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At least 613 records · Page 34

Dark Energy Survey Year 3 results: optimized $w$CDM simulation-based inference with weak lensing map-level hybrid statistics

We present cosmological constraints from the Dark Energy Survey Year 3 (DES Y3) weak lensing data using hierarchical hybrid statistics within a Bayesian simulation-based inference framework that is based on the Gower Street simulations. To maximize the precision of the inference, we have developed a new, information-theory based, data compression of the weak lensing maps to just seven highly informative summary statistics. The hybrid scheme exploits the high information content of the power spectrum, compressing both the power spectrum and neural-based summaries that are designed to extract further information. Our simulation-based approach enables principled forward modelling of all major sources of systematic uncertainty and survey properties into realistic mock observations, including the survey mask, photometric redshift uncertainties, intrinsic galaxy alignments, multiplicative shear calibration bias, source galaxy clustering, non-Gaussian shape noise, and non-linear structure formation. The summary statistics are then used in a Bayesian simulation-based inference pipeline. The inference is validated through coverage tests and checks for robustness against baryonic feedback. Assuming a $w$CDM cosmology, our analysis yields $S_8 = 0.808 \pm 0.017$, $Ω_{\rm m} = 0.325 \pm 0.024$, and $w < -0.766$ (marginalized posterior 68 per cent credible intervals). This rigorous combination of information theory, physics- and neural network-based extreme data compression, and principled Bayesian analysis improves the figure of merit for $(Ω_{\rm m}, S_8, w)$ by 60 per cent over the previous state-of-the-art, and by almost a factor of 3 over two-point analyses of the same data. They are the most precise joint constraints on $(Ω_{\rm m}, S_8, w)$ from weak gravitational lensing data alone of any survey to date. We intend to apply this analysis to the more recent DES Y6 data.

Williamson, J. [University Coll. London]↗

Statistics of Point Vortex Turbulence in Non-neutral Flows and in Flows with Translational and Rotational Symmetries

A theory (Esler and Ashbee in J Fluid Mech 779:275–308, 2015) describing the statistics of N freely-evolving point vortices in a bounded two-dimensional domain is extended. First, the case of a non-neutral vortex gas is addressed, and it is shown that the density of states function can be identified with the probability density function of an infinite sum of independent non-central chi-squared random variables, the details of which depend only on the shape of the domain. Equations for the equilibrium energy spectrum and other statistical quantities follow, the validity of which are verified against direct numerical simulations of the equations of motion. Second, domains with additional conserved quantities associated with a symmetry (e.g., circle, periodic channel) are investigated, and it is shown that the treatment of the non-neutral case can be modified to account for the additional constraint.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An efficient direct solver for rarefied gas flows with arbitrary statistics

A new numerical methodology associated with a unified treatment is presented to solve the Boltzmann–BGK equation of gas dynamics for the classical and quantum gases described by the Bose–Einstein and Fermi–Dirac statistics. Utilizing a class of globally-stiffly-accurate implicit–explicit Runge–Kutta scheme for the temporal evolution, associated with the discrete ordinate method for the quadratures in the momentum space and the weighted essentially non-oscillatory method for the spatial discretization, the proposed scheme is asymptotic-preserving and imposes no non-linear solver or requires the knowledge of fugacity and temperature to capture the flow structures in the hydrodynamic (Euler) limit. The proposed treatment overcomes the limitations found in the work by Yang and Muljadi (2011) [33] due to the non-linear nature of quantum relations, and can be applied in studying the dynamics of a gas with internal degrees of freedom with correct values of the ratio of specific heat for the flow regimes for all Knudsen numbers and energy wave lengths. The present methodology is numerically validated with the unified treatment by the one-dimensional shock tube problem and the two-dimensional Riemann problems for gases of arbitrary statistics. Descriptions of ideal quantum gases including rotational degrees of freedom have been successfully achieved under the proposed methodology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter–Gummel scheme to non-Boltzmann (e.g. Fermi–Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗

Statistical Emulation of Climate Model Projections Based on Precomputed GCM Runs*

The authors describe a new approach for emulating the output of a fully coupled climate model under arbitrary forcing scenarios that is based on a small set of precomputed runs from the model. Temperature and precipitation are expressed as simple functions of the past trajectory of atmospheric CO 2 concentrations, and a statistical model is fit using a limited set of training runs. The approach is demonstrated to be a useful and computationally efficient alternative to pattern scaling and captures the nonlinear evolution of spatial patterns of climate anomalies inherent in transient climates. The approach does as well as pattern scaling in all circumstances and substantially better in many; it is not computationally demanding; and, once the statistical model is fit, it produces emulated climate output effectively instantaneously. In conclusion, it may therefore find wide application in climate impacts assessments and other policy analyses requiring rapid climate projections.

