The Shane Wirtanen counts: Observability of the galaxy correlation function

For an explicit test of the ability to recover the galaxy two-point correlation function from the Lick catalog of Shane and Wirtanen, we have applied the reduction and analysis methods of Seidner et al. and Groth and Peebles to model galaxy distributions that have known plate and field "errors" and that are high-fidelity simulations of the Lick sample. The model galaxy space distribution is constructed with the Soneira-Peebles prescription, which generates model distributions which have two-, three-, and four-point correlation functions in good agreement with the observed correlation functions. The space distribution is projected onto the sky with and without plate "errors." The Seidner et al. analysis recovers the plate factors in the former case with an error of 6.3%, as originally estimated. The two-point correlation function estimated from the "corrected" model catalog reproduces the built-in correlation function including the break from the power law. This is also true if the angular scale of the break is increased or decreased by a factor of 1.76 from the observed value. We also compare a map of the corrected counts with a map of the counts projected without plate errors and find that the corrected map is a good visual representation of the galaxy distribution. Finally, we construct a simulation which includes systematic variations in plate sensitivity with observer and time-so called "plate shape gradients." Once again, the correlation function of the model catalog reproduces the built in correlation function

Detection of Cosmic Shear with the HST Survey Strip

Weak lensing by large-scale structure provides a unique method to directly measure matter fluctuations in the universe, and has recently been detected from the ground. Here, we report the first detection of this `cosmic shear' based on space-based images. The detection was derived from the Hubble Space Telescope (HST) Survey Strip (or Groth Strip), a 4' by 42' set of 28 contiguous WFPC2 pointings with I<27. The small size of the HST Point-Spread Function (PSF) affords both a lower statistical noise, and a much weaker sensitivity to systematic effects, a crucial limiting factor of cosmic shear measurements. Our method and treatment of systematic effects were discussed in an earlier paper (Rhodes, Refregier & Groth 2000). We measure an rms shear of 1.8% on the WFPC2 chip scale (1.27'), in agreement with the predictions of cluster-normalized CDM models. Using a Maximum Likelihood (ML) analysis, we show that our detection is significant at the 99.5% confidence level (CL), and measure the normalization of the matter power spectrum to be sigma8*Omega_m^(0.48) = 0.51 (+0.14,-0.17), in a LambdaCDM universe. These 68% CL errors include (Gaussian) cosmic variance, systematic effects and the uncertainty in the redshift distribution of the background galaxies. Our result is consistent with earlier lensing measurements from the ground, and with the normalization derived from cluster abundance. We discuss how our measurement can be improved with the analysis of a large number of independent WFPC2 fields.Comment: 4 pages, 2 figure

Arya: Nearly linear-time zero-knowledge proofs for correct program execution

There have been tremendous advances in reducing interaction, communication and verification time in zero-knowledge proofs but it remains an important challenge to make the prover efficient. We construct the first zero-knowledge proof of knowledge for the correct execution of a program on public and private inputs where the prover computation is nearly linear time. This saves a polylogarithmic factor in asymptotic performance compared to current state of the art proof systems. We use the TinyRAM model to capture general purpose processor computation. An instance consists of a TinyRAM program and public inputs. The witness consists of additional private inputs to the program. The prover can use our proof system to convince the verifier that the program terminates with the intended answer within given time and memory bounds. Our proof system has perfect completeness, statistical special honest verifier zero-knowledge, and computational knowledge soundness assuming linear-time computable collision-resistant hash functions exist. The main advantage of our new proof system is asymptotically efficient prover computation. The prover’s running time is only a superconstant factor larger than the program’s running time in an apples-to-apples comparison where the prover uses the same TinyRAM model. Our proof system is also efficient on the other performance parameters; the verifier’s running time and the communication are sublinear in the execution time of the program and we only use a log-logarithmic number of rounds

Foundations of Fully Dynamic Group Signatures

Group signatures are a central cryptographic primitive that has received a considerable amount of attention from the cryptographic community. They allow members of a group to anonymously sign on behalf of the group. Membership is overseen by a designated group manager. There is also a tracing authority that can revoke anonymity by revealing the identity of the signer if and when needed, to enforce accountability and deter abuse. For the primitive to be applicable in practice, it needs to support fully dynamic groups, i.e. users can join and leave at any time. In this work we take a close look at existing security definitions for fully dynamic group signatures. We identify a number of shortcomings in existing security definitions and fill the gap by providing a formal rigorous security model for the primitive. Our model is general and is not tailored towards a specific design paradigm and can therefore, as we show, be used to argue about the security of different existing constructions following different design paradigms. Our definitions are stringent and when possible incorporate protection against maliciously chosen keys. In the process, we identify a subtle issue inherent to one design paradigm, where new members might try to implicate older ones by means of back-dated signatures. This is not captured by existing models. We propose some inexpensive fixes for some existing constructions to avoid the issue

