non-Gaussian Effects Research Articles

High-Precision Retrieving Ocean Parameters Based on a New Improved Second-Order Model With Considering Non-Gaussian Effects

High-Precision Retrieving Ocean Parameters Based on a New Improved Second-Order Model With Considering Non-Gaussian Effects

Exploring the effects of primordial non-Gaussianity at galactic scales

While large scale primordial non-Gaussianity is strongly constrained by present-day data, there are no such constraints at Mpc scales. Here we investigate the effect of significant small-scale primordial non-Gaussianity on structure formation and the galaxy formation process with collisionless simulations: specifically, we explore four different types of non-Gaussianities. All of these prescriptions lead to a distinct and potentially detectable feature in the matter power spectrum around the non-linear scale. The feature might have interesting consequences for the S 8 tension. We then show in particular that a negatively-skewed distribution of the potential random field, hence positively skewed in terms of overdensities, with f NL of the order of 1000 at these scales, implies that typical galaxy-sized halos reach half of their present-day mass at an earlier stage and have a quieter merging history at z < 3 than in the Gaussian case. Their environment between 0.5 and 4 virial radii at z = 0 is less dense than in the Gaussian case. This quieter history and less dense environment has potentially interesting consequences in terms of the formation of bulges and bars. Moreover, we show that the two most massive subhalos around their host tend to display an interesting anti-correlation of velocities, indicative of kinematic coherence. All these hints will need to be statistically confirmed in larger-box simulations with scale-dependent non-Gaussian initial conditions, followed by hydrodynamical zoom-in simulations to explore the detailed consequences of small-scale non-Gaussianities on galaxy formation.

Effects of finite non-Gaussianity on evolution of a random wind wave field.

We examine the long-term evolution of a random wind wave field generated by constant forcing, by comparing numerical simulations of the kinetic equationand direct numerical simulations (DNS) of the dynamical equations. While the integral characteristics of the spectra are in reasonably good agreement, the spectral shapes differ considerably at large times, the DNS spectral shape being in much better agreement with field observations. Varying the number of resonant and approximately resonant wave interactions in the DNS numerical scheme, we show that when the ratio of nonlinear and linear parts of the Hamiltonian tends to zero, the DNS spectral shape approaches the shape predicted by the kinetic equation. We attribute the discrepancies between the kinetic equationmodeling, on one side, and the DNS and observations, on the other, to the neglect of non-Gaussianity in the derivation of the kinetic equation.

Non-Gaussianity effects on the primordial black hole abundance for sharply-peaked primordial spectrum

We perturbatively study the effect of non-Gaussianities on the mass fraction of primordial black holes (PBHs) at the time of formation by systematically taking its effect into account in the one-point probability distribution function of the primordial curvature perturbation. We focus on the bispectrum and trispectrum and derive formulas that describe their effects on the skewness and kurtosis of the distribution function. Then considering the case of narrowly peaked spectra, we obtain simple formulas that concisely express the effect of the bi- and trispectra. In particular, together with the g NL and τ NL parameters of the trispectrum, we find that non-Gaussianity parameters for various types of the bispectrum are linearly combined to give an effective parameter, f NL eff, that determines the PBH mass fraction in the narrow spectral shape limit.

Bistatic Radar Scattering from Non-Gaussian Height Distributed Rough Surfaces

In modeling a rough surface, it is common to assume a Gaussian height distribution. This hypothesis cannot describe an eventual asymmetry between crests and troughs of natural surfaces. We analyzed the bistatic scattering from a rough surface with non-Gaussian height distributions using the Kirchhoff scattering theory. Two extreme cases of Gamma-distributed surfaces were compared in particular: exponential and Gaussian distributions. The bistatic angular dependence was examined under various root mean square (RMS) heights and power spectrum densities. Contribution sources to the coherent and incoherent scattering components were singled out relating to the surface height distribution. For an exponential height surface, the coherent scattering strengthens even as the surface becomes rough. The non-Gaussian effect on the incoherent scattering is connected with surface power spectrum density. The height distribution impacts differ in the different regions of the bistatic scattering plane and thus complicate the differentiation of the scattering patterns due to height distribution.

