Nonlinear Bias Research Articles

The renormalization group for large-scale structure: origin of galaxy stochasticity

The renormalization group equations for large-scale structure (RG-LSS) describe how the bias and stochastic (noise) parameters — both of matter and biased tracers such as galaxies — evolve as a function of the cutoff Λ of the effective field theory. In previous work, we derived the RG-LSS equations for the bias parameters using the Wilson-Polchinski framework. Here, we extend these results to include stochastic contributions, corresponding to terms in the effective action that are higher order in the current J. We derive the general local interaction terms that describe stochasticity at all orders in perturbations,and a closed set of nonlinear RG equations for their coefficients. These imply thata single nonlinear bias term generates all stochastic moments through RG evolution. Further, theevolution is controlled by a different, lower scale than the nonlinear scale. This has implications for the optimal choice of the renormalization scale when comparing the theory with data to obtain cosmological constraints.

Fast simulation mapping: From standard to modified gravity cosmologies using the bias assignment method

Context. We assess the effectiveness of a non-parametric bias model in generating mock halo catalogues for modified gravity (MG) cosmologies, relying on the distribution of dark matter from either MG or Λ cold dark matter (ΛCDM) simulations. Aims. We aim to generate halo catalogues that effectively capture the distinct impact of MG, ensuring high accuracy in both two- and three-point statistics for a comprehensive analysis of large-scale structures. We investigated the inclusion of MG in non-local bias to directly map the tracers onto ΛCDM fields, which would significantly reduce computational costs. Methods. We employed the bias assignment method (BAM) to model halo distribution statistics by leveraging seven high-resolution COLA simulations of MG cosmologies. Taking cosmic-web dependences into account when learning the bias relations, we designed two experiments to map the MG effects: one utilising the consistent MG density fields and the other employing the benchmark ΛCDM density field. Results. BAM generates MG halo catalogues from both calibration experiments with excellent summary statistics, achieving a ~1% accuracy in the power spectrum across a wide range of k modes, with minimal differences well below 10% for modes subject to cosmic variance, particularly below k < 0.07 h Mpc−1. The reduced bispectrum remains consistent with the reference catalogues within 10% for the studied configuration. Our results demonstrate that a non-linear and non-local bias description can model the effects of MG starting from a ΛCDM field.

CLASS-OneLoop: accurate and unbiased inference from spectroscopic galaxy surveys

The power spectrum is the most commonly applied summary statistics to extract cosmological information from the observed three-dimensional distribution of galaxies in spectroscopic surveys. We present CLASS-OneLoop, a new numerical tool, fully integrated into the Boltzmann code CLASS, enabling the calculation of the one-loop power spectrum of biased tracers in spectroscopic surveys. Built upon the Eulerian moment expansion framework for redshift-space distortions, the implemented model incorporates a complete set of nonlinear biases, counterterms, and stochastic contributions, and includes the infrared resummation and the Alcock-Paczynski effect. The code features an evaluation of the loops by either direct numerical integration or Fast Fourier Transform, and employs a fast-slow parameter decomposition, which is essential for accelerating MCMC runs. After presenting performance and validation tests, as an illustration of the capabilities of the code, we apply it to fit the measured redshift-space halo power spectrum wedges on a ΛCDM subset of the AbacusSummit simulation suite and considering scales up to kmax = 0.3 h/Mpc. We find that the one-loop model adeptly recovers the fiducial cosmology of the simulation, while a simplified model commonly used in the literature for sensitivity forecasts yields significantly biased results. Furthermore, we conduct Monte Carlo Markov Chain (MCMC) forecasts for a DESI-like survey, considering a model with a dynamical dark energy component. Our results demonstrate the ability to independently constrain cosmological and nuisance parameters, even in the presence of a large parameter space with twenty-nine variables.

