Abstract
Computing the inverse covariance matrix (or precision matrix) of large data vectors is crucial in weak lensing (and multiprobe) analyses of the large-scale structure of the Universe. ...Analytically computed covariances are noise-free and hence straightforward to invert; however, the model approximations might be insufficient for the statistical precision of future cosmological data. Estimating covariances from numerical simulations improves on these approximations, but the sample covariance estimator is inherently noisy, which introduces uncertainties in the error bars on cosmological parameters and also additional scatter in their best-fitting values. For future surveys, reducing both effects to an acceptable level requires an unfeasibly large number of simulations. In this paper we describe a way to expand the precision matrix around a covariance model and show how to estimate the leading order terms of this expansion from simulations. This is especially powerful if the covariance matrix is the sum of two contributions, $\smash{\sf{C} = \sf{A}+\sf{B}}$, where $\smash{\sf{A}}$ is well understood analytically and can be turned off in simulations (e.g. shape noise for cosmic shear) to yield a direct estimate of $\smash{\sf{B}}$. We test our method in mock experiments resembling tomographic weak lensing data vectors from the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope (LSST). For DES we find that 400 N-body simulations are sufficient to achieve negligible statistical uncertainties on parameter constraints. For LSST this is achieved with 2400 simulations. The standard covariance estimator would require >105 simulations to reach a similar precision. We extend our analysis to a DES multiprobe case finding a similar performance.
ABSTRACT
We comprehensively analyse the cosmology dependence of counts-in-cells statistics. We focus on the shape of the one-point probability distribution function (PDF) of the matter density field ...at mildly non-linear scales. Based on large-deviation statistics, we parametrize the cosmology dependence of the matter PDF in terms of the linear power spectrum, the growth factor, the spherical collapse dynamics, and the non-linear variance. We extend our formalism to include massive neutrinos, finding that the total matter PDF is highly sensitive to the total neutrino mass Mν and can disentangle it from the clustering amplitude σ8. Using more than a million PDFs extracted from the Quijote simulations, we determine the response of the matter PDF to changing parameters in the νΛCDM model and successfully cross-validate the theoretical model and the simulation measurements. We present the first νΛCDM Fisher forecast for the matter PDF at multiple scales and redshifts, and its combination with the matter power spectrum. We establish that the matter PDF and the matter power spectrum are highly complementary at mildly non-linear scales. The matter PDF is particularly powerful for constraining the matter density Ωm, clustering amplitude σ8 and the total neutrino mass Mν. Adding the mildly non-linear matter PDF to the mildly non-linear matter power spectrum improves constraints on Ωm by a factor of 5 and σ8 by a factor of 2 when considering the three lowest redshifts. In our joint analysis of the matter PDF and matter power spectrum at three redshifts, the total neutrino mass is constrained to better than 0.01 eV with a total volume of 6 (Gpc h−1)3. We discuss how density-split statistics can be used to translate those encouraging results for the matter PDF into realistic observables in galaxy surveys.
ABSTRACT
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the ...maximum a posteriori probability values, as the intervals indicate concordance or discordance between models and with measurements from other data. Intermediate statistics (e.g. the power spectrum) are usually measured and inferences are made by fitting models to these rather than the raw data, assuming that the likelihood for these statistics has multivariate Gaussian form. The covariance matrix used to calculate the likelihood is often estimated from simulations, such that it is itself a random variable. This is a standard problem in Bayesian statistics, which requires a prior to be placed on the true model parameters and covariance matrix, influencing the joint posterior distribution. As an alternative to the commonly used independence Jeffreys prior, we introduce a prior that leads to a posterior that has approximately frequentist matching coverage. This is achieved by matching the covariance of the posterior to that of the distribution of true values of the parameters around the maximum likelihood values in repeated trials, under certain assumptions. Using this prior, credible intervals derived from a Bayesian analysis can be interpreted approximately as confidence intervals, containing the truth a certain proportion of the time for repeated trials. Linking frequentist and Bayesian approaches that have previously appeared in the astronomical literature, this offers a consistent and conservative approach for credible intervals quoted on model parameters for problems where the covariance matrix is itself an estimate.
ABSTRACT
We present the integrated three-point shear correlation function iζ± – a higher order statistic of the cosmic shear field – which can be directly estimated in wide-area weak lensing surveys ...without measuring the full three-point shear correlation function, making this a practical and complementary tool to two-point statistics for weak lensing cosmology. We define it as the one-point aperture mass statistic Map measured at different locations on the shear field correlated with the corresponding local two-point shear correlation function ξ±. Building upon existing work on the integrated bispectrum of the weak lensing convergence field, we present a theoretical framework for computing the integrated three-point function in real space for any projected field within the flat-sky approximation and apply it to cosmic shear. Using analytical formulae for the non-linear matter power spectrum and bispectrum, we model iζ± and validate it on N-body simulations within the uncertainties expected from the sixth year cosmic shear data of the Dark Energy Survey. We also explore the Fisher information content of iζ± and perform a joint analysis with ξ± for two tomographic source redshift bins with realistic shape noise to analyse its power in constraining cosmological parameters. We find that the joint analysis of ξ± and iζ± has the potential to considerably improve parameter constraints from ξ± alone, and can be particularly useful in improving the figure of merit of the dynamical dark energy equation of state parameters from cosmic shear data.
