Higher Order Statistics Research Articles

Furutsu-Novikov–like Cross-Correlation–Response Relations for Systems Driven by Shot Noise

We consider a dynamic system that is driven by an intensity-modulated Poisson process with intensity Λ(t)=λ(t)+ϵν(t). We derive an exact relation between the input-output cross-correlation in the spontaneous state (ϵ=0) and the linear response to the modulation (ϵ>0). If ϵ is sufficiently small, linear-response theory captures the full response. The relation can be regarded as a variant of the Furutsu-Novikov theorem for the case of shot noise. As we show, the relation is still valid in the presence of additional independent noise. Furthermore, we derive an extension to Cox-process input, which provides an instance of colored shot noise. We discuss applications to particle detection and to neuroscience. Using the new relation, we obtain a fluctuation-response relation for a leaky integrate-and-fire neuron. We also show how the new relation can be used in a remote control problem in a recurrent neural network. The relations are numerically tested for both stationary and nonstationary dynamics. Lastly, extensions to marked Poisson processes and to higher-order statistics are presented. Published by the American Physical Society 2024

Radiomics-Based Diagnosis in Dentomaxillofacial Radiology: A Systematic Review.

Radiomics is a quantitative tool for digital image analysis. This systematic review aims to investigate the scientific articles to evaluate the potential implications of Radiomics analysis in Dentomaxillofacial Radiology (DMFR). Studies regarding Radiomics applications in DMFR and human samples, in vivo study, a case reports/series if ≧5 samples were included, while case reports/series if < 5 samples, articles other than in English, abstracts without full text, and studies published before 2015 were excluded. Fifty-one articles were selected from 3789 literatures. The QUADAS-2 tool was used for risk of bias assessment. The accuracy of predicting dentomaxillofacial pathologies was considered as the primary outcome, and the modeling type of Radiomics was considered as the secondary outcome. A meta-analysis could not be performed due to the lack of information and standardization among the reported accuracies. The reported accuracies were found between 0.66 and 99.65%. Logistic regression (n = 6) was found to be the most common Radiomics modeling type, followed by Support Vector Machine and Decision Tree (n = 5). Second-order statistics (n = 38) was the most common type of Radiomics application, followed by first-order (n = 26), higher-order (n = 20), and shape-based (n = 15) statistics. Further work is needed to increase standardization in the Radiomics workflow. Quantitative image analysis is an alternative tool for conventional visual radiographic evaluation. Radiomics systems depend on elements such as imaging modality, feature type, data mining, or statistical method. Radiomics applications do not justify digital transformation on their own, but the potential of its integration into the digital workflow is considerable.

Spectra data calibration based on deep residual modeling of independent component regression

Independent component regression (ICR) has recently become quite popular in spectra data calibration, due to its advantages in non-Gaussian data modeling and high-order statistics feature extraction. Inspired by the idea of deep learning, this paper extends the basic ICR model to the deep form by introducing a layer-wise residual learning strategy. Based on the residual information generated from last layer of the deep learning model, more and more different patterns of independent components can be extracted layer-by-layer. Then, a further information compression step is taken to combine and also to condense those independent components obtained from different layers of the deep model. Two detailed benchmark case studies are implemented to evaluate the calibration performance of the develop model, based on which the effectiveness of both layer-by-layer component extraction and further information compression are well confirmed.

