algorithms) to speed up the computation. |
The bootstrap function. generating 999 samples and computing the estimates. took roughly 1 minute. showing the feasibilitv of the procedure for large data sets. | The bootstrap function, generating 999 samples and computing the estimates, took roughly 1 minute, showing the feasibility of the procedure for large data sets. |
The speed of the marked. point bootstrap is due to the [act that the marks that. are resaanpled have already been computed as part of the estimation. | The speed of the marked point bootstrap is due to the fact that the marks that are resampled have already been computed as part of the estimation. |
The additional computational burden of the bootstrap is sampling the points and keeping track of the number of times each point is resaniplect | The additional computational burden of the bootstrap is sampling the points and keeping track of the number of times each point is resampled. |
, In this paper. we introduced the marked point bootstrap as a method to bootstrap spatial data for estimating errors without specific model assumptions. | In this paper, we introduced the marked point bootstrap as a method to bootstrap spatial data for estimating errors without specific model assumptions. |
In particular. we described how the method can be applied to estimators of the (wo- and three-point correlation functions. | In particular, we described how the method can be applied to estimators of the two- and three-point correlation functions. |
With the non-parametric bootstrap. errors are obtained [rom the actual data. | With the non-parametric bootstrap, errors are obtained from the actual data. |
There is no need choose a model. select parameter values or generate mock catalogs using N-body simulations. | There is no need choose a model, select parameter values or generate mock catalogs using $N$ -body simulations. |
Thus errors obtained from non-parametric bootstrap can be used to compare with errors obtained from other methods with more specific model assumptions. | Thus errors obtained from non-parametric bootstrap can be used to compare with errors obtained from other methods with more specific model assumptions. |
For non-parametric spatial bootstrap. we propose the marked point bootstrap over the more conmon block bootstrap or subsampling methods. | For non-parametric spatial bootstrap, we propose the marked point bootstrap over the more common block bootstrap or subsampling methods. |
There are several advantages of the marked point bootstrap. | There are several advantages of the marked point bootstrap. |
Firstly. bv using information from actual pairs or (riplets of points in (he data. bootstrap confidence intervals using (the marked point bootstrap attain better empirical coverage than confidence intervals constructed using block bootstrap (see [or a comparison of these (wo methods). | Firstly, by using information from actual pairs or triplets of points in the data, bootstrap confidence intervals using the marked point bootstrap attain better empirical coverage than confidence intervals constructed using block bootstrap (see \citealt{loh02a} for a comparison of these two methods). |
Our observations of ΤΟ Oph and LEU Set throw doubt on the currently proposed. identification of these old novae. | Our observations of V794 Oph and EU Sct throw doubt on the currently proposed identification of these old novae. |
We thank Dr. D. O'Donoghue for the use of his EACLE program for Fourier analysis of the light curves. | We thank Dr. D. O'Donoghue for the use of his EAGLE program for Fourier analysis of the light curves. |
PAW is supported. by funds. mace available from. the National ltesearch Foundation aad by strategic funds made available to BW from the University of Cape Town. | PAW is supported by funds made available from the National Research Foundation and by strategic funds made available to BW from the University of Cape Town. |
DW's research is supported by the University. | BW's research is supported by the University. |
amount of CPU time needed. | amount of CPU time needed. |
A version which circumvents this problem is being developed. | A version which circumvents this problem is being developed. |
For this test we adopt the problem mentioned by Lelloch Lazarell (1994)... | For this test we adopt the problem mentioned by Lefloch Lazareff \shortcite{lefloch1}. |
