Conditional Mass Function Research Articles

The LORELI database: 21 cm signal inference with 3D radiative hydrodynamics simulations

The Square Kilometer Array is expected to measure the 21 cm signal from the Epoch of Reionization (EoR) in the coming decade, and its pathfinders may provide a statistical detection even earlier. The currently reported upper limits provide tentative constraints on the astrophysical parameters of the models of the EoR. In order to interpret such data with 3D radiative hydrodynamics simulations using Bayesian inference, we present the latest developments of the LICORICE code. Relying on an implementation of the halo conditional mass function to account for unresolved star formation, this code now allows accurate simulations of the EoR at 2563 resolution. We use this version of LICORICE to produce the first iteration of LORELI, a public dataset now containing hundreds of 21 cm signals computed from radiative hydrodynamics simulations. We train a neural network on LORELI to provide a fast emulator of the LICORICE power spectra, LOREMU, which has ∼5% rms error relative to the simulated signals. LOREMU is used in a Markov chain Monte Carlo framework to perform Bayesian inference, first on a mock observation composed of a simulated signal and thermal noise corresponding to 100 h observations with the SKA. We then apply our inference pipeline to the latest measurements from the HERA interferometer. We report constraints on the X-ray emissivity, and confirm that cold reionization scenarios are unlikely to accurately represent our Universe.

The Novel Bivariate Distribution: Statistical Properties and Real Data Applications

This article proposes a novel class of bivariate distributions that are completely defined by stating their conditionals as Poisson exponential distributions. Numerous statistical properties of this distribution are also examined here, including the conditional probability mass function (PMF) and moments of the new class. The techniques of maximum likelihood and pseudolikelihood are used to estimate the model parameters. Additionally, the effectiveness of the bivariate Poisson exponential conditional (BPEC) distribution is compared to that of the bivariate Poisson conditional (BPC), the bivariate Poisson (BP), the bivariate Poisson–Lindley (BPL), and the bivariate negative binomial (BNB) distributions using a real-world dataset. The findings of Akaike information criterion (AIC) and Bayesian information criterion (BIC) reveal that the BPEC distribution performs better than the other distributions considered in this study. As a result, the authors claim that this distribution may be used to fit dependent and overspread count data.

Non-Linear Moving Barrier and the Ordinary and Conditional Mass Function

We study the problem of the determination of a high precision cosmological mass function, which is of fundamental importance in several problems of astrophysics, like the building up of an halo model. The determination of a mass function through numerical simulation is time demanding, and restrict to particular cosmological parameters. Analytical methods, allow to determine high precision mass functions, without the limitations of the simulations. We improve on previous analytical models, reaching high level of precision. In particular, we improve the scheme of Del Popolo presented in older and more recent papers, based on the excursion set approach. We further improve the mass function with respect to the quoted papers, using an higher order first crossing distribution, and an improved barrier with respect previous papers. As a result, we can obtain a mass function with a precision of 1%, in the mass range ≃ (109−1015) h−1M☉, and in the redshift range 0 < z s< 10. The paper also shows how the use of the quoted improved first-crossing distribution, improves the agreement between the conditional mass function, and simulations.

Testing the conditional mass function of dark matter haloes against numerical N-body simulations

We compare the predicted conditional mass function (CMF) of dark matter halos from two theoretical prescriptions against numerical N-body simulations, both in overdense and underdense regions and at different Eulerian scales ranging from $5$ to $30\,h^{-1}\,$Mpc. In particular, we consider in detail a locally-implemented rescaling of the unconditional mass function (UMF) already discussed in the literature, and also a generalization of the standard rescaling method described in the extended Press-Schechter formalism. First, we test the consistency of these two rescalings by verifying the normalization of the CMF at different scales, and showing that none of the proposed cases provides a normalized CMF. In order to satisfy the normalization condition, we include a modification in the rescaling procedure. After this modification, the resulting CMF generally provides a better description of numerical results. We finally present an analytical fit to the ratio between the CMF and the UMF (also known as the matter-to-halo bias function) in underdense regions, which could be of special interest to speed-up the computation of the halo abundance when studying void statistics. In this case, the CMF prescription based on the locally-implemented rescaling provides a slightly better description of the numerical results when compared to the standard rescaling.

