436 research outputs found
The Effects of Halo Assembly Bias on Self-Calibration in Galaxy Cluster Surveys
Self-calibration techniques for analyzing galaxy cluster counts utilize the
abundance and the clustering amplitude of dark matter halos. These properties
simultaneously constrain cosmological parameters and the cluster
observable-mass relation. It was recently discovered that the clustering
amplitude of halos depends not only on the halo mass, but also on various
secondary variables, such as the halo formation time and the concentration;
these dependences are collectively termed assembly bias. Applying modified
Fisher matrix formalism, we explore whether these secondary variables have a
significant impact on the study of dark energy properties using the
self-calibration technique in current (SDSS) and the near future (DES, SPT, and
LSST) cluster surveys. The impact of the secondary dependence is determined by
(1) the scatter in the observable-mass relation and (2) the correlation between
observable and secondary variables. We find that for optical surveys, the
secondary dependence does not significantly influence an SDSS-like survey;
however, it may affect a DES-like survey (given the high scatter currently
expected from optical clusters) and an LSST-like survey (even for low scatter
values and low correlations). For an SZ survey such as SPT, the impact of
secondary dependence is insignificant if the scatter is 20% or lower but can be
enhanced by the potential high scatter values introduced by a highly correlated
background. Accurate modeling of the assembly bias is necessary for cluster
self-calibration in the era of precision cosmology.Comment: 13 pages, 5 figures, replaced to match published versio
Hybrid Probabilistic Trajectory Optimization Using Null-Space Exploration
In the context of learning from demonstration, human examples are usually imitated in either Cartesian or joint space. However, this treatment might result in undesired movement trajectories in either space. This is particularly important for motion skills such as striking, which typically imposes motion constraints in both spaces. In order to address this issue, we consider a probabilistic formulation of dynamic movement primitives, and apply it to adapt trajectories in Cartesian and joint spaces simultaneously. The probabilistic treatment allows the robot to capture the variability of multiple demonstrations and facilitates the mixture of trajectory constraints from both spaces. In addition to this proposed hybrid space learning, the robot often needs to consider additional constraints such as motion smoothness and joint limits. On the basis of Jacobian-based inverse kinematics, we propose to exploit robot null-space so as to unify trajectory constraints from Cartesian and joint spaces while satisfying additional constraints. Evaluations of hand-shaking and striking tasks carried out with a humanoid robot demonstrate the applicability of our approach
Kernelized movement primitives
Imitation learning has been studied widely as a convenient way to transfer human skills to robots. This learning approach is aimed at extracting relevant motion patterns from human demonstrations and subsequently applying these patterns to different situations. Despite the many advancements that have been achieved, solutions for coping with unpredicted situations (e.g., obstacles and external perturbations) and high-dimensional inputs are still largely absent. In this paper, we propose a novel kernelized movement primitive (KMP), which allows the robot to adapt the learned motor skills and fulfill a variety of additional constraints arising over the course of a task. Specifically, KMP is capable of learning trajectories associated with high-dimensional inputs owing to the kernel treatment, which in turn renders a model with fewer open parameters in contrast to methods that rely on basis functions. Moreover, we extend our approach by exploiting local trajectory representations in different coordinate systems that describe the task at hand, endowing KMP with reliable extrapolation capabilities in broader domains. We apply KMP to the learning of time-driven trajectories as a special case, where a compact parametric representation describing a trajectory and its first-order derivative is utilized. In order to verify the effectiveness of our method, several examples of trajectory modulations and extrapolations associated with time inputs, as well as trajectory adaptations with high-dimensional inputs are provided
Generalized Task-Parameterized Skill Learning
Programming by demonstration has recently gained much attention due to its user-friendly and natural way to transfer human skills to robots. In order to facilitate the learning of multiple demonstrations and meanwhile generalize to new situations, a task-parameterized Gaussian mixture model (TP-GMM) has been recently developed. This model has achieved reliable performance in areas such as human-robot collaboration and dual-arm manipulation. However, the crucial task frames and associated parameters in this learning framework are often set by the human teacher, which renders three problems that have not been addressed yet: (i) task frames are treated equally, without considering their individual importance, (ii) task parameters are defined without taking into account additional task constraints, such as robot joint limits and motion smoothness, and (iii) a fixed number of task frames are pre-defined regardless of whether some of them may be redundant or even irrelevant for the task at hand. In this paper, we generalize the task-parameterized learning by addressing the aforementioned problems. Moreover, we provide a novel learning perspective which allows the robot to refine and adapt previously learned skills in a low dimensional space. Several examples are studied in both simulated and real robotic systems, showing the applicability of our approach