A box filled with atomic hydrogen of particle density ny=10 cm and temperature Loon.= LOOK is exposed to ionizing radiation. with the photon lux increasing from zero linearly with time with a rate db/di=5.07:10.7 cmPss 7. | A box filled with atomic hydrogen of particle density $n_0=10$ $^{-3}$ and temperature $T_{\rm cold}=100$ K is exposed to ionizing radiation, with the photon flux increasing from zero linearly with time with a rate ${\rm d}\Phi/{\rm d}t=5.07 \cdot 10^{-2}$ $^{-2}$ $^{-2}$. |
There exists an analytical solution to this problem. which is self similar in the sense hat physical values at position ο measured in the direction of the photon flow at time / are only functions of w/t. | There exists an analytical solution to this problem, which is self similar in the sense that physical values at position $x$ measured in the direction of the photon flow at time $t$ are only functions of $x/t$. |
his means: the structure is stretched with time. | This means: the structure is stretched with time. |
Phe convergence of the code towards the correct. solution with increasing resolution can be tested. in one calculation. since for all appearing structures the ratio between structure sizes ancl smoothing lengths increases lincarly with timo. | The convergence of the code towards the correct solution with increasing resolution can be tested in one calculation, since for all appearing structures the ratio between structure sizes and smoothing lengths increases linearly with time. |
The resulting structure is the following: an isothermal shock is driven into the neutral medium. sweeping up a dense laver of material. | The resulting structure is the following: an isothermal shock is driven into the neutral medium, sweeping up a dense layer of material. |
This is followed. by an ionization [ront which leaves the ionized material in quasi-static equilibrium (sce Ligs. 6..7)). (1994) | This is followed by an ionization front which leaves the ionized material in quasi-static equilibrium (see Figs. \ref{fig:test2dens}, \ref{fig:test2vel}) |
(1994) (1979).. | \shortcite{lefloch1} \shortcite{lefloch1} \shortcite{VanLeer}. |
4.3 | \ref{sect:test1} |
formation in Abell 1664. | formation in Abell 1664. |
Similar cooling rates have been estimated for most of the other galaxies in our sample etal. 2008). | Similar cooling rates have been estimated for most of the other galaxies in our sample \citep{odea08}. |
We note that there is FUV continuum and Lyo emission in Abell 1795 and Abell 2597 which ts closely associated with the radio sources - suggesting a contribution from Jet induced star formation (O'Deaetal.2004). | We note that there is FUV continuum and $\alpha$ emission in Abell 1795 and Abell 2597 which is closely associated with the radio sources - suggesting a contribution from jet induced star formation \citep{odea04}. |
. However. the radio jets in Abell 1835 and RXJ 2129400 show no relationship with the FUV emission. | However, the radio jets in Abell 1835 and RXJ 2129+00 show no relationship with the FUV emission. |
While both Abell 1795 and Abell 2597 host star formation. it is ata lower level than estimated for the 7 of our sample. | While both Abell 1795 and Abell 2597 host star formation, it is at a lower level than estimated for the 7 of our sample. |
In addition the 7 BCGsstudied here are generally have less powerful radio sources than those in Abell 1795 and Abell 2597. | In addition the 7 BCGs studied here are generally have less powerful radio sources than those in Abell 1795 and Abell 2597. |
The combination of higher SFR and lower radio power in our BCGs suggests that the radio sources have a smaller relative impact on the triggering and/or properties of the star formation and associated emission line nebulae. | The combination of higher SFR and lower radio power in our BCGs suggests that the radio sources have a smaller relative impact on the triggering and/or properties of the star formation and associated emission line nebulae. |
Further. the lack of FUV emission aligned with the radio jets indicates that the contribution from scattered AGN light is small. | Further, the lack of FUV emission aligned with the radio jets indicates that the contribution from scattered AGN light is small. |