HOW THE DENSITY ENVIRONMENT CHANGES THE INFLUENCE OF THE DARK MATTER–BARYON STREAMING VELOCITY ON COSMOLOGICAL STRUCTURE FORMATION

ABSTRACT We study the dynamical effect of the relative velocity between dark matter and baryonic fluids, which remained supersonic after the epoch of recombination. The impact of this supersonic motion on the formation of cosmological structures was first formulated by Tseliakhovich &amp; Hirata, in terms of the linear theory of small-scale fluctuations coupled to large-scale, relative velocities in mean-density regions. In their formalism, they limited the large-scale density environment to be that of the global mean density. We improve on their formulation by allowing variation in the density environment as well as the relative velocities. This leads to a new type of coupling between large-scale and small-scale modes. We find that the small-scale fluctuation grows in a biased way: faster in the overdense environment and slower in the underdense environment. We also find that the net effect on the global power spectrum of the density fluctuation is to boost its overall amplitude from the prediction by Tseliakhovich &amp; Hirata. Correspondingly, the conditional mass function of cosmological halos and the halo bias parameter are both affected in a similar way. The discrepancy between our prediction and that of Tseliakhovich &amp; Hirata is significant, and therefore, the related cosmology and high-redshift astrophysics should be revisited. The mathematical formalism of this study can be used for generating cosmological initial conditions of small-scale perturbations in generic, overdense (underdense) background patches.

Imprint off(R)gravity on nonlinear structure formation

We test the imprint of f(R) modified gravity on the halo mass function, using N-body simulations and a theoretical model developed in (Kopp et al. 2013). We find a very good agreement between theory and simulations. We extend the theoretical model to the conditional mass function and apply it to the prediction of the linear halo bias in f(R) gravity. Using the halo model we obtain a prediction for the non-linear matter power spectrum accurate to ~10% at z=0 and up to k=2h/Mpc. We also study halo profiles for the f(R) models and find a deviation from the standard general relativity result up to 40%, depending on the halo masses and redshift. This has not been pointed out in previous analysis. Finally we study the number density and profiles of voids identified in these f(R) N-body simulations. We underline the effect of the bias and the sampling to identify voids. We find significant deviation from GR when measuring the f(R) void profiles with fR0<-10^{-6}.

Simulating the large-scale structure of HI intensity maps

Intensity mapping of neutral hydrogen (HI) is a promising observational probe of cosmology and large-scale structure. We present wide field simulations of HI intensity maps based on N-body simulations of a 2.6 Gpc / h box with 20483 particles (particle mass 1.6 × 1011 M⊙ / h). Using a conditional mass function to populate the simulated dark matter density field with halos below the mass resolution of the simulation (108 M⊙ / h < Mhalo < 1013 M⊙ / h), we assign HI to those halos according to a phenomenological halo to HI mass relation. The simulations span a redshift range of 0.35 ≲ z ≲ 0.9 in redshift bins of width Δ z ≈ 0.05 and cover a quarter of the sky at an angular resolution of about 7′. We use the simulated intensity maps to study the impact of non-linear effects and redshift space distortions on the angular clustering of HI. Focusing on the autocorrelations of the maps, we apply and compare several estimators for the angular power spectrum and its covariance. We verify that these estimators agree with analytic predictions on large scales and study the validity of approximations based on Gaussian random fields, particularly in the context of the covariance. We discuss how our results and the simulated maps can be useful for planning and interpreting future HI intensity mapping surveys.

Optimal decision of multi-inconsistent information systems based on information fusion

This paper discusses the fusion of multi-inconsistent decision information systems. First, basic definitions and properties of rough sets, belief and plausibility functions are reviewed. Then, conditional mass function, conditional belief function and conditional plausibility function based on the decision set are defined. We then study the optimal decision of a test set and the reduction of an inconsistent decision information system based on the conditional mass function. Meanwhile, conditional mass function, conditional belief function and conditional plausibility function based on the conditional attribute set are also discussed and we define an uncertainty degree of an inconsistent information system based on the quasi-probability measure. Further, we study fusion method of inconsistent decision information systems using conditional mass functions based on a decision set. Finally, we define a conditional uncertainty measure and give a method to obtain the optimal decision and the confidence level.