Under-Determined DOA Estimation: A Method Based on Higher-Order Statistics and Non-Uniform Arrays

Under-Determined DOA Estimation: A Method Based on Higher-Order Statistics and Non-Uniform Arrays

Theoretical wavelet ℓ1-norm from one-point probability density function prediction

Context. Weak gravitational lensing, which results from the bending of light by matter along the line of sight, is a potent tool for exploring large-scale structures, particularly in quantifying non-Gaussianities. It is a pivotal objective for upcoming surveys. In the realm of current and forthcoming full-sky weak-lensing surveys, convergence maps, which represent a line-of-sight integration of the matter density field up to the source redshift, facilitate field-level inference. This provides an advantageous avenue for cosmological exploration. Traditional two-point statistics fall short of capturing non-Gaussianities, necessitating the use of higher-order statistics to extract this crucial information. Among the various available higher-order statistics, the wavelet ℓ1 -norm has proven its efficiency in inferring cosmology. However, the lack of a robust theoretical framework mandates reliance on simulations, which demand substantial resources and time. Aims. Our novel approach introduces a theoretical prediction of the wavelet ℓ1-norm for weak-lensing convergence maps that is grounded in the principles of large-deviation theory. This method builds upon recent work and offers a theoretical prescription for an aperture mass one-point probability density function. Methods. We present for the first time a theoretical prediction of the wavelet ℓ1-norm for convergence maps that is derived from the theoretical prediction of their one-point probability distribution. Additionally, we explored the cosmological dependence of this prediction and validated the results on simulations. Results. A comparison of our predicted wavelet ℓ1 -norm with simulations demonstrates a high level of accuracy in the weakly nonlinear regime. Moreover, we show its ability to capture cosmological dependence. This paves the way for a more robust and efficient parameter-inference process.

Exact average many-body interatomic interaction model for random alloys

Understanding the physical origin of mechanisms in random alloys that lead to the formation of microstructures requires an understanding of their average behavior and, equally important, the role of local fluctuations around the average. Material properties of random alloys can be computed using direct simulations on random configurations. However, some properties are very difficult to compute, for others it is not even fully understood how to compute them using random sampling, in particular, interaction energies between multiple defects. To that end, we develop an atomistic model that does the averaging on the level of interatomic potentials. With such an average interatomic interaction model the problem of averaging via random sampling is bypassed since the problem of computing material properties on random configurations reduces to the problem of computing material properties on single crystals, the average alloy, which can be done using standard techniques.To be predictive, we develop our average model on the class of linear machine-learning interatomic potentials (MLIPs). To that end, using tools from higher-order statistics, we derive an analytic expansion of average many-body per-atom energies of linear MLIPs in terms of average tensor products of the feature vectors of the underlying machine-learning model that scales linearly with the size of an atomic neighborhood. In order to avoid forming higher-order tensors composed of products of feature vectors, we develop an implementation using equivariant tensor network (ETN) potentials, a class of linear MLIPs, that contracts the feature vectors to small-sized tensors, and then takes the average. We validate the average ETN potential by demonstrating the convergence of direct Monte Carlo simulations to the exact value for properties of the NbMoTaW medium-entropy alloy. Simulating average properties of dislocations has thus far only been possible with average embedded atom method potentials that, however, predict artificial polarized cores. Here, we show that average ETN potentials predict the compact screw dislocation core structure, in agreement with density functional theory. Hence, we anticipate that our model will become useful for understanding mechanistic origins of material properties and for developing predictive models of mechanical properties of random alloys.

Identification of ocular artifact in EEG signals using VMD and Hurst exponent.

Electroencephalographic (EEG) readings are usually infected with unavoidable artifacts, especially physiological ones. One such physiological artifact is the ocular artifacts (OAs) that are generally related to eyes and are characterized by high magnitude and a specific spike pattern in the prefrontal region of the brain. During the long-duration EEG acquisition, the retrieval of important information becomes quite complicated in prefrontal regions as ocular artifacts dominate the EEG recorded, making it difficult to discern underlying brain activity. With the progress and development in signal processing techniques, artifact handling has become a progressive field of investigation. This paper presents a framework for the detection and correction of ocular artifacts. This study emphasizes improving the quality and reducing the time complexity by using higher-order statistics (HOS) for artifact identification and variational mode decomposition (VMD) for OA correction. An overall SNR of 14 dB, MAE of 0.09, and PSNR of 33.59 dB has been attained by the proposed framework. It was observed that the proposed HOS-VMD surpassed the state-of-the-art mode decomposition techniques.

