text:
# Publications

2014
Guo H, Zheng Z, Zehavi I, Xu H, Eisenstein DJ, Weinberg DH, Bahcall NA, Berlind AA, Comparat J, McBride CK, et al. The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: modeling of the luminosity and colour dependence in the Data Release 10. ArXiv e-prints [Internet]. 2014;1401:3009. Publisher's VersionAbstract
We investigate the luminosity and colour dependence of clustering ofCMASS galaxies in the Sloan Digital Sky Survey-III Baryon OscillationSpectroscopic Survey Tenth Data Release. The halo occupationdistribution framework is adopted to model the projected two-pointcorrelation function measurements on small and intermediate scales (from$0.02$ to $60\,h^{-1}{\rm {Mpc}}$) and to interpret the observed trendsand infer the connection of galaxies to dark matter halos. We find thatluminous red galaxies reside in massive halos of mass$M{\sim}10^{13}$--$10^{14}\,h^{-1}{\rm M_\odot}$ and more luminousgalaxies are more clustered and hosted by more massive halos. The strongsmall-scale clustering requires a fraction of these galaxies to besatellites in massive halos, with the fraction at the level of 5--8 percent and decreasing with luminosity. The characteristic mass of a halohosting on average one satellite galaxy above a luminosity threshold isabout a factor $8.7$ larger than that of a halo hosting a central galaxyabove the same threshold. At a fixed luminosity, progressively reddergalaxies are more strongly clustered on small scales, which can beexplained by having a larger fraction of these galaxies in the form ofsatellites in massive halos. Our clustering measurements on scales below$0.4\,h^{-1}{\rm {Mpc}}$ allow us to study the small-scale spatialdistribution of satellites inside halos. While the clustering ofluminosity-threshold samples can be well described by aNavarro-Frenk-White (NFW) profile, that of the reddest galaxies prefersa steeper or more concentrated profile. Finally, we also use galaxysamples of constant number density at different redshifts to study theevolution of luminous galaxies, and find the clustering to be consistentwith passive evolution in the redshift range of $0.5 \lesssim z \lesssim0.6$.
Tojeiro R, Ross AJ, Burden A, Samushia L, Manera M, Percival WJ, Beutler F, Cuesta AJ, Dawson K, Eisenstein DJ, et al. The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: galaxy clustering measurements in the low redshift sample of Data Release 11. ArXiv e-prints [Internet]. 2014;1401:1768. Publisher's VersionAbstract
We present the distance measurement to z = 0.32 using the 11th datarelease of the Sloan Digital Sky Survey-III Baryon Acoustic OscillationSurvey (BOSS). We use 313,780 galaxies of the low-redshift (LOWZ) sampleover 7,341 square-degrees to compute $D_V = (1264 \pm Anderson L, Aubourg E, Bailey S, Beutler F, Bolton AS, Brinkmann J, Brownstein JR, Chuang C-H, Cuesta AJ, Dawson KS, et al. The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measuring DA and H at z = 0.57 from the baryon acoustic peak in the Data Release 9 spectroscopic Galaxy sample. Monthly Notices of the Royal Astronomical Society [Internet]. 2014:156. Publisher's VersionAbstract We present measurements of the angular diameter distance to and Hubbleparameter at z = 0.57 from the measurement of the baryon acoustic peakin the correlation of galaxies from the Sloan Digital Sky Survey IIIBaryon Oscillation Spectroscopic Survey. Our analysis is based on asample from Data Release 9 of 264 283 galaxies over 3275 square degreesin the redshift range 0.43 < z < 0.70. We use two differentmethods to provide robust measurement of the acoustic peak positionacross and along the line of sight in order to measure the cosmologicaldistance scale. We find DA(0.57) = 1408 ± 45 Mpc andH(0.57) = 92.9 ± 7.8 km s-1 Mpc-1 for ourfiducial value of the sound horizon. These results from the anisotropicfitting are fully consistent with the analysis of the sphericallyaveraged acoustic peak position presented in Anderson et al. Ourdistance measurements are a close match to the predictions of thestandard cosmological model featuring a cosmological constant and zerospatial curvature. Ross AJ, Samushia L, Burden A, Percival WJ, Tojeiro R, Manera M, Beutler F, Brinkmann J, Brownstein JR, Carnero A, et al. The clustering of galaxies in the SDSS-III DR10 Baryon Oscillation Spectroscopic Survey: no detectable colour dependence of distance scale or growth rate measurements. Monthly Notices of the Royal Astronomical Society [Internet]. 2014;437:1109-1126. Publisher's VersionAbstract We study the clustering of galaxies, as a function of their colour, fromData Release Ten (DR10) of the Sloan Digital Sky Survey III (SDSS-III)Baryon Oscillation Spectroscopic Survey. DR10 contains 540 505 galaxieswith 0.43 < z < 0.7; from these we select 122 967 for a Blue'sample and 131 969 for a Red' sample based on k + e corrected (to z =0.55) r - i colours and i-band magnitudes. The samples are chosen suchthat both contain more than 100 000 galaxies, have similar redshiftdistributions and maximize the difference in clustering amplitude. TheRed sample has a 40 per cent larger bias than the Blue(bRed/bBlue = 1.39 ± 0.04), implying thatthe Red galaxies occupy dark matter haloes with an average mass that is0.5 log10 M⊙ greater. Spherically averagedmeasurements of the correlation function, ξ0, and thepower spectrum are used to locate the position of the baryon acousticoscillation (BAO) feature of both samples. Using ξ0, weobtain distance scales, relative to the distance of our referenceΛ cold dark matter cosmology, of 1.010 ± 0.027 for the Redsample and 1.005 ± 0.031 for the Blue. After applyingreconstruction, these measurements improve to 1.013 ± 0.020 forthe Red sample and 1.008 ± 0.026 for the Blue. For each sample,measurements of ξ0 and the second multipole moment,ξ2, of the anisotropic correlation function are used todetermine the rate of structure growth, parametrized byfσ8. We find fσ8, Red = 0.511 ±0.083, fσ8, Blue = 0.509 ± 0.085 andfσ8, Cross = 0.423 ± 0.061 (from thecross-correlation between the Red and Blue samples). We use thecovariance between the bias and growth measurements obtained from eachsample and their cross-correlation to produce an optimally combinedmeasurement of fσ8, comb = 0.443 ± 0.055. Thisresult compares favourably to that of the full 0.43 < z < 0.7sample (fσ8, full = 0.422 ± 0.051) despite thefact that, in total, we use less than half of the number of galaxiesanalysed in the full sample measurement. In no instance do we detectsignificant differences in distance scale or structure growthmeasurements obtained from the Blue and Red samples. Our results areconsistent with theoretical predictions and our tests on mock samples,which predict that any colour-dependent systematic uncertainty on themeasured BAO position is less than 0.5 per cent. Percival WJ, Ross AJ, Sánchez AG, Samushia L, Burden A, Crittenden R, Cuesta AJ, Magana MV, Manera M, Beutler F, et al. The clustering of Galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: including covariance matrix errors. Monthly Notices of the Royal Astronomical Society [Internet]. 