Yield and quality grade outcomes as affected by molecular breeding values for commercial beef cattle.

Although genetic tests for many economically important beef cattle traits are commercially available, additional information is needed to help the industry better understand how the results from these tests translate into phenotypic outcomes. This information has important implications for marker-assisted management. The objective of this research was to determine the relationship between molecular breeding values (MBV) characterizing yield grade and marbling and distributions of phenotypic outcomes for yield grade and quality grade. Using data collected from commercially-fed cattle, mixed-model regression equations were estimated for yield grade and quality grade outcomes for both the full sample of commercial cattle (n= 8,995) and a subsample of black-hided steers (n = 4,790). Significant yield grade (P < 0.01) and marbling (P < 0.01) MBV effects were found. However, the yield grade MBV held up better at predicting phenotypic outcomes than the marbling MBV. Estimated conditional probability mass functions of yield and quality grade outcomes for the general population and black-hided steers were similar. Since distributions for black-hided steers were expected to be more applicable from a management perspective, we focused our analysis on these animals. For example, black-hided steers with "low" genetic potential for yield grade and marbling had about a 29% chance of achieving the base price or better on a price grid (yield grade 3 or lower and quality grade Low Choice or better). Increasing genetic potential for marbling increased the likelihood of achieving this same outcome. However, increasing genetic potential for yield grade was unlikely to increase overall carcass quality given its large deleterious effect on quality grade outcomes. Instead, simultaneous improvements in genetic potential for yield grade and marbling offered much more reliable improvements in overall carcass quality. For example, an animal with "moderate" genetic potential for both yield grade and marbling had a 46% chance of achieving the base price or better on a price grid, and an animal with the maximum observed MBV for these traits had a 66% chance of achieving this same outcome. Although the yield grade MBV held up better at predicting phenotypic outcomes, shifts in the distributions of yield grade and quality grade suggested that these increases were largely determined by the marbling MBV.

Halo abundances within the cosmic web

We investigate the dependence of the mass function of dark-matter haloes on their environment within the cosmic web of large-scale structure. A dependence of the halo mass function on large-scale mean density is a standard element of cosmological theory, allowing mass-dependent biasing to be understood via the peak-background split. On the assumption of a Gaussian density field, this analysis can be extended to ask how the mass function depends on the geometrical environment: clusters, filaments, sheets and voids, as classified via the tidal tensor (the Hessian matrix of the gravitational potential). In linear theory, the problem can be solved exactly, and the result is attractively simple: the conditional mass function has no explicit dependence on the local tidal field, and is a function only of the local density on the filtering scale used to define the tidal tensor. There is nevertheless a strong implicit predicted dependence on geometrical environment, because the local density couples statistically to the derivatives of the potential. We compute the predictions of this model and study the limits of their validity by comparing them to results deduced empirically from N-body simulations. We have verified that, to a good approximation, the abundance of haloes in different environments depends only on their densities, and not on their tidal structure. In this sense we find relative differences between halo abundances in different environments with the same density which are smaller than ∼13 per cent. Furthermore, for sufficiently large filtering scales, the agreement with the theoretical prediction is good, although there are important deviations from the Gaussian prediction at small, non-linear scales. We discuss how to obtain improved predictions in this regime, using the ‘effective-universe’ approach.

Bridging Probability and Possibility via Bayesian Theorem

The connection between probability and possibility has been studied for decades. Several studies have intended to provide a unified interpretation for these concepts; other studies attempt to discover their transformation relationship. This paper addresses these problems using a unified perspective. By extending the viewpoint of interpreting the grade of membership as a conditional probability, we introduce the conditional probability mass function and likelihood mass function to describe randomness and fuzziness, respectively. We draw the conclusion that conditional probability is undetermined itself and can be used for describing either randomness or fuzziness, depending on how it is interpreted. A fuzzy Bayesian theorem is presented based on the fuzziness interpretation of conditional probability. Additionally, a probability-possibility conversion is derived by assigning different interpretations for conditional probability of the Bayesian theorem, which is notably similar to Klir's normalized transformation. An example of target recognition demonstrates that the fuzzy Bayesian classifier outperforms the usual Bayesian classifier.

