Nonlinear Scaling Research Articles

Detection of Cosmological 21 cm Emission with the Canadian Hydrogen Intensity Mapping Experiment

We present a detection of 21 cm emission from large-scale structure (LSS) between redshift 0.78 and 1.43 made with the Canadian Hydrogen Intensity Mapping Experiment. Radio observations acquired over 102 nights are used to construct maps that are foreground filtered and stacked on the angular and spectral locations of luminous red galaxies (LRGs), emission-line galaxies (ELGs), and quasars (QSOs) from the eBOSS clustering catalogs. We find decisive evidence for a detection when stacking on all three tracers of LSS, with the logarithm of the Bayes factor equal to 18.9 (LRG), 10.8 (ELG), and 56.3 (QSO). An alternative frequentist interpretation, based on the likelihood ratio test, yields a detection significance of 7.1σ (LRG), 5.7σ (ELG), and 11.1σ (QSO). These are the first 21 cm intensity mapping measurements made with an interferometer. We constrain the effective clustering amplitude of neutral hydrogen (H i), defined as , where ΩH i is the cosmic abundance of H i, b H i is the linear bias of H i, and 〈f μ 2〉 = 0.552 encodes the effect of redshift-space distortions at linear order. We find for LRGs (z = 0.84), for ELGs (z = 0.96), and for QSOs (z = 1.20), with constraints limited by modeling uncertainties at nonlinear scales. We are also sensitive to bias in the spectroscopic redshifts of each tracer, and we find a nonzero bias Δ v = − 66 ± 20 km s−1 for the QSOs. We split the QSO catalog into three redshift bins and have a decisive detection in each, with the upper bin at z = 1.30 producing the highest-redshift 21 cm intensity mapping measurement thus far.

Optical and SAR Image Registration Based on Multi-Scale Orientated Map of Phase Congruency

Optical and Synthetic Aperture Radar (SAR) images are highly complementary, and their registrations are a fundamental task for other remote sensing applications. Traditional feature-matching algorithms fail to solve the significant nonlinear radiation difference (NRD) caused by different sensors. To address this problem, a robust registration algorithm with the multi-scale orientated map of phase congruency (MSPCO) is proposed. First, a nonlinear diffusion scale space is established to obtain the scale invariance of feature points. Compared with the linear Gaussian scale space, the nonlinear diffusion scale space can better preserve the edge and texture information. Second, to ensure the quantity and repeatability of features, corner points and edge points are detected on the moment map of phase congruency, respectively, which is the foundation to the next feature matching. Third, the MSPCO descriptor is constructed via the orientation of phase congruency (PCO). PCO is highly robust to NRD, and the different scales of PCOs enhance the robustness of the descriptor. Finally, a feature-matching strategy based on an effective scale ratio is proposed, which reduces the number of comparisons among features and improves computational efficiency. The experimental results show that the proposed method is better than the existing feature-based methods in terms of the number of correct matches and registration accuracy. The registration accuracy is only inferior to that of the most advanced template matching method, and the accuracy difference is within 0.3 pixels, which fully demonstrates the robustness and accuracy of the proposed method in optical and SAR image registration.

A Modified NLCS Algorithm for High-Speed Bistatic Forward-Looking SAR Focusing with Spaceborne Illuminator

The coupling and spatial variation of range and azimuth parameters is the biggest challenge for bistatic forward-looking SAR (BFSAR) imaging. In contrast with the monostatic SAR and translational invariant bistatic SAR (TI-BSAR), the range cell migration (RCM), and Doppler parameters of high-speed bistatic forward-looking SAR (HS-BFSAR) have two-dimensional spatial variation characteristics, which makes it difficult to obtain SAR images with satisfactory global focusing. Firstly, based on the configuration of the spaceborne illuminator and high-speed forward-looking receiving platform, the accurate range-Doppler domain expression of the echo signal is derived in this paper. Secondly, using this analytical expression, a range nonlinear chirp scaling (NLCS) is proposed to equalize the RCM and equivalent range frequency modulation (FM) rate so that they can be uniformly processed in the two-dimensional frequency domain. Next, in the azimuth processing, the proposed method decomposes the Doppler contribution of the transmitter and receiver, respectively. Then, an azimuth NLCS is used to eliminate the spatial variation of the azimuth FM rate. Finally, a range-dependent azimuth filter is constructed to achieve azimuth compression. Simulation results validate the efficiency and effectiveness of the proposed algorithm.