Uncertainty in Sea State Observations from Satellite Altimeters and Buoys during the Jason-3/Sentinel-6 MF Tandem Experiment

The Copernicus Sentinel-6 Michael Freilich (S6-MF) and Jason-3 (J3) Tandem Experiment (S6-JTEX) provided over 12 months of closely collocated altimeter sea state measurements, acquired in “low-resolution” (LR) and synthetic aperture radar “high-resolution” (HR) modes onboard S6-MF. The consistency and uncertainties associated with these measurements of sea state are examined in a region of the eastern North Pacific. Discrepancies in mean significant wave height (Hs, 0.01 m) and root-mean-square deviation (0.06 m) between J3 and S6-MF LR are found to be small compared to differences with buoy data (0.04, 0.29 m). S6-MF HR data are found to be highly correlated with LR data (0.999) but affected by a nonlinear sea state-dependent bias. However, the bias can be explained robustly through regression modelling based on Hs. Subsequent triple collocation analysis (TCA) shows very little difference in measurement error (0.18 ± 0.03 m) for the three altimetry datasets, when analysed with buoy data (0.22 ± 0.02 m) and ERA5 reanalysis (0.27 ± 0.02 m), although statistical precision, limited by total collocations (N = 535), both obscures interpretation and motivates the use of a larger dataset. However, we identify uncertainties in the collocation methodology, with important consequences for methods such as TCA. Firstly, data from some commonly used buoys are found to be statistically questionable, possibly linked to erroneous buoy operation. Secondly, we develop a methodology based on altimetry data to show how statistically outlying data also arise due to sampling over local sea state gradients. This methodology paves the way for accurate collocation closer to the coast, bringing larger collocation sample sizes and greater statistical robustness.

Learning View Synthesis for Desktop Telepresence with Few RGBD Cameras.

Recent telepresence systems have shown significant improvements in quality compared to prior systems. However, they struggle to achieve both low cost and high quality at the same time. In this work, we envision a future where telepresence systems become a commodity and can be installed on typical desktops. To this end, we present a high-quality view synthesis method that uses a cost-effective capture system that consists of commodity hardware accessible to the general public. We propose a neural renderer that uses a few RGBD cameras as input to synthesize novel views of a user and their surroundings. At the core of the renderer is Multi-Layer Point Cloud (MPC), a novel 3D representation that improves reconstruction accuracy by removing non-linear biases in depth cameras. Our temporally-aware renderer further improves the stability of synthesized videos by conditioning on past information. Additionally, we propose Spatial Skip Connections (SSC) to improve image upsampling under limited GPU memory. Experimental results show that our renderer outperforms recent methods in terms of view synthesis quality. Our method generalizes to new users and challenging content (e.g., hand gestures and clothing deformation) without costly per-video optimization, object templates, or heavy pre-processing. The code and dataset will be made available.

Effective mass function of radio meteoroids as a modulating factor in determining atmospheric scale height

Abstract A long-standing problem in meteor science has been the persistent presence of bias in the measured value of atmospheric scale heights obtained from radio meteor echoes. A common practice of fitting a linear function for bias correction follows the assumption that the systematic bias is devoid of seasonal asymmetry. This would be true if the mass and the velocity distribution of meteoroids remain invariant, both spatially and temporally. But so far no such convincing evidence has been published. On the contrary, fundamental arguments suggest that an universal mass function of radio meteoroids is counter-intuitive. This parameter cannot remain invariant due to the intrinsic variability in the meteor response function resulting from the Earth’s motion on the plane of ecliptic. In this paper, we show that an inverse relation exists between the width of meteor height distribution, expressed in unit of atmospheric scale height, and the exponent of the mass function. The overall mean of this exponent for the Sodankylä radar is 1.91 ± 0.02, modulated by a seasonal variation from the mean of the order of ∼±0.1. The stated inverse relation is applied to correct for the effect of mass distribution on the height distribution. Allowing for variable mass correction effectively removes the nonlinear bias in the measured scale heights in the meteor ionisation region.