2014:244. Publisher's VersionAbstract We present improved methodology for including covariance matrices in theerror budget of Baryon Oscillation Spectroscopic Survey (BOSS) galaxyclustering measurements, revisiting Data Release 9 (DR9) analyses, anddescribing a method that is used in DR10/11 analyses presented incompanion papers. The precise analysis method adopted is becomingincreasingly important, due to the precision that BOSS can now reach:even using as many as 600 mock catalogues to estimate covariance oftwo-point clustering measurements can still lead to an increase in theerrors of ˜20 per cent, depending on how the cosmologicalparameters of interest are measured. In this paper, we extend previouswork on this contribution to the error budget, deriving formulae forerrors measured by integrating over the likelihood, and to thedistribution of recovered best-fitting parameters fitting thesimulations also used to estimate the covariance matrix. Both aresituations that previous analyses of BOSS have considered. We apply theformulae derived to baryon acoustic oscillation (BAO) and redshift-spacedistortion (RSD) measurements from BOSS in our companion papers. Tofurther aid these analyses, we consider the optimum number of bins touse for two-point measurements using the monopole power spectrum orcorrelation function for BAO, and the monopole and quadrupole moments ofthe correlation function for anisotropic-BAO and RSD measurements. 2013 Weinberg DH, Mortonson MJ, Eisenstein DJ, Hirata C, Riess AG, Rozo E. Observational probes of cosmic acceleration. Physics Reports [Internet]. 2013;530:87-255. Publisher's VersionAbstract The accelerating expansion of the universe is the most surprisingcosmological discovery in many decades, implying that the universe isdominated by some form of "dark energy" with exotic physical properties,or that Einstein's theory of gravity breaks down on cosmological scales.The profound implications of cosmic acceleration have inspired ambitiousefforts to understand its origin, with experiments that aim to measurethe history of expansion and growth of structure with percent-levelprecision or higher. We review in detail the four most well establishedmethods for making such measurements: Type Ia supernovae, baryonacoustic oscillations (BAO), weak gravitational lensing, and theabundance of galaxy clusters. We pay particular attention to thesystematic uncertainties in these techniques and to strategies forcontrolling them at the level needed to exploit "Stage IV" dark energyfacilities such as BigBOSS, LSST, Euclid, and WFIRST. We briefly reviewa number of other approaches including redshift-space distortions, theAlcock-Paczynski effect, and direct measurements of the Hubble constantH0. We present extensive forecasts for constraints on thedark energy equation of state and parameterized deviations from GeneralRelativity, achievable with Stage III and Stage IV experimental programsthat incorporate supernovae, BAO, weak lensing, and cosmic microwavebackground data. We also show the level of precision required forclusters or other methods to provide constraints competitive with thoseof these fiducial programs. We emphasize the value of a balanced programthat employs several of the most powerful methods in combination, bothto cross-check systematic uncertainties and to take advantage ofcomplementary information. Surveys to probe cosmic acceleration producedata sets that support a wide range of scientific investigations, andthey continue the longstanding astronomical tradition of mapping theuniverse in ever greater detail over ever larger scales. Agarwal N, Ho S, Myers AD, Seo H-J, Ross AJ, Bahcall N, Brinkmann J, Eisenstein DJ, Muna D, Palanque-Delabrouille N, et al. Characterizing unknown systematics in large scale structure surveys. ArXiv e-prints [Internet]. 2013;1309:2954. Publisher's VersionAbstract Photometric large scale structure (LSS) surveys probe the largestvolumes in the Universe, but are inevitably limited by systematicuncertainties. Imperfect photometric calibration leads to biases in ourmeasurements of the density fields of LSS tracers such as galaxies andquasars, and as a result in cosmological parameter estimation. Earlierstudies have proposed using cross-correlations between differentredshift slices or cross-correlations between different surveys toreduce the effects of such systematics. In this paper we develop amethod to characterize unknown systematics. We demonstrate that while wedo not have sufficient information to correct for unknown systematics inthe data, we can obtain an estimate of their magnitude. We define aparameter to estimate contamination from unknown systematics usingcross-correlations between different redshift slices and proposediscarding bins in the angular power spectrum that lie outside a certaincontamination tolerance level. We show that this method improvesestimates of the bias using simulated data and further apply it tophotometric luminous red galaxies in the Sloan Digital Sky Survey as acase study. Kim A, Padmanabhan N, Aldering G, Allen S, Baltay C, Cahn R, D'Andrea C, Dalal N, Dawson K, Denney K, et al. Distance Probes of Dark Energy. ArXiv e-prints [Internet]. 2013;1309:5382. Publisher's VersionAbstract This document presents the results from the Distances subgroup of theCosmic Frontier Community Planning Study (Snowmass 2013). We summarizethe current state of the field as well as future prospects andchallenges. In addition to the established probes using Type IAsupernovae and baryon acoustic oscillations, we also considerprospective methods based on clusters, active galactic nuclei,gravitational wave sirens and strong lensing time delays. Iršič V, Slosar A, Bailey S, Eisenstein DJ, Font-Ribera A, Le Goff J-M, Lundgren B, McDonald P, O'Connell R, Palanque-Delabrouille N, et al. Detection of Lyβ auto-correlations and Lyα-Lyβ cross-correlations in BOSS Data Release 9. Journal of Cosmology and Astro-Particle Physics [Internet]. 2013;09:016. Publisher's VersionAbstract The Lyman-β forest refers to a region in the spectra of distantquasars that lies between the rest-frame Lyman-β and Lyman-γemissions. The forest in this region is dominated by a combination ofabsorption due to resonant Lyα and Lyβ scattering. Whenconsidering the 1D Lyβ forest in addition to the 1D Lyαforest, the full statistical description of the data requires four 1Dpower spectra: Lyα and Lyβ auto-power spectra and theLyα-Lyβ real and imaginary cross-power spectra. We describehow these can be measured using an optimal quadratic estimator thatnaturally disentangles Lyα and Lyβ contributions. Using asample of approximately 60,000 quasar sight-lines from the BOSS DataRelease 9, we make the measurement of the one-dimensional power spectrumof fluctuations due to the Lyβ resonant scattering. While we havenot corrected our measurements for resolution damping of the power andother systematic effects carefully enough to use them for cosmologicalconstraints, we can robustly conclude the following: i) Lyβ powerspectrum and Lyα-Lyβ cross spectra are detected with highstatistical significance; ii) the cross-correlation coefficient is ≈1 on large scales; iii) the Lyβ measurements are contaminated bythe associated OVI absorption, which is analogous to the SiIIIcontamination of the Lyα forest. Measurements of the Lyβforest will allow extension of the usable path-length for the Lyαmeasurements while allowing a better understanding of the physics ofintergalactic medium and thus more robust cosmological constraints. Aird J, Coil AL, Moustakas J, Diamond-Stanic AM, Blanton MR, Cool RJ, Eisenstein DJ, Wong KC, Zhu G. PRIMUS: An Observationally Motivated Model to Connect the Evolution of the Active Galactic Nucleus and Galaxy Populations out to z ~ 1. The Astrophysical Journal [Internet]. 