Improved mixed dark matter halo model for ultralight axions

We present a complete halo model for mixed dark matter composed of cold dark matter (CDM) and ultralight axionlike particles (ULAs). Our model treats ULAs as a biased tracer of CDM, in analogy to treatments of massive neutrinos and neutral hydrogen. The model accounts for clustering of ULAs around CDM host halos, and fully models the cross correlations of both components. The model inputs include the ULA Jeans scale, and soliton density profile. Our model can be used to predict the matter power spectrum, $P(k)$, on nonlinear scales for subpopulations of ULAs across the mass range ${10}^{\ensuremath{-}33}\text{ }\text{ }\mathrm{eV}\ensuremath{\le}m\ensuremath{\le}{10}^{\ensuremath{-}21}\text{ }\mathrm{eV}$, and can be calibrated against future mixed DM simulations to improve its accuracy. The mixed DM halo model also allows us to assess the importance of various approximations.

Separable Paravector Orientation Tensors for Enhancing Retinal Vessels.

Robust detection of retinal vessels remains an unsolved research problem, particularly in handling the intrinsic real-world challenges of highly imbalanced contrast between thick vessels and thin ones, inhomogeneous background regions, uneven illumination, and complex geometries of crossing/bifurcations. This paper presents a new separable paravector orientation tensor that addresses these difficulties by characterizing the enhancement of retinal vessels to be dependent on a nonlinear scale representation, invariant to changes in contrast and lighting, responsive for symmetric patterns, and fitted with elliptical cross-sections. The proposed method is built on projecting vessels as a 3D paravector valued function rotated in an alpha quarter domain, providing geometrical, structural, symmetric, and energetic features. We introduce an innovative symmetrical inhibitory scheme that incorporates paravector features for producing a set of directional contrast-independent elongated-like patterns reconstructing vessel tree in orientation tensors. By fitting constraint elliptical volumes via eigensystem analysis, the final vessel tree is produced with a strong and uniform response preserving various vessel features. The validation of proposed method on clinically relevant retinal images with high-quality results, shows its excellent performance compared to the state-of-the-art benchmarks and the second human observers.

Optomechanical effects in nanocavity-enhanced resonant Raman scattering of a single molecule

In this article, we address the optomechanical effects in surface-enhanced resonant Raman scattering (SERRS) from a single molecule in a nano-particle on mirror (NPoM) nanocavity by developing a quantum master equation theory, which combines macroscopic quantum electrodynamics and electron-vibration interaction within the framework of open quantum system theory. We supplement the theory with electromagnetic simulations and time-dependent density functional theory calculations in order to study the SERRS of a methylene blue molecule in a realistic NPoM nanocavity. The simulations allow us not only to identify the conditions to achieve conventional optomechanical effects, such as vibrational pumping, non-linear scaling of Stokes and anti-Stokes scattering, but also to discovery distinct behaviors, such as the saturation of exciton population, the emergence of Mollow triplet side-bands, and higher-order Raman scattering. All in all, our study might guide further investigations of optomechanical effects in resonant Raman scattering.

Full forward model of galaxy clustering statistics with AbacusSummit light cones

ABSTRACT Novel summary statistics beyond the standard 2-point correlation function (2PCF) are necessary to capture the full astrophysical and cosmological information from the small-scale (r < 30h−1Mpc) galaxy clustering. However, the analysis of beyond-2PCF statistics on small scales is challenging because we lack the appropriate treatment of observational systematics for arbitrary summary statistics of the galaxy field. In this paper, we develop a full forward modelling pipeline for a wide range of summary statistics using the large high-fidelity AbacusSummit light cones that account for many systematic effects as well as remain flexible and computationally efficient to enable posterior sampling. We apply our forward model approach to a fully realistic mock galaxy catalog and demonstrate that we can recover unbiased constraints on the underlying galaxy–halo connection model using two separate summary statistics: the standard 2PCF and the novel k-th nearest neighbour (kNN) statistics, which are sensitive to correlation functions of all orders. We will demonstrate its strong constraining power on extended galaxy–halo connection models and cosmology in follow up papers. We expect this to become a powerful approach when applying to upcoming surveys such as DESI where we can leverage a multitude of summary statistics across a wide redshift range to maximally extract information from the non-linear scales.