Third-order intrinsic alignment of SDSS BOSS LOWZ galaxies

Cosmic shear is a powerful probe of cosmology, but it is affected by the intrinsic alignment (IA) of galaxy shapes with the large-scale structure. Upcoming surveys such as Euclid and Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) require an accurate understanding of IA, particularly for higher-order cosmic shear statistics that are vital for extracting the most cosmological information. In this paper, we report the first detection of third-order IA correlations using the LOWZ galaxy sample from the Sloan Digital Sky Survey (SDSS) Baryon Oscillation Spectroscopic Survey (BOSS). We compare our measurements with predictions from the MICE cosmological simulation and an analytical model inspired by the Non-linear Linear Alignment (NLA) model and informed by second-order correlations. We also explore the dependence of the third-order correlation on the galaxies' luminosity. We find that the amplitude $A_ IA $ of the IA signal is non-zero at the $4.7 level for scales between Mpc Mpc Mpc Mpc $ the inferred $A_ IA $ agrees both with the prediction from the simulation and estimates from second-order statistics within 1sigma but deviations arise at smaller scales. Our results demonstrate the feasibility of measuring third-order IA correlations and using them for constraining IA models. The agreement between second- and third-order IA constraints also opens the opportunity for a consistent joint analysis and IA self-calibration, promising tighter parameter constraints for upcoming cosmological surveys.

Comparisons of experimentally and numerically determined statistics for predicting low-occurrence wind speeds around a 1:1:2 block model

Accurate prediction of low-occurrence wind speeds around urban structures is crucial for safe building design. Although Large-eddy simulation (LES) is commonly used as a high-fidelity model as compared with the Reynolds-Averaged Navier–Stokes (RANS) simulations, the present validation process relies on the comparison of fundamental statistics of the mean and standard deviations. The discrepancies in LESs and wind-tunnel experiments (WTEs) are unclear in terms of physical quantities characterizing the unsteadiness of the simulated turbulent flow such as probability density and power spectral densities, and low-occurrence winds speeds. Therefore, this study aims to evaluate the effectiveness of LES in predicting unsteady wind behavior around a 1:1:2 block model. The study identifies prominent differences to improve the accuracy of unsteady numerical simulations especially for the purpose of predicting low-occurrence wind speeds. Various advection schemes in LESs were investigated, including first-order upwind, second-order linear, and dynamic interpolation schemes. The results show significant discrepancies, particularly in higher-order statistics and low-occurrence wind speeds, with WTE consistently exhibiting higher energy levels across all frequencies. These findings highlight the need to refine advection schemes to enhance their predictive accuracy. LESs with minimal numerical errors from discretization schemes can substantially improve urban wind assessments and contribute to the design of safer structures.

A novel method for estimating avian roost sizes using passive acoustic recordings

Abstract Communal bird roosts serve as information centres and a means of thermoregulation for many species. While some communally roosting species are major pests and cause dis‐amenities, others are of conservation concern. Estimating the population of roosting birds can provide a useful proxy of population size and possibly a more reliable estimate than other sampling techniques. However, estimating these populations is challenging as some roosts are large and often occluded in foliage. Previous acoustic methods such as paired sampling, microphone arrays and use of call rate have been used to estimate bird abundances; however, these are less suited for estimating large roost populations where hundreds of individuals are calling in unison. To address this challenge, we explored using machine learning techniques to estimate a roost population of the Javan myna, Acridotheres javanicus, an invasive species in Singapore. While one may expect to use sound intensity to estimate roost sizes, it is affected by various factors such as distance to the recorder, local propagation conditions (e.g. buildings and trees), weather conditions, and noise from other sources. Here, we used a deep neural network to extract higher order statistics from the sound recordings and use those to help estimate roost sizes. Additionally, we validated our method using automated visual analysis with a dual‐camera setup and manual bird counts. Our estimated bird counts over time using our acoustic model matched the automated visual estimates and manual bird counts at a selected Javan myna roost, thus validating our approach. Our acoustic model estimated close to 400 individual mynas roosting in a single tree. Analyses of additional recordings of Javan myna roosts conducted on two separate occasions and at a different roost location using our acoustic model showed that our roost estimates over time also matched our automated visual estimates well. Practical implication: Our novel approach of estimating communal roost sizes can be achieved robustly using a simple portable acoustic recording system. Our method has multiple applications such as testing the efficacy of avian roost population control measures (e.g. roost tree pruning) and monitoring the populations of threatened bird species that roost communally.