A Morphological and Multicolor Survey for Faint QSOs in the Groth-Westphal Strip

Quasars representative of the populous faint end of the luminosity function are frustratingly dim with m~24 at intermediate redshift; moreover groundbased surveys for such faint QSOs suffer substantial morphological contamination by compact galaxies having similar colors. In order to establish a more reliable ultrafaint QSO sample, we used the APO 3.5-m telescope to take deep groundbased U-band CCD images in fields previously imaged in V,I with WFPC2/HST. Our approach hence combines multicolor photometry with the 0.1" spatial resolution of HST, to establish a morphological and multicolor survey for QSOs extending about 2 magnitudes fainter than most extant groundbased surveys. We present results for the "Groth-Westphal Strip", in which we identify 10 high likelihood UV-excess candidates having stellar or stellar-nucleus+galaxy morphology in WFPC2. For m(606)<24.0 (roughly B<24.5) the surface density of such QSO candidates is 420 (+180,-130) per square degree, or a surface density of 290 (+160,-110) per square degree with an additional V-I cut that may further exclude compact emission line galaxies. Even pending confirming spectroscopy, the observed surface density of QSO candidates is already low enough to yield interesting comparisons: our measures agree extremely well with the predictions of several recent luminosity function models.Comment: 29 pages including 6 tables and 7 figures. As accepted for publication in The Astronomical Journal (minor revisions

Luminosity Functions of Elliptical Galaxies at z < 1.2

The luminosity functions of E/S0 galaxies are constructed in 3 different redshift bins (0.2 < z < 0.55, 0.55 < z < 0.8, 0.8 < z < 1.2), using the data from the Hubble Space Telescope Medium Deep Survey (HST MDS) and other HST surveys. These independent luminosity functions show the brightening in the luminosity of E/S0s by about 0.5~1.0 magnitude at z~1, and no sign of significant number evolution. This is the first direct measurement of the luminosity evolution of E/S0 galaxies, and our results support the hypothesis of a high redshift of formation (z > 1) for elliptical galaxies, together with weak evolution of the major merger rate at z < 1.Comment: To be published in ApJ Letters, 4 pages, AAS Latex, 4 figures, and 2 table

A Proper Motion Survey for White Dwarfs with the Wide Field Planetary Camera 2

We have performed a search for halo white dwarfs as high proper motion objects in a second epoch WFPC2 image of the Groth-Westphal strip. We identify 24 high proper motion objects with mu > 0.014 ''/yr. Five of these high proper motion objects are identified as strong white dwarf candidates on the basis of their position in a reduced proper motion diagram. We create a model of the Milky Way thin disk, thick disk and stellar halo and find that this sample of white dwarfs is clearly an excess above the < 2 detections expected from these known stellar populations. The origin of the excess signal is less clear. Possibly, the excess cannot be explained without invoking a fourth galactic component: a white dwarf dark halo. We present a statistical separation of our sample into the four components and estimate the corresponding local white dwarf densities using only the directly observable variables, V, V-I, and mu. For all Galactic models explored, our sample separates into about 3 disk white dwarfs and 2 halo white dwarfs. However, the further subdivision into the thin and thick disk and the stellar and dark halo, and the subsequent calculation of the local densities are sensitive to the input parameters of our model for each Galactic component. Using the lowest mean mass model for the dark halo we find a 7% white dwarf halo and six times the canonical value for the thin disk white dwarf density (at marginal statistical significance), but possible systematic errors due to uncertainty in the model parameters likely dominate these statistical error bars. The white dwarf halo can be reduced to around 1.5% of the halo dark matter by changing the initial mass function slightly. The local thin disk white dwarf density in our solution can be made consistent with the canonical value by assuming a larger thin disk scaleheight of 500 pc.Comment: revised version, accepted by ApJ, results unchanged, discussion expande

Foundations of Fully Dynamic Group Signatures

Group signatures allow members of a group to anonymously sign on behalf of the group. Membership is administered by a designated group manager. The group manager can also reveal the identity of a signer if and when needed to enforce accountability and deter abuse. For group signatures to be applicable in practice, they need to support fully dynamic groups, i.e., users may join and leave at any time. Existing security definitions for fully dynamic group signatures are informal, have shortcomings, and are mutually incompatible. We fill the gap by providing a formal rigorous security model for fully dynamic group signatures. Our model is general and is not tailored toward a specific design paradigm and can therefore, as we show, be used to argue about the security of different existing constructions following different design paradigms. Our definitions are stringent and when possible incorporate protection against maliciously chosen keys. We consider both the case where the group management and tracing signatures are administered by the same authority, i.e., a single group manager, and also the case where those roles are administered by two separate authorities, i.e., a group manager and an opening authority. We also show that a specialization of our model captures existing models for static and partially dynamic schemes. In the process, we identify a subtle gap in the security achieved by group signatures using revocation lists. We show that in such schemes new members achieve a slightly weaker notion of traceability. The flexibility of our security model allows to capture such relaxation of traceability

A Slow Merger History of Field Galaxies Since z~1

Using deep infrared observations conducted with the CISCO imager on the Subaru Telescope, we investigate the field-corrected pair fraction and the implied merger rate of galaxies in redshift survey fields with Hubble Space Telescope imaging. In the redshift interval, 0.5 < z < 1.5, the fraction of infrared-selected pairs increases only modestly with redshift to 7% +- 6% at z~1. This is nearly a factor of three less than the fraction, 22% +- 8%, determined using the same technique on HST optical images and as measured in a previous similar study. Tests support the hypothesis that optical pair fractions at z~1 are inflated by bright star-forming regions that are unlikely to be representative of the underlying mass distribution. By determining stellar masses for the companions, we estimate the mass accretion rate associated with merging galaxies. At z~1, we estimate this to be 2x10^{9 +- 0.2} solar masses per galaxy per Gyr. Although uncertainties remain, our results suggest that the growth of galaxies via the accretion of pre-existing fragments remains as significant a phenomenon in the redshift range studied as that estimated from ongoing star formation in independent surveys.Comment: 5 pages, accepted for publication in ApJ Letter