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Baumard et al. attribute to humans a sense of fairness. However, the properties of this sense are so underspecified that the evolutionary account offered is not well-motivated. We contrast this with the framework of Universal Moral Grammar, which has sought a descriptively adequate account of the structure of the moral domain as a precondition for understanding the evolution of morality.

We use FIRE-2 zoom simulations of Milky Way size disk galaxies to derive easy-to-use relationships between the observed circular speed of the Galaxy at the Solar location, \\(v_\\mathrm{c}\\), and dark matter properties of relevance for direct detection experiments: the dark matter density, the dark matter velocity dispersion, and the speed distribution of dark matter particles near the Solar location. We find that both the local dark matter density and 3D velocity dispersion follow tight power laws with \\(v_\\mathrm{c}\\). Using this relation together with the observed circular speed of the Milky Way at the Solar radius, we infer the local dark matter density and velocity dispersion near the Sun to be \\(\\rho = 0.42\\pm 0.06\\ \\mathrm{GeV}\\,\\mathrm{cm^{-3}}\\) and \\(\\sigma_{\\rm 3D} = 280^{+19}_{-18}\\,\\mathrm{km\\,s^{-1}}\\). We also find that the distribution of dark matter particle speeds is well-described by a modified Maxwellian with two shape parameters, both of which correlate with the observed \\(v_{\\rm c}\\). We use that modified Maxwellian to predict the speed distribution of dark matter near the Sun and find that it peaks at a most probable speed of \\(257\\,\\mathrm{km\\,s^{-1}}\\) and begins to truncate sharply above \\(470\\,\\mathrm{km\\,s^{-1}}\\). This peak speed is somewhat higher than expected from the standard halo model, and the truncation occurs well below the formal escape speed to infinity, with fewer very-high-speed particles than assumed in the standard halo model.

This thesis explores conceptions of judgement which have been central to various philosophical and scientific traditions. Beginning with Hume, I situate his conception of judgement within his overarching constructivist program, his science of man. Defending Hume from criticism regarding the naturalistic credentials of this program, I argue that Hume’s science of man, along with the conception of judgement which is integral to it, is appropriately understood as a forerunner to contemporary cognitive science. Despite this, I contend that Hume’s conception of judgement prompts a problem regarding the intentionality of judgement – a problem which he does not adequately address. In the second part of my thesis I show how the intentionality problem which Hume grapples with is also crucial, constituting a point of departure, for Kant’s transcendental undertaking. Following Kant’s reasoning, I illustrate how an original concern with this intentionality issue leads Kant to a distinct conception of judgement, according to which concepts only exist in the context of a judgement. Having arrived at Kant’s conception of a judgement, the remainder of the thesis is devoted to the issue of judgement forms. Kant’s postulation of these forms is closely related to his conception of judgement, and I seek to establish both how these forms ought to be understood and how they might be derived. In relation to this latter issue, I suggest that there may a role for contemporary work in Generative Grammar. Specifically, I suggest that it may be viable to understand the forms of judgement as grammatical in nature, thereby securing an interdisciplinary connection between a philosophy of judgement and the empirical investigation of grammar.

We present an efficient estimator for higher-order galaxy clustering using small groups of nearby galaxies, or multiplets. Using the Luminous Red Galaxy (LRG) sample from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2, we identify galaxy multiplets as discrete objects and measure their cross-correlations with the general galaxy field. Our results show that the multiplets exhibit stronger clustering bias as they trace more massive dark matter halos than individual galaxies. When comparing the observed clustering statistics with the mock catalogs generated from the N-body simulation AbacusSummit, we find that the mocks underpredict multiplet clustering despite reproducing the galaxy two-point auto-correlation reasonably well. This discrepancy indicates that the standard Halo Occupation Distribution (HOD) model is insufficient to describe the properties of galaxy multiplets, revealing the greater constraining power of this higher-order statistic on galaxy-halo connection and the possibility that multiplets are specific to additional assembly bias. We demonstrate that incorporating secondary biases into the HOD model improves agreement with the observed multiplet statistics, specifically by allowing galaxies to preferentially occupy halos in denser environments. Our results highlight the potential of utilizing multiplet clustering, beyond traditional two-point correlation measurements, to break degeneracies in models describing the galaxy-dark matter connection.