We have also noted that most of our galaxies exhibit asymmetries in their distribution of star formation and 4+ of them show lopsided X-ray contours. | We have also noted that most of our galaxies exhibit asymmetries in their distribution of star formation and 4 of them show lopsided X-ray contours. |
Feedback from an AGN (jets and bubbles) would not be expected to push the X-ray emitting gas off-center. | Feedback from an AGN (jets and bubbles) would not be expected to push the X-ray emitting gas off-center. |
However disturbances in the IGM could lead to higher cooling rates in the gas as the cluster relaxes and slowly evolves to equilibrium (e.g.. Russelletal.2010). | However disturbances in the IGM could lead to higher cooling rates in the gas as the cluster relaxes and slowly evolves to equilibrium (e.g., \citealt{russell10}) ). |
We thank the referee for à prompt and constructive report. | We thank the referee for a prompt and constructive report. |
This work is based on observations. made with the NASA/ESATelescope. obtained at the Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy. Inc.. under NASA contract 5-265355. | This work is based on observations made with the NASA/ESA, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract 5-26555. |
Support forAST program 11230 was provided by NASA through a grant from the Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy. Inc.. under NASA contract NAS 5-26555. | Support for program 11230 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. |
This research made use of (1) the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Administration: and (2) NASA's Astrophysics Data System Abstract Service. | This research made use of (1) the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration; and (2) NASA's Astrophysics Data System Abstract Service. |
The National Radio Astronomy Observatory 1s a facility of the National Science Foundation operated under cooperative agreement by Associated Universities. Inc. KPO was supported by an NSF REU program at the University of Rochester. | The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. KPO was supported by an NSF REU program at the University of Rochester. |
offsets on large scales are of the order of tens and mindreds of pe (Cen A. ASF and 3€ 31) to tens of kpc (PINS 1127) 115). | offsets on large scales are of the order of tens and hundreds of pc (Cen A, M87 and 3C 31) to tens of kpc (PKS $1127-145$ ). |
These also suggest that the observed radio/X-rav aud optical/N-rav offsets in the six large scale jets are due to svuchrotrou time laes. | These also suggest that the observed radio/X-ray and optical/X-ray offsets in the six large scale jets are due to synchrotron time lags. |
According to equations (13) and (11). the optical/X-rav offset at a knot should be ~LO? times smaller than he radio/optical offset at the same knot. | According to equations (13) and (14), the optical/X-ray offset at a knot should be $\sim 10^{-3}$ times smaller than the radio/optical offset at the same knot. |
In \LS7. though shortened due to jet expansion. the radio/optical offse5 of —0.21dE0.017 at knot IIST-1 aud ~0.340.017aw ; snot D are larger than the correspoudiug optical offsets which are too small to be measured at current accuracy of 0,037. (NEushall et al. | In M87, though shortened due to jet expansion, the radio/optical offsets of $\sim0.24\pm 0.01\arcsec$ at knot HST-1 and $\sim0.3\pm 0.01\arcsec$ at knot D are larger than the corresponding optical/X-ray offsets which are too small to be measured at current accuracy of $\arcsec$ (Marshall et al. |
2002). | 2002). |
This coufinus hat offsets in AIS? are due to svuchrotrou time lags. | This confirms that offsets in M87 are due to synchrotron time lags. |
Among the six sources. MIST is the only one that has data or both optical/N-ray aud racio/optical offsets. | Among the six sources, M87 is the only one that has data for both optical/X-ray and radio/optical offsets. |
Probably. he optical/X-ray offsets in the rest five sources were also sanaller than the corresponding radio/optical offsets. if hey could be measured. | Probably, the optical/X-ray offsets in the rest five sources were also smaller than the corresponding radio/optical offsets, if they could be measured. |