2013;775:41. Publisher's VersionAbstract We present an observationally motivated model to connect the activegalactic nucleus (AGN) and galaxy populations at 0.2 < z < 1.0 andpredict the AGN X-ray luminosity function (XLF). We start withmeasurements of the stellar mass function of galaxies (from the PrismMulti-object Survey) and populate galaxies with AGNs using models forthe probability of a galaxy hosting an AGN as a function of specificaccretion rate. Our model is based on measurements indicating that thespecific accretion rate distribution is a universal function across awide range of host stellar masses with slope γ1 ≈-0.65 and an overall normalization that evolves with redshift. Wetest several simple assumptions to extend this model to high specificaccretion rates (beyond the measurements) and compare the predictionsfor the XLF with the observed data. We find good agreement with a modelthat allows for a break in the specific accretion rate distribution at apoint corresponding to the Eddington limit, a steep power-law tail tosuper-Eddington ratios with slope \gamma _2=-2.1^{+0.3}_{-0.5}, and ascatter of 0.38 dex in the scaling between black hole and host stellarmass. Our results show that samples of low luminosity AGNs are dominatedby moderately massive galaxies ( {M_*}\sim 10^{10}{--}10^{11} {M}_\odot)growing with a wide range of accretion rates due to the shape of thegalaxy stellar mass function rather than a preference for AGN activityat a particular stellar mass. Luminous AGNs may be a severely skewedpopulation with elevated black hole masses relative to their hostgalaxies and in rare phases of rapid accretion. Skibba RA, Smith SMM, Coil AL, Moustakas J, Aird J, Blanton MR, Bray AD, Cool RJ, Eisenstein DJ, Mendez AJ, et al. PRIMUS: Galaxy Clustering as a Function of Luminosity and Color at 0.2. ArXiv e-prints [Internet]. 2013;1310:1093. Publisher's VersionAbstract We present measurements of the luminosity and color-dependence of galaxyclustering at 0.2 Kazin EA, Sánchez AG, Cuesta AJ, Beutler F, Chuang C-H, Eisenstein DJ, Manera M, Padmanabhan N, Percival WJ, Prada F, et al. The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measuring H(z) and DA(z) at z = 0.57 with clustering wedges. Monthly Notices of the Royal Astronomical Society [Internet]. 2013;435:64-86. Publisher's VersionAbstract We analyse the 2D correlation function of the Sloan Digital SkySurvey-III Baryon Oscillation Spectroscopic Survey (BOSS) CMASS sampleof massive galaxies of the ninth data release to measure cosmicexpansion H and the angular diameter distance DA at a meanredshift of = 0.57. We apply, for the first time, a newcorrelation function technique called clustering wedgesξΔμ(s). Using a physically motivated model, theanisotropic baryonic acoustic feature in the galaxy sample is detectedat a significance level of 4.7σ compared to a featureless model.The baryonic acoustic feature is used to obtain model-independentconstraints cz/H/rs = 12.28 ± 0.82 (6.7 percentaccuracy) and DA/rs = 9.05 ± 0.27 (3.0 percent) with a correlation coefficient of -0.5, where rs is thesound horizon scale at the end of the baryonic drag era. We conductthorough tests on the data and 600 simulated realizations, findingrobustness of the results regardless of the details of the analysismethod. Combining this with rs constraints from the cosmicmicrowave background, we obtain H(0.57) = 90.8 ± 6.2 kms-1 Mpc-1 and DA(0.57) = 1386 ±45 Mpc. We use simulations to forecast results of the final BOSS CMASSdata set. We apply the reconstruction technique on the simulationsdemonstrating that the sharpening of the anisotropic baryonic acousticfeature should improve the detection as well as tighten constraints of Hand DA by ˜30 per cent on average. Font-Ribera A, Kirkby D, Busca N, Miralda-Escudé J, Ross NP, Slosar A, Aubourg É, Bailey S, Bhardwaj V, Bautista J, et al. Quasar-Lyman$\alpha$Forest Cross-Correlation from BOSS DR11 : Baryon Acoustic Oscillations. ArXiv e-prints [Internet]. 2013;1311:1767. Publisher's VersionAbstract We measure the large-scale cross-correlation of quasars with the Lymanalpha forest absorption, using over 164,000 quasars from Data Release 11of the SDSS-III Baryon Oscillation Spectroscopic Survey. We extend theprevious study of roughly 60,000 quasars from Data Release 9 to largerseparations, allowing a measurement of the Baryonic Acoustic Oscillation(BAO) scale along the line of sight$c/(H(z=2.36) ~ r_s) = 9.0 \pm 0.3$and across the line of sight$D_A(z=2.36)~ / ~ r_s = 10.8 \pm 0.4$,consistent with CMB and other BAO data. Using the best fit value of thesound horizon from Planck data ($r_s=147.49 Mpc$), we can translatethese results to a measurement of the Hubble parameter of$H(z=2.36) =226 \pm 8 km/s$and of the angular diameter distance of$D_A(z=2.36) =1590 \pm 60 Mpc\$. The measured cross-correlation function and an updateof the code to fit the BAO scale (baofit) are made publicly available.
Majewski SR, Hasselquist S, Łokas EL, Nidever DL, Frinchaboy PM, García Pérez AE, Johnston KV, Mészáros S, Shetrone M, Allende Prieto C, et al. Discovery of a Dynamical Cold Point in the Heart of the Sagittarius dSph Galaxy with Observations from the APOGEE Project. The Astrophysical Journal Letters [Internet]. 2013;777:L13. Publisher's VersionAbstract
The dynamics of the core of the Sagittarius (Sgr) dwarf spheroidal(dSph) galaxy are explored using high-resolution (R ~ 22, 500), H-band,near-infrared spectra of over 1000 giant stars in the central 3deg2 of the system, of which 328 are identified as Sgrmembers. These data, among some of the earliest observations from theSloan Digital Sky Survey III/Apache Point Observatory Galactic EvolutionExperiment (APOGEE) and the largest published sample of high resolutionSgr dSph spectra to date, reveal a distinct gradient in the velocitydispersion of Sgr from 11 to 14 km s–1 for radii>0.°8 from center to a dynamical cold point of 8 kms–1 in the Sgr center—a trend differing from thatfound in previous kinematical analyses of Sgr over larger scales thatsuggests a more or less flat dispersion profile at these radii.Well-fitting mass models with either cored and cusped dark matterdistributions can be found to match the kinematical results, althoughthe cored profile succeeds with significantly more isotropic stellarorbits than required for a cusped profile. It is unlikely that the coldpoint reflects an unusual mass distribution. The dispersion gradient mayarise from variations in the mixture of populations with distinctkinematics within the dSph; this explanation is suggested (e.g., bydetection of a metallicity gradient across similar radii), but notconfirmed, by the present data. Despite these remaining uncertaintiesabout their interpretation, these early test data (including some frominstrument commissioning) demonstrate APOGEE's usefulness for precisiondynamical studies, even for fields observed at extreme airmasses.
Xu X, Cuesta AJ, Padmanabhan N, Eisenstein DJ, McBride CK. Measuring DA and H at z=0.35 from the SDSS DR7 LRGs using baryon acoustic oscillations. Monthly Notices of the Royal Astronomical Society [Internet]. 2013;431:2834-2860. Publisher's VersionAbstract
