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At least 73 records · Page 4

SZ–X-Ray Surface Brightness Fluctuations in the SPT-XMM Clusters

The hot plasma in galaxy clusters, the intracluster medium, is expected to be shaped by subsonic turbulent motions, which are key for heating, cooling, and transport mechanisms. The turbulent motions contribute to the nonthermal pressure, which, if not accounted for, consequently imparts a hydrostatic mass bias. Accessing information about turbulent motions is thus of major astrophysical and cosmological interest. Characteristics of turbulent motions can be indirectly accessed through surface brightness fluctuations. This study expands on our pilot investigations of surface brightness fluctuations in the Sunyaev–Zel’dovich and in X-ray data by examining, for the first time, a large sample of 60 clusters using both SPT-SZ and XMM-Newton data and spans the redshift range 0.2 < z < 1.5, thus constraining the respective pressure and density fluctuations within 0.6 R $_{500}$. We deem density fluctuations to be of sufficient quality for 32 clusters, finding mild correlations between the peak of the amplitude spectra of density fluctuations and various dynamical parameters. We infer turbulent velocities from density fluctuations with an average Mach number $\mathcal{M}$ 3D = 0.52 ± 0.14, in agreement with numerical simulations. For clusters with inferred turbulent Mach numbers from fluctuations in both pressure, $\mathcal{M}$ P , and density, $\mathcal{M}$ ρ , we find broad agreement between $\mathcal{M}$ P and $\mathcal{M}$ ρ . Our results suggest either a bimodal or a skewed unimodal Mach number distribution, with the majority of clusters being turbulence-dominated (subsonic) while the remainder are shock-dominated (supersonic).

79 ASTRONOMY AND ASTROPHYSICS

ELG×LRG Distribution through Dark Matter Halo Dynamics

We investigate the clustering and halo occupation distribution (HOD) of DESI Y1 emission-line (ELGs) and luminous red (LRGs) galaxies at 0.8 < z < 1.1, including their cross-correlation (ELG×LRG), using the A BACUS S UMMIT suite and a new Halo Occupation Model (H OME ) for galaxy multitracers. This integrates intrahalo dynamics, halo exclusion, and quenching, bridging insights from hydrodynamical, HOD, abundance-matching, and semianalytic studies. Leveraging full phase-space information from the Uchuu N-body simulation, and sampling satellites from dark-matter particle positions via physically motivated prescriptions, Home reproduces the anisotropic clustering down to s = 200 h −1 kpc with unprecedented accuracy. Model parameters are inferred solely from two-point statistics using a two-level Bayesian framework, yielding high-fidelity ELG, LRG, and cross-reference catalogs. We find that satellite ELGs behave as incoherent flows within their parent halos, dominating the clustering below 4 h −1 Mpc. The HOD from the best-fit Home has the following properties: (i) 90.50% (85.91%) of ELGs (LRGs) are central galaxies without satellites, residing in halos of M vir ∼ 6.6 × 10 11 (1.2 × 10 13 ) h −1 M ⊙ ; (ii) the ELG×LRG cross-correlation is governed by central-central pairs and shaped by halo exclusion on 2–5 h −1 Mpc scales; (iii) 9.50% (14.09%) of ELGs (LRGs) are satellites, of which 1.09% (3.52%) inhabit halos with a central galaxy of the same species in a maximally conformal configuration, 7.02% (0.005%) orbit complementary hosts in a minimally conformal state, and 0.58% (10.57%) are orphans. The high sensitivity of Home precisely captures the dynamics of satellites in different host environments, opening a promising avenue for understanding systematics and the dynamical nature of dark matter, potentially distinguishing gravity models.

Favole, Ginevra [Universidad de La Laguna (Spain);

Direct inference of nuclear equation-of-state parameters from gravitational-wave observations

The observation of neutron star mergers with gravitational waves (GWs) has provided a new method to constrain the dense-matter equation of state (EOS) and to better understand its nuclear physics. However, inferring nuclear microphysics from GW observations necessitates the sampling of EOS model parameters that serve as input for each EOS used during the GW data analysis. The sampling of the EOS parameters requires solving the Tolman–Oppenheimer–Volkoff (TOV) equations a large number of times—a process that slows down each likelihood evaluation in the analysis on the order of a few seconds. Here, we employ emulators for the TOV equations built using multilayer perceptron neural networks to enable direct inference of nuclear EOS parameters from GW strain data. Our emulators allow us to rapidly solve the TOV equations, taking in EOS parameters and outputting the associated tidal deformability of a neutron star in only a few tens of milliseconds. We implement these emulators in PyCBC to directly infer the EOS parameters using the event GW170817, providing posteriors on these parameters informed solely by GWs. We benchmark these runs against analyses performed using the full TOV solver and find that the emulators achieve speed ups of nearly two orders of magnitude, with negligible differences in the recovered posteriors. Additionally, we constrain the slope and curvature of the symmetry energy at the 90% upper credible interval to be $L$ sym ≲ 106 MeV and $K$ sym ≲ 26 MeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Data-driven projection pursuit adaptation of polynomial chaos expansions for dependent high-dimensional parameters

