Spreading in Social Systems: Reflections

In this final chapter, we consider the state-of-the-art for spreading in social systems and discuss the future of the field. As part of this reflection, we identify a set of key challenges ahead. The challenges include the following questions: how can we improve the quality, quantity, extent, and accessibility of datasets? How can we extract more information from limited datasets? How can we take individual cognition and decision making processes into account? How can we incorporate other complexity of the real contagion processes? Finally, how can we translate research into positive real-world impact? In the following, we provide more context for each of these open questions.Comment: 7 pages, chapter to appear in "Spreading Dynamics in Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur

High Resolution STIS/HST and HIRES/Keck Spectra of Three Weak MgII Absorbers Toward PG 1634+706

High resolution optical (HIRES/Keck) and UV (STIS/HST) spectra, covering a large range of chemical transitions, are analyzed for three single-cloud weak MgII absorption systems along the line of sight toward the quasar PG 1634+706. Weak MgII absorption lines in quasar spectra trace metal-enriched environments that are rarely closely associated with the most luminous galaxies (>0.05L^*). The two weak MgII systems at z=0.81 and z=0.90 are constrained to have >=solar metallicity, while the metallicity of the z=0.65 system is not as well-constrained, but is consistent with >1/10th solar. These weak MgII clouds are likely to be local pockets of high metallicity in a lower metallicity environment. All three systems have two phases of gas, a higher density region that produces narrower absorption lines for low ionization transitions, such as MgII, and a lower density region that produces broader absorption lines for high ionization transitions, such as CIV. The CIV profile for one system (at z=0.81) can be fit with a single broad component (b~10 km/s), but those for the other two systems require one or two additional offset high ionization clouds. Two possible physical pictures for the phase structure are discussed: one with a low-ionization, denser phase embedded in a lower density surrounding medium, and the other with the denser clumps surrounding more highly ionized gas.Comment: 32 pages, 4 figures; to appear in ApJ on May 20, 200

Tracing the Filamentary Structure of the Galaxy Distribution at z~0.8

We study filamentary structure in the galaxy distribution at z ~ 0.8 using data from the Deep Extragalactic Evolutionary Probe 2 (DEEP2) Redshift Survey and its evolution to z ~ 0.1 using data from the Sloan Digital Sky Survey (SDSS). We trace individual filaments for both surveys using the Smoothed Hessian Major Axis Filament Finder, an algorithm which employs the Hessian matrix of the galaxy density field to trace the filamentary structures in the distribution of galaxies. We extract 33 subsamples from the SDSS data with a geometry similar to that of DEEP2. We find that the filament length distribution has not significantly changed since z ~ 0.8, as predicted in a previous study using a \LamdaCDM cosmological N-body simulation. However, the filament width distribution, which is sensitive to the non-linear growth of structure, broadens and shifts to smaller widths for smoothing length scales of 5-10 Mpc/h from z ~ 0.8 to z ~ 0.1, in accord with N-body simulations.Comment: 10 pages, 8 figures, accepted for the publication in MNRA

Present-Day Descendants of z=3 Ly-{\alpha} Emitting Galaxies in the Millennium-II Halo Merger Trees

Using the Millennium-II Simulation dark matter sub-halo merger histories, we created mock catalogs of Lyman Alpha Emitting (LAE) galaxies at z=3.1 to study the properties of their descendants. Several models were created by selecting the sub-halos to match the number density and typical dark matter mass determined from observations of these galaxies. We used mass-based and age-based selection criteria to study their effects on descendant populations at z~2, 1 and 0. For the models that best represent LAEs at z=3.1, the z=0 descendants have a median dark matter halo mass of 10^12.7 M_Sun, with a wide scatter in masses (50% between 10^11.8 and 10^13.7 M_Sun). Our study differentiated between central and satellite sub-halos and found that ~55% of z=0 descendants are central sub-halos with M_Median~10^12 M_Sun. This confirms that central z=0 descendants of z=3.1 LAEs have halo masses typical of L* type galaxies. The satellite sub-halos reside in group/cluster environments with dark matter masses around 10^14 M_Sun. The median descendant mass is robust to various methods of age determination, but it could vary by a factor of 5 due to current observational uncertainties in the clustering of LAEs used to determine their typical z=3.1 dark matter mass.Comment: Accepted for publication in Ap

Crawling the Cosmic Network: Identifying and Quantifying Filamentary Structure

We present the Smoothed Hessian Major Axis Filament Finder (SHMAFF), an algorithm that uses the eigenvectors of the Hessian matrix of the smoothed galaxy distribution to identify individual filamentary structures. Filaments are traced along the Hessian eigenvector corresponding to the largest eigenvalue, and are stopped when the axis orientation changes more rapidly than a preset threshold. In both N-body simulations and the Sloan Digital Sky Survey (SDSS) main galaxy redshift survey data, the resulting filament length distributions are approximately exponential. In the SDSS galaxy distribution, using smoothing lengths of 10 h^{-1} Mpc and 15 h^{-1} Mpc, we find filament lengths per unit volume of 1.9x10^{-3} h^2 Mpc^{-2} and 7.6x10^{-4} h^2 Mpc^{-2}, respectively. The filament width distributions, which are much more sensitive to non-linear growth, are also consistent between the real and mock galaxy distributions using a standard cosmology. In SDSS, we find mean filament widths of 5.5 h^{-1} Mpc and 8.4 h^{-1} Mpc on 10 h^{-1} Mpc and 15 h^{-1} Mpc smoothing scales, with standard deviations of 1.1 h^{-1} Mpc and 1.4 h^{-1} Mpc, respectively. Finally, the spatial distribution of filamentary structure in simulations is very similar between z=3 and z=0 on smoothing scales as large as 15 h^{-1} Mpc, suggesting that the outline of filamentary structure is already in place at high redshift.Comment: 10 pages, 11 figures, accepted to MNRA

Crawling the Cosmic Network: Exploring the Morphology of Structure in the Galaxy Distribution

Although coherent large-scale structures such as filaments and walls are apparent to the eye in galaxy redshift surveys, they have so far proven difficult to characterize with computer algorithms. This paper presents a procedure that uses the eigenvalues and eigenvectors of the Hessian matrix of the galaxy density field to characterize the morphology of large-scale structure. By analysing the smoothed density field and its Hessian matrix, we can determine the types of structure - walls, filaments, or clumps - that dominate the large-scale distribution of galaxies as a function of scale. We have run the algorithm on mock galaxy distributions in a LCDM cosmological N-body simulation and the observed galaxy distributions in the Sloan Digital Sky Survey. The morphology of structure is similar between the two catalogues, both being filament-dominated on 10-20 h^{-1} Mpc smoothing scales and clump-dominated on 5 h^{-1} Mpc scales. There is evidence for walls in both distributions, but walls are not the dominant structures on scales smaller than ~25 h^{-1} Mpc. Analysis of the simulation suggests that, on a given comoving smoothing scale, structures evolve with time from walls to filaments to clumps, where those found on smaller smoothing scales are further in this progression at a given time.Comment: 37 pages, 14 figures. Accepted to MNRAS