A new LSTNet-based temperature prediction model for permanent magnet

Permanent magnet synchronous motors (PMSMs) can effectively protect against demagnetization by accurate permanent magnet (PM) temperature prediction; nevertheless, due to the nonlinear properties and intricate internal structure of PMSMs, accurate PM temperature prediction methods still encounter difficulties. This paper proposes a new PM temperature prediction model (LSTNet-Improved) based on long- and short-term time series network (LSTNet) to increase the prediction accuracy of PM temperature. By adding a multi-scale convolutional (MSC) layer to the convolutional neural network (CNN) layer of LSTNet, the short-term detail-dependent information between PMSM variables can be obtained by the model, and adds a CNN skip (CNN-skip) layer in place of the gate recurrent unite skip (GRU-skip) layer to find the long- and short-term local repetitive patterns between the variables, which yields additional feature information. Furthermore, a nonlinear bias term (MNB) is added to the original multi-head attention layer in order to solve the complex nonlinear relationship between multivariate time series. These layers are applied after the CNN-skip layer and gated recurrent unite (GRU) layers, respectively. This allows the model to become more robust and automatically learn to the complex nonlinear relationship between the sequences, focus on the important feature information, and lessen the impact of redundant information on the PMs’ temperature prediction task. The experimental results show that the goodness of fit (R2), root mean square error (RMSE) and mean absolute error (MAE) of the proposed model are 99.93%, 14.55% and 9.45%, respectively, and compared with LSTNet, the R2 is improved by 0.09%, the RMSE and MAE are reduced by 7.03% and 6.51%. These results confirm that the model can correctly predict the PM temperature, efficiently extract both long- and short-term patterns among the variables of the PMSM, and effectively focus on the key feature information in the intricate nonlinear series.

Variable structure bidimensional reference pattern-based anti-bias track to track association

Aiming at distributed sensors with nonlinear biases, this paper proposes an anti-bias track-to-track association algorithm named variable structure bidimensional reference pattern (VSBRP). Firstly, we theoretically analyze the limitations of the original reference-pattern (REP) in dealing with sensor nonlinear bias. Subsequently, to eliminate the adverse effects of sensor bias on track-to-track association, we reformulate the reference-pattern feature by organizing the position and velocity information, with the aim of estimating the relative bias using multiple dimensions of information. Additionally, we propose to regulate the structure of REP in real-time according to missed and false tracks, thereby improving the robustness of the target tracking system. Numerical simulations are performed to demonstrate the effectiveness and superiority of the proposed method.

Enhancing solids deposit prediction in gully pots with explainable hybrid models: A review.

Urban flooding has made it necessary to gain a better understanding of how well gully pots perform when overwhelmed by solids deposition due to various climatic and anthropogenic variables. This study investigates solids deposition in gully pots through the review of eight models, comprising four deterministic models, two hybrid models, a statistical model, and a conceptual model, representing a wide spectrum of solid depositional processes. Traditional models understand and manage the impact of climatic and anthropogenic variables on solid deposition but they are prone to uncertainties due to inadequate handling of complex and non-linear variables, restricted applicability, inflexibility and data bias. Hybrid models which integrate traditional models with data-driven approaches have proved to improve predictions and guarantee the development of uncertainty-proof models. Despite their effectiveness, hybrid models lack explainability. Hence, this study presents the significance of eXplainable Artificial Intelligence (XAI) tools in addressing the challenges associated with hybrid models. Finally, crossovers between various models and a representative workflow for the approach to solids deposition modelling in gully pots is suggested. The paper concludes that the application of explainable hybrid modeling can serve as a valuable tool for gully pot management as it can address key limitations present in existing models.

Reconciling the efficacy and effectiveness of masking on epidemic outcomes.

During the COVID-19 pandemic, mask wearing in public settings has been a key control measure. However, the reported effectiveness of masking has been much lower than laboratory measures of efficacy, leading to doubts on the utility of masking. Here, we develop an agent-based model that comprehensively accounts for individual masking behaviours and infectious disease dynamics, and test the impact of masking on epidemic outcomes. Using realistic inputs of mask efficacy and contact data at the individual level, the model reproduces the lower effectiveness as reported in randomized controlled trials. Model results demonstrate that transmission within households, where masks are rarely used, can substantially lower effectiveness, and reveal the interaction of nonlinear epidemic dynamics, control measures and potential measurement biases. Overall, model results show that, at the individual level, consistent masking can reduce the risk of first infection and, over time, reduce the frequency of repeated infection. At the population level, masking can provide direct protection to mask wearers, as well as indirect protection to non-wearers, collectively reducing epidemic intensity. These findings suggest it is prudent for individuals to use masks during an epidemic, and for policymakers to recognize the less-than-ideal effectiveness of masking when devising public health interventions.