Uncertainty quantification (UQ) and inference involving a large number of parameters are valuable tools for problems associated with heterogeneous and non-stationary behaviors. The difficulty with these problems is exacerbated when these parameters are statistically dependent requiring statistical characterization over joint measures. Probabilistic modeling methodologies stand as effective tools in the realms of UQ and inference. Among these, polynomial chaos expansions (PCE), when adapted to low-dimensional quantities of interest (QoI), provide effective yet accurate approximations for these QoI in terms of an adapted orthogonal basis. These adaptation techniques have been cast as projection pursuits in Gaussian Hilbert space in what has been referred to as a projection pursuit adaptation (PPA) by Xiaoshu Zeng and Roger Ghanem (2023). The PPA method efficiently identifies an optimal low-dimensional space for representing the QoI and simultaneously evaluates an optimal PCE within that space. The quality of this approximation clearly depends on the size of the training dataset, which is typically a function of the adapted reduced dimension. Here, the complexity of the problem is thus mediated by the complexity of the low-dimensional quantity of interest and not the complexity of the high-dimensional parameter space.

Data-driven

DAmodel: hierarchical Bayesian modelling of DA white dwarfs for spectrophotometric calibration

We use hierarchical Bayesian modelling to calibrate a network of 32 all-sky faint DA white dwarf (DA WD) spectrophotometric standards (⁠16.5 < V , 19.5⁠) alongside three CALSPEC standards, from 912 Å to 32 μm. The framework is the first of its kind to jointly infer photometric zero points and WD parameters (surface gravity log g⁠, effective temperature T eff ⁠, extinction A V ⁠, dust relation parameter R V ) by simultaneously modelling both photometric and spectroscopic data. We model panchromatic Hubble Space Telescope Wide Field Camera 3 (HST/WFC3) UVIS and IR photometry, HST/STIS UV spectroscopy, and ground-based optical spectroscopy to sub-per cent precision. Photometric residuals for the sample are the lowest yet yielding < 0.004 mag RMS on average from the UV to the NIR, achieved by jointly inferring time-dependent changes in system sensitivity and WFC3/IR count-rate nonlinearity. Our GPU-accelerated implementation enables efficient sampling via Hamiltonian Monte Carlo, critical for exploring the high-dimensional posterior space. The hierarchical nature of the model enables population analysis of intrinsic WD and dust parameters. Inferred spectral energy distributions from this model will be essential for calibrating the James Webb Space Telescope as well as next-generation surveys, including Vera Rubin Observatory’s Legacy Survey of Space and Time and the Nancy Grace Roman Space Telescope.

methods: statistical

Solving high-dimensional inverse problems using amortized likelihood-free inference with noisy and incomplete data

Here, we present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously. We apply the proposed method to an inversion problem in groundwater hydrology to estimate the posterior distribution of the log-conductivity field conditioned on spatially sparse time-series observations of the system’s hydraulic head responses. The conductivity field is represented with 706 degrees of freedom in the considered problem. Comparison with the likelihood-based iterative ensemble smoother PEST-IES method demonstrates that the proposed method accurately estimates the parameter posterior distribution and the observations’ predictive posterior distribution at a fraction of the inference time of PEST-IES.

conditional invertible neural network

First Estimation of Model Parameters for Neutrino-Induced Nucleon Knockout Using Simulation-Based Inference

To enable an accurate determination of oscillation parameters, accelerator-based neutrino experiments require detailed simulations of nuclear interaction physics in the GeV regime. While substantial effort from both theory and experiment is currently being invested to improve the fidelity of these simulations, their present deficiencies typically oblige experimental collaborations to resort to empirical tuning of simulation model parameters. As the precision requirements of the field continue to become more stringent, machine learning techniques may provide a powerful means of handling corresponding growth in the complexity of future neutrino interaction model tuning exercises. To study the suitability of simulation-based inference (SBI) for this physics application, in this paper we revisit a tuned configuration of the GENIE neutrino event generator that was originally developed by the MicroBooNE collaboration. Despite closely reproducing the adopted values of four physics parameters when confronted with the tuned cross-section predictions as input, we find that our trained SBI algorithm prefers modestly different values (within MicroBooNE's assigned uncertainties) and achieves slightly better goodness-of-fit when inference is run on the experimental data set originally used by MicroBooNE. We also find that our trained algorithm can create a fair approximation of an alternative neutrino scattering simulation, NuWro, that shares only a subset of its physics model parameters with GENIE.