Uncertainty quantification of turbulent systems via physically consistent and data-informed reduced-order models

This work presents a data-driven, energy-conserving closure method for the coarse-scale evolution of the mean and covariance of turbulent systems. Spatiotemporally non-local neural networks are employed for calculating the impact of non-Gaussian effects to the low-order statistics of dynamical systems with an energy-preserving quadratic nonlinearity. This property, which characterizes the advection term of turbulent flows, is encoded via an appropriate physical constraint in the training process of the data-informed closure. This condition is essential for the stability and accuracy of the simulations as it appropriately captures the energy transfers between unstable and stable modes of the system. The numerical scheme is implemented for a variety of turbulent systems, with prominent forward and inverse energy cascades. These problems include prototypical models such as an unstable triad system and the Lorentz-96 system, as well as more complex models: The two-layer quasi-geostrophic flows and incompressible, anisotropic jets where passive inertial tracers are being advected on. Training data are obtained through high-fidelity direct numerical simulations. In all cases, the hybrid scheme displays its ability to accurately capture the energy spectrum and high-order statistics of the systems under discussion. The generalizability properties of the trained closure models in all the test cases are explored, using out-of-sample realizations of the systems. The presented method is compared with existing first-order closure schemes, where only the mean equation is evolved. This comparison showcases that correctly evolving the covariance of the system outperforms first-order schemes in accuracy, at the expense of increased computational cost.

Peaks and primordial black holes: the effect of non-Gaussianity

In light of recent developments in the field, we re-evaluate the effect of local-type non-Gaussianity on the primordial black hole (PBH) abundance (and consequently, upon constraints on the primordial power spectrum arising from PBHs). We apply peaks theory to the full, non-linear compaction, finding that, whilst the effect of non-Gaussianity is qualitatively similar to previous findings, the effect is much less significant. It is found the non-Gaussianity parameters f NL local and g NL local typically need to be approximately 1 or 2 orders of magntiude larger respectively to have a similar to that previously found. The effect will be to weaken the dependance of PBH constraints on the primordial power spectrum on the non-Gaussianity parameters, as well as to dramatically weaken constraints on the non-Gaussianity parameters (and/or PBH abundance) arising from the non-observation of dark matter isocurvature modes. We also consider the correlation between the curvature perturbation ζ and the compaction C, finding that, whilst PBHs may form at rare peaks in C these do not necessarily correspond to rare peaks in ζ — casting some doubt on many of the existing calculations of the PBH abundance.

Functional Data Analysis for Extracting the Intrinsic Dimensionality of Spectra: Application to Chemical Homogeneity in the Open Cluster M67

Abstract High-resolution spectroscopic surveys of the Milky Way have entered the Big Data regime and have opened avenues for solving outstanding questions in Galactic archeology. However, exploiting their full potential is limited by complex systematics, whose characterization has not received much attention in modern spectroscopic analyses. In this work, we present a novel method to disentangle the component of spectral data space intrinsic to the stars from that due to systematics. Using functional principal component analysis on a sample of 18,933 giant spectra from APOGEE, we find that the intrinsic structure above the level of observational uncertainties requires ≈10 functional principal components (FPCs). Our FPCs can reduce the dimensionality of spectra, remove systematics, and impute masked wavelengths, thereby enabling accurate studies of stellar populations. To demonstrate the applicability of our FPCs, we use them to infer stellar parameters and abundances of 28 giants in the open cluster M67. We employ Sequential Neural Likelihood, a simulation-based Bayesian inference method that learns likelihood functions using neural density estimators, to incorporate non-Gaussian effects in spectral likelihoods. By hierarchically combining the inferred abundances, we limit the spread of the following elements in M67: Fe ≲ 0.02 dex; C ≲ 0.03 dex; O, Mg, Si, Ni ≲ 0.04 dex; Ca ≲ 0.05 dex; N, Al ≲ 0.07 dex (at 68% confidence). Our constraints suggest a lack of self-pollution by core-collapse supernovae in M67, which has promising implications for the future of chemical tagging to understand the star formation history and dynamical evolution of the Milky Way.