Constraints on S8 from a full-scale and full-shape analysis of redshift-space clustering and galaxy–galaxy lensing in BOSS

ABSTRACT We present a novel simulation-based cosmological analysis of galaxy–galaxy lensing and galaxy redshift-space clustering. Compared to analysis methods based on perturbation theory, our simulation-based approach allows us to probe a much wider range of scales, $0.4 \, h^{-1} \, \mathrm{Mpc}$ to $63 \, h^{-1} \, \mathrm{Mpc}$, including highly non-linear scales, and marginalizes over astrophysical effects such as assembly bias. We apply this framework to data from the Baryon Oscillation Spectroscopic Survey LOWZ sample cross-correlated with state-of-the-art gravitational lensing catalogues from the Kilo Degree Survey and the Dark Energy Survey. We show that gravitational lensing and redshift-space clustering when analysed over a large range of scales place tight constraints on the growth-of-structure parameter $S_8 = \sigma _8 \sqrt{\Omega _{\rm m} / 0.3}$. Overall, we infer S8 = 0.792 ± 0.022 when analysing the combination of galaxy–galaxy lensing and projected galaxy clustering and S8 = 0.771 ± 0.027 for galaxy redshift-space clustering. These findings highlight the potential constraining power of full-scale studies over studies analysing only large scales and also showcase the benefits of analysing multiple large-scale structure surveys jointly. Our inferred values for S8 fall below the value inferred from the CMB, S8 = 0.834 ± 0.016. While this difference is not statistically significant by itself, our results mirror other findings in the literature whereby low-redshift large-scale structure probes infer lower values for S8 than the CMB, the so-called S8-tension.

The CIDER simulations: non-linear structure formation in the constrained interacting dark energy scenario

ABSTRACTWe present for the first time a suite of cosmological simulations for a particular class of interacting Dark Energy cosmologies characterized by a background expansion history constrained to be indistinguishable from ΛCDM. Such Constrained Interacting Dark Energy scenario – or CIDER – has been recently proposed in the literature and has the appealing feature of suppressing structure formation at late times, thereby possibly alleviating the persisting σ8 tension while leaving background observables unaffected. A crucial step to assess the viability of such scenarios is then represented by quantifying their impact on structure formation at non-linear scales, which is what we start investigating with the simulations discussed in the present work. We show that – for reasonable parameter choices – the reconstructed scalar potential is close to an exponential for most of the matter dominated epoch, and that the non-linear evolution of structures in these models imprints specific footprints on matter and halo statistics that may allow to break degeneracies with standard cosmological parameters.

The bacco simulation project: bacco hybrid Lagrangian bias expansion model in redshift space

ABSTRACT We present an emulator that accurately predicts the power spectrum of galaxies in redshift space as a function of cosmological parameters. Our emulator is based on a second-order Lagrangian bias expansion that is displaced to Eulerian space using cosmological N-body simulations. Redshift space distortions are then imprinted using the non-linear velocity field of simulated particles and haloes. We build the emulator using a forward neural network trained with the simulations of the BACCO project, which covers an eight-dimensional parameter space including massive neutrinos and dynamical dark energy. We show that our emulator provides unbiased cosmological constraints from the monopole, quadrupole, and hexadecapole of a mock galaxy catalogue that mimics the BOSS-CMASS sample down to non-linear scales ($k\sim 0.6{h\, {\rm Mpc}^{-1}}$). This work opens up the possibility of robustly extracting cosmological information from small scales using observations of the large-scale structure of the universe.