54 ENVIRONMENTAL SCIENCES↗

A NEW STATISTICAL PERSPECTIVE TO THE COSMIC VOID DISTRIBUTION

In this study, we obtain the size distribution of voids as a three-parameter redshift-independent log-normal void probability function (VPF) directly from the Cosmic Void Catalog (CVC). Although many statistical models of void distributions are based on the counts in randomly placed cells, the log-normal VPF that we obtain here is independent of the shape of the voids due to the parameter-free void finder of the CVC. We use three void populations drawn from the CVC generated by the Halo Occupation Distribution (HOD) Mocks, which are tuned to three mock SDSS samples to investigate the void distribution statistically and to investigate the effects of the environments on the size distribution. As a result, it is shown that void size distributions obtained from the HOD Mock samples are satisfied by the three-parameter log-normal distribution. In addition, we find that there may be a relation between the hierarchical formation, skewness, and kurtosis of the log-normal distribution for each catalog. We also show that the shape of the three-parameter distribution from the samples is strikingly similar to the galaxy log-normal mass distribution obtained from numerical studies. This similarity between void size and galaxy mass distributions may possibly indicate evidence of nonlinear mechanisms affecting both voids and galaxies, such as large-scale accretion and tidal effects. Considering the fact that in this study, all voids are generated by galaxy mocks and show hierarchical structures in different levels, it may be possible that the same nonlinear mechanisms of mass distribution affect the void size distribution.

79 ASTRONOMY AND ASTROPHYSICS↗

The Global Statistical Response of the Outer Radiation Belt During Geomagnetic Storms

Using the total radiation belt electron content calculated from Van Allen Probe phase space density, the time-dependent and global response of the outer radiation belt during storms is statistically studied. Using phase space density reduces the impacts of adiabatic changes in the main phase, allowing a separation of adiabatic and nonadiabatic effects and revealing a clear modality and repeatable sequence of events in storm time radiation belt electron dynamics. This sequence exhibits an important first adiabatic invariant (μ)-dependent behavior in the seed (150 MeV/G), relativistic (1,000 MeV/G), and ultrarelativistic (4,000 MeV/G) populations. The outer radiation belt statistically shows an initial phase dominated by loss followed by a second phase of rapid acceleration, while the seed population shows little loss and immediate enhancement. Lastly, the time sequence of the transition to the acceleration is also strongly μ dependent and occurs at low μ first, appearing to be repeatable from storm to storm.

58 GEOSCIENCES↗

A hierarchical analysis of the impact of methodological decisions on statistical downscaling of daily precipitation and air temperatures

Despite the widespread application of statistical downscaling tools, uncertainty remains regarding the role of model formulation in determining model skill for daily maximum and minimum temperature (Tmax and Tmin), and precipitation occurrence and intensity. Impacts of several key aspects of statistical transfer function form on model skill are evaluated using a framework resistant to model overspecification. We focus on: (a) model structure: simple (generalized linear models, GLMs) versus complex (artificial neural networks, ANNs) models. (b) Predictor selection: Fixed number of predictors chosen a priori versus stepwise selection of predictors and inclusion of grid point values versus predictors derived from application of principal components analysis (PCA) to spatial fields. We also examine the influence of domain size on model performance. For precipitation downscaling, we consider the role of the threshold used to characterize a wet day and apply three approaches (Poisson and Gamma distributions in GLM and ANN) to downscale wet-day precipitation amounts. While no downscaling formulation is optimal for all predictands and at 10 locations representing diverse U.S. climates, and due to the exclusion of variance inflation all of the downscaling formulations fail to reproduce the range of observed variability, models with larger suites of prospective predictors generally have higher skill. For temperature downscaling, ANNs generally outperform GLM, with greater improvements for T min than T max . Furthermore, use of PCA-derived predictors does not systematically improve model skill, but does improve skill for temperature extremes. Model skill for precipitation occurrence generally increases as the wet-day threshold increases and models using PCA-derived predictors tend to outperform those based on grid cell predictors. Each model for wet-day precipitation intensity overestimates annual total precipitation and underestimates the proportion derived from extreme precipitation events, but ANN-based models and those with larger predictor suites tend to have the smallest bias.