Minkowski functionals and the nonlinear perturbation theory in the large-scale structure: Second-order effects

The second-order formula of Minkowski functionals in weakly non-Gaussian fields is compared with the numerical $N$-body simulations. Recently, the weakly non-Gaussian formula of Minkowski functionals is extended to include the second-order effects of non-Gaussianity in general dimensions. We apply this formula to the three-dimensional density field in the large-scale structure of the Universe. The parameters of the second-order formula include several kinds of skewness and kurtosis parameters. We apply tree level of nonlinear perturbation theory to estimate these parameters, including novel calculations of quartic cumulants. First we compare the theoretical values with those of numerical simulations on the basis of parameter values, and next we test the performance of the analytic formula combined with the perturbation theory. The second-order formula outperforms the first-order formula in general. The performance of the perturbation theory depends on the smoothing radius applied in defining the Minkowski functionals. The quantitative comparisons are presented in detail.

Non-Gaussian effects of the Saha\u2019s ionization in the early universe

Tsallis’ thermostatistical has received increasing attention due to its success in describing phenomena that manifest unusual thermodynamic properties. In this context, the generalized Saha equation must follow a condition of generalized thermal equilibrium of matter and radiation. The present work aims to explore the non-Gaussian effects on Saha’s ionization via Tsallis statistics. To accomplish this, we generalized the number density taking into account a non-Gaussian Fermi-Dirac distribution and then set out the Saha equation for the cosmological recombination. As a result, we highlight two new non-Gaussian effects: (i) two generalized chemical equilibrium conditions, one for the relativistic regime and the other for the non-relativistic one; and (ii) the hydrogen binding q-energy. We demonstrated that to yield smooth shifts in the binding energy, the a-parameter must be very small. We also showed that binding q-energy exhibits symmetrical behavior around the value of the standard binding energy. Besides, we used the q-energy in order to access other hydrogen energy levels, and we ascertained the values of the a-parameter that access those levels and their relationship to temperature. Finally, we employed these results to examine the non-Gaussian effects of the deuterium bottleneck, recombination, and the particle anti-particle excess.

Features of transport in non-Gaussian random porous systems

The goal of this work is to employ a semi-analytical framework to investigate key features associated with the transport behavior of an inert solute in non-Gaussian random fields. We focus our analysis on the transport dynamics of a solute plume through a porous medium characterized by spatially heterogeneous non-Gaussian log-conductivity fields, Y. We rest on a stochastic Lagrangian framework to provide semi-analytical formulations to evaluate the statistical moments and cumulative distribution function (CDF) of solute concentration. The heterogeneous structure of the log-conductivity field is modeled as a Generalized Sub-Gaussian process. This model has been shown to capture non-Gaussian and scale-dependent features displayed by several variables, including key parameters of porous media. Our results suggest that the effects of non-Gaussianity in Y on solute concentration statistics are more pronounced at locations near the solute source zone and at early times. The impact of the analyzed non-Gaussian nature of the field of Y is also significant at the lower tails of the distribution. We also explore conditions under which when the concentration CDF in Generalized Sub-Gaussian Y fields can be approximated by the widely used beta distribution. Furthermore, the methodology used in this work is an alternative to the commonly used numerical Monte Carlo method and can be employed as a benchmark tool in computational stochastic mass transport problems in porous media.

Multi-wavelength spectroscopic probes: prospects for primordial non-Gaussianity and relativistic effects

Next-generation cosmological surveys will observe larger cosmic volumes than ever before, enabling us to access information on the primordial Universe, as well as on relativistic effects. We consider forthcoming 21cm intensity mapping surveys (SKAO) and optical galaxy surveys (DESI and Euclid), combining the information via multi-tracer cross-correlations that suppress cosmic variance on ultra-large scales.In order to fully incorporate wide-angle effects and redshift-bin cross-correlations, together with lensing magnification and other relativistic effects, we use the angular power spectra, Cℓ (zi ,zj ). Applying a Fisher analysis, we forecast the expected precision on f NL and the detectability of lensing and other relativistic effects. We find that the full combination of two pairs of 21cm and galaxy surveys, one pair at low redshift and one at high redshift, could deliver σ(f NL) ∼ 1.5, detect the Doppler effect with a signal-to-noise ratio ∼8 and measure the lensing convergence contribution at ∼2% precision. In a companion paper, we show that the best-fit values of f NL and of standard cosmological parameters are significantly biased if the lensing contribution neglected.