Tame-Narvaez, Karla [Fermilab] (ORCID:000000022249

Joint state-parameter estimation for the reduced fracture model via the united filter

Here, in this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media are critical in subsurface hydrology, geophysics, and reservoir geomechanics. Reduced fracture models, which represent fractures as lower-dimensional interfaces, enable efficient multi-scale simulations. However, reduced fracture models also face accuracy challenges due to modeling errors and uncertainties in physical parameters such as permeability and fracture geometry. To address these challenges, we propose a United Filter method, which integrates the Ensemble Score Filter (EnSF) for state estimation with the Direct Filter for parameter estimation. EnSF, based on a score-based diffusion model framework, produces ensemble representations of the state distribution without deep learning. Meanwhile, the Direct Filter, a recursive Bayesian inference method, estimates parameters directly from state observations. The United Filter combines these methods iteratively: EnSF estimates are used to refine parameter values, which are then fed back to improve state estimation. Numerical experiments demonstrate that the United Filter method surpasses the state-of-the-art Augmented Ensemble Kalman Filter, delivering more accurate state and parameter estimation for reduced fracture models. This framework also provides a robust and efficient solution for PDE-constrained inverse problems with uncertainties and sparse observations.

Bayesian inference

A Theoretical Operational Model for Complex Experiments and its Invariance Theorems

We develop and systematize the Theoretical–Operational Model (TOM), a framework that treats preparation and measurement —including their operational residues— as intrinsic structures of physical theory. The central contribution is a principled geometric–algebraic organization of admissible operational deformations, formulated using quantum channels, renormalization-style flows, and information-geometric tools. Within this structure, operational residues and background processes are represented as effective morphisms attached to these operational components, whose invariants yield constraints on how theoretical parameters vary under specified classes of deformations. Illustrations drawn from muon–electron conversion, long-baseline neutrino oscillations, and quark–gluon-plasma phenomenology show how TOM maps operational effects into inferences about theoretical parameters, enables systematic cross-experimental comparisons, and stabilizes parameter estimation against defined deformation families. By embedding the operational layer—together with its residues—within a structured theoretical setting, TOM supports both theory testing and theory development, clarifying the conceptual relation between experimental realization and the physical quantities represented by the theory.

Pronskikh, Vitaly [Fermilab] (ORCID:00000002518174

Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical GP-UCB algorithm, but the additional random exploration step accelerates their convergence, nearly achieving the optimal convergence rate. Furthermore, to facilitate Bayesian inference with intractable likelihoods, we propose to utilize optimization iterates for maximum a posteriori estimation to build a Gaussian process surrogate model for the unnormalized log-posterior density. We provide bounds for the Hellinger distance between the true and the approximate posterior distributions in terms of the number of design points. We demonstrate the effectiveness of our Bayesian optimization algorithms in nonconvex benchmark objective functions, in a machine learning hyperparameter tuning problem, and in a black-box engineering design problem. The effectiveness of our posterior approximation approach is demonstrated in two Bayesian inference problems for parameters of dynamical systems.

Bayesian inference

Detailed characterization of runaway electron driven whistler waves in low-density DIII-D discharges

RE-driven whistler waves during quiescent DIII-D shots have been investigated further. The waves are confirmed to be mostly perpendicularly propagating and are observed for the first time with frequencies up to 700 MHz. Phase-spectral analysis has been used to infer their toroidal mode numbers, n, which are expected to scale with the wavenumber, k, of the mode. Though we derive a theoretical scaling of k ≈ 4n, the measured mode numbers are found to exhibit a very weak dependence on k. In addition, increases in synchrotron emission have been found to consistently lag whistler wave bursts by roughly 3–5 ms, suggesting the waves are causing pitch-angle scattering, since the emitted synchrotron radiation is a strong function of the REs' perpendicular energy. The stronger the wave bursts, the greater the subsequent increase in synchrotron emission. A predator-prey model is used to describe these nonlinear wave-particle interactions, from which the wave damping rates and the loss parameter can be inferred. The damping rates are found to be of the order of (1.6 ± 0.8) × 10 4 /s, and the unitless loss parameter is found to be approximately 2, suggesting that the loss mechanism is diffusive. These observations will serve to validate models of RE-driven waves in tokamak plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Demonstrate new plasticity models for doped UO 2 that capture dislocation mechanisms