An Uncertainty-Aware Minimal Intervention Control Strategy Learned from Demonstrations
Motivated by the desire to have robots physically present in human environments, in recent years we have witnessed an emergence of different approaches for learning active compliance. Some of the most compelling solutions exploit a minimal intervention control principle, correcting deviations from a goal only when necessary, and among those who follow this concept, several probabilistic techniques have stood out from the rest. However, these approaches are prone to requiring several task demonstrations for proper gain estimation and to generating unpredictable robot motions in the face of uncertainty. Here we present a Programming by Demonstration approach for uncertainty-aware impedance regulation, aimed at making the robot compliant - and safe to interact with - when the uncertainty about its predicted actions is high. Moreover, we propose a data-efficient strategy, based on the energy observed during demonstrations, to achieve minimal intervention control, when the uncertainty is low. The approach is validated in an experimental scenario, where a human collaboratively moves an object with a 7-DoF torque-controlled robot
Non-parametric Imitation Learning of Robot Motor Skills
Unstructured environments impose several challenges when robots are required to perform different tasks and adapt to unseen situations. In this context, a relevant problem arises: how can robots learn to perform various tasks and adapt to different conditions? A potential solution is to endow robots with learning capabilities. In this line, imitation learning emerges as an intuitive way to teach robots different motor skills. This learning approach typically mimics human demonstrations by extracting invariant motion patterns and subsequently applies these patterns to new situations. In this paper, we propose a novel kernel treatment of imitation learning, which endows the robot with imitative and adaptive capabilities. In particular, due to the kernel treatment, the proposed approach is capable of learning human skills associated with high-dimensional inputs. Furthermore, we study a new concept of correlation-adaptive imitation learning, which allows for the adaptation of correlations exhibited in high-dimensional demonstrated skills. Several toy examples and a collaborative task with a real robot are provided to verify the effectiveness of our approach
The Aemulus Project III: Emulation of the Galaxy Correlation Function
Using the N-body simulations of the AEMULUS Project, we construct an emulator
for the non-linear clustering of galaxies in real and redshift space. We
construct our model of galaxy bias using the halo occupation framework,
accounting for possible velocity bias. The model includes 15 parameters,
including both cosmological and galaxy bias parameters. We demonstrate that our
emulator achieves ~ 1% precision at the scales of interest, 0.1<r<10 h^{-1}
Mpc, and recovers the true cosmology when tested against independent
simulations. Our primary parameters of interest are related to the growth rate
of structure, f, and its degenerate combination fsigma_8. Using this emulator,
we show that the constraining power on these parameters monotonically increases
as smaller scales are included in the analysis, all the way down to 0.1 h^{-1}
Mpc. For a BOSS-like survey, the constraints on fsigma_8 from r<30 h^{-1} Mpc
scales alone are more than a factor of two tighter than those from the fiducial
BOSS analysis of redshift-space clustering using perturbation theory at larger
scales. The combination of real- and redshift-space clustering allows us to
break the degeneracy between f and sigma_8, yielding a 9% constraint on f alone
for a BOSS-like analysis. The current AEMULUS simulations limit this model to
surveys of massive galaxies. Future simulations will allow this framework to be
extended to all galaxy target types, including emission-line galaxies.Comment: 14 pages, 8 figures, 1 table; submitted to ApJ; the project webpage
is available at https://aemulusproject.github.io ; typo in Figure 7 and
caption updated, results unchange
The Aemulus Project I: Numerical Simulations for Precision Cosmology
The rapidly growing statistical precision of galaxy surveys has lead to a
need for ever-more precise predictions of the observables used to constrain
cosmological and galaxy formation models. The primary avenue through which such
predictions will be obtained is suites of numerical simulations. These
simulations must span the relevant model parameter spaces, be large enough to