Box replication effects in weak lensing light-cone construction

Abstract Weak gravitational lensing simulations serve as indispensable tools for obtaining precise cosmological constraints. In particular, it is crucial to address the systematic uncertainties in theoretical predictions, given the rapid increase in galaxy numbers and the reduction in observational noise. Both on-the-fly and post-processing methods for constructing lensing light-cones encounter limitations due to the finite simulated volume, necessitating the replication of the simulation box to encompass the volume to high redshifts. To address this issue, our primary focus lies on investigating and quantifying the impact of box replication on the convergence power spectrum and higher-order moments of lensing fields. Subsequently, a univariate model is utilized to estimate the amplitude parameter A by fitting four statistics measured from partial-sky light-cones along specific angles, to the averaged result from random directions. The investigation demonstrates that the systematic bias stemming from the box replication phenomenon falls within the bounds of statistical errors for the majority of cases. However, caution should be exercised when considering high-order statistics on a small sky coverage (≲ 25 deg2). For this case, we have developed a code that facilitates the identification of optimal viewing angles for the light-cone construction. This code has been made publicly accessible https://github.com/czymh/losf.

Task-based modulation of higher-order lexical statistics in the ventral and dorsal visual streams

Task-based modulation of higher-order lexical statistics in the ventral and dorsal visual streams

Hybrid non-linear probabilistic model using Monte Carlo simulation and hybrid support vector regression for evaporation predictions

ABSTRACT This study presents a hybrid model combining support vector regression (SVR) with the grey wolf optimizer (GWO) for evaluating evaporation dynamics. The model was tested using 50 years of meteorological data from Zabol and Chabahar stations in Iran, and compared against standard SVR. Results show that the SVR-GWO significantly outperforms SVR, reducing predictive errors by over 41% on average. For Zabol, the SVR-GWO markedly improved performance, particularly in July where R2 increased from 0.867 to 0.973. The model more closely matched observed statistics, especially for mean and standard deviation, though challenges remain in reproducing higher-order statistics. Interestingly, the 5000-function evaluation proved nearly as effective as 500 000, suggesting computational efficiency. This integrated approach, incorporating Monte Carlo simulations and kernel density estimation, provides valuable probabilistic insights into evaporation dynamics, offering a promising tool for drought vulnerability assessment and water resources planning in regions with complex climatic patterns.

Models and methods for RZ-signals distinction in non-Gaussian noise for information-measurement systems

Abstract Polynomial Decision Rules (DR) for the problems of discrete RZ (Return-to-Zero) signal distinction in asymmetric-excess non-Gaussian noise are proposed. A new approach is proposed, which is based on the use of a modified moment quality criterion of statistical hypothesis testing and the application of higher-order statistics to describe the characteristics of non-Gaussian noise. Simulation of the DR with different parameters of the signal and noise was carried out. It is shown that taking into account the coefficients of skewness and kurtosis of the non-Gaussian noise the efficiency of signal distinction increases with non-linear processing DR compared to known results, which are optimal for the Gaussian noise model. The conducted studies demonstrate a reduction in false decisions in the processing of RZ signals when considering the coefficients of skewness and kurtosis of non-Gaussian noise. Such an increase in efficiency can exceed twofold, depending on the noise parameters. It is shown that the efficiency of the proposed approach is much higher for small SNR (Signal-to-Noise Ratio) values, for example, less than 1.

