Shannon Information and Kolmogorov Complexity

We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual information versus Kolmogorov (`algorithmic') mutual information, probabilistic sufficient statistic versus algorithmic sufficient statistic (related to lossy compression in the Shannon theory versus meaningful information in the Kolmogorov theory), and rate distortion theory versus Kolmogorov's structure function. Part of the material has appeared in print before, scattered through various publications, but this is the first comprehensive systematic comparison. The last mentioned relations are new.Comment: Survey, LaTeX 54 pages, 3 figures, Submitted to IEEE Trans Information Theor

Propagation of Ultra-High-Energy Cosmic Ray Nuclei in Cosmic Magnetic Fields and Implications for Anisotropy Measurements

(Abridged) Recent results from the Pierre Auger Observatory (PAO) indicate that the composition of ultra-high-energy cosmic rays (UHECRs) with energies above $10^{19}$ eV may be dominated by heavy nuclei. An important question is whether the distribution of arrival directions for such UHECR nuclei can exhibit observable anisotropy or positional correlations with their astrophysical source objects despite the expected strong deflections by intervening magnetic fields. For this purpose, we have simulated the propagation of UHECR nuclei including models for both the extragalactic magnetic field and the Galactic magnetic field. Assuming that only iron nuclei are injected steadily from sources with equal luminosity and spatially distributed according to the observed large scale structure in the local Universe, at the number of events published by the PAO so far, the arrival distribution of UHECRs would be consistent with no auto-correlation at 95% confidence if the mean number density of UHECR sources $n_s >~ 10^{-6}$ Mpc$^{-3}$, and consistent with no cross-correlation with sources within 95% errors for $n_s >~ 10^{-5}$ Mpc$^{-3}$. On the other hand, with 1000 events above $5.5 \times 10^{19}$ eV in the whole sky, next generation experiments can reveal auto-correlation with more than 99% probability even for $n_s <~ 10^{-3}$ Mpc$^{-3}$, and cross-correlation with sources with more than 99% probability for $n_s <~ 10^{-4}$ Mpc$^{-3}$. In addition, we find that the contribution of Centaurus A is required to reproduce the currently observed UHECR excess in the Centaurus region. Secondary protons generated by photodisintegration of primary heavy nuclei during propagation play a crucial role in all cases, and the resulting anisotropy at small angular scales should provide a strong hint of the source location if the maximum energies of the heavy nuclei are sufficiently high.Comment: 17 pages, 15 figure

Microlensing toward crowded fields: Theory and applications to M31

We present a comprehensive treatment of the pixel-lensing theory and apply it to lensing experiments and their results toward M31. Using distribution functions for the distances, velocities, masses, and luminosities of stars, we derive lensing event rates as a function of the event observables. In contrast to the microlensing regime, in the pixel-lensing regime (crowded or unresolved sources) the observables are the maximum excess flux of the source above a background and the full width at half-maximum (FWHM) time of the event. To calculate lensing event distribution functions depending on these observables for the specific case of M31, we use data from the literature to construct a model of M31, reproducing consistently photometry, kinematics and stellar population. We predict the halo- and self-lensing event rates for bulge and disk stars in M31 and treat events with and without finite source signatures separately. We use the M31 photon noise profile and obtain the event rates as a function of position, field of view, and S/N threshold at maximum magnification. We calculate the expected rates for WeCAPP and for a potential Advanced Camera for Surveys (ACS) lensing campaign. The detection of two events with a peak signal-to-noise ratio larger than 10 and a timescale larger than 1 day in the WeCAPP 2000/2001 data is in good agreement with our theoretical calculations. We investigate the luminosity function of lensed stars for noise characteristics of WeCAPP and ACS. For the pixel-lensing regime, we derive the probability distribution for the lens masses in M31 as a function of the FWHM timescale, flux excess and color, including the errors of these observables.Comment: 45 pages, 27 figures LaTeX; corrected typos; published in the Astrophysical Journal Supplemen

Constraining halo occupation properties of X-ray AGNs using clustering of Chandra sources in the Bootes survey region

We present one of the most precise measurement to date of the spatial clustering of X-ray selected AGNs using a sample derived from the Chandra X-ray Observatory survey in the Bootes field. The real-space two-point correlation function over a redshift interval from z=0.17 to z~3 is well described by the power law, xi(r)=(r/r0)^-gamma, for comoving separations r<~20h^-1 Mpc. We find gamma=1.84+-0.12 and r0 consistent with no redshift trend within the sample (varying between r0=5.5+-0.6 h^-1 Mpc for =0.37 and r0=6.9+-1.0 h^-1 Mpc for =1.28). Further, we are able to measure the projections of the two-point correlation function both on the sky plane and in the line of sight. We use these measurements to show that the Chandra/Bootes AGNs are predominantly located at the centers of dark matter halos with the circular velocity Vmax>320 km/s or M_200 > 4.1e12 h^-1 Msun, and tend to avoid satellite galaxies in halos of this or higher mass. The halo occupation properties inferred from the clustering properties of Chandra/Bootes AGNs --- the mass scale of the parent dark matter halos, the lack of significant redshift evolution of the clustering length, and the low satellite fraction --- are broadly consistent with the Hopkins et al. scenario of quasar activity triggered by mergers of similarly-sized galaxies.Comment: Accepted to ApJ. The revision matches the accepted version. The most significant changes include the recalculation of uncertainties using mock catalogs and explicit comparison with the AGN HOD studies based on projected correlation function, w(rp

Horizon of quantum black holes in various dimensions

We adapt the horizon wave-function formalism to describe massive static spherically symmetric sources in a general $(1+D)$-dimensional space-time, for $D>3$ and including the $D=1$ case. We find that the probability $P_{\rm BH}$ that such objects are (quantum) black holes behaves similarly to the probability in the $(3+1)$ framework for $D> 3$. In fact, for $D\ge 3$, the probability increases towards unity as the mass grows above the relevant $D$-dimensional Planck scale $m_D$. At fixed mass, however, $P_{\rm BH}$ decreases with increasing $D$, so that a particle with mass $m\simeq m_D$ has just about $10\%$ probability to be a black hole in $D=5$, and smaller for larger $D$. This result has a potentially strong impact on estimates of black hole production in colliders. In contrast, for $D=1$, we find the probability is comparably larger for smaller masses, but $P_{\rm BH} < 0.5$, suggesting that such lower dimensional black holes are purely quantum and not classical objects. This result is consistent with recent observations that sub-Planckian black holes are governed by an effective two-dimensional gravitation theory. Lastly, we derive Generalised Uncertainty Principle relations for the black holes under consideration, and find a minimum length corresponding to a characteristic energy scale of the order of the fundamental gravitational mass $m_D$ in $D>3$. For $D=1$ we instead find the uncertainty due to the horizon fluctuations has the same form as the usual Heisenberg contribution, and therefore no fundamental scale exists.Comment: Latex, 16 pages, 8 figures. Final version to appear in PL

LABOCA mapping of the infrared dark cloud MSXDC G304.74+01.32

Infrared dark clouds (IRDCs) likely represent very early stages of high-mass star/star cluster formation. In this study, we aim to determine the physical properties and spatial distribution of dense clumps in the IRDC MSXDC G304.74+01.32 (G304.74), and bring these characteristics into relation to theories concerning the origin of IRDCs and their fragmentation into clumps and star-forming cores. G304.74 was mapped in the 870 $\mu$m dust continuum with the LABOCA bolometer on APEX. Archival MSX and IRAS infrared data were used to study the nature and properties of the submillimetre clumps within the cloud. There are 8 clumps within G304.74 which are not associated with mid-infrared (MIR) emission. Some of them are candidates for being/harbouring high-mass starless cores (HMSCs). We compared the clump masses and their spatial distribution in G304.74 with those in several other recently studied IRDCs. There is a high likelihood that the clump mass distributions in G304.74 and in several other IRDCs represent the samples of the same parent distribution. In most cases the spatial distributions of clumps in IRDCs do not deviate significantly from random distributions. This is consistent with the idea that the origin of IRDCs, and their further sub-fragmentation down to scales of clumps is caused by supersonic turbulence in accordance with results from giant molecular clouds.Comment: 15 pages, 8 figures, accepted for publication in Astronomy and Astrophysic

The Bs oscillation amplitude analysis

The properties of the amplitude method for \Bs oscillation analyses are studied in detail. The world combination of measured amplitudes is converted into a likelihood profile as a function of oscillation frequency. A procedure is proposed to estimate the probability that the minimum observed is due to a statistical fluctuation. This method, applied to the data available at the time of 1999 Winter Conferences, gives $1 - CL \approx 0.03$ .Comment: 27 pages, 16 figur

Is the Number of Giant Arcs in LCDM Consistent With Observations?

We use high-resolution N-body simulations to study the galaxy-cluster cross-sections and the abundance of giant arcs in the $\Lambda$CDM model. Clusters are selected from the simulations using the friends-of-friends method, and their cross-sections for forming giant arcs are analyzed. The background sources are assumed to follow a uniform ellipticity distribution from 0 to 0.5 and to have an area identical to a circular source with diameter 1\arcsec. We find that the optical depth scales as the source redshift approximately as \tau_{1''} = 2.25 \times 10^{-6}/[1+(\zs/3.14)^{-3.42}] (0.6<\zs<7). The amplitude is about 50% higher for an effective source diameter of 0.5\arcsec. The optimal lens redshift for giant arcs with the length-to-width ratio ($L/W$) larger than 10 increases from 0.3 for \zs=1, to 0.5 for \zs=2, and to 0.7-0.8 for \zs>3. The optical depth is sensitive to the source redshift, in qualitative agreement with Wambsganss et al. (2004). However, our overall optical depth appears to be only $\sim$ 10% to 70% of those from previous studies. The differences can be mostly explained by different power spectrum normalizations ($\sigma_8$) used and different ways of determining the $L/W$ ratio. Finite source size and ellipticity have modest effects on the optical depth. We also found that the number of highly magnified (with magnification $|\mu|>10$) and ``undistorted'' images (with $L/W<3$) is comparable to the number of giant arcs with $|\mu|>10$ and $L/W>10$. We conclude that our predicted rate of giant arcs may be lower than the observed rate, although the precise `discrepancy' is still unclear due to uncertainties both in theory and observations.Comment: Revised version after the referee's reports (32 pages,13figures). The paper has been significantly revised with many additions. The new version includes more detailed comparisons with previous studies, including the effects of source size and ellipticity. New discussions about the redshift distribution of lensing clusters and the width of giant arcs have been adde