In light water reactors, fuel vendors are investigating the use of dopants to modify the properties of UO 2 pellets, with the goal of improving pellet-cladding mechanical interactions during operation. Dopants are expected to ‘soften’ the pellets; that is, the doped pellets have higher plastic deformation than conventional UO 2 . This leads to a reduction in the severity of mechanical pellet-cladding interactions, helping to reduce the hoop strain on the cladding. By minimizing the strain exerted by the pellet on the cladding, it is anticipated that cladding performance under accident conditions can be enhanced (i.e., lowering the risk of burst during a LOCA). Dopants such as chromium (Cr) promote grain growth during pellet fabrication, leading to larger grains; therefore, understanding the link between chemistry, microstructure and mechanical deformation (enhanced creep rates) behavior of UO 2 is critical to helping operators further substantiate the benefits of doping UO 2 . Historically, the nuclear energy industry has relied on empirical models to make assessments of performance. Compared to empirical models, mechanistic physics-based models provide benefits, such as, fewer data points for validation and better extrapolation where experimental data is scarce or non-existent. In this report, Bayesian inference techniques have been applied to a previously developed lower length-scale-informed diffusional creep model. The objective is to i) infer lower-length-scale parameter distributions from available experiment and then ii) determine the uncertainties in the measurable quantity (in this case creep rates) after propagating the inferred lower length scale parameter uncertainties. The approach requires many evaluations of the model, which becomes computationally insurmountable; therefore, a neural-network model is trained to data obtained by sampling the full model over the most important parameters. This neural-network is then used in the Bayesian inference approach to determine probability distributions in the parameter values that represent the uncertainty in the model given what is known from the experiments (posterior). A significant reduction compared to conservative initial (prior) uncertainties is achieved through inference against the experimental data, demonstrating the efficacy of this approach. Furthermore, by accounting for uncertainties in the experimental conditions and sample non-stoichiometry, it is possible to resolve apparent discrepancies in experimental measurements within a self-consistent grain boundary (Coble) creep model that is sensitive to chemistry. This work has been written up and submitted to Nuclear Technology for a special issue on accelerated fuel qualification (AFQ). This uncertainty quantification (UQ) work not only improves the diffusional model, while accounting for uncertainty, but also establishes a framework which can readily be applied to the mechanistic models of dislocation deformation developed in this study. The most likely values from the Bayesian analysis are incorporated into our UO 2 diffusional creep model and a lower length scale-informed irradiation UO 2 creep mechanistic model to generate a dataset. This dataset has been provided to our INL collaborators for training an artificial neural network surrogate model, which will be implemented in the BISON fuel performance code to assess how the results differ from those currently obtained using a fully empirical model and that of using the nominal (uncalibrated) atomic scale parameters in our mechanistic model. Plastic deformation (creep and glide) in UO 2 is a complex phenomenon, governed by multiple underlying processes such as local defect concentrations, applied stresses, and microstructural characteristics. Consequently, there is a need for a meso-scale model with polycrystalline resolution capable of extrapolating to large grain sizes applicable to doped UO 2 , where data is limited and the model can help bridge the knowledge gap. By integrating atomistic data into the polycrystal LApx code, it becomes possible to predict dislocation climb and glide plasticity that simple analytical models cannot accurately represent. The application of atomic-scale data within LApx demonstrated the importance of climb and glide mechanisms in reproducing high-stress UO 2 behavior. Behaviors such as this are crucial to capture and implement in BISON, as parts of the fuel pellet can reach temperatures where glide can occur before pellet cracking. This model which captures dislocation based mechanisms for UO 2 is then used to stand up the doped model accounting for larger grain sizes. It was found that larger grain sizes can lead to enhanced deformation rates in the glide regime, and therefore can help with the pellet cladding mechanical interaction. Therefore if the fuel pellet reaches conditions (stress/temperature) where glide is active, the enhanced creep rates for larger grains in the glide regime (doped UO 2 ) can help with pellet cladding mechanical interactions. Plastic deformation in UO 2 involves multiple mechanisms, including diffusional creep, dislocation climb, and glide. This milestone contains two parts: (1) UQ of a pre-existing lower length scale informed mechanistic diffusional creep model, and (2) development of a new LApx based model for dislocation-mediated creep mechanisms in UO 2 , with application to large-grain doped UO 2 .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