We present measurements of the angular diameter distanceDA(z) and the Hubble parameter H(z) at z = 0.35 using theanisotropy of the baryon acoustic oscillation (BAO) signal measured inthe galaxy clustering distribution of the Sloan Digital Sky Survey(SDSS) Data Release 7 (DR7) luminous red galaxy (LRG) sample. Our workis the first to apply density-field reconstruction to an anisotropicanalysis of the acoustic peak. Reconstruction partially removes theeffects of non-linear evolution and redshift-space distortions in orderto sharpen the acoustic signal. We present the theoretical frameworkbehind the anisotropic BAO signal and give a detailed account of thefitting model we use to extract this signal from the data. Our methodfocuses only on the acoustic peak anisotropy, rather than the moremodel-dependent anisotropic information from the broad-band power. Wetest the robustness of our analysis methods on 160 Large Suite of DarkMatter Simulation DR7 mock catalogues and find that our models areunbiased at the ˜0.2 per cent level in measuring the BAOanisotropy. After reconstruction we measure DA(z = 0.35) =1050 ± 38 Mpc and H(z = 0.35) = 84.4 ± 7.0 kms-1 Mpc-1 assuming a sound horizon ofrs = 152.76 Mpc. Note that these measurements are correlatedwith a correlation coefficient of 0.57. This represents a factor of 1.4improvement in the error on DA relative to thepre-reconstruction case; a factor of 1.2 improvement is seen for H.
Lee K-G, Bailey S, Bartsch LE, Carithers W, Dawson KS, Kirkby D, Lundgren B, Margala D, Palanque-Delabrouille N, Pieri MM, et al. The BOSS Lyα Forest Sample from SDSS Data Release 9. The Astronomical Journal [Internet]. 2013;145:69. Publisher's VersionAbstract
We present the BOSS Lyman-α (Lyα) Forest Sample from SDSSData Release 9, comprising 54,468 quasar spectra with z qso> 2.15 suitable for Lyα forest analysis. This data set probesthe intergalactic medium with absorption redshifts 2.0 < zα < 5.7 over an area of 3275 deg2, andencompasses an approximate comoving volume of 20 h -3Gpc3. With each spectrum, we have included several productsdesigned to aid in Lyα forest analysis: improved sky masks thatflag pixels where data may be unreliable, corrections for known biasesin the pipeline estimated noise, masks for the cores of damped Lyαsystems and corrections for their wings, and estimates of the unabsorbedcontinua so that the observed flux can be converted to a fractionaltransmission. The continua are derived using a principal component fitto the quasar spectrum redward of rest-frame Lyα (λ >1216 Å), extrapolated into the forest region and normalized by alinear function to fit the expected evolution of the Lyα forest
Mendez AJ, Coil AL, Aird J, Diamond-Stanic AM, Moustakas J, Blanton MR, Cool RJ, Eisenstein DJ, Wong KC, Zhu G. PRIMUS: Infrared and X-Ray AGN Selection Techniques at 0.2 < z < 1.2. The Astrophysical Journal [Internet]. 2013;770:40. Publisher's VersionAbstract
We present a study of Spitzer/IRAC and X-ray active galactic nucleus(AGN) selection techniques in order to quantify the overlap, uniqueness,contamination, and completeness of each. We investigate how the overlapand possible contamination of the samples depend on the depth of boththe IR and X-ray data. We use Spitzer/IRAC imaging, Chandra andXMM-Newton X-ray imaging, and spectroscopic redshifts from the PRismMUlti-object Survey to construct galaxy and AGN samples at 0.2 < z< 1.2 over 8 deg2. We construct samples over a wide rangeof IRAC flux limits (SWIRE to GOODS depth) and X-ray flux limits (10 ksto 2 Ms). We compare IR-AGN samples defined using both the IRAC colorselection of Stern et al. and Donley et al. with X-ray-detected AGNsamples. For roughly similar depth IR and X-ray surveys, we find that
Tassev S, Zaldarriaga M, Eisenstein DJ. Solving large scale structure in ten easy steps with COLA. Journal of Cosmology and Astro-Particle Physics [Internet]. 2013;06:036. Publisher's VersionAbstract
We present the COmoving Lagrangian Acceleration (COLA) method: an N-bodymethod for solving for Large Scale Structure (LSS) in a frame that iscomoving with observers following trajectories calculated in LagrangianPerturbation Theory (LPT). Unlike standard N-body methods, the COLAmethod can straightforwardly trade accuracy at small-scales in order togain computational speed without sacrificing accuracy at large scales.This is especially useful for cheaply generating large ensembles ofaccurate mock halo catalogs required to study galaxy clustering and weaklensing, as those catalogs are essential for performing detailed erroranalysis for ongoing and future surveys of LSS. As an illustration, weran a COLA-based N-body code on a box of size 100 Mpc/h with particlesof mass ≈ 5 × 109Msolar/h. Running thecode with only 10 timesteps was sufficient to obtain an accuratedescription of halo statistics down to halo masses of at least1011Msolar/h. This is only at a modest speedpenalty when compared to mocks obtained with LPT. A standard detailedN-body run is orders of magnitude slower than our COLA-based code. Thespeed-up we obtain with COLA is due to the fact that we calculate thelarge-scale dynamics exactly using LPT, while letting the N-body codesolve for the small scales, without requiring it to capture exactly theinternal dynamics of halos. Achieving a similar level of accuracy inhalo statistics without the COLA method requires at least 3 times moretimesteps than when COLA is employed.
Ahn CP, Alexandroff R, Allende Prieto C, Anders F, Anderson SF, Anderton T, Andrews BH, Aubourg É, Bailey S, Bastien FA, et al. The Tenth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the SDSS-III Apache Point Observatory Galactic Evolution Experiment. ArXiv e-prints [Internet]. 2013;1307:7735. Publisher's VersionAbstract
The Sloan Digital Sky Survey (SDSS) has been in operation since 2000April. This paper presents the tenth public data release (DR10) from itscurrent incarnation, SDSS-III. This data release includes the firstspectroscopic data from the Apache Point Observatory Galaxy EvolutionExperiment (APOGEE), along with spectroscopic data from the BaryonOscillation Spectroscopic Survey (BOSS) taken through 2012 July. TheAPOGEE instrument is a near-infrared R~22,500 300-fiber spectrographcovering 1.514--1.696 microns. The APOGEE survey is studying thechemical abundances and radial velocities of roughly 100,000 red giantstar candidates in the bulge, bar, disk, and halo of the Milky Way. DR10includes 178,397 spectra of 57,454 stars, each typically observed threeor more times, from APOGEE. Derived quantities from these spectra(radial velocities, effective temperatures, surface gravities, andmetallicities) are also included.DR10 also roughly doubles the number ofBOSS spectra over those included in the ninth data release. DR10includes a total of 1,507,954 BOSS spectra, comprising 927,844 galaxyspectra; 182,009 quasar spectra; and 159,327 stellar spectra, selectedover 6373.2 square degrees.
Dawson KS, Schlegel DJ, Ahn CP, Anderson SF, Aubourg É, Bailey S, Barkhouser RH, Bautista JE, Beifiori A, Berlind AA, et al. The Baryon Oscillation Spectroscopic Survey of SDSS-III. The Astronomical Journal [Internet]. 2013;145:10. Publisher's VersionAbstract
The Baryon Oscillation Spectroscopic Survey (BOSS) is designed tomeasure the scale of baryon acoustic oscillations (BAO) in theclustering of matter over a larger volume than the combined efforts ofall previous spectroscopic surveys of large-scale structure. BOSS uses1.5 million luminous galaxies as faint as i = 19.9 over 10,000deg2 to measure BAO to redshifts z < 0.7. Observations ofneutral hydrogen in the Lyα forest in more than 150,000 quasarspectra (g < 22) will constrain BAO over the redshift range 2.15