It should be poiuted out that. uulike bright kuots. a weak knot iav be caused by a siugle shock. | It should be pointed out that, unlike bright knots, a weak knot may be caused by a single shock. |
Weak X-rav knots thus may not have correspouding optical or radio knots before disappearing. | Weak X-ray knots thus may not have corresponding optical or radio knots before disappearing. |
The faint knots. AL/AXI. AD/AND and AG/ANG in Cen A. and Dx and F in M87 are probably a single shock wave. aud the offsets at these knots mav not be caused by svuchrotron time laes. | The faint knots, A4/AX4, A5/AX5 and A6/AX6 in Cen A, and Dx and F in M87 are probably a single shock wave, and the offsets at these knots may not be caused by synchrotron time lags. |
Iu some sources. the large scale Nav jets may be dominated by inverse-Compton scattering of racdio-cluitting or even lower energv clectrous (Schwartz ct al. | In some sources, the large scale X-ray jets may be dominated by inverse-Compton scattering of radio-emitting or even lower energy electrons (Schwartz et al. |
2000. Schawartz 2002: Tavecchio et al. | 2000, Schwartz 2002; Tavecchio et al. |
2000: Celotti et al. | 2000; Celotti et al. |
2001). | 2001). |
Iu these sources. X-ray knots cannot be closer to the core than the corresponding radio knots. as indicated by multibaud monitoring of fares in PISS 191010 iu which N-ravs are due to inverse-Compton scattering aud the X-rav flare in 1997 lageed behiud the radio flare ~16 davs (Murscher 2000). | In these sources, X-ray knots cannot be closer to the core than the corresponding radio knots, as indicated by multiband monitoring of flares in PKS $1510-10$ in which X-rays are due to inverse-Compton scattering and the X-ray flare in 1997 lagged behind the radio flare $\sim 16$ days (Marscher 2000). |
In the six sources. because the bright X-rav knots precede their radio (and optical) counterparts. the N-rav jets cannot be due to inverse-Comptou emission. | In the six sources, because the bright X-ray knots precede their radio (and optical) counterparts, the X-ray jets cannot be due to inverse-Compton emission. |
Iun conclusion. shocks iu most large scale jets can re-accelerate clectrous to enereies high enough to cuit svuchrotrou N-ravs: The observed radio/N-rav anc optical/N-rav offsets at brieht knots in Ms7. Cen A. 3C 66D. 3C 31. 3C 273. aud PINS 1127115 are probably caused by svuchrotron time lags. sugeestiug that the large scale N-rav and optical jets in these sources are dominated by svuchrotron emission. | In conclusion, shocks in most large scale jets can re-accelerate electrons to energies high enough to emit synchrotron X-rays; The observed radio/X-ray and optical/X-ray offsets at bright knots in M87, Cen A, 3C 66B, 3C 31, 3C 273, and PKS $1127-145$ are probably caused by synchrotron time lags, suggesting that the large scale X-ray and optical jets in these sources are dominated by synchrotron emission. |
We thank the auonviuous referee aud D.E. ILuzis for constructive suesestions. commients and disceussious. | We thank the anonymous referee and D.E. Harris for constructive suggestions, comments and discussions. |
This work was financially supported by the DI21 Project of the Ikoreau eovermuicut. | This work was financially supported by the BK21 Project of the Korean government. |
This very simple formalism based on conservation of mass captures the essence of Dohnanvis (?)) more elaborate pioneering treatment. | This very simple formalism based on conservation of mass captures the essence of Dohnanyi's \citeyear{dohnanyi69}) ) more elaborate pioneering treatment. |
Based on laboratory experiments which involved solid bodies dominated by material strength. Dohnanyi chose rjxr. | Based on laboratory experiments which involved solid bodies dominated by material strength, Dohnanyi chose $r_B\propto r$ . |
When rgocx rand N(r)oxr| aye inserted into Eq. L.. | When $r_B\propto r$ and $N(r)\propto r^{1-q}$ are inserted into Eq. \ref{steadystate}, |
we retrieve the g=7/2 of Dohnanyi and several subsequent authors (lorexample.??).. | we retrieve the $q=7/2$ of Dohnanyi and several subsequent authors \citep[for example,
][]{williams94,tanaka96}. |
This slope is much steeper than the best-fit «mall-end q=2.3 found by 2.. who rule out q=7/2 at better than confidence. | This slope is much steeper than the best-fit small-end $q=2.3$ found by \cite{bernstein03}, who rule out $q=7/2$ at better than confidence. |