Spatial clustering of high-redshift Lyman-break galaxies

We present a physically motivated semi-analytic model to understand the clustering of high redshift LBGs. We show that the model parameters constrained by the observed luminosity function, can be used to predict large scale (\theta > 80 arcsec) bias and angular correlation function of galaxies. These predictions are shown to reproduce the observations remarkably well. We then adopt these model parameters to calculate the halo occupation distribution (HOD) using the conditional mass function. The halo model using this HOD is shown to provide a reasonably good fit to the observed clustering of LBGs at both large (\theta>80") and small (\theta < 10") angular scales for z=3-5 and several limiting magnitudes. However, our models underpredict the clustering amplitude at intermediate angular scales, where quasi-linear effects are important. The average mass of halos contributing to the observed clustering is found to be 6.2 x 10^{11} M_\odot and the characteristic mass of a parent halo hosting satellite galaxies is 1.2 \times 10^{12} M_\odot for a limiting absolute magnitude of -20.5 at z=4. For a given threshold luminosity these masses decrease with increasing z and at any given z these are found to increase with increasing value of threshold luminosity. We find that approximately 40 % of the halos above a minimum mass M_{min}, can host detectable central galaxies and about 5-10 % of these halos are likely to also host a detectable satellite. The satellites form typically a dynamical timescale prior to the formation of the parent halo. The small angular scale clustering is due to central-satellite pairs and is quite sensitive to changes in the duration of star formation in a halo. The present data favor star formation in a halo lasting typically for a few dynamical time-scales. Our models also reproduce different known trends between parameters related to star formation.

Halo statistics in non-Gaussian cosmologies: the collapsed fraction, conditional mass function and halo bias from the path-integral excursion set method

Characterizing the level of primordial non-Gaussianity (PNG) in the initial conditions for structure formation is one of the most promising ways to test inflation and differentiate among different scenarios. The scale-dependent imprint of PNG on the large-scale clustering of galaxies and quasars has already been used to place significant constraints on the level of PNG in our observed Universe. Such measurements depend upon an accurate and robust theory of how PNG affects the bias of galactic halos relative to the underlying matter density field. We improve upon previous work by employing a more general analytical method - the path-integral extension of the excursion set formalism - which is able to account for the non-Markovianity caused by PNG in the random-walk model used to identify halos in the initial density field. This non-Markovianity encodes information about environmental effects on halo formation which have so far not been taken into account in analytical bias calculations. We compute both scale-dependent and -independent corrections to the halo bias, along the way presenting an expression for the conditional collapsed fraction for the first time, and a new expression for the conditional halo mass function. To leading order in our perturbative calculation, we recover the halo bias results of Desjacques et. al. (2011), including the new scale-dependent correction reported there. However, we show that the non-Markovian dynamics from PNG can lead to marked differences in halo bias when next-to-leading order terms are included. We quantify these differences here. [abridged]

Excursion set theory for modified gravity: correlated steps, mass functions and halo bias

We show how correlated steps introduces significant contributions to the modification of the halo mass function in modified gravity models, taking the chameleon models as an example, in the framework of the excursion set approach. This correction applies to both Lagrangian and Eulerian environments discussed in previous studies. Correlated steps also enhances the modifications due to the fifth force in the conditional mass function as well as the halo bias. We found that abundance and clustering measurements from different environments can provide strong constraints on the chameleon models.