There is a converging body of evidence supporting a measurable slowdown of the Atlantic Meridional Overturning Circulation (AMOC) as climate warms and Northern Hemisphere ice sheets inexorably ...shrink. Within this context, we assess the variability of the AMOC during the Holocene based on a marine sediment core retrieved from the deep northwest Atlantic, which sensitively recorded large‐scale deglacial transitions in deep water circulation. While there is a diffuse notion of Holocene variability in Labrador and Nordic Seas overturning, we report a largely invariable deep water circulation for the last ~11,000 years, even during the meltwater pulse associated with the 8.2‐ka event. Sensitivity tests along with high‐resolution 231Pa/230Th data constrain the duration and the magnitude of possible Holocene AMOC variations. The generally constant baseline during the Holocene suggests attenuated natural variability of the large‐scale AMOC on submillennial timescales and calls for compensating effects involving the upstream components of North Atlantic Deep Water.
Key Points
High‐resolution 231Pa/230Th record from the Bermuda Rise for the past 11,000 years presented
Low variability of Holocene AMOC derived from 231Pa/230Th, εNd and δ13C
Duration and magnitude of the 8.2‐ka event constrained by sensitivity tests
Many different biofabrication approaches as well as a variety of bioinks have been developed by researchers working in the field of tissue engineering. A main challenge for bioinks often remains the ...difficulty to achieve shape fidelity after printing. In order to overcome this issue, a homogeneous pre-crosslinking technique, which is universally applicable to all alginate-based materials, was developed. In this study, the Young's Modulus after post-crosslinking of selected hydrogels, as well as the chemical characterization of alginate in terms of M/G ratio and molecular weight, were determined. With our technique it was possible to markedly enhance the printability of a 2% (w/v) alginate solution, without using a higher polymer content, fillers or support structures. 3D porous scaffolds with a height of around 5 mm were printed. Furthermore, the rheological behavior of different pre-crosslinking degrees was studied. Shear forces on cells as well as the flow profile of the bioink inside the printing nozzle during the process were estimated. A high cell viability of printed NIH/3T3 cells embedded in the novel bioink of more than 85% over a time period of two weeks could be observed.
Levosimendan’s calcium sensitizing effects in heart muscle cells are well established; yet, its potential impact on skeletal muscle cells has not been evidently determined. Despite controversial ...results, levosimendan is still expected to interact with skeletal muscle through off-target sites (further than troponin C). Adding to this debate, we investigated levosimendan’s acute impact on fast-twitch skeletal muscle biomechanics in a length-dependent activation study by submersing single muscle fibres in a levosimendan-supplemented solution. We employed our MyoRobot technology to investigate the calcium sensitivity of skinned single muscle fibres alongside their stress–strain response in the presence or absence of levosimendan (100 µM). While control data are in agreement with the theory of length-dependent activation, levosimendan appears to shift the onset of the ‘descending limb’ of active force generation to longer sarcomere lengths without notably improving myofibrillar calcium sensitivity. Passive stretches in the presence of levosimendan yielded over twice the amount of enlarged restoration stress and Young’s modulus in comparison to control single fibres. Both effects have not been described before and may point towards potential off-target sites of levosimendan.
In this paper the weighted ENO (essentially non-oscillatory) scheme developed for the one-dimensional case by Liu, Osher, and Chan is applied to the case of unstructured triangular grids in two space ...dimensions. Ideas from Jiang and Shu, especially their new way of smoothness measuring, are considered. As a starting point for the unstructured case we use an ENO scheme like the one introduced by Abgrall. Beside the application of the weighted ENO ideas the whole reconstruction algorithm is analyzed and described in detail. Here we also concentrate on technical problems and their solution. Finally, some applications are given to demonstrate the accuracy and robustness of the resulting new method. The whole reconstruction algorithm described here can be applied to any kind of data on triangular unstructured grids, although it is used in the framework of compressible flow computation in this paper only.
Gelatin methacryloyl (GelMA)-based hydrogels have become highly studied as modular tissue culture platforms due to the combination of the bioactivity of gelatin and tailorability of ...photo-crosslinkable hydrogels. However, current production and characterization workflows still rely on manual, time-consuming, and low-throughput processes, ultimately limiting widespread adaption. To address these challenges, an open-source technology platform is engineered and validated for automated high-throughput production of GelMA-based 3D constructs by integrating automated pipetting capabilities for viscous and non-viscous liquids. Firstly, the platform is applied in combination with inexpensive absorbance measurements to systematically optimize the mixing sequence for GelMA-based precursor solutions. This enables a decrease in the relative standard deviation of the prepared mixtures from 63% to 2.5%, demonstrating a significantly improved reproducibility. Next, the applicability and high-throughput capacity are demonstrated by the reproducible generation of GelMA dilution series with 0.5 and 2% (w/v) concentration steps as well as double network hydrogels consisting of 2% (w/v) alginate and 5% (w/v) GelMA. Finally, a simple and user-friendly methodology is described that integrates Design of Experiments approaches to systematically study the combinatorial effects of material and crosslinking parameters and to establish a parameter library for on-demand production of mechanically defined GelMA-based hydrogels. The platform enables reproducible production and offers an open-source and accessible alternative to high-priced liquid-handling robots and bioprinters.
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•Open-source platform overcomes manual and time-consuming processes for gelatin methacryloyl (GelMA)-based hydrogels•High-throughput production with automated workflows yields substantial increase in reproducibility compared to manual tasks•Materials library enables automatically production of mechanically defined 3D constructs with known parameters•Platform offers an open-source and accessible alternative to high-priced liquid-handling robots and bioprinters
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