obtain the precision demanded by upcoming data, and be thoroughly validated in
order to ensure accuracy. In this paper we present one such suite of
simulations, forming the basis for the AEMULUS Project, a collaboration devoted
to precision emulation of galaxy survey observables. We have run a set of 75
(1.05 h^-1 Gpc)^3 simulations with mass resolution and force softening of
3.51\times 10^10 (Omega_m / 0.3) ~ h^-1 M_sun and 20 ~ h^-1 kpc respectively in
47 different wCDM cosmologies spanning the range of parameter space allowed by
the combination of recent Cosmic Microwave Background, Baryon Acoustic
Oscillation and Type Ia Supernovae results. We present convergence tests of
several observables including spherical overdensity halo mass functions, galaxy
projected correlation functions, galaxy clustering in redshift space, and
matter and halo correlation functions and power spectra. We show that these
statistics are converged to 1% (2%) for halos with more than 500 (200)
particles respectively and scales of r>200 ~ h^-1 kpc in real space or k ~ 3 h
Mpc^-1 in harmonic space for z\le 1. We find that the dominant source of
uncertainty comes from varying the particle loading of the simulations. This
leads to large systematic errors for statistics using halos with fewer than 200
particles and scales smaller than k ~ 4 h^-1 Mpc. We provide the halo catalogs
and snapshots detailed in this work to the community at
https://AemulusProject.github.io.Comment: 16 pages, 12 figures, 3 Tables Project website:
https://aemulusproject.github.io
Cosmological Constraints from the Large Scale Weak Lensing of SDSS MaxBCG Clusters
We derive constraints on the matter density \Om and the amplitude of matter
clustering \sig8 from measurements of large scale weak lensing (projected
separation R=5-30\hmpc) by clusters in the Sloan Digital Sky Survey MaxBCG
catalog. The weak lensing signal is proportional to the product of \Om and the
cluster-mass correlation function \xicm. With the relation between optical
richness and cluster mass constrained by the observed cluster number counts,
the predicted lensing signal increases with increasing \Om or \sig8, with mild
additional dependence on the assumed scatter between richness and mass. The
dependence of the signal on scale and richness partly breaks the degeneracies
among these parameters. We incorporate external priors on the richness-mass
scatter from comparisons to X-ray data and on the shape of the matter power
spectrum from galaxy clustering, and we test our adopted model for \xicm
against N-body simulations. Using a Bayesian approach with minimal restrictive
priors, we find \sig8(\Om/0.325)^{0.501}=0.828 +/- 0.049, with marginalized
constraints of \Om=0.325_{-0.067}^{+0.086} and \sig8=0.828_{-0.097}^{+0.111},
consistent with constraints from other MaxBCG studies that use weak lensing
measurements on small scales (R<=2\hmpc). The (\Om,\sig8) constraint is
consistent with and orthogonal to the one inferred from WMAP CMB data,
reflecting agreement with the structure growth predicted by GR for an LCDM
cosmological model. A joint constraint assuming LCDM yields \Om=0.298 +/- 0.020
and \sig8=0.831 +/- 0.020. Our cosmological parameter errors are dominated by
the statistical uncertainties of the large scale weak lensing measurements,
which should shrink sharply with current and future imaging surveys.Comment: 20 pages, 12 figures, MNRAS Submitted. For a brief video explaining
the key result of this paper, see http://www.youtube.com/user/OSUAstronomy,
or http://v.youku.com/v_show/id_XNDI3ODA3NzY4.html in countries where YouTube
is not accessibl
The Aemulus Project II: Emulating the Halo Mass Function
Existing models for the dependence of the halo mass function on cosmological
parameters will become a limiting source of systematic uncertainty for cluster
cosmology in the near future. We present a halo mass function emulator and
demonstrate improved accuracy relative to state-of-the-art analytic models. In
this work, mass is defined using an overdensity criteria of 200 relative to the
mean background density. Our emulator is constructed from the AEMULUS
simulations, a suite of 40 N-body simulations with snapshots from z=3 to z=0.
These simulations cover the flat wCDM parameter space allowed by recent Cosmic
Microwave Background, Baryon Acoustic Oscillation and Type Ia Supernovae
results, varying the parameters w, Omega_m, Omega_b, sigma_8, N_{eff}, n_s, and
H_0. We validate our emulator using five realizations of seven different
cosmologies, for a total of 35 test simulations. These test simulations were
not used in constructing the emulator, and were run with fully independent
initial conditions. We use our test simulations to characterize the modeling
uncertainty of the emulator, and introduce a novel way of marginalizing over
the associated systematic uncertainty. We confirm non-universality in our halo
mass function emulator as a function of both cosmological parameters and
redshift. Our emulator achieves better than 1% precision over much of the
relevant parameter space, and we demonstrate that the systematic uncertainty in
our emulator will remain a negligible source of error for cluster abundance
studies through at least the LSST Year 1 data set.Comment: https://aemulusproject.github.io
- âŠ