Double-peaked inflation model: Scalar induced gravitational waves and primordial-black-hole suppression from primordial non-Gaussianity

A significant abundance of primordial black hole (PBH) dark matter can be produced by curvature perturbations with power spectrum $\Delta_\zeta^2(k_{\mathrm{peak}})\sim \mathcal{O}(10^{-2})$ at small scales, associated with the generation of observable scalar induced gravitational waves (SIGWs). However, the primordial non-Gaussianity may play a non-negligible role, which is not usually considered. We propose two inflation models that predict double peaks of order $\mathcal{O}(10^{-2})$ in the power spectrum and study the effects of primordial non-Gaussianity on PBHs and SIGWs. This model is driven by a power-law potential, and has a noncanonical kinetic term whose coupling function admits two peaks. By field-redefinition, it can be recast into a canonical inflation model with two quasi-inflection points in the potential. We find that the PBH abundance will be altered saliently if non-Gaussianity parameter satisfies $|f_{\mathrm{NL}}(k_{\text{peak}},k_{\text{peak}},k_{\text{peak}})|\gtrsim \Delta^2_{\zeta}(k_{\mathrm{peak}})/(23\delta^3_c) \sim \mathcal{O}(10^{-2})$. Whether the PBH abundance is suppressed or enhanced depends on the $f_{\mathrm{NL}}$ being positive or negative, respectively. In our model, non-Gaussianity parameter $f_{\mathrm{NL}}(k_{\mathrm{peak}},k_{\mathrm{peak}},k_{\mathrm{peak}})\sim \mathcal{O}(1)$ takes positive sign, thus PBH abundance is suppressed dramatically. On the contrary, SIGWs are insensitive to primordial non-Gaussianity and hardly affected, so they are still within the sensitivities of space-based GWs observatories and Square Kilometer Array.

Variance of the fatigue damage in non-Gaussian stochastic processes with narrow-band power spectrum

This paper presents two theoretical models to assess the variance of the fatigue damage in stationary narrow-band and non-Gaussian stochastic processes. The models extend two solutions existing in the literature and restricted to Gaussian processes. The new models here developed exploit a non-linear transformation that links Gaussian and non-Gaussian domains based on skewness and kurtosis coefficients, which are used to quantify the deviation from the Gaussian distribution. Monte Carlo numerical simulations in time-domain are performed to confirm the correctness of the proposed non-Gaussian models, and to investigate the sensitivity of the variance of the damage to the skewness, kurtosis, and inverse slope of the stress versus life (S-N) curve. An example is finally presented to demonstrate the increase of the failure probability due to non-Gaussian effects in the stochastic loading.

Non-extensive processes associated with heating of the Galactic disc

We analyse the mechanisms ruling galactic disc heating through the dynamics of space velocities U, V and W, extracted from the Geneva-Copenhagen catalogue. To do this, we use a model based on non-extensive statistical mechanics, where we derive the probability distribution functions that quantify the non-Gaussian effects. Furthermore, we find that the deviation q –1 at a given stellar age follows a non-random behaviour. As a result, the q-index behaviour indicates that the vertical component W, perpendicular to the Galactic plane, does not “heat up” at random, which is in disagreement with previous works that attributed the evolution of W to randomness. Finally, our results bring a new perspective to this matter and open the way for studying Galactic kinematic components through the eyes of more robust statistical models that consider non-Gaussian effects.The authors would like to dedicate this paper to all the victims of the COVID-19 pandemic around the world.

Dynamics identification and forecasting of COVID-19 by switching Kalman filters.

The COVID-19 pandemic has captivated scientific activity since its early days. Particular attention has been dedicated to the identification of underlying dynamics and prediction of future trend. In this work, a switching Kalman filter formalism is applied on dynamics learning and forecasting of the daily new cases of COVID-19. The main feature of this dynamical system is its ability to switch between different linear Gaussian models based on the observations and specified probabilities of transitions between these models. It is thus able to handle the problem of hidden state estimation and forecasting for models with non-Gaussian and nonlinear effects. The potential of this method is explored on the daily new cases of COVID-19 both at the state-level and the country-level in the US. The results suggest a common disease dynamics across states that share certain features. We also demonstrate the ability to make short to medium term predictions with quantifiable error bounds.