54 ENVIRONMENTAL SCIENCES↗

Statistical Shape Modeling of Cam Femoroacetabular Impingement

In this study, statistical shape modeling (SSM) was used to quantify three-dimensional (3D) variation and morphologic differences between femurs with and without cam femoroacetabular impingement (FAI). 3D surfaces were generated from CT scans of femurs from 41 controls and 30 cam FAI patients. SSM correspondence particles were optimally positioned on each surface using a gradient descent energy function. Mean shapes for control and patient groups were defined from the resulting particle configurations. Morphological differences between group mean shapes and between the control mean and individual patients were calculated. Principal component analysis was used to describe anatomical variation present in both groups. The first 6 modes (or principal components) captured statistically significant shape variations, which comprised 84% of cumulative variation among the femurs. Shape variation was greatest in femoral offset, greater trochanter height, and the head-neck junction. The mean cam femur shape protruded above the control mean by a maximum of 3.3 mm with sustained protrusions of 2.5-3.0 mm along the anterolateral head-neck junction and distally along the anterior neck, corresponding well with reported cam lesion locations and soft-tissue damage. This study provides initial evidence that SSM can describe variations in femoral morphology in both controls and cam FAI patients and may be useful for developing new measurements of pathological anatomy. SSM may also be applied to characterize cam FAI severity and provide templates to guide patient-specific surgical resection of bone.

statistical shape modeling↗

Highly accelerated life testing (HALT): A review from a statistical perspective

Despite its use in one form or another for at least four decades, HALT and related techniques [e.g., highly accelerated-stress screening (HASS) and stress audits (HASA)] are not well understood within the statistical community and remain controversial. This largely reflects a conflict in motivation between engineers, testing under harsh conditions to discover and eliminate failure modes, and statisticians, taking a more cautious approach to develop quantitative estimates of parameters such as mean time between failures (MTBF). Here, this review article will clarify HALT concepts and methods and explain where it fits within the universe of methods that involve the application of accelerating factors to compress the time required to evaluate or enhance product reliability. A major distinction is between methods such as HALT, a high-stress test-analyze-fix-test iterative process directed at improving reliability by discovering and fixing weak points in a design, and quantitative accelerated life testing (QALT), whose goal is the estimation of product life for a fixed design. We discuss methods such as physics of failure that offer some hope of bridging the gap between the qualitative nature of HALT, and purely quantitative statistical methods. We present a variety of engineering applications of HALT including metal fatigue, piping and pressure vessels, structural damage, radiation damage, and rotating machinery. We also discuss potential synergies between HALT and QALT, such as rapid identification, through HALT, of failure modes requiring quantitative analysis. For further study, extensive references to the applicable literature are provided as well as an appendix that describes related methods.

97 MATHEMATICS AND COMPUTING↗

Gaussian Beta Ensembles at High Temperature: Eigenvalue Fluctuations and Bulk Statistics

We study the limiting behavior of Gaussian beta ensembles in the regime where βn=const as n→∞. The results are (1) Gaussian fluctuations for linear statistics of the eigenvalues, and (2) Poisson convergence of the bulk statistics. (2) is an alternative proof of the result by Benaych-Georges and Péché (J Stat Phys 161(3):633–656, 2015) with the explicit form of the intensity measure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The CMS Statistical Analysis and Combination Tool: Combine

This paper describes the Combine software package used for statistical analyses by the CMS Collaboration. The package, originally designed to perform searches for a Higgs boson and the combined analysis of those searches, has evolved to become the statistical analysis tool presently used in the majority of measurements and searches performed by the CMS Collaboration. It is not specific to the CMS experiment, and this paper is intended to serve as a reference for users outside of the CMS Collaboration, providing an outline of the most salient features and capabilities. Readers are provided with the possibility to run Combine and reproduce examples provided in this paper using a publicly available container image. Since the package is constantly evolving to meet the demands of ever-increasing data sets and analysis sophistication, this paper cannot cover all details of Combine. However, the online documentation referenced within this paper provides an up-to-date and complete user guide.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Prediction of the Al-rich part of the Al-Cu phase diagram using cluster expansion and statistical mechanics