Galaxy bias in the era of LSST: perturbative bias expansions

Upcoming imaging surveys will allow for high signal-to-noise measurements of galaxy clustering at small scales. In this work, we present the results of the Rubin Observatory Legacy Survey of Space and Time (LSST) bias challenge, the goal of which is to compare the performance of different nonlinear galaxy bias models in the context of LSST Year 10 (Y10) data. Specifically, we compare two perturbative approaches, Lagrangian perturbation theory (LPT) and Eulerian perturbation theory (EPT) to two variants of Hybrid Effective Field Theory (HEFT), with our fiducial implementation of these models including terms up to second order in the bias expansion as well as nonlocal bias and deviations from Poissonian stochasticity. We consider a variety of different simulated galaxy samples and test the performance of the bias models in a tomographic joint analysis of LSST-Y10-like galaxy clustering, galaxy-galaxy-lensing and cosmic shear. We find both HEFT methods as well as LPT and EPT combined with non-perturbative predictions for the matter power spectrum to yield unbiased constraints on cosmological parameters up to at least a maximal scale of k max = 0.4 Mpc-1 for all samples considered, even in the presence of assembly bias. While we find that we can reduce the complexity of the bias model for HEFT without compromising fit accuracy, this is not generally the case for the perturbative models. We find significant detections of non-Poissonian stochasticity in all cases considered, and our analysis shows evidence that small-scale galaxy clustering predominantly improves constraints on galaxy bias rather than cosmological parameters. These results therefore suggest that the systematic uncertainties associated with current nonlinear bias models are likely to be subdominant compared to other sources of error for tomographic analyses of upcoming photometric surveys, which bodes well for future galaxy clustering analyses using these high signal-to-noise data.

Nonlinear bias toward complex contagion in uncertain transmission settings.

Current epidemics in the biological and social domains are challenging the standard assumptions of mathematical contagion models. Chief among them are the complex patterns of transmission caused by heterogeneous group sizes and infection risk varying by orders of magnitude in different settings, like indoor versus outdoor gatherings in the COVID-19 pandemic or different moderation practices in social media communities. However, quantifying these heterogeneous levels of risk is difficult, and most models typically ignore them. Here, we include these features in an epidemic model on weighted hypergraphs to capture group-specific transmission rates. We study analytically the consequences of ignoring the heterogeneous transmissibility and find an induced superlinear infection rate during the emergence of a new outbreak, even though the underlying mechanism is a simple, linear contagion. The dynamics produced at the individual and group levels are therefore more similar to complex, nonlinear contagions, thus blurring the line between simple and complex contagions in realistic settings. We support this claim by introducing a Bayesian inference framework to quantify the nonlinearity of contagion processes. We show that simple contagions on real weighted hypergraphs are systematically biased toward the superlinear regime if the heterogeneity of the weights is ignored, greatly increasing the risk of erroneous classification as complex contagions. Our results provide an important cautionary tale for the challenging task of inferring transmission mechanisms from incidence data. Yet, it also paves the way for effective models that capture complex features of epidemics through nonlinear infection rates.

A nonlinear data-driven approach to bias correction of XCO2 for NASA's OCO-2 ACOS version 10

Abstract. Measurements of column-averaged dry air mole fraction of CO2 (termed XCO2) from the Orbiting Carbon Observatory-2 (OCO-2) contain systematic errors and regional-scale biases, often induced by forward model error or nonlinearity in the retrieval. Operationally, these biases are corrected for by a multiple linear regression model fit to co-retrieved variables that are highly correlated with XCO2 error. The operational bias correction is fit in tandem with a hand-tuned quality filter which limits error variance and reduces the regime of interaction between state variables and error to one that is largely linear. While the operational correction and filter are successful in reducing biases in retrievals, they do not allow for throughput or correction of data in which biases become nonlinear in predictors or features. In this paper, we demonstrate a clear improvement in the reduction in error variance over the operational correction by using a set of nonlinear machine learning models, one for land and one for ocean soundings. We further illustrate how the operational quality filter can be relaxed when used in conjunction with a nonlinear bias correction, which allows for an increase in sounding throughput by 14 % while maintaining the residual error in the operational correction. The method can readily be applied to future Atmospheric CO2 Observations from Space (ACOS) algorithm updates, to OCO-2's companion instrument OCO-3, and to other retrieved atmospheric state variables of interest.