On the performance of L2E estimation in modelling heterogeneous count responses with extreme values

In healthcare studies, count data sets measured with covariates often exhibit heterogeneity and contain extreme values. To analyse such count data sets, we use a finite mixture of regression model framework and investigate a robust estimation approach, called the L2E [D.W. Scott, On fitting and adapting of density estimates, Comput. Sci. Stat. 30 (1998), pp. 124–133], to estimate the parameters. The L2E is based on an integrated L2 distance between parametric conditional and true conditional mass functions. In addition to studying the theoretical properties of the L2E estimator, we compare the performance of L2E with the maximum likelihood (ML) estimator and a minimum Hellinger distance (MHD) estimator via Monte Carlo simulations for correctly specified and gross-error contaminated mixture of Poisson regression models. These show that the L2E is a viable robust alternative to the ML and MHD estimators. More importantly, we use the L2E to perform a comprehensive analysis of a Western Australia hospital inpatient obstetrical length of stay (LOS) (in days) data that contains extreme values. It is shown that the L2E provides a two-component Poisson mixture regression fit to the LOS data which is better than those based on the ML and MHD estimators. The L2E fit identifies admission type as a significant covariate that profiles the predominant subpopulation of normal-stayers as planned patients and the small subpopulation of long-stayers as emergency patients.

THE STELLAR-SUBHALO MASS RELATION OF SATELLITE GALAXIES

We extend the abundance matching technique (AMT) to infer the satellite-subhalo and central-halo mass relations (MRs) of galaxies, as well as the corresponding satellite conditional mass functions (CMFs). We use the observed galaxy stellar mass function (GSMF) decomposed into centrals and satellites and the LCDM halo/subhalo mass functions as inputs. We explore the effects of defining the subhalo mass at the time of accretion (m_acc) vs. at the time of observation (m_obs). We test the standard assumption that centrals and satellites follow the same MRs, showing that this assumption leads to predictions in disagreement with observations, specially for m_obs. Instead, when the satellite-subhalo MRs are constrained following our AMT, they are always different from the central-halo MR: the smaller the stellar mass (Ms), the less massive is the subhalo of satellites as compared to the halo of centrals of the same Ms. On average, for Ms<2x10^11Msol, the dark mass of satellites decreased by 60-65% with respect to their masses at accretion time. The resulting MRs for both definitions of subhalo mass yield satellite CMFs in agreement with observations. Also, when these MRs are used in a HOD model, the predicted correlation functions agree with observations. We show that the use of m_obs leads to less uncertain MRs than m_acc, and discuss implications of the obtained satellite-subhalo MR. For example, we show that the tension between abundance and dynamics of MW satellites in LCDM gives if the slope of the GSMF faint-end slope upturns to -1.6.

Conditional probabilities in the excursion set theory: generic barriers and non-Gaussian initial conditions

The excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the dark matter halo mass function. The computation of the mass function is mapped into the so-called first-passage time problem in the presence of a moving barrier. The excursion set theory is also a powerful formalism to study other properties of dark matter halos such as halo bias, accretion rate, formation time, merging rate and the formation history of halos. This is achieved by computing conditional probabilities with non-trivial initial conditions, and the conditional two-barrier first-crossing rate. In this paper we use the path integral formulation of the excursion set theory to calculate analytically these conditional probabilities in the presence of a generic moving barrier, including the one describing the ellipsoidal collapse, and for both Gaussian and non-Gaussian initial conditions. While most of our analysis associated with Gaussian initial conditions assumes Markovianity (top-hat in momentum space smoothing, rather than generic filters), the non-Markovianity of the random walks induced by non-Gaussianity is consistently accounted for. We compute, for a generic barrier, the first two scale-independent halo bias parameters, the conditional mass function and the halo formation time probability, including the effects of non-Gaussianities. We also provide the expression for the two-constant-barrier first-crossing rate when non-Markovian effects are induced by a top-hat filter function in real space.

Non-Gaussian Halo Bias Re-examined: Mass-dependent Amplitude from the Peak-Background Split and Thresholding

Recent results of N-body simulations have shown that current theoretical models are not able to correctly predict the amplitude of the scale-dependent halo bias induced by primordial non-Gaussianity, for models going beyond the simplest, local quadratic case. Motivated by these discrepancies, we carefully examine three theoretical approaches based on (1) the statistics of thresholded regions, (2) a peak-background split method based on separation of scales, and (3) a peak-background split method using the conditional mass function. We first demonstrate that the statistics of thresholded regions, which is shown to be equivalent at leading order to a local bias expansion, cannot explain the mass-dependent deviation between theory and N-body simulations. In the two formulations of the peak-background split on the other hand, we identify an important, but previously overlooked, correction to the non-Gaussian bias that strongly depends on halo mass. This new term is in general significant for any primordial non-Gaussianity going beyond the simplest local fNL model. In a separate paper, we compare these new theoretical predictions with N-body simulations, showing good agreement for all simulated types of non-Gaussianity.

