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We present posterior sample redshift distributions for the Hyper Suprime-Cam Subaru Strategic Program Weak Lensing three-year (HSC Y3) analysis. Using the galaxies’ photometry and spatial cross-correlations, we conduct a combined Bayesian Hierarchical Inference of the sample redshift distributions. The spatial cross-correlations are derived using a subsample of Luminous Red Galaxies (LRGs) with accurate redshift information available up to a photometric redshift of z < 1.2. We derive the photometry-based constraints using a combination of two empirical techniques calibrated on spectroscopic and multiband photometric data that cover a spatial subset of the shear catalogue. The limited spatial coverage induces a cosmic variance error budget that we include in the inference. Our cross-correlation analysis models the photometric redshift error of the LRGs to correct for systematic biases and statistical uncertainties. We demonstrate consistency between the sample redshift distributions derived using the spatial cross-correlations, the photometry, and the posterior of the combined analysis. Based on this assessment, we recommend conservative priors for sample redshift distributions of tomographic bins used in the three-year cosmological Weak Lensing analyses.

Recovering credible cosmological parameter constraints in a weak lensing shear analysis requires an accurate model that can be used to marginalize over nuisance parameters describing potential sources of systematic uncertainty, such as the uncertainties on the sample redshift distribution n(z). Due to the challenge of running Markov chain Monte Carlo (MCMC) in the high-dimensional parameter spaces in which the n(z) uncertainties may be parametrized, it is common practice to simplify the n(z) parametrization or combine MCMC chains that each have a fixed n(z) resampled from the n(z) uncertainties. In this work, we propose a statistically principled Bayesian resampling approach for marginalizing over the n(z) uncertainty using multiple MCMC chains. We self-consistently compare the new method to existing ones from the literature in the context of a forecasted cosmic shear analysis for the HSC three-year shape catalogue, and find that these methods recover statistically consistent error bars for the cosmological parameter constraints for predicted HSC three-year analysis, implying that using the most computationally efficient of the approaches is appropriate. However, we find that for data sets with the constraining power of the full HSC survey data set (and, by implication, those upcoming surveys with even tighter constraints), the choice of method for marginalizing over n(z) uncertainty among the several methods from the literature may modify the 1σ uncertainties on Ωm–S8 constraints by ∼4 per cent, and a careful model selection is needed to ensure credible parameter intervals.

Cosmological weak lensing measurements rely on a precise measurement of the shear two-point correlation function (2PCF) along with a deep understanding of systematics that affect it. In this work, we demonstrate a general framework for detecting and modelling the impact of PSF systematics on the cosmic shear 2PCF and mitigating its impact on cosmological analysis. Our framework can detect PSF leakage and modelling error from all spin-2 quantities contributed by the PSF second and higher moments, rather than just the second moments, using the cross-correlations between galaxy shapes and PSF moments. We interpret null tests using the HSC Year 3 (Y3) catalogs with this formalism and find that leakage from the spin-2 combination of PSF fourth moments is the leading contributor to additive shear systematics, with total contamination that is an order-of-magnitude higher than that contributed by PSF second moments alone. We conducted a mock cosmic shear analysis for HSC Y3 and find that, if uncorrected, PSF systematics can bias the cosmological parameters Ωm and S8 by ∼0.3σ. The traditional second moment-based model can only correct for a 0.1σ bias, leaving the contamination largely uncorrected. We conclude it is necessary to model both PSF second and fourth moment contaminations for HSC Y3 cosmic shear analysis. We also reanalyse the HSC Y1 cosmic shear analysis with our updated systematics model and identify a 0.07σ bias on Ωm when using the more restricted second moment model from the original analysis. We demonstrate how to self-consistently use the method in both real space and Fourier space, assess shear systematics in tomographic bins, and test for PSF model overfitting.

Weak gravitational lensing is one of the most powerful tools for cosmology, while subject to challenges in quantifying subtle systematic biases. The point spread function (PSF) can cause biases in weak lensing shear inference when the PSF model does not match the true PSF that is convolved with the galaxy light profile. Although the effect of PSF size and shape errors – i.e. errors in second moments – is well studied, weak lensing systematics associated with errors in higher moments of the PSF model require further investigation. The goal of our study is to estimate their potential impact for LSST weak lensing analysis. We go beyond second moments of the PSF by using image simulations to relate multiplicative bias in shear to errors in the higher moments of the PSF model. We find that the current level of errors in higher moments of the PSF model in data from the Hyper Suprime-Cam survey can induce a ∼0.05 per cent shear bias, making this effect unimportant for ongoing surveys but relevant at the precision of upcoming surveys such as LSST.

Branched DNA motifs serve as the basic construction elements for all synthetic DNA nanostructures. However, precise control of branching orientation remains a key challenge to further heighten the overall structural order. In this study, we use two strategies to control the branching orientation. The first one is based on immobile Holliday junctions which employ specific nucleotide sequences at the branch points which dictate their orientation. The second strategy is to use angle‐enforcing struts to fix the branching orientation with flexible spacers at the branch points. We have also demonstrated that the branching orientation control can be achieved dynamically, either by canonical Watson–Crick base pairing or non‐canonical nucleobase interactions (e.g., i‐motif and G‐quadruplex). With precise angle control and feedback from the chemical environment, these results will enable novel DNA nanomechanical sensing devices, and precisely‐ordered three‐dimensional architectures.

Branched DNA motifs serve as the basic construction elements for all synthetic DNA nanostructures. However, precise control of branching orientation remains a key challenge to further heighten the overall structural order. In this study, we use two strategies to control the branching orientation. The first one is based on immobile Holliday junctions which employ specific nucleotide sequences at the branch points which dictate their orientation. The second strategy is to use angle‐enforcing struts to fix the branching orientation with flexible spacers at the branch points. We have also demonstrated that the branching orientation control can be achieved dynamically, either by canonical Watson–Crick base pairing or non‐canonical nucleobase interactions (e.g., i‐motif and G‐quadruplex). With precise angle control and feedback from the chemical environment, these results will enable novel DNA nanomechanical sensing devices, and precisely‐ordered three‐dimensional architectures.