Indeed. work on the structure of small solar svstem bodies suggests that many of them are gravitationallv bound rubble piles rather than solid monoliths. | Indeed, work on the structure of small solar system bodies suggests that many of them are gravitationally bound rubble piles rather than solid monoliths. |
Basecl on oscillating lighteurves of the large ΑΟ (20000) Varuna (radius 22100km). ? find that (his bodies has density ~Lgem* and is therefore unlikely to be solid. | Based on oscillating lightcurves of the large KBO (20000) Varuna (radius $R>100\;\km$ ), \cite{jewitt02} find that this bodies has density $\sim 1\;\g\;\cm^{-3}$ and is therefore unlikely to be solid. |
However. other effects may also be responsible for the lighteurve shape (see.forexample.?).. | However, other effects may also be responsible for the lightcurve shape \citep[see, for example,][]{goldreich04}. |
The rotation statistics of much smaller bodies (22~10 km) in the more easily observed region between the asteroid belt and (he sun also suggest that siall bodies in the solar svstem are rubble piles rather (han monoliths. | The rotation statistics of much smaller bodies $R\sim 10\;\km$ ) in the more easily observed region between the asteroid belt and the sun also suggest that small bodies in the solar system are rubble piles rather than monoliths. |
That no small asteroids are observed (to rotate faster than their breakup speed suggests (hat those which were spun up bevond breakup simply broke apart (2): (hiis in (urn suggests that these asteroids have no tensile strength. | That no small asteroids are observed to rotate faster than their breakup speed suggests that those which were spun up beyond breakup simply broke apart \citep{harris96}; this in turn suggests that these asteroids have no tensile strength. |
A study including 26 small asteroids came to similar conclusions about. asteroid internal structure (2).. | A study including 26 small near-earth asteroids came to similar conclusions about asteroid internal structure \citep{pravec98}. |
The most detailed probe available of the structure of small IKNDOs is research. ou short-period comets. kilometer-sized bodies which are thought to have originated in the Ixuiper belt. | The most detailed probe available of the structure of small KBOs is research on short-period comets, kilometer-sized bodies which are thought to have originated in the Kuiper belt. |
Work on the breakup and impact of comet Shoemaker-Levy 9. thought to be 12 km in size. indicates that its strength before breakup was ~60dyncm7 or less (2): a body like Shoemaker-Levy 9 would have material strength energv ad most about ten times less than its gravitational energv. | Work on the breakup and impact of comet Shoemaker-Levy 9, thought to be 1–2 km in size, indicates that its strength before breakup was $\sim60\;\dyn\;\cm^{-2}$ or less \citep{asphaug96}; a body like Shoemaker-Levy 9 would have material strength energy at most about ten times less than its gravitational energy. |
These indications motivate an investigation of the influence of negligible material strength on (he lragmentation spectirum. | These indications motivate an investigation of the influence of negligible material strength on the fragmentation spectrum. |
We might therefore replace the rjxr destruction criterion used by Dohnanyi with the requirement (hat the kinetic energy of the bullet be equal to the total gravitational energy ol the target: where Coeox rds (he escape velocity [rom a target of size r. ancl. again. e is (he bodies? constant. velocity dispersion. | We might therefore replace the $r_B\propto r$ destruction criterion used by Dohnanyi with the requirement that the kinetic energy of the bullet be equal to the total gravitational energy of the target: where $v_{\rm esc}\propto r$ is the escape velocity from a target of size $r$, and, again, $v$ is the bodies' constant velocity dispersion. |
Then Physically. r4 is the size of a body whose escape velocity equals the velocitydispersion of the svstem. | Then Physically, $r_{\rm eq}$ is the size of a body whose escape velocity equals the velocitydispersion of the system. |
When density pIgem. and the Nuiper Belts current velocity dispersion pocPKms1 fare used. rego10*km~ the radius of Pluto. | When density $\rho\sim
