Function-based Intersubject Alignment of Human Cortical Anatomy

Making conclusions about the functional neuroanatomical organization of the human brain requires methods for relating the functional anatomy of an individual's brain to population variability. We have developed a method for aligning the functional neuroanatomy of individual brains based on the patterns of neural activity that are elicited by viewing a movie. Instead of basing alignment on functionally defined areas, whose location is defined as the center of mass or the local maximum response, the alignment is based on patterns of response as they are distributed spatially both within and across cortical areas. The method is implemented in the two-dimensional manifold of an inflated, spherical cortical surface. The method, although developed using movie data, generalizes successfully to data obtained with another cognitive activation paradigm—viewing static images of objects and faces—and improves group statistics in that experiment as measured by a standard general linear model (GLM) analysis

The Average Star Formation Histories of Galaxies in Dark Matter Halos from z=0-8

We present a robust method to constrain average galaxy star formation rates, star formation histories, and the intracluster light as a function of halo mass. Our results are consistent with observed galaxy stellar mass functions, specific star formation rates, and cosmic star formation rates from z=0 to z=8. We consider the effects of a wide range of uncertainties on our results, including those affecting stellar masses, star formation rates, and the halo mass function at the heart of our analysis. As they are relevant to our method, we also present new calibrations of the dark matter halo mass function, halo mass accretion histories, and halo-subhalo merger rates out to z=8. We also provide new compilations of cosmic and specific star formation rates; more recent measurements are now consistent with the buildup of the cosmic stellar mass density at all redshifts. Implications of our work include: halos near 10^12 Msun are the most efficient at forming stars at all redshifts, the baryon conversion efficiency of massive halos drops markedly after z ~ 2.5 (consistent with theories of cold-mode accretion), the ICL for massive galaxies is expected to be significant out to at least z ~ 1-1.5, and dwarf galaxies at low redshifts have higher stellar mass to halo mass ratios than previous expectations and form later than in most theoretical models. Finally, we provide new fitting formulae for star formation histories that are more accurate than the standard declining tau model. Our approach places a wide variety of observations relating to the star formation history of galaxies into a self-consistent framework based on the modern understanding of structure formation in LCDM. Constraints on the stellar mass-halo mass relationship and star formation rates are available for download at http://www.peterbehroozi.com/data.html .Comment: Revised to match ApJ accepted version, with additional corrections to Figs. 18+19 (superseding published version

Fast Bootstrapping and Permutation Testing for Assessing Reproducibility and Interpretability of Multivariate fMRI Decoding Models

Multivariate decoding models are increasingly being applied to functional magnetic imaging (fMRI) data to interpret the distributed neural activity in the human brain. These models are typically formulated to optimize an objective function that maximizes decoding accuracy. For decoding models trained on full-brain data, this can result in multiple models that yield the same classification accuracy, though some may be more reproducible than others—i.e. small changes to the training set may result in very different voxels being selected. This issue of reproducibility can be partially controlled by regularizing the decoding model. Regularization, along with the cross-validation used to estimate decoding accuracy, typically requires retraining many (often on the order of thousands) of related decoding models. In this paper we describe an approach that uses a combination of bootstrapping and permutation testing to construct both a measure of cross-validated prediction accuracy and model reproducibility of the learned brain maps. This requires re-training our classification method on many re-sampled versions of the fMRI data. Given the size of fMRI datasets, this is normally a time-consuming process. Our approach leverages an algorithm called fast simultaneous training of generalized linear models (FaSTGLZ) to create a family of classifiers in the space of accuracy vs. reproducibility. The convex hull of this family of classifiers can be used to identify a subset of Pareto optimal classifiers, with a single-optimal classifier selectable based on the relative cost of accuracy vs. reproducibility. We demonstrate our approach using full-brain analysis of elastic-net classifiers trained to discriminate stimulus type in an auditory and visual oddball event-related fMRI design. Our approach and results argue for a computational approach to fMRI decoding models in which the value of the interpretation of the decoding model ultimately depends upon optimizing a joint space of accuracy and reproducibility

Observing the End of Cold Flow Accretion using Halo Absorption Systems

We use cosmological SPH simulations to study the cool, accreted gas in two Milky Way-size galaxies through cosmic time to z=0. We find that gas from mergers and cold flow accretion results in significant amounts of cool gas in galaxy halos. This cool circum-galactic component drops precipitously once the galaxies cross the critical mass to form stable shocks, Mvir = Msh ~ 10^12 Msun. Before reaching Msh, the galaxies experience cold mode accretion (T<10^5 K) and show moderately high covering fractions in accreted gas: f_c ~ 30-50% for R10^16 cm^-2. These values are considerably lower than observed covering fractions, suggesting that outflowing gas (not included here) is important in simulating galaxies with realistic gaseous halos. Within ~500 Myr of crossing the Msh threshold, each galaxy transitions to hot mode gas accretion, and f_c drops to ~5%. The sharp transition in covering fraction is primarily a function of halo mass, not redshift. This signature should be detectable in absorption system studies that target galaxies of varying host mass, and may provide a direct observational tracer of the transition from cold flow accretion to hot mode accretion in galaxies.Comment: 6 pages, 2 figures. Minor changes to match published version (results unchanged

Constraints on the relationship between stellar mass and halo mass at low and high redshift