Quantum nonlinear ac transport theory at low frequency

Based on the nonequilibrium Green’s function (NEGF), we develop a quantum nonlinear theory to study time-dependent ac transport properties in the low frequency and nonlinear bias voltage regimes. By expanding NEGF in terms of time to the linear order in Wigner representation, we can explicitly include the time-dependent self-consistent Coulomb interaction induced by external ac bias. Hence this theory automatically satisfies two basic requirements, i.e. current conservation and gauge invariance. Within this theory, the nonlinear ac current can be evaluated at arbitrarily large bias voltages under the low frequency limit. In addition, we obtain the expression of time-dependent current under the wide band limit and derive the relation between the nonlinear electrochemical capacitance and the bias voltage, which are very useful in predicting the dynamical properties of nanoelectronic devices. This quantum theory can be directly combined with density functional theory to investigate time-dependent ac transport from first-principles calculation.

Soliton polarization dynamics in a fiber laser of zero dispersion.

Polarization properties of a soliton generated in a fiber laser of zero dispersion are investigated. Similar to the solitons generated in a fiber laser of all anomalous dispersion, the polarization ellipse of the soliton rotated during pulse evolution inside the cavity. The number of rotations relies on the cavity averaged birefringence with nonlinear bias. The larger the cavity averaged birefringence is, the bigger the bias is. When the period multiplying of solitons appears, the number of rotations depends on both multiplying periods and the cavity averaged birefringence. Multiple polarization states can be observed at a fixed position in the cavity depending on the multiplying period. When the cavity length is equal to n times of the averaged beat length, the polarization ellipse of the soliton rotates n∗m times at a fixed position, where m is equal to the multiplying period.

Rapid quantitative analysis of Rongalite adulteration in rice flour using autoencoder and residual-based model associated with portable Raman spectroscopy

Rice flour is a raw material for various foods and is used as a substitute for wheat flour. However, some merchants adulterate rice flour with the illegal additive Rongalite to extend the shelf life and earn illegal profits. Rongalite is highly carcinogenic, and ingestion of more than 10 g can even cause death. high-performance liquid chromatography (HPLC) and mass spectrometry (MS) are currently the main methods for detecting food adulteration, however, the existing methods have many limitations, complex operation, expensive instrumentation, etc. Raman spectroscopy has the advantages of convenience and non-destructive samples, but Raman spectroscopy can be affected by interference such as fluorescence background that affects detection, in addition to the problem of difficult quantitative analysis due to nonlinear bias. In this article, we used the preprocessing method of Savitzky-Golay smoothing filtering and VTPspline to improve the quality of the spectra and proposed the SARNet, which combines autoencoder and residual network to achieve the quantitative analysis of Rongalite content in rice flour. The new model combines a linear model with a nonlinear model, which can solve the nonlinear problem effectively. Experiments showed that the new SARNet model achieved state-of-the-art results, achieving the best R2 of 0.9703 and RMSEP of 0.0075. The lowest Rongalite concentration detected by the portable Raman spectrometer was 0.49%. In summary, the proposed method using portable Raman spectroscopy combined with machine learning has low detection bias and high accuracy, which can realize quantitative analyses of adulterated Rongalite in rice flour quickly. The method provides an accurate and nondestructive analytical tool in the field of food detection.

Breaking the τT–f degeneracy of the kinetic Sunyaev–Zel’dovich cosmology in redshift space

ABSTRACT The ‘optical depth–linear growth rate’ (τT − f) degeneracy is a long-standing problem in the kinetic Sunyaev–Zel’dovich (kSZ) cosmology. It can be broken in redshift space, where the velocity field leaves its own distinct imprint on the galaxies’ redshift space positions and provides valuable information of the linear growth rate. We validate this idea with the Fisher matrix and Monte Carlo Markov chain techniques in this work, finding that the level of this degeneracy breaking is further enhanced on non-linear scales due to the non-linear evolution of the density and velocity fields, if we have a good prior knowledge of the non-linear bias of galaxies. This result emphasizes the importance of the redshift space analysis of the kSZ effect and its potential as a powerful cosmological probe, especially on non-linear scales. As a by-product, we develop a non-linear model of the redshift space density-weighted pairwise kSZ power spectrum. The fitted f and τT values from this model are shown to be accurate within 1σ–2σ ranges of the fiducial ones when confronted to the mock galaxies mimicking a DESI + CMB-S4 survey combination, even on small scales of k ∼ 0.5h Mpc−1.