text:
Gamasutra is part of the Informa Tech Division of Informa PLC

This site is operated by a business or businesses owned by Informa PLC and all copyright resides with them. Informa PLC's registered office is 5 Howick Place, London SW1P 1WG. Registered in England and Wales. Number 8860726.

View All     Post     RSS
August 1, 2021
Press Releases
August 1, 2021
Games Press
If you enjoy reading this site, you might also want to check out these UBM Tech sites:

Simple mechanics, complex puzzle creation - Part 3: Fun challenges

by Andrea Baldiraghi on 11/02/16 06:16:00 pm

The following blog post, unless otherwise noted, was written by a member of Gamasutra’s community.
The thoughts and opinions expressed are those of the writer and not Gamasutra or its parent company.

In part 1, we defined our game building blocks and mechanics and observed the exponential growth of possible game states and level complexity. In part 2, we found a way to verify our levels as to guarantee the 3 basic rules of our game (no dead ends, with and without max-combo, a no-combo solution can’t be shorter than a combo one) and we assigned a 3-star rating system for our correct levels.

Our final goal though is to create fair, fun and interesting challenges, and a correct level only satisfies the fairness constraint so we are going to try and define additional rules to improve our rating system and highlight the fun and interesting components of a level.

These rules must represent the feedback from playtesting sample levels both by the designer and players with different levels of experience in videogames. They must try to define “fun” and ‘interesting” while staying consistent with the communication we are creating between the game and the player through our mechanics and levels sequence. Let’s see an example of the content of this communication.

Silent tutorial, natural learning

Skiddy has a total of 12 worlds. The first contains only red Skiddies. The next 4 worlds present a single new object each. Following worlds will combine these objects, creating even more complex puzzles.

The first few levels of each world act as a “silent tutorial” to guide players toward a natural learning of each new object’s properties, understanding through playing.

We can see this in the progression of the first 4 levels of World 1:

 Level 1 - The minimum playable level: 2 Skiddies to get max combo, an empty plane and one exit Level 2 - The plane is not a rectangle, there can be static obstacles Level 3 - There can be more than one exit. Vertical symmetry makes left and right solutions equivalent Level 4 - We can’t clear single Skiddies but we can still break the max-combo with 2 double combos

These sequence of 4 simple levels subtly teaches a lot of game mechanics, but we can go one level further and analyze the moves we are allowed to make in a couple of easy levels to see how the “natural learning” idea works within a single board.

Level 1-1, we learn how to get medals and break the combo

We can’t move up, so we immediately reduce the choice to three directions to limit a beginner’s confusion. After noticing the bottom exit, usually our first instinct is to go down, in this way we clear 1 Skiddy in 1 move. We are left with another lonely one to bounce around and clear the level in at least 2 more moves. We get no medals, but we learn that it’s ok to clear Skiddies one by one. Now we want to get some medals so we try again, doing something different. If we move either left or right, we get the 2 Skiddies stuck together and in this level, there is no way of separating them. Whichever way we move now we will end up with a combo. On the left side, we can go down and clear the level in only 2 moves. This is the minimum and will net us all 3 medals. On the right side, we can either go down-left-down or back left and down, so we clear the level in 4 or 3 moves (typically 4 because on first instinct we generally tend to not backtrack). We learn the difference between combo only (1 medal) and combo in minimum moves (3 medals).

This level also shows how a simple change creates problematic results.

If we move the bottom exit to the middle, we change two things:

1. There would be no way to break the combo
2. The only way for the player to learn about the importance of minimum move would be a frustrating ping-pong left and right

Level 1-1 is a simple but comprehensive example of what we learned from our first playtest sessions and helps us defined some positive and negative characteristic of a level.

Positive:

1. It’s my choice to break the combo. Until all same-color Skiddies are in the level I must be able to get the max combo no matter how I moved before
2. It’s easy to break the combo if I don’t pay attention. It’s rewarding to focus on my moves
3. Level layouts, symmetry and block placement have a meaningful purpose

Negative:

1. Getting the max combo in less moves than it takes to break it reduces the challenge
2. Levels that are easy to solve just randomly moving around are boring
3. Correct levels with a feeling of random or unbalanced block placement are not interesting or visually confusing

Lets’ analyze and try to implement point no.1. in our editor.

1 Until all same-color Skiddies are in the level I must be able to get the max combo

To clarify this situation, here’s an example of a level where we break the max combo:

The perfect  solution for this level is Down, Left, Down. Starting by moving left we clear the yellow Skiddies in a combo but then it’s impossible to get the red ones in a position that will not break theirs. Even not willingly breaking any color combo, the max combo is now impossible.

While play-testing this became subconsciously expected and felt almost as important as not having dead ends so we decided that it was a necessary condition to get at least 3 stars in our rating system.

To track this, first we define a method (CheckCanCombo) to check if the level state related to a node can still lead to a max combo:

//this class contains all information related to our level game board.
//we can unpack all this information from the Node.Value field and recreate
//any state while traversing our tree

Class Board {
…

Int NumR; //hold the initial count of red skiddies in this level

List <Blocks> Moveables; //moveable blocks in this level
//(colored skiddies, crates, ice blocks, etc..)

//checks if from this node we can still reach the max combo
//returns 0 if can combo, 2 if cannot combo (1 is reserved for later)
public int CheckCanCombo() {

if (NumR > 0) {
int countreds = 0;
//count each color skiddy
foreach (Block b in Moveables) {
if(b.IsType(RedSkiddy)) {
countreds++;
}

//if a color has less than all items, it cannot lead to a combo,
//0 means we can still get a combo for this color or the last block for this
//color was cleared. If it’s the last one, the node will be excluded in the
//final check because the related node State is not set to MaxCombo
if (countreds > 0 && countreds != NumR) {
return 2;
}
else return 0;
}
}

…
}

Then we add a field (CanCombo) to our node class (defined in part 1 and 2) to track the result.