In this work, the thermodynamic properties of α-Al and other phases (GP zones, θ&#x27;&#x27;, θ&#x27; and θ) in the Al-rich part of the Al-Cu system have been obtained by means of the cluster expansion formalism in combination with statistical mechanics. This information was used to build the Al-rich part of the Al-Cu phase-diagram taking into account vibrational entropic contributions for θ&#x27;, as those of the other phases were negligible. The simulation predictions of the phase boundaries between α-Al and either θ&#x27;&#x27;, θ&#x27; or θ phases as a function of temperature are in good agreement with experimental data and extend the phase boundaries to a wider temperature range. The DFT calculations reveal the presence of a number of metastable Guinier-Preston-zone type configurations that may coexist with α-Al and θ&#x27;&#x27; at low temperatures. They also demonstrate that θ&#x27; is the stable phase below 550K but it is replaced by θ above this temperature due to the vibrational entropic contribution to the Gibbs energy of θ&#x27;. This work shows how the combination of cluster expansion and statistical mechanics can be used to expand our knowledge of the phase diagram of metallic alloys and to provide Gibbs free energies of different phases that can be used as input in mesoscale simulations of precipitation.

36 MATERIALS SCIENCE↗

Temporal evolution of soil moisture statistical fractal and controls by soil texture and regional groundwater flow

Soil moisture statistical fractal is an important tool for downscaling remotely-sensed observations and has the potential to play a key role in multi-scale hydrologic modeling. The fractal was first introduced two decades ago, but relatively little is known regarding how its scaling exponents evolve in time in response to climatic forcings. Previous studies have neglected the process of moisture re-distribution due to regional groundwater flow. Here, we used a physically-based surface-subsurface processes model and numerical experiments to elucidate the patterns and controls of fractal temporal evolution in two U.S. Midwest basins. Groundwater flow was found to introduce large-scale spatial structure, thereby reducing the scaling exponents (τ), which has implications for the transferability of calibrated parameters to predict τ. However, the groundwater effects depend on complex interactions with other physical controls such as soil texture and land use. The fractal scaling exponents, while in general showing a seasonal mode that correlates with mean moisture content, display hysteresis after storm events that can be divided into three phases, consistent with literature findings: (a) wetting, (b) re-organizing, and (c) dry-down. Modeling experiments clearly show that the hysteresis is attributed to soil texture, whose "patchiness" is the primary contributing factor. We generalized phenomenological rules for the impacts of rainfall, soil texture, groundwater flow, and land use on τevolution. Grid resolution has a mild influence on the results and there is a strong correlation between predictions of τ from different resolutions. Overall, our results suggest that groundwater flow should be given more consideration in studies of the soil moisture statistical fractal, especially in regions with a shallow water table.

54 ENVIRONMENTAL SCIENCES↗

High precision statistical Landau gauge lattice gluon propagator computation vs. the Gribov–Zwanziger approach

In this article we report on lattice results for the Landau gauge gluon propagator using large statistical ensembles. In particular, the compatibility of the lattice data with the tree level predictions of the Refined Gribov–Zwanziger and the Very Refined Gribov–Zwanziger actions is analysed, complementing earlier work using small-scale statistics. Our results show that the data is well described by the tree level estimate only up to momenta p≲1 GeV and clearly favours the so-called Refined Gribov–Zwanziger scenario propagator. For the Very Refined Gribov–Zwanziger action, these results imply a particular relation between d=2 condensates. Furthermore, we also provide a global fit of the lattice data that interpolates between the above scenario at low momenta and the usual continuum one-loop renormalization improved perturbation theory after introducing an infrared log-regularizing term.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Higher order corrected thermodynamics and statistics of Kerr–Newman–Gödel black hole

In this paper, we consider the rotating charged Gödel black hole and study the effect of the higher order corrections of the entropy on the thermodynamics and statistics quantities of the Kerr–Newman–Gödel black hole. The leading order correction is logarithmic while higher-order terms are proportional to the inverse of the area of the black hole. We obtain modified thermodynamics and statistics and find that correction terms are important in the stability of the black hole.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