STATISTICAL PROPERTIES OF SUPERCLUSTER-LIKE FILAMENTS FROM COSMOLOGICAL SIMULATIONS

We study large-scale structures from numerical simulations, paying particular attention to supercluster-like structures. A grid-density-contour based algorithm is adopted to locate connected groups. With the increase of the linking density threshold, the foam- like cosmic web is subsequently broken into individual supercluster-like groups and further halos which are in accordance to groups with the linking density threshold {\rho}/{\rho}= 1 + {\delta} = 80. By analyzing sets of cosmological simulations with varying cosmological parameters, we find that an universal mass function exists not only for halos but also for low-density supercluster-like groups until the linking density threshold decreases to a density where the global percolation of large-scale structures occurs. We further show that the mass functions of different groups can be well described by the Jenkins form with the parameters being dependent on the linking density threshold. On the other hand, these low- density supercluster-like groups cannot be directly associated with the predictions from the excursion set theory with effective barriers obtained from dynamical collapse models, and the peak exclusion effect must be taken into account. Including such an effect, the mass function of groups with the linking density threshold 1 + {\delta} = 16 is in good agreements with that from the excursion set theory with a nearly flat effective barrier. A simplified analysis of the ellipsoidal collapse model indicates that the barrier for collapses along two axes to form filaments is approximately flat in scales, thus we define groups identified with 1 + {\delta} = 16 as filaments. We then further study the halo-filament conditional mass function and the filament-halo conditional mass function, and compare them with the predictions from the two-barrier excursion set theory. The shape statistics for filaments are also presented.

Lyα-EMITTING GALAXIES ATz= 2.1 IN ECDF-S: BUILDING BLOCKS OF TYPICAL PRESENT-DAY GALAXIES?

We discovered a sample of 250 Ly-Alpha emitting (LAE) galaxies at z=2.1 in an ultra-deep 3727 A narrow-band MUSYC image of the Extended Chandra Deep Field-South. LAEs were selected to have rest-frame equivalent widths (EW) > 20 A and emission line fluxes > 2.0 x 10^(-17)erg /cm^2/s, after carefully subtracting the continuum contributions from narrow band photometry. The median flux of our sample is 4.2 x 10^(-17)erg/cm^2/s, corresponding to a median Lya luminosity = 1.3 x 10^(42) erg/s at z=2.1. At this flux our sample is > 90% complete. Approximately 4% of the original NB-selected candidates were detected in X-rays by Chandra, and 7% were detected in the rest-frame far-UV by GALEX. At luminosity>1.3 x 10^42 erg/s, the equivalent width distribution is unbiased and is represented by an exponential with scale-length of 83+/-10 A. Above this same luminosity threshold, we find a number density of 1.5+/-0.5 x 10^-3 Mpc^-3. Neither the number density of LAEs nor the scale-length of their EW distribution show significant evolution from z=3 to z=2. We used the rest frame UV luminosity to estimate a median star formation rate of 4 M_(sun) /yr. The median rest frame UV slope, parametrized by B-R, is that typical of dust-free, 0.5-1 Gyr old or moderately dusty, 300-500 Myr old populations. Approximately 40% of the sample occupies the z~2 star-forming galaxy locus in the UVR two color diagram. Clustering analysis reveals that LAEs at z=2.1 have r_0=4.8+/-0.9 Mpc and a bias factor b=1.8+/-0.3. This implies that z=2.1 LAEs reside in dark matter halos with median masses Log(M/M_(sun))=11.5^(+0.4)_(-0.5), which are among of the lowest-mass halos yet probed at this redshift. We used the Sheth-Tormen conditional mass function to study the descendants of these LAEs and found that their typical present-day descendants are local galaxies with L* properties, like the Milky Way.