Iterated rational quadratic kernel - High-order unscented Kalman filtering algorithm for spacecraft tracking

The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods. However, reentry flight is accompanied by complex flight environments, which brings to the uncertain, complex, and strongly coupled non-Gaussian detection noise. As a result, there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application. To address these issues, a new iterated rational quadratic (RQ) kernel high-order unscented Kalman filtering (IRQ-HUKF) algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed. Firstly, the characteristic analysis of the RQ kernel is investigated in detail, which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing high-order moments of the RQ kernel. Subsequently, the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion, termed the iterated RQ kernel-UKF (RQ-UKF) algorithm by derived analytically, which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing high-order moments and heavy-tailed characteristics. Meanwhile, to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems, the high-order Sigma Points (SP) as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF. Finally, to further improve the flexibility of the IRQ-HUKF algorithm in practical application, an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence (KLD) method and parametric sensitivity analysis of the RQ kernel. The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.

Spectral incremental dynamic methodology for nonlinear structural systems endowed with fractional derivative elements subjected to fully non-stationary stochastic excitation

A novel spectral incremental dynamic analysis methodology for analysing structural response in nonlinear systems with fractional derivative elements is presented, aligning with modern seismic design codes, like Eurocode 8. Drawing inspiration from the concept of fully non-stationary stochastic processes, the vector of the imposed seismic excitations is characterised by time and frequency evolving power spectra stochastically compatible with elastic response spectra of specified damping ratio and ground acceleration. The proposed method efficiently determines the nonlinear system time-dependent probability density functions for the non-stationary system response amplitude by employing potent nonlinear stochastic dynamics concepts, such as stochastic averaging and statistical linearisation. Unlike traditional incremental dynamic analysis curves found in the literature, the herein proposed method introduces a three-dimensional alternative counterpart, that of stochastic engineering demand parameter surfaces, providing with higher-order statistics of the system response. An additional noteworthy aspect involves the derivation of response evolutionary power spectra as function of spectral acceleration, offering a deeper insight into the underlying system dynamics. Besides its capabilities, the method maintains the coveted element of a particularly low associated computational cost, increasing its attractiveness and practicality among diverse applications of engineering interest. Numerical examples comprising the bilinear hysteretic model endowed with fractional derivative elements subject to an Eurocode 8 elastic design spectrum demonstrate the capabilities and reliability of the proposed methodology. Its accuracy is assessed by juxtaposing the derived results with germane Monte Carlo Simulation data.

Ray-tracing versus Born approximation in full-sky weak lensing simulations of the MillenniumTNG project

ABSTRACT Weak gravitational lensing is a powerful tool for precision tests of cosmology. As the expected deflection angles are small, predictions based on non-linear N-body simulations are commonly computed with the Born approximation. Here, we examine this assumption using DORIAN, a newly developed full-sky ray-tracing scheme applied to high-resolution mass-shell outputs of the two largest simulations in the MillenniumTNG suite, each with a 3000 Mpc box containing almost 1.1 trillion cold dark matter particles in addition to 16.7 billion particles representing massive neutrinos. We examine simple two-point statistics like the angular power spectrum of the convergence field, as well as statistics sensitive to higher order correlations such as peak and minimum statistics, void statistics, and Minkowski functionals of the convergence maps. Overall, we find only small differences between the Born approximation and a full ray-tracing treatment. While these are negligibly small at power-spectrum level, some higher order statistics show more sizeable effects; ray-tracing is necessary to achieve per cent level precision. At the resolution reached here, full-sky maps with 0.8 billion pixels and an angular resolution of 0.43 arcmin, we find that interpolation accuracy can introduce appreciable errors in ray-tracing results. We therefore implemented an interpolation method based on non-uniform fast Fourier transforms (NUFFT) along with more traditional methods. Bilinear interpolation introduces significant smoothing, while nearest grid point sampling agrees well with NUFFT, at least for our fiducial source redshift, $z_s=1.0$, and for the 1 arcmin smoothing we use for higher order statistics.