Quijote-PNG: The Information Content of the Halo Power Spectrum and Bispectrum

We investigate how much can be learnt about four types of primordial non-Gaussianity (PNG) from small-scale measurements of the halo field. Using the quijote-png simulations, we quantify the information content accessible with measurements of the halo power spectrum monopole and quadrupole, the matter power spectrum, the halo–matter cross spectrum, and the halo bispectrum monopole. This analysis is the first to include small, nonlinear scales, up to , and to explore whether these scales can break degeneracies with cosmological and nuisance parameters making use of thousands of N-body simulations. We perform all the halo measurements in redshift space with a single sample comprised of all halos with mass >3.2 × 1013 h −1 M ⊙. For local PNG, measurements of the scale-dependent bias effect from the power spectrum using sample variance cancellation provide significantly tighter constraints than measurements of the halo bispectrum. In this case measurements of the small scales add minimal additional constraining power. In contrast, the information on equilateral and orthogonal PNG is primarily accessible through the bispectrum. For these shapes, small-scale measurements increase the constraining power of the halo bispectrum by up to 4×, though the addition of scales beyond k ≈ 0.3 h Mpc−1 improves constraints largely through reducing degeneracies between PNG and the other parameters. These degeneracies are even more powerfully mitigated through combining power spectrum and bispectrum measurements. However, even with combined measurements and small-scale information, equilateral non-Gaussianity remains highly degenerate with σ 8 and our bias model.

The Clustering Properties of AGNs/Quasars in CatWISE2020 Catalog

We study the clustering properties of 1,307,530 AGNs/quasars in the CatWISE2020 catalog prepared using the Wide-field Infrared Survey Explorer and Near-Earth Object Wide-field Infrared Survey Explorer survey data. For angular moments ℓ ⪆ 10 (⪅18°) down to nonlinear scales, the results are in agreement with the standard ΛCDM cosmology, with a galaxy bias roughly matching that of the NRAO VLA Sky Survey (NVSS) AGNs. We further explore the redshift dependence of the fraction of infrared-bright AGNs on stellar mass, , and find , ruling out a nonevolution hypothesis at a ≈4.6σ confidence level. The results are consistent with the measurements obtained with NVSS AGNs, though considerably more precise thanks to the significantly higher number density of objects in CatWISE2020. The excess dipole and high clustering signal above angular scale ≈18° remains anomalous.

Causal modifications of gravity and their observational bounds

Since general relativity is the unique theory of massless spin 2 particles at large distances, the most reasonable way to have significant modifications is to introduce one or more light scalars that mediate a new long-range force. Most existing studies of such scalars invoke models that exhibit some kind of "screening" at short distances to hide the force from solar system tests. However, as is well known, such modifications also exhibit superluminality, which can be interpreted as a form of acausality. In this work we explore explicitly subluminal and causal scalar field models. In particular, we study a conformally coupled scalar $\phi$, with a small coupling to matter to obey solar system bounds, and a non-canonical kinetic term $K(X)$ ($X=(\partial\phi)^2/2$) that obeys all subluminality constraints and is hyperbolic. We consider $K(X)$ that is canonical for small $X$, but beyond some nonlinear scale enters a new scaling regime of power $p$, with $1/2<p<1$ (the DBI kinetic term is the limit $p=1/2$ and a canonical scalar is $p=1$). As opposed to screening (and superluminality), this new force becomes more and more important in the regime of high densities (and subluminality). We then turn to the densest environments to put bounds on this new interaction. We compute constraints from precession in binary systems such as Hulse-Taylor, we compute corrections to neutron star hydrostatic equilibrium, and we compute power in radiation, both tensor mode corrections and the new scalar mode, which can be important during mergers.