// A node contains information about board configuration and relations to other nodes
class Node {
int Value;		//encodes our pieces’ layout and board score
NodeState State;	//max-combo, ok or dead-end?
Node[4] Child;	//the states originating form the next 4 moves
int Index; 		//generating move(none, up, right, down, left)
//			    	-1    0   1      2     3
Node Parent;    //state before last move, used to traverse our solution
int Depth;		//how many moves it took to reach this node

int CanCombo;   //tracks if the max combo is still reachable from this node
//0 can, 2 cannot combo (1 is reserved for later)
}

Our root is created with CanCombo = 0 as anyway all blocks are available, then whenever we create a child node from a parent node that can still reach the combo, we perform the check. The first time that we reach a node that breaks the combo, we can save the move sequence so the editor can show us where it breaks.

//creation from an existing node
Node node = new Node(value) {
Value = value;
State = DeadEnd		//we do not know if we can reach a solution
Parent = CurrentNode;	//set the parent for solution traversal
Index = index;		//we track the originating move
Depth = currentNode.Depth + 1;

if (CurrentNode.CanCombo < 2) {
//only if parent can reach the max combo
node.CanCombo = board.CheckCanCombo();
}
else {
//save the move sequence so we can see it in the editor
Board.FirstBreaker = GetFirstBreakerSolution(currentNode);
}
}

Then we define a method to check if at some point the combo was broken.

//We enumerate through all our unique nodes and check if a node that could still lead
//to the max combo (CanCombo == 0) didn’t actually lead to it (State != MaxCombo)

public bool BreakComboCheck() {
foreach (Node n in Uniques) {
if (n.CanCombo == 0) {
if (!n.State == NodeState.MaxCombo)
return false;
}
}
return true;
}

And at the end of our rating check, we can add this after the DeadEnd search, together with the other conditions to get our 3 stars.

    …

Rating = 0;

Rating = 1;
bool comboUnbroken = BreakComboCheck();

if (noCombo && withCombo) {
Rating = 2;
if (comboUnbroken) {
if (Perfect == Moves) {
Rating = 3;
…
}
…

Thanks to the previous state propagation, this important rule was fairly easy to implement, we can move to point no.2.

2 - It’s easy to break the combo if I don’t pay attention. It’s rewarding to focus on my moves

What this means in practice is that it must never take more moves to clear a single Skiddy (or more than one but not all if we have more than 2) from one color group than it takes to get the combo for that group (as we saw in level 1-1). Let’s clarify with a negative example:

Here we can get the red combo in 1 move by going down, but it takes 2 moves to break it going right then down.

Tracking this is even easier than point one, we just need a field (SingleSkiddyOut) in our tree class and when we perform our CheckCanCombo during node creation we save our depth if necessary.

       …

if (CurrentNode.CanCombo < 2) { //only if parent can reach the max combo
node.CanCombo = board.CheckCanCombo();

//if at this point we broke the combo, it means we cleared some but
//not all skiddies of a color group. We save the number of moves.
if (node.CanCombo == 2 && singleSkiddyOut == 0 ) {
SingleSkiddyOut = currentNode.Depth + 1;
}

…

And when we rate the board we just check if it’s greater than the number of moves it takes to get a perfect.

This simple rule improves a level’s quality a lot, so we add a 4th star to our rating.

    …

Rating = 0;

Rating = 1;
bool comboUnbroken = BreakComboCheck();

if (noCombo && withCombo) {
Rating = 2;
if (comboUnbroken) {
if (Perfect == Moves) {
Rating = 3;

//breaking the combo is not harder then getting a perfect
if (SingleSkiddyOut <= Perfect) {
Rating = 4;
}
…

We can move to the last point:

3 - Level layouts, symmetry and block placement have a meaningful purpose

We briefly discussed placement of static blocks in level 1-1 analysis but before we continue we need to take a look at how we introduced other obstacles in later levels.

In Level 2-1 we learn how to use a pit, a block that will stop Skiddies on their movement but can be slid over with an additional move. This can be useful to align us to an exit or to change direction mid-level.

 Initially we perceive a new obstacle as a negative challenge Our first reaction is to move away But we find that we cannot reach the exit using walls only We are guided back to try the new object Discovering its properties And we learn how to use it to solve the levels

The function of this new block, as that of any other dynamic object we will get later is to challenge the player while contributing to the level solution. It would make no sense to just have these objects around yet solving the level without interacting with them, so we track that any special block is contributing to the final solution.

We do this by checking 2 things:

1. If we remove all the special blocks and get the same solutions, they are not contributing anything
2. For each and every solution leading to a perfect, every special block must be interacted with (e.g.: every pit must be traversed by a Skiddy, every crate must be pushed around, etc...)

As before, we can clarify this with the example of a wrong level:

In this example, we can get a perfect solution moving Up, Left, Down, Right and Down, with both Skiddies sliding over the pit. If we remove the pit though, because of the level layout, we get the exact perfect solution as the Skiddies can use walls to stop in the correct position. This level will fail the 4th star check

These checks are a bit more complicated than the previous ones so we omit code for brevity but in the end if our level contains special blocks, we can check this as part of our 4th star rating.

    …

Rating = 0;

Rating = 1;
bool comboUnbroken = BreakComboCheck();

if (noCombo && withCombo) {
Rating = 2;
if (comboUnbroken) {
if (Perfect == Moves) {
Rating = 3;
//breaking the combo is not harder then getting a perfect
if (factory.FirstSkiddyOut <= Perfect) {
…
//we either don’t have special blocks or thei are
//all used in every perfect solution
if (!HasSpecials || UsingSpecials(factory)) {
Rating = 4;
}
…

In the final version of our editor there’s an additional 5th star for levels with a second color with only 1 Skiddy. This levels get 5 stars only if it’s possible to clear this single Skiddy in no more than 1 move after clearing the first combo. (It’s tedious to bounce around a lonely Skiddy without combo chance).  For the sake of our discussion, we don’t need to dwell on its implementation details. All levels featured in the game are 4 or 5 Stars.

We have now reached a satisfying situation, where our editor can analyze our level and, based on the game designer’s requirements, correctly determine if it respects all the required rules and rate it accordingly.

Our levels are now guaranteed to satisfy the following conditions:

1. Without dead ends – 1 Star
2. With and without max-combo -2 Stars
3. The no-combo solution is always longer than a combo one
4. It’s always possible to get the max combo regardless of the level state, unless I break it voluntarily – 3 Stars
5.  I can always break the combo in less moves than it takes to get the perfect
6. If there are special blocks they all contribute to the perfect solution. – 4 Stars
7. If there’s a single Skiddy for a color, it can be cleared in 1 move after the combo for the other color – 5 stars

This removes human error in this critical (and, frankly, impossible to always verify by hand) test phase and avoids that level that appears to be good but has hidden negative characteristics not found by the designer or by human players.