We use a statistical approach to determine the relationship between the stellar masses of galaxies and the masses of the dark matter halos in which they reside. We obtain a parameterized stellar-to-halo mass (SHM) relation by populating halos and subhalos in an N-body simulation with galaxies and requiring that the observed stellar mass function be reproduced. We find good agreement with constraints from galaxy-galaxy lensing and predictions of semi-analytic models. Using this mapping, and the positions of the halos and subhalos obtained from the simulation, we find that our model predictions for the galaxy two-point correlation function (CF) as a function of stellar mass are in excellent agreement with the observed clustering properties in the SDSS at z=0. We show that the clustering data do not provide additional strong constraints on the SHM function and conclude that our model can therefore predict clustering as a function of stellar mass. We compute the conditional mass function, which yields the average number of galaxies with stellar masses in the range [m, m+dm] that reside in a halo of mass M. We study the redshift dependence of the SHM relation and show that, for low mass halos, the SHM ratio is lower at higher redshift. The derived SHM relation is used to predict the stellar mass dependent galaxy CF and bias at high redshift. Our model predicts that not only are massive galaxies more biased than low mass ones at all redshifts, but the bias increases more rapidly with increasing redshift for massive galaxies than for low mass ones. We present convenient fitting functions for the SHM relation as a function of redshift, the conditional mass function, and the bias as a function of stellar mass and redshift.Comment: 21 pages, 17 figures, discussion enlarged, one more figure, updated references, accepted for publication in Ap

Constraining the LRG Halo Occupation Distribution using Counts-in-Cylinders

The low number density of the Sloan Digital Sky Survey (SDSS) Luminous Red Galaxies (LRGs) suggests that LRGs occupying the same dark matter halo can be separated from pairs occupying distinct dark matter halos with high fidelity. We present a new technique, Counts-in-Cylinders (CiC), to constrain the parameters of the satellite contribution to the LRG Halo-Occupation Distribution (HOD). For a fiber collision-corrected SDSS spectroscopic LRG subsample at 0.16 < z < 0.36, we find the CiC multiplicity function is fit by a halo model where the average number of satellites in a halo of mass M is = ((M - Mcut)/M1)^alpha with Mcut = 5.0 +1.5/-1.3 (+2.9/-2.6) X 10^13 Msun, M1 = 4.95 +0.37/-0.26 (+0.79/-0.53) X 10^14 Msun, and alpha = 1.035 +0.10/-0.17 (+0.24/-0.31) at the 68% and 95% confidence levels using a WMAP3 cosmology and z=0.2 halo catalog. Our method tightly constrains the fraction of LRGs that are satellite galaxies, 6.36 +0.38/-0.39, and the combination Mcut/10^{14} Msun + alpha = 1.53 +0.08/-0.09 at the 95% confidence level. We also find that mocks based on a halo catalog produced by a spherical overdensity (SO) finder reproduce both the measured CiC multiplicity function and the projected correlation function, while mocks based on a Friends-of-Friends (FoF) halo catalog has a deficit of close pairs at ~1 Mpc/h separations. Because the CiC method relies on higher order statistics of close pairs, it is robust to the choice of halo finder. In a companion paper we will apply this technique to optimize Finger-of-God (FOG) compression to eliminate the 1-halo contribution to the LRG power spectrum.Comment: 40 pages, 9 figures, submitted to Astrophysical Journa

Fitting functions for a disk-galaxy model with different LCDM-halo profiles

We present an adaptation of the standard scenario of disk-galaxy formation to the concordant LCDM cosmology aimed to derive analytical expressions for the scale length and rotation speed of present-day disks that form within four different, cosmologically motivated protogalactic dark matter halo-density profiles. We invoke a standard galaxy-formation model that includes virial equilibrium of spherical dark halos, specific angular momentum conservation during gas cooling, and adiabatic halo response to the gas inflow. The mean mass-fraction and mass-to-light ratio of the central stellar disk are treated as free parameters whose values are tuned to match the zero points of the observed size-luminosity and circular speed-luminosity relations of galaxies. We supply analytical formulas for the characteristic size and rotation speed of disks built inside Einasto r^{1/6}, Hernquist, Burkert, and Navarro-Frenk-White dark matter halos. These expressions match simultaneously the observed zero points and slopes of the different correlations that can be built in the RVL space of disk galaxies from plausible values of the galaxy- and star-formation efficiencies

The pseudo-evolution of halo mass

A dark matter halo is commonly defined as a spherical overdensity of matter with respect to a reference density, such as the critical density or the mean matter density of the Universe. Such definitions can lead to a spurious pseudo-evolution of halo mass simply due to redshift evolution of the reference density, even if its physical density profile remains constant over time. We estimate the amount of such pseudo-evolution of mass between z=1 to 0 for halos identified in a large N-body simulation, and show that it accounts for almost the entire mass evolution of the majority of halos with M200 of about 1E12 solar masses and can be a significant fraction of the apparent mass growth even for cluster-sized halos. We estimate the magnitude of the pseudo-evolution assuming that halo density profiles remain static in physical coordinates, and show that this simple model predicts the pseudo-evolution of halos identified in numerical simulations to good accuracy, albeit with significant scatter. We discuss the impact of pseudo-evolution on the evolution of the halo mass function and show that the non-evolution of the low-mass end of the halo mass function is the result of a fortuitous cancellation between pseudo-evolution and the absorption of small halos into larger hosts. We also show that the evolution of the low mass end of the concentration-mass relation observed in simulations is almost entirely due to the pseudo-evolution of mass. Finally, we discuss the implications of our results for the interpretation of the evolution of various scaling relations between the observable properties of galaxies and galaxy clusters and their halo masses.Comment: 15 pages, 9 figures. Minor changes. Published Versio