KiDS-1000: Combined halo-model cosmology constraints from galaxy abundance, galaxy clustering, and galaxy-galaxy lensing

We present constraints on the flat Λ cold dark matter cosmological model through a joint analysis of galaxy abundance, galaxy clustering, and galaxy-galaxy lensing observables with the Kilo-Degree Survey. Our theoretical model combines a flexible conditional stellar mass function, which describes the galaxy-halo connection, with a cosmological N-body simulation-calibrated halo model, which describes the non-linear matter field. Our magnitude-limited bright galaxy sample combines nine-band optical-to-near-infrared photometry with an extensive and complete spectroscopic training sample to provide accurate redshift and stellar mass estimates. Our faint galaxy sample provides a background of accurately calibrated lensing measurements. We constrain the structure growth parameter to S8 = σ8√Ωm/0.3 =√0.773−0.030+0.028 and the matter density parameter to Ωm = 0.290−0.017+0.021. The galaxy-halo connection model adopted in the work is shown to be in agreement with previous studies. Our constraints on cosmological parameters are comparable to, and consistent with, joint ‘3 × 2pt’ clustering-lensing analyses that additionally include a cosmic shear observable. This analysis therefore brings attention to the significant constraining power in the often excluded non-linear scales for galaxy clustering and galaxy-galaxy lensing observables. By adopting a theoretical model that accounts for non-linear halo bias, halo exclusion, scale-dependent galaxy bias, and the impact of baryon feedback, this work demonstrates the potential for, and a way towards, including non-linear scales in cosmological analyses. Varying the width of the satellite galaxy distribution with an additional parameter yields a strong preference for sub-Poissonian variance, improving the goodness of fit by 0.18 in terms of the reduced χ2 value (and increasing the p-value by 0.25) compared to a fixed Poisson distribution.

Impact of climate change on hydrologic components using CORDEX Africa climate model in Gilgel Gibe 1 watershed Ethiopia

This study aimed to assess the impact of climate change on the hydrological components of Gilgel Gibe-1 using the ensemble of Coordinated Regional Climate Downscaling Experiments (CORDEX) Africa Domain namely REMO2009, HIRAM5, CCLM4-8 and RCA4 Regional Climate Models (RCMs) simulations. The performance of these RCM models was evaluated using the observed data from 1985 to 2005 and the ensemble was shown to simulate rainfall and air temperature better than individual RCMs. Then the RCMs ensemble data for historical and future projections from 2026 to 2055 years under RCP4.5 and RCP8.5 were corrected for bias and used to evaluate the impact of climate change. A non-linear bias correction and the monthly mean biases corrections method is used to adjust precipitation and temperature respectively. The future projection shows that; rainfall is expected to increase from August to December with maximum values of 1.97–235.23% under RCP4.5. The maximum temperature is expected to increase with maximum value of 1.62 °C under RCP8.5 in the study area. The calibrated and validated Soil and Water Assessment Tool (SWAT) model was used to investigate the impact of climate change on hydrologic components such as surface runoff, lateral flow, water yield, evapotranspiration and sediment yield. The SWAT model was calibrated and validated using monthly stream flow with the statistical performance of R2 value of 0.82 and NSE value of 0.72 for calibration and R2 of 0.79 and NSE of 0.67 for validation. Surface runoff and sediment yield are expected to increase from August to December under RCP4.5 and from August to February under RCP8.5. Overall both surface runoff and sediment yield are expected to increase in the future.

Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model

A Multifractional Process with Random Exponent (MPRE) is used to model the dynamics of log-prices in a financial market. Under this assumption, we show that the Hurst-Hölder exponent of the MPRE follows the fractional Ornstein–Uhlenbeck process which in the Fractional Stochastic Volatility Model of Comte and Renault (1998) describes the dynamics of the log-volatility. We provide evidence that several biases of the estimation procedures can generate artificial rough volatility in surrogated as well as real financial data.