BMINN: Learning chemical potentials and parameters from voltage data for multi-phase battery modeling

Free-energy landscapes and chemical potentials govern the dynamics of phase transitions, transport, and stability in functional materials, yet they remain experimentally inaccessible under realistic operating conditions. Here we introduce a Bayesian model-integrated neural network (BMINN) that embeds physics-based formulations of non-autonomous partial differential-algebraic equations into probabilistic learning. This approach reconstructs hidden thermodynamics directly from macroscopic current-voltage data, providing quantitative access to metastable states, staging transitions, and energy barriers without synchrotron probes. Demonstrated on lithium-graphite electrodes, BMINN recovers full Gibbs free-energy landscapes with fidelity validated against operando X-ray diffraction. The framework generalizes across dynamical regimes, enabling accurate voltage prediction, internal state estimation, and inference of governing parameters. Beyond batteries, BMINN exemplifies a broadly applicable strategy for learning missing physics in multiphase, non-equilibrium systems, offering a new pathway to uncover hidden thermodynamic functions across condensed matter and materials physics.

25 ENERGY STORAGE

Uncertainty quantification of material parameters in modeling coupled metal and high explosive experiments

Experiments involving the coupling of metal and high explosives (HE) are of notable defense-related interest, and we seek to refine the uncertainty quantification associated with models of such experiments. In particular, our focus is on how uncertainty related to the metal constitutive model challenges our ability to infer high explosive model parameters when analyzing focused science experiments. We consider three focused experiments involving an HE accelerating metal: small plate tests with tantalum/LX-14 and tantalum/LX-17 pairings as well as a tantalum/LX-17 cylinder test. For all three models, we perform sensitivity analysis to ascertain the influence of metal strength on the coupled experimental response. Moreover, we calibrate each model in a Bayesian setting and study the quantification of metal strength on the inference of the HE parameters. Based on our results, we offer guidance for future metal/HE experiments.

36 MATERIALS SCIENCE

Bayesian model-data comparison incorporating theoretical uncertainties

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of properly accounting for theoretical uncertainties. In this Letter, we present a Bayesian framework that explicitly quantifies these uncertainties by statistically modeling theory errors, guided by qualitative knowledge of a theory’s varying reliability across the input domain. We demonstrate the effectiveness of this approach using two systems: a simple ball drop experiment and multi-stage heavy-ion simulations. In both cases incorporating model discrepancy leads to improved parameter estimates, with systematic improvements observed as additional experimental observables are integrated.

Bayesian methods

Progress in end-to-end optimization of fundamental physics experimental apparata with differentiable programming

In this article we examine recent developments in the research area concerning the creation of end-to-end models for the complete optimization of measuring instruments. The models we consider rely on differentiable programming methods and on the specification of a software pipeline including all factors impacting performance — from the data-generating processes to their reconstruction and the inference on the parameters of interest — along with the careful specification of a utility function well aligned with the end goals of the experiment. Building on previous studies originated within the MODE Collaboration, we focus specifically on applications involving instruments for particle physics experimentation, as well as industrial and medical applications that share the detection of radiation as their data-generating mechanism. This report illustrates the most recent advancements in the area, and outlines, for each of the discussed applications as well as for automatic differentiation itself, ongoing and future work.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

Characterization of DESI fiber assignment incompleteness effect on 2-point clustering and mitigation methods for DR1 analysis

We present an in-depth analysis of the fiber assignment incompleteness in the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1). This incompleteness is caused by the restricted mobility of the robotic fiber positioner in the DESI focal plane, which limits the number of galaxies that can be observed at the same time, especially at small angular separations. As a result, the observed clustering amplitude is suppressed in a scale-dependent manner, which, if not addressed, can severely impact the inference of cosmological parameters. We discuss the methods adopted for simulating fiber assignment on mocks and data. In particular, we introduce the fast fiber assignment (FFA) emulator, which was employed to obtain the power spectrum covariance adopted for the DR1 full-shape analysis. We present the mitigation techniques, organised in two classes: measurement stage and model stage. We then use high fidelity mocks as a reference to quantify both the accuracy of the FFA emulator and the effectiveness of the different measurement-stage mitigation techniques. This complements the studies conducted in a parallel paper for the model-stage techniques, namely the θ-cut approach. We find that pairwise inverse probability (PIP) weights with angular upweighting recover the “true” clustering in all the cases considered, in both Fourier and configuration space. Notably, we present the first ever power spectrum measurement with PIP weights from real data.

cosmological simulations