We present jax-cosmo, a library for automatically differentiable cosmological theory calculations. It uses the JAX library, which has created a new coding ecosystem, especially in probabilistic programming. As well as batch acceleration, just-in-time compilation, and automatic optimization of code for different hardware modalities (CPU, GPU, TPU), JAX exposes an automatic differentiation (autodiff) mechanism. Thanks to autodiff, jax-cosmo gives access to the derivatives of cosmological likelihoods with respect to any of their parameters, and thus enables a range of powerful Bayesian inference algorithms, otherwise impractical in cosmology, such as Hamiltonian Monte Carlo and Variational Inference. In its initial release, jax-cosmo implements background evolution, linear and non-linear power spectra (using halofit or the Eisenstein and Hu transfer function), as well as angular power spectra with the Limber approximation for galaxy and weak lensing probes, all differentiable with respect to the cosmological parameters and their other inputs. We illustrate how autodiff can be a game-changer for common tasks involving Fisher matrix computations, or full posterior inference with gradient-based techniques. In particular, we show how Fisher matrices are now fast, exact, no longer require any fine tuning, and are themselves differentiable. Finally, using a Dark Energy Survey Year 1 3x2pt analysis as a benchmark, we demonstrate how jax-cosmo can be combined with Probabilistic Programming Languages to perform posterior inference with state-of-the-art algorithms including a No U-Turn Sampler, Automatic Differentiation Variational Inference,and Neural Transport HMC. We further demonstrate that Normalizing Flows using Neural Transport are a promising methodology for model validation in the early stages of analysis.

In Stage-IV imaging surveys, a significant amount of the cosmologically useful information is due to sources whose images overlap with those of other sources on the sky. The cosmic shear signal is primarily encoded in the estimated shapes of observed galaxies and thus directly impacted by overlaps. We introduce a framework based on the Fisher formalism to analyze effects of overlapping sources (blending) on the estimation of cosmic shear. For the Rubin Observatory Legacy Survey of Space and Time (LSST), we present the expected loss in statistical sensitivity for the ten-year survey due to blending. We find that for approximately 62% of galaxies that are likely to be detected in full-depth LSST images, at least 1% of the flux in their pixels is from overlapping sources. We also find that the statistical correlations between measures of overlapping galaxies and, to a much lesser extent the higher shot noise level due to their presence, decrease the effective number density of galaxies, \\(N_{eff}\\), by \\(\\sim\\)18%. We calculate an upper limit on \\(N_{eff}\\) of 39.4 galaxies per arcmin\\(^2\\) in \\(r\\) band. We study the impact of varying stellar density on \\(N_{eff}\\) and illustrate the diminishing returns of extending the survey into lower Galactic latitudes. We extend the Fisher formalism to predict the increase in pixel-noise bias due to blending for maximum-likelihood (ML) shape estimators. We find that noise bias is sensitive to the particular shape estimator and measure of ensemble-average shape that is used, and properties of the galaxy that include redshift-dependent quantities such as size and luminosity.

We present new Galactic dust reddening maps of the high Galactic latitude sky using DESI imaging and spectroscopy. We directly measure the reddening of 2.6 million stars by comparing the observed stellar colors in \\(g-r\\) and \\(r-z\\) from DESI imaging with the synthetic colors derived from DESI spectra from the first two years of the survey. The reddening in the two colors is on average consistent with the Fitzpatrick (1999) extinction curve with \\(R_V=3.1\\). We find that our reddening maps differ significantly from the commonly used Schlegel et al. (1998) (SFD) reddening map (by up to 80 mmag in \\(E(B-V)\\)), and we attribute most of this difference to systematic errors in the SFD map. To validate the reddening map, we select a galaxy sample with extinction correction based on our reddening map, and this yields significantly better uniformity than the SFD extinction correction. Finally, we discuss the potential systematic errors in the DESI reddening measurements, including the photometric calibration errors that are the limiting factor on our accuracy. The \\(E(g-r)\\) and \\(E(r-z)\\) maps presented in this work, and for convenience their corresponding \\(E(B-V)\\) maps with SFD calibration, are publicly available.

We model the expansion history of the Universe as a Gaussian Process and find constraints on the dark energy density and its low-redshift evolution using distances inferred from the Luminous Red Galaxy (LRG) and Lyman-alpha (Ly\\(\\alpha\\)) datasets of the Baryon Oscillation Spectroscopic Survey, supernova data from the Joint Light-curve Analysis (JLA) sample, Cosmic Microwave Background (CMB) data from the Planck satellite, and local measurement of the Hubble parameter from the Hubble Space Telescope (\\(\\mathsf H0\\)). Our analysis shows that the CMB, LRG, Ly\\(\\alpha\\), and JLA data are consistent with each other and with a \\(\\Lambda\\)CDM cosmology, but the \\({\\mathsf H0}\\) data is inconsistent at moderate significance. Including the presence of dark radiation does not alleviate the \\({\\mathsf H0}\\) tension in our analysis. While some of these results have been noted previously, the strength here lies in that we do not assume a particular cosmological model. We calculate the growth of the gravitational potential in General Relativity corresponding to these general expansion histories and show that they are well-approximated by \\(\\Omega_{\\rm m}^{0.55}\\) given the current precision. We assess the prospects for upcoming surveys to measure deviations from \\(\\Lambda\\)CDM using this model-independent approach.