1\;\g\;\cm^{-3}$ and the Kuiper Belt's current velocity dispersion $v\sim 1\;\km\;\s^{-1}$ are used, $r_{\rm eq} \sim 10^3\;\km \sim$ the radius of Pluto. |
Equivalently. a target of size | Equivalently, a target of size |
open pitch angle. | open pitch angle. |
The spectrum shown in Figure 7 is (tvpical for a Sbtvpe galaxy. with faint Lla and [N II] emission lines according to the Kennicutt(1992). spectroscopic atlas of galaxies. | The spectrum shown in Figure \ref{figure7} is typical for a Sb–type galaxy with faint $\alpha$ and [N II] emission lines according to the \citet{ken92} spectroscopic atlas of galaxies. |
The (BB) color profile with an outer average value of 221.5 is equite red for a Sb spiral although Reduzzi&Rampazzo(1996) show a few similar examples and light conlanunation from IC: 829 cannot be excluded. | The (B–R) color profile with an outer average value of $\approx$ 1.5 is quite red for a Sb spiral although \citet{RR96} show a few similar examples and light contamination from IC 829 cannot be excluded. |
This galaxy shows open spiral arms which depart [rom a bar. | This galaxy shows open spiral arms which depart from a bar. |
This latter structure can be seen in (he surface brightness. geometric proliles (Figure 3)) and in the residual map (Figure 5)). | This latter structure can be seen in the surface brightness, geometric profiles (Figure \ref{figure3}) ) and in the residual map (Figure \ref{figure5}) ). |
The spectrum shown in Figure 7 is consistent with the SDa classification of the galaxy according to Ixennieutt(1992). | The spectrum shown in Figure \ref{figure7} is consistent with the SBa classification of the galaxy according to \citet{ken92}. |
. The galaxy is a faint and nearly edgeon late(wpe spiral with a warped outer envelope and a probable inner bar structure (see PLA. profile variation in Figure 3)). The spectrum is quite noisy but shows the prominent |O 11]A3727 [feature and possibly IL7 and [O HI|A5007 eenmission lines. | The galaxy is a faint and nearly edge–on late–type spiral with a warped outer envelope and a probable inner bar structure (see P.A. profile variation in Figure \ref{figure3}) ).The spectrum is quite noisy but shows the prominent [O $\lambda$ 3727 feature and possibly $\beta$ and [O $\lambda$ 5007 emission lines. |
The surface brightness profile of the galaxy shows two components which suggest a SO classification. | The surface brightness profile of the galaxy shows two components which suggest a S0 classification. |
The shape profile shows moderately (254)) boxy isophotes in the outskirts aud the position angle profile does not reveal a signilicant isophotal twisting. | The shape profile shows moderately $\leq$ ) boxy isophotes in the outskirts and the position angle profile does not reveal a significant isophotal twisting. |
The color (D.R) x 1.5 is tvpical of early(vpe galaxies. | The color (B–R) $\approx$ 1.5 is typical of early–type galaxies. |
No emission lines are visible in the verv low signalto.noise spectrum shown in Figure 7.. | No emission lines are visible in the very low signal–to–noise spectrum shown in Figure \ref{figure7}. |
No [fant features are found after the model subtraction (Figure 6)). | No faint features are found after the model subtraction (Figure \ref{figure6}) ). |
The galaxy is a nucleated dwarl elliptical. with no other obvious features emerging either [rom the surface photometry or from (he faint spectrum. | The galaxy is a nucleated dwarf elliptical, with no other obvious features emerging either from the surface photometry or from the faint spectrum. |
According to the surface photometry presented in Figure 4.. the galaxy is an earlytype lenticular seen edgeon with small P.A. variations (X107). | According to the surface photometry presented in Figure \ref{figure4}, , the galaxy is an early–type lenticular seen edge–on with small P.A. variations $\leq$ $^{\circ}$ ). |
The residual | The residual |
where the mass-accretion rate AF=ωνης and 7 is an efficiency typically taken to be 0.1. | where the mass-accretion rate $\dot{M} = L_x / \eta c^2$ and $\eta$ is an efficiency typically taken to be $0.1$. |
We can also consider the viscous time-scale in a standard @-disc. | We can also consider the viscous time-scale in a standard $\alpha$ -disc. |
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