We can now create levels that are fair and fun, yet we are still missing the final element to answer our initial question. Given two levels with the same elements and equal rating, what makes one better than the other? What makes an interesting level?

In the 4th and last part we will try to implement some level design rules so that our editor can help us in the creation phase and avoid testing levels that can be discarded in advance.

Disclaimer: As a first experience in designing/programming a video game, we are aware our methods might not be the best but they served the purpose and aided the design and the code to evolve and complement each other.  If readers have questions or suggestions regarding the subject matter and how to improve it, we at BigBangPixel would sincerely like to discuss it, so write us at [email protected]

License: Skiddy and all related assets including levels and editors are Copyright 2012 by BigBangPixel and all rights are reserved. The information published in this article can be used by anyone for non-assignable, non-transferable, non-commercial use or educational purposes.  Any other use, including any redistribution in

whole or in part, requires explicit, written permission from BigBangPixel.

Related Jobs

Insomniac Games — Burbank, California, United States
[07.30.21]

Technical Artist - Pipeline
Insomniac Games — Burbank, California, United States
[07.30.21]

Engine Programmer
Legends of Learning — Baltimore, Maryland, United States
[07.30.21]

Senior Gameplay Engineer - \$160k - Remote OK
Bytro Labs GmbH — Hamburg, Germany
[07.30.21]

Senior Product Owner / Live-Ops Owner (f/m/x)

format: plain


text:
# Brown clustering

Brown clustering is a hard hierarchical agglomerative clustering problem based on distributional information proposed by Peter Brown, Vincent Della Pietra, Peter deSouza, Jennifer Lai, and Robert Mercer.[1] It is typically applied to text, grouping words into clusters that are assumed to be semantically related by virtue of their having been embedded in similar contexts.

## Introduction

In natural language processing, Brown clustering[2] or IBM clustering[3] is a form of hierarchical clustering of words based on the contexts in which they occur, proposed by Peter Brown, Vincent Della Pietra, Peter deSouza, Jennifer Lai, and Robert Mercer of IBM in the context of language modeling.[1] The intuition behind the method is that a class-based language model (also called cluster n-gram model[3]), i.e. one where probabilities of words are based on the classes (clusters) of previous words, is used to address the data sparsity problem inherent in language modeling.

Jurafsky and Martin give the example of a flight reservation system that needs to estimate the likelihood of the bigram "to Shanghai", without having seen this in a training set.[3] The system can obtain a good estimate if it can cluster "Shanghai" with other city names, then make its estimate based on the likelihood of phrases such as "to London", "to Beijing" and "to Denver".

## Technical definition

Brown groups items (i.e., types) into classes, using a binary merging criterion based on the log-probability of a text under a class-based language model, i.e. a probability model that takes the clustering into account. Thus, average mutual information (AMI) is the optimization function, and merges are chosen such that they incur the least loss in global mutual information.

As a result, the output can be thought of not only as a binary tree but perhaps more helpfully as a sequence of merges, terminating with one big class of all words. This model has the same general form as a hidden Markov model, reduced to bigram probabilities in Brown's solution to the problem. MI is defined as:

${\displaystyle \operatorname {MI} (c_{i},c_{j})=\Pr(\langle c_{i},c_{j}\rangle )\log _{2}{\frac {\Pr(\langle c_{i},c_{j}\rangle )}{\Pr(\langle c_{i},*\rangle )\Pr(\langle *,c_{j}\rangle )}}}$

Finding the clustering that maximizes the likelihood of the data is computationally expensive. The approach proposed by Brown et al. is a greedy heuristic.

The work also suggests use of Brown clusterings as a simplistic bigram class-based language model. Given cluster membership indicators ci for the tokens wi in a text, the probability of the word instance wi given preceding word wi-1 is given by:[3]

${\displaystyle \Pr(w_{i}|w_{i-1})=\Pr(w_{i}|c_{i})\Pr(c_{i}|c_{i-1})}$

This has been criticised[citation needed] as being of limited utility, as it only ever predicts the most common word in any class, and so is restricted to |c| word types; this is reflected in the low relative reduction in perplexity found when using this model and Brown.

## Variations

Other works have examined trigrams in their approaches to the Brown clustering problem.[4]

Brown clustering as proposed generates a fixed number of output classes. It is important to choose the correct number of classes, which is task-dependent.[5] The cluster memberships of words resulting from Brown clustering can be used as features in a variety of machine-learned natural language processing tasks.[2]

A generalization of the algorithm was published in the AAAI conference in 2016, including a succinct formal definition of the 1992 version and then also the general form.[6] Core to this is the concept that the classes considered for merging do not necessarily represent the final number of classes output, and that altering the number of classes considered for merging directly affects the speed and quality of the final result.

There are no known theoretical guarantees on the greedy heuristic proposed by Brown et al. (as of February 2018). However, the clustering problem can be framed as estimating the parameters of the underlying class-based language model: it is possible to develop a consistent estimator for this model under mild assumptions.[7]


text:
# [Tex/LaTex] How to write conditional equations with one-sided curly brackets

best practicesequations

I want to write a conditional expression such as the following.

What is the best way to express such conditional expressions in Latex?

I think this is a job for cases from the amsmath package

\documentclass{article}
\usepackage{amsmath}

\begin{document}
$f(x)= \begin{cases} \frac{x^2-x}{x},& \text{if } x\geq 1\\ 0, & \text{otherwise} \end{cases}$
\end{document}

or if you would prefer a displaystyle fraction, then you could use dcases from the mathtools package, which extends (and loads) the amsmath package.

\documentclass{article}
\usepackage{mathtools}

\begin{document}
$f(x)= \begin{dcases} \frac{x^2-x}{x},& \text{if } x\geq 1\\ 0, & \text{otherwise} \end{dcases}$
\end{document}


text:
## anonymous 4 years ago Let y= 6 x^5 - 9. Find A, B, and C so that (dy)/(dx) = Ax^B +C. A =

1. anonymous

what on earth kind of questions are these? why don't they just ask for the derivative?

2. anonymous

I know they want me to find A.B.C.D

3. anonymous

BUT I just used that wolfram and got the anwser

4. anonymous

but how do you find if x=2?

5. anonymous

not sure what you mean, but this is the ordinary power rule $y=6x^5-9$ $y'=5\times 6x^{5-1}=30x^4$


text:
# Lorentz Transformation (1 Viewer)

### Users Who Are Viewing This Thread (Users: 0, Guests: 1)

#### yukcream

I am not sure wheather
matrix T^v_u = {T^u_v}^-1
or T^v_u = {T^v_u} is true?
T is a lorentz transformation for 4 vector~

Yuk

#### Tom Mattson

Staff Emeritus
Gold Member
Start by writing down the matrix representation of a general Lorentz transformation.

yukcream said:
I am not sure wheather
matrix T^v_u = {T^u_v}^-1
In matrix language, that is $T^T=T^{-1}$. In other words, you are asking if the transpose of $T$ equals the inverse of $T$.

Try writing it out explicitly and see if it does.

or T^v_u = {T^v_u} is true?
Is there a typo here? Because here you just seem to be asking if $T^{\mu}_{\nu}$ equals itself, unless there is something else implied by the { } braces.