Interacting dark energy from the joint analysis of the power spectrum and bispectrum multipoles with the EFTofLSS

ABSTRACT Interacting dark energy models have been suggested as alternatives to the standard cosmological model, ΛCDM. We focus on a phenomenologically interesting class of dark scattering models that is characterized by pure momentum exchange between dark energy and dark matter. This model extends the parameter space with respect to ΛCDM by two parameters, w and A, which define the dark energy equation of state and the strength of the coupling between dark energy and dark matter, respectively. In order to test non-standard cosmologies with Stage-IV galaxy clustering surveys, it is crucial to model mildly non-linear scales and perform precision versus accuracy tests. We use the Effective Field Theory of Large-Scale Structure; and we perform validation tests by means of an MCMC analysis using a large set of N-body simulations. We find that adding the bispectrum monopole to the power spectrum multipoles improves the constraints on the dark energy parameters by $\sim 30 {{\ \rm per\ cent}}$ for $k_{\mathrm{max}, B}^{l=0} = 0.11$ h Mpc−1, without introducing biases in the parameter estimation. We also find that the same improvement can be achieved with more moderate scale cuts and the use of bias relations, or with the addition of the bispectrum quadrupole. Finally, we study degeneracies between the dark energy parameters and the scalar amplitude As and discuss the corresponding projection effects, as well as degeneracies with other cosmological parameters.

Constructive Approximation on Graded Meshes for the Integral Fractional Laplacian

We consider the homogeneous Dirichlet problem for the integral fractional Laplacian $$(-\Delta )^s$$ . We prove optimal Sobolev regularity estimates in Lipschitz domains provided the solution is $$C^s$$ up to the boundary. We present the construction of graded bisection meshes by a greedy algorithm and derive quasi-optimal convergence rates for approximations to the solution of such a problem by continuous piecewise linear functions. The nonlinear Sobolev scale dictates the relation between regularity and approximability.

Fast and realistic large-scale structure from machine-learning-augmented random field simulations

ABSTRACT Producing thousands of simulations of the dark matter distribution in the Universe with increasing precision is a challenging but critical task to facilitate the exploitation of current and forthcoming cosmological surveys. Many inexpensive substitutes to full N-body simulations have been proposed, even though they often fail to reproduce the statistics of the smaller non-linear scales. Among these alternatives, a common approximation is represented by the lognormal distribution, which comes with its own limitations as well, while being extremely fast to compute even for high-resolution density fields. In this work, we train a generative deep learning model, mainly made of convolutional layers, to transform projected lognormal dark matter density fields to more realistic dark matter maps, as obtained from full N-body simulations. We detail the procedure that we follow to generate highly correlated pairs of lognormal and simulated maps, which we use as our training data, exploiting the information of the Fourier phases. We demonstrate the performance of our model comparing various statistical tests with different field resolutions, redshifts, and cosmological parameters, proving its robustness and explaining its current limitations. When evaluated on 100 test maps, the augmented lognormal random fields reproduce the power spectrum up to wavenumbers of $1 \, h \, \rm {Mpc}^{-1}$, and the bispectrum within 10 per cent, and always within the error bars, of the fiducial target simulations. Finally, we describe how we plan to integrate our proposed model with existing tools to yield more accurate spherical random fields for weak lensing analysis.

Explicit time embedding based cascade attention network for information popularity prediction

Predicting information cascade popularity is a fundamental problem in social networks. Capturing temporal attributes and cascade role information (e.g., cascade graphs and cascade sequences) is necessary for understanding the information cascade. Current methods rarely focus on unifying this information for popularity predictions, which prevents them from effectively modeling the full properties of cascades to achieve satisfactory prediction performances. In this paper, we propose an explicit Time embedding based Cascade Attention Network (TCAN) as a novel popularity prediction architecture for large-scale information networks. TCAN integrates temporal attributes (i.e., periodicity, linearity, and non-linear scaling) into node features via a general time embedding approach (TE), and then employs a cascade graph attention encoder (CGAT) and a cascade sequence attention encoder (CSAT) to fully learn the representation of cascade graphs and cascade sequences. We use two real-world datasets (i.e., Weibo and APS) with tens of thousands of cascade samples to validate our methods. Experimental results show that TCAN obtains mean logarithm squared errors of 2.007 and 1.201 and running times of 1.76 h and 0.15 h on both datasets, respectively. Furthermore, TCAN outperforms other representative baselines by 10.4%, 3.8%, and 10.4% in terms of MSLE, MAE, and R-squared on average while maintaining good interpretability.

Data-driven constitutive relation reveals scaling law for hydrodynamic transport coefficients.