A new track fitting algorithm dedicated for handling non-Gaussian detector effects using flexible and parameterized models

We present a new track fitting algorithm for high energy physics experiments dedicated for handling the non-Gaussian detector effects. It uses a comprehensive propagation model to predict the particle trajectory, as well as flexible and parameterized models (FPM method) to describe the contributions from multiple scattering, to estimate of the positions of hits, and to calculate the energy losses. The track fitting algorithm with the FPM method then minimizes a global non-linear chi-square function to obtain the full information of a track.

Quantum work statistics close to equilibrium

We study the statistics of work, dissipation, and entropy production of a quantum quasi-isothermal process, where the system remains close to the thermal equilibrium along the transformation. We derive a general analytic expression for the work distribution and the cumulant generating function. All work cumulants split into a classical (non-coherent) and quantum (coherent) term, implying that close to equilibrium there are two independent channels of dissipation at all levels of the statistics. For non-coherent or commuting protocols, only the first two cumulants survive, leading to a Gaussian distribution with its first two moments related through the classical fluctuation-dissipation relation. On the other hand, quantum coherence leads to positive skewness and excess kurtosis in the distribution, and we demonstrate that these non-Gaussian effects are a manifestation of asymmetry in relation to the resource theory of thermodynamics. Furthermore, we also show that the non-coherent and coherent contributions satisfy independently the Evans-Searles fluctuation theorem, which sets strong bounds on the statistics, with negative values of the dissipation being exponentially suppressed. Our findings are illustrated in a driven two-level system and an Ising chain, where quantum signatures of the work distribution in the macroscopic limit are discussed.

Multimode CV‐QKD with non‐Gaussian operations

Non-Gaussian operations have been studied intensively in recent years due to their ability to increase the secret key rate for certain CV-QKD protocols. However, most previous studies on such protocols are carried out in a single-mode setting, even though in reality any quantum state contains multi-mode components in frequency space. In this work we investigate the use of non-Gaussian operations in a multi-mode CV-QKD system. Our main finding is that, contrary to single-mode CV-QKD systems, in generic multi-mode CV-QKD systems it is possible to use non-Gaussian operations to increase the optimized secret key rate. More specifically, we find that at losses of order 30dB, which represents a distance of order 160km and the effective maximum distance for CV-QKD, the key rate for multi-mode non-Gaussian operations can be orders of magnitude higher than single-mode operations. Our results are important for real-world CV-QKD systems especially those dependent on quantum error correction - a process that requires non-Gaussian effects.

PBH in single field inflation: the effect of shape dispersion and non-Gaussianities

Primordial black holes (PBHs) may result from high peaks in a random field of cosmological perturbations. In single field inflationary models, such perturbations can be seeded as the inflaton overshoots a small barrier on its way down the potential. PBHs are then produced through two distinct mechanisms, during the radiation era. The first one is the familiar collapse of large adiabatic overdensities. The second one is the collapse induced by relic bubbles where the inflaton field is trapped in a false vacuum. The latter are due to rare backward fluctuations of the inflaton which prevented it from overshooting the barrier in horizon sized regions. We consider (numerically and analytically) the effect of non-Gaussianities on the threshold for overdensities to collapse into a PBH. Since typical high peaks have some dispersion in their shape or profile, we also consider the effect of such dispersion on the corresponding threshold for collapse. With these results we estimate the most likely channel for PBH production as a function of the non-Gaussianity parameter fNL. We also compare the threshold for collapse coming from the perturbative versus the non perturbative template for the non-Gaussianity arising in this model. We show that i) for fNL ≳ 3.5, the population of PBH coming from false vacuum regions dominates over that which comes from the collapse of large adiabatic overdensities, ii) the non-perturbative template of the non-Gaussianities is important to get accurate results. iii) the effect of the dispersion is small in determining the threshold for the compaction function, although it can be appreciable in determining the threshold amplitude for the curvature perturbation at low fNL. We also confirm that the volume averaged compaction function provides a very accurate universal estimator for the threshold.