#### yukcream

It is great that you can understand my notation~ you are so smart!!

It is my fault that I want to ask is T^v_u = {T^v_u} -1?

thanks for help
yuk

#### Tom Mattson

Staff Emeritus
Gold Member
yukcream said:
It is great that you can understand my notation~ you are so smart!!
Your notation is a lot like LaTeX, which is what I used to make my math symbols. So, I'm not really that smart. :tongue2:

It is my fault that I want to ask is T^v_u = {T^v_u} -1?
OK, so now you're asking if $T$ is equal to its own inverse. Again, try to write down the matrix and see if that is so.

#### yukcream

Actually T is a special transformation~ called Lorentz transformation. In 4 vector case they are not equal~ but my lecturer asked me to prove T = T inverse~ I wonder is there is any typing error in his assignment given? or the position of the indexs may affect the result? They are not the same in fact!

yuk yuk

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving


text:
# Is the acceleration of the expansion of the universe caused by expansion of spacetime itself?

When considering the accelerating expansion of the universe, it is often stated that dark energy is required to cause acceleration of expansion in order to overcome the pull of gravity.

However, it seems that if the rate of expansion is great enough, this would overcome the effect of gravity that is causing deceleration.

In other words, the distance gain of the expanding universe is happening at a rate greater than the force pull of gravity. So although gravity does work to reduce the expansion velocity, the additional distance gained causes an increasing amount of space to expand. I.e. things are accelerating faster apart because at each step, there is more space between them to expand (which is increasingly greater than the gravity pull).

Let me try to define this better:

Given two bodies in the universe very far apart a,b.

vel_expand - the rate at which the distance between a,b is increasing due to the expansion of spacetime between them

acc_from_expand - the increase of vel_expand caused because of the greater distance between a,b

So as a,b move apart, the space between them increases (which is an increase in the amount of expanding space time between them), which causes a greater increase due to expansion of space time - i.e. an acceleration of expansion due to the expansion itself.

Now on the opposite side of the equation is the pull of gravity (the curvature of space time) caused by the mass of a,b. However, gravity decreases at an inverse square to the distance so it quickly becomes smaller as distance changes.

So as distances become large between a,b there is a point where the acceleration due to expansion of spacetime between a,b is greater than the deceleration due to gravity between them.

So at that point they will continue to expand apart at an accelerating rate.

(This concept is similar to the edge of the observable universe. The distance from which speed of light can overcome the expansion of the universe.)

Maybe this is all completely wrong. But I would like any feedback on whether this makes any sense.

Also in my description, the acceleration of expansion would be a function of the distance between objects - so the further apart 2 bodies in the universe, the faster they would be accelerating apart. I don’t know if that matches measurements - but I have read that there are discrepancies between the rate of expansion measured in the background radiation versus white dwarves vs supernovas.

Does my concept make sense?

If so, is there an article that discusses the acceleration of the expansion of the universe due to the expansion of the universe itself?

If not, where am I wrong in my concept?

• Also, is the the space time constant that Einstein added to the general theory of relativity? (Which in my description is the concept that space time itself expands at a fixed rate)? – Rick Love May 27 '19 at 20:01
• I don't know if this is helpful, but I didn't get "an acceleration of expansion due to the expansion itself". First of all, it should be clarified that expansion of space is expansion of universe (i.e. it's not like the universe is expanding within space, but I somehow think that you already know this). Do you mean that the cause of expansion lies within spacetime itself, so more expansion will lead to even more expansion? – Helen May 27 '19 at 22:38
• If the latter is the intended meaning, then it could have to do with one of the proposed causes of the expansion, i.e. vacuum energy. Also, let's add as was also noted in the answer that objects further apart will not accelerate away from each other more. – Helen May 27 '19 at 22:41
• @RickLove why the deselection? – Árpád Szendrei May 28 '19 at 4:48

You are correct, space itself is expanding, but only in the intergalactic viods of space.

Inside galaxies, space is not expanding, because gravity dominates.

We cannot say that two solar systems in the Milky Way would recede because of space expansion between them.

Space is expanding between the galaxies, where gravity is not dominant, but dark energy is dominant.

The problem lies in the definition of distance (or speed of recession) in GR at an intergalactic scale. There is no such definition of distance (or speed of recession).

It is very hard to define at what rate two galaxies are recessing, and we have no experimental evidence on the expansion of space itself.

So you are saying that if two galaxies are farther apart, they will be accelerating faster then two galaxies that are closer. This is not correct to say. Over large distances, the universe expands uniformly. Though, what you are saying might be right if you say that inside galaxy clusters, space is expanding slower (because of gravity) then in the voids of galaxy groups, space is expanding faster (because gravity has even less influence there).

• I would clarify that if expansion is uniform across the universe, it still occurs in areas of larger gravity, it is simply negligible compared to gravity. Also, I would question whether expansion is uniform across the universe or if there are factors not considered that could be affecting it. – Rick Love May 28 '19 at 3:28

No, the accelerated expansion of the universe is caused by cosmological constant. The cc has negative pressure $$p$$. You may have a look at the Friedmann acceleration equation whereby the term $$-(\rho + 3p)$$ is decisive. The universe expands accelerated if this term is positive which requires that the matter density $$\rho$$ is dominated by the cosmological constant (notice $$p$$ is negative).

Second, spacetime doesn't expand. Note that space doesn't expand by itself. Instead "expansion of the universe" means increasing distances between comoving objects. Whether the notions space expands or distant galaxies are moving away from each other depends on the chosen coordinates. So neither of these views - being not invariant - may be considered as a measurable physical phenomenon. Space expands in FRW-coordinates and galaxies move away in normal-coordinates.


text:
## Asynchronous weighted additive Schwarz methods

Andreas Frommer, Hartmut Schwandt, and Daniel B. Szyld

### Abstract

A class of asynchronous Schwarz methods for the parallel solution of nonsingular linear systems of the form $Ax=f$ is investigated. This class includes, in particular, an asynchronous algebraic Schwarz method as well as asynchronous multisplitting. Theorems are obtained demonstrating convergence for the cases when $A^{-1}$ is nonnegative and when $A$ is an $H$-matrix. The results shown are for both the situations with or without overlap between the domains in which an underlying mesh is divided, if such a mesh exists. Numerical experiments on systems of up to over ten million variables on up to 256 processors are presented. They illustrate the convergence properties of the method, as well as the fact that when the domains are not all of the same size, the asynchronous method can be up to 50% faster than the corresponding synchronous one.

Full Text (PDF) [136 KB], BibTeX

### Key words

Asynchronous methods, monotone matrices, H-matrices, linear system, parallel algorithms, multisplittings, additive Schwartz.

65F10, 65Y05.

### Links to the cited ETNA articles

 [5] Vol. 3 (1995), pp. 24-38 Rafael Bru, Violeta Migallón, José Penadés, and Daniel B. Szyld: Parallel, synchronous and asynchronous two-stage multisplitting methods