Finding extended hydrodynamics equationsvalid from the dense gas region to the rarefied gas region remains a great challenge. The key to success is to obtain accurate constitutive relations for stress and heat flux. Data-driven models offer a new phenomenological approach to learning constitutive relations from data. Such models enable complex constitutive relations that extend Newton's law of viscosity and Fourier's law of heat conduction by regression on higher derivatives. However, the choices of derivatives in these models are ad hoc without a clear physical explanation. We investigated data-driven models theoretically on a linear system. We argue that these models are equivalent to nonlinear length scale scaling laws of transport coefficients. The equivalence to scaling laws justified the physical plausibility and revealed the limitation of data-driven models. Our argument also points out that modeling the scaling law could avoid practical difficulties in data-driven models like derivative estimation and variable selection on noisy data. We further proposed a constitutive relation model based on scaling law and tested it on the calculation of Rayleigh scattering spectra. The result shows our data-driven model has a clear advantage over the Chapman-Enskog expansion and moment methods.

Interface instabilities in hydrodynamic relativistic jets

ABSTRACT Both the dynamics and the observational properties of relativistic jets are determined by their interaction with the ambient medium. A crucial role is played by the contact discontinuity at the jet boundary, which in the presence of jet collimation may become subject to Rayleigh–Taylor instability (RTI) and Richtmyer–Meshkov instability (RMI). Here, we study the evolution of these instabilities in non-magnetized relativistic jets using special relativistic three-dimensional hydrodynamic simulations. We show that the growth of initial perturbations is consistent with relativistic RTI operating in the jet collimation region. The contribution of RMI becomes important downstream from the collimation shock in agreement with the theoretical expectations. Both instabilities reach non-linear scales above the shock convergence point and trigger strong turbulence, mixing the jet with the ambient matter. We devise an analytic solution for the mixing rate and show that it is sensitive to the external density gradients. Our results may be applied to different types of astrophysical objects. In particular, different contribution of interface instabilities is a natural explanation for the observed dichotomy between FR-I and FR-II radiogalaxies. The rapid slow-down in the jet of M87 is consistent with baryon entrainment from the circumnuclear matter with the observed density distribution. In microquasars, baryon loading triggered by interface instabilities is a probable reason for the low observed Lorentz factors. We show that the observed variability in gamma-ray bursts cannot come from mixing driven by interface instabilities and likely originates from the engine, suggesting the presence of magnetic fields in the jet.

Improved ship imaging algorithm for geosynchronous synthetic aperture radar (SAR) featured by subaperture time window selection optimization and inverse SAR translational compensation

An inverse synthetic aperture radar processing-based algorithm is improved for ship imaging in geosynchronous synthetic aperture radars (GEO SARs) to solve the technical challenges including long accumulation time and complex target motion characteristics. The improvement on the existing algorithm mainly involves four aspects. First, the formula for calculating the appropriate time length of subaperture is derived, according to the principle that the accumulated power of the ship’s echo corresponding to the subaperture duration ensures that the signal-to-noise ratio satisfies the requirement of GEO SARs. The derived formula solves the problem that how long the subaperture length should be taken with regards to a long accumulation time of GEO SAR when imaging ships. Second, we propose an optimization criterion for determining the appropriate subaperture time window by ensuring that the maximum number of ship pixels is detected in the subaperture image. The proposed criterion is used to optimize the location of the subaperture time window in the long accumulation time. Third, the SPECAN algorithm used in the scene imaging process is replaced by an improved nonlinear chirp scaling (NLCS) algorithm to improve the imaging accuracy of the scene. Our improvement on the traditional NLCS algorithm focuses on improving precisions of some of the formulas in the traditional algorithm. Furthermore, a translational compensation algorithm is proposed by considering the influence of spatial variance of slant range history of GEO SARs. The proposed translational compensation algorithm improves the compensation accuracy since the spatial variance of different scatterers in the scene is considered. A series of simulation experiments related with ship imaging in GEO SARs were carried out to verify the correctness of the proposed algorithm and the improvement on the imaging quality compared with that of the existing algorithm.