Statistical blade tip timing measurement, Part II: High-order cumulant architecture

Blade tip timing (BTT) is a potential non-contact vibration measurement technique for rotating blades owing to its high efficiency and long service life. However, probe layout design and vibration parameter identification are critical challenges in BTT due to its inherent undersampling. To address this issue, we have proposed the concept of statistical BTT measurement which promotes efficient layouts and parameter identification methods by shifting the recovery target from the signal to itself to its statistics. In the first paper of series papers, we have developed covariance architecture for BTT measurement and signal post-processing. In this second part of series papers, we set out to develop BTT measurement from a higher-order statistic perspective. Specifically, we find that the 2qth-order cumulant retains the vibration information (frequency and amplitude) of the signal itself and it can be recovered at lower sampling rates than what is prescribed by the covariance architecture. On this basis, we propose a higher-order cumulant architecture for BTT measurement, which contains two aspects: higher-order difference layout (HODL) and higher-order cumulant-based parameter identifications. HODL is a special family of layouts that physically guarantee the availability of consecutive higher-order cumulant estimations and thus leads to a satisfactory parameter identification. To facilitate application, a series of concrete HODLs are provided for users, including a four-level nested layout and its enhanced version, and optimal fourth-order difference layout. The quantitative comparison in the simulations and experiments shows the effectiveness of the proposed higher-order cumulant architecture. Compared with the architectures developed from covariance and signal itself perspective, the proposed higher-order cumulant architecture is not only more robust to noise but also further reduces the number of required probes.

Constraining modified gravity with weak lensing peaks

Abstract It is well established that maximizing the information extracted from upcoming and ongoing stage-IV weak-lensing surveys requires higher-order summary statistics that complement the standard two-point statistics. In this work, we focus on weak-lensing peak statistics to test two popular modified gravity models, f(R) and nDGP, using the FORGE and BRIDGE weak-lensing simulations, respectively. From these simulations we measure the peak statistics as a function of both cosmological and modified gravity parameters simultaneously. Our findings indicate that the peak abundance is sensitive to the strength of modified gravity, while the peak two-point correlation function is sensitive to the nature of the screening mechanism in a modified gravity model. We combine these simulated statistics with a Gaussian Process Regression emulator and a Gaussian likelihood to generate stage-IV forecast posterior distributions for the modified gravity models. We demonstrate that, assuming small scales can be correctly modelled, peak statistics can be used to distinguish GR from f(R) and nDGP models at the two-sigma level with a stage-IV survey area of $300 \, \rm {deg}^2$ and $1000 \, \rm {deg}^2$, respectively. Finally, we show that peak statistics can constrain log10(|fR0|) = −6 to 2% precision, and log10(H0rc) = 0.5 to 25% precision.

Full shape cosmology analysis from BOSS in configuration space using neural network acceleration

Recently, a new wave of full modeling analyses have emerged within the Large-Scale Structure community, leading mostly to tighter constraints on the estimation of cosmological parameters, when compared with standard approaches used over the last decade by collaboration analyses of stage III experiments. However, the majority of these full-shape analyses have primarily been conducted in Fourier space, with limited emphasis on exploring the configuration space. Investigating n-point correlations in configuration space demands a higher computational cost compared to Fourier space because it typically requires an additional integration step. This can pose a limitation when using these approaches, especially when considering higher-order statistics. One avenue to mitigate the high computation time is to take advantage of neural network acceleration techniques. In this work, we present a full shape analysis of Sloan Digital Sky Survey III/BOSS in configuration space using a neural network accelerator. We show that the efficacy