130 research outputs found
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An average-case analysis of bin packing with uniformly distributed item sizes
We analyze the one-dimensional bin-packing problem under the assumption that bins have unit capacity, and that items to be packed are drawn from a uniform distribution on [0,1]. Building on some recent work by Frederickson, we give an algorithm which uses n/2+0(n^½) bins on the average to pack n items. (Knodel has achieved a similar result.) The analysis involves the use of a certain 1-dimensional random walk. We then show that even an optimum packing under this distribution uses n/2+0(n^1/2) bins on the average, so our algorithm is asymptotically optimal, up to constant factors on the amount of wasted space. Finally, following Frederickson, we show that two well-known greedy bin-packing algorithms use no more bins than our algorithm; thus their behavior is also in asymptotically optimal in this sense
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On the average difference between the solutions to linear and integer knapsack problems
We analyze the expected difference between the solutions to the integer and linear versions of the 0-1 Knapsack Problem. This difference is of interest since it may help understand the efficiency of a fast backtracking algorithm for the integer 0-1 Knapsack Problem. We show that, under a fairly reasonable input distribution, the expected difference is 0(log^2 n/n) and Ω(1/n)
A Measurement of Secondary Cosmic Microwave Background Anisotropies from the 2500 Square-degree SPT-SZ Survey
We present measurements of secondary cosmic microwave background (CMB) anisotropies and cosmic infrared background (CIB) fluctuations using data from the South Pole Telescope (SPT) covering the complete 2540 deg^2 SPT-SZ survey area. Data in the three SPT-SZ frequency bands centered at 95, 150, and 220 GHz, are used to produce six angular power spectra (three single-frequency auto-spectra and three cross-spectra) covering the multipole range 2000 2500 at these frequencies. The main contributors to the power spectra at these angular scales and frequencies are the primary CMB, CIB, thermal and kinematic Sunyaev-Zel'dovich effects (tSZ and kSZ), and radio galaxies. We include a constraint on the tSZ power from a measurement of the tSZ bispectrum from 800 deg^2 of the SPT-SZ survey. We measure the tSZ power at 143 GHz to be D^(tSZ)_(3000) = 4.08^(+0.58)_(-0.67) µK^2 and the kSZ power to be D^(kSZ)_(3000) = 2.9 \pm 1.3 µK^2. The data prefer positive kSZ power at 98.1% CL. We measure a correlation coefficient of ξ = 0.113^(+0.057)_(-0.054) between sources of tSZ and CIB power, with ξ < 0 disfavored at a confidence level of 99.0%. The constraint on kSZ power can be interpreted as an upper limit on the duration of reionization. When the post-reionization homogeneous kSZ signal is accounted for, we find an upper limit on the duration Δz < 5.4 at 95% CL
Angular Power Spectra of the Millimeter Wavelength Background Light from Dusty Star-forming Galaxies with the South Pole Telescope
We use data from the first 100 square-degree field observed by the South Pole
Telescope (SPT) in 2008 to measure the angular power spectrum of temperature
anisotropies contributed by the background of dusty star-forming galaxies
(DSFGs) at millimeter wavelengths. From the auto and cross-correlation of 150
and 220 GHz SPT maps, we significantly detect both Poisson distributed and, for
the first time at millimeter wavelengths, clustered components of power from a
background of DSFGs. The spectral indices between 150 and 220 GHz of the
Poisson and clustered components are found to be 3.86 +- 0.23 and 3.8 +- 1.3
respectively, implying a steep scaling of the dust emissivity index beta ~ 2.
The Poisson and clustered power detected in SPT, BLAST (at 600, 860, and 1200
GHz), and Spitzer (1900 GHz) data can be understood in the context of a simple
model in which all galaxies have the same graybody spectrum with dust
emissivity index of beta = 2 and dust temperature T_d = 34 K. In this model,
half of the 150 GHz background light comes from redshifts greater than 3.2. We
also use the SPT data to place an upper limit on the amplitude of the kinetic
Sunyaev-Zel'dovich power spectrum at l = 3000 of 13 uK^2 at 95% confidence.Comment: 18 pages, 9 figure
A measurement of secondary cosmic microwave background anisotropies with two years of South Pole Telescope observations
We present the first three-frequency South Pole Telescope (SPT) cosmic
microwave background (CMB) power spectra. The band powers presented here cover
angular scales 2000 < ell < 9400 in frequency bands centered at 95, 150, and
220 GHz. At these frequencies and angular scales, a combination of the primary
CMB anisotropy, thermal and kinetic Sunyaev-Zel'dovich (SZ) effects, radio
galaxies, and cosmic infrared background (CIB) contributes to the signal. We
combine Planck and SPT data at 220 GHz to constrain the amplitude and shape of
the CIB power spectrum and find strong evidence for non-linear clustering. We
explore the SZ results using a variety of cosmological models for the CMB and
CIB anisotropies and find them to be robust with one exception: allowing for
spatial correlations between the thermal SZ effect and CIB significantly
degrades the SZ constraints. Neglecting this potential correlation, we find the
thermal SZ power at 150 GHz and ell = 3000 to be 3.65 +/- 0.69 muK^2, and set
an upper limit on the kinetic SZ power to be less than 2.8 muK^2 at 95%
confidence. When a correlation between the thermal SZ and CIB is allowed, we
constrain a linear combination of thermal and kinetic SZ power: D_{3000}^{tSZ}
+ 0.5 D_{3000}^{kSZ} = 4.60 +/- 0.63 muK^2, consistent with earlier
measurements. We use the measured thermal SZ power and an analytic, thermal SZ
model calibrated with simulations to determine sigma8 = 0.807 +/- 0.016.
Modeling uncertainties involving the astrophysics of the intracluster medium
rather than the statistical uncertainty in the measured band powers are the
dominant source of uncertainty on sigma8 . We also place an upper limit on the
kinetic SZ power produced by patchy reionization; a companion paper uses these
limits to constrain the reionization history of the Universe.Comment: 25 pages; 14 figures; Submitted to ApJ (Updated to reflect referee
comments
A Measurement of the Cosmic Microwave Background Damping Tail from the 2500-square-degree SPT-SZ survey
We present a measurement of the cosmic microwave background (CMB) temperature
power spectrum using data from the recently completed South Pole Telescope
Sunyaev-Zel'dovich (SPT-SZ) survey. This measurement is made from observations
of 2540 deg of sky with arcminute resolution at GHz, and improves
upon previous measurements using the SPT by tripling the sky area. We report
CMB temperature anisotropy power over the multipole range . We
fit the SPT bandpowers, combined with the seven-year Wilkinson Microwave
Anisotropy Probe (WMAP7) data, with a six-parameter LCDM cosmological model and
find that the two datasets are consistent and well fit by the model. Adding SPT
measurements significantly improves LCDM parameter constraints; in particular,
the constraint on tightens by a factor of 2.7. The impact of
gravitational lensing is detected at , the most significant
detection to date. This sensitivity of the SPT+WMAP7 data to lensing by
large-scale structure at low redshifts allows us to constrain the mean
curvature of the observable universe with CMB data alone to be
. Using the SPT+WMAP7 data, we measure the
spectral index of scalar fluctuations to be in the LCDM
model, a preference for a scale-dependent spectrum with .
The SPT measurement of the CMB damping tail helps break the degeneracy that
exists between the tensor-to-scalar ratio and in large-scale CMB
measurements, leading to an upper limit of (95%,C.L.) in the LCDM+
model. Adding low-redshift measurements of the Hubble constant () and the
baryon acoustic oscillation (BAO) feature to the SPT+WMAP7 data leads to
further improvements. The combination of SPT+WMAP7++BAO constrains
in the LCDM model, a detection of , ... [abridged]Comment: 21 pages, 10 figures. Replaced with version accepted by ApJ. Data
products are available at http://pole.uchicago.edu/public/data/story12
Extragalactic millimeter-wave sources in South Pole Telescope survey data: source counts, catalog, and statistics for an 87 square-degree field
We report the results of an 87 square-degree point-source survey centered at
R.A. 5h30m, decl. -55 deg. taken with the South Pole Telescope (SPT) at 1.4 and
2.0 mm wavelengths with arc-minute resolution and milli-Jansky depth. Based on
the ratio of flux in the two bands, we separate the detected sources into two
populations, one consistent with synchrotron emission from active galactic
nuclei (AGN) and one consistent with thermal emission from dust. We present
source counts for each population from 11 to 640 mJy at 1.4 mm and from 4.4 to
800 mJy at 2.0 mm. The 2.0 mm counts are dominated by synchrotron-dominated
sources across our reported flux range; the 1.4 mm counts are dominated by
synchroton-dominated sources above ~15 mJy and by dust-dominated sources below
that flux level. We detect 141 synchrotron-dominated sources and 47
dust-dominated sources at S/N > 4.5 in at least one band. All of the most
significantly detected members of the synchrotron-dominated population are
associated with sources in previously published radio catalogs. Some of the
dust-dominated sources are associated with nearby (z << 1) galaxies whose dust
emission is also detected by the Infrared Astronomy Satellite (IRAS). However,
most of the bright, dust-dominated sources have no counterparts in any existing
catalogs. We argue that these sources represent the rarest and brightest
members of the population commonly referred to as sub-millimeter galaxies
(SMGs). Because these sources are selected at longer wavelengths than in
typical SMG surveys, they are expected to have a higher mean redshift
distribution and may provide a new window on galaxy formation in the early
universe.Comment: 35 emulateapj pages, 12 figures, 5 table
Extragalactic millimeter-wave point source catalog, number counts and statistics from 771 square degrees of the SPT-SZ Survey
We present a point source catalog from 771 square degrees of the South Pole
Telescope Sunyaev Zel'dovich (SPT-SZ) survey at 95, 150, and 220 GHz. We detect
1545 sources above 4.5 sigma significance in at least one band. Based on their
relative brightness between survey bands, we classify the sources into two
populations, one dominated by synchrotron emission from active galactic nuclei,
and one dominated by thermal emission from dust-enshrouded star-forming
galaxies. We find 1238 synchrotron and 307 dusty sources. We cross-match all
sources against external catalogs and find 189 unidentified synchrotron sources
and 189 unidentified dusty sources. The dusty sources without counterparts are
good candidates for high-redshift, strongly lensed submillimeter galaxies. We
derive number counts for each population from 1 Jy down to roughly 9, 5, and 11
mJy at 95, 150, and 220 GHz. We compare these counts with galaxy population
models and find that none of the models we consider for either population
provide a good fit to the measured counts in all three bands. The disparities
imply that these measurements will be an important input to the next generation
of millimeter-wave extragalactic source population models.Comment: 23 pages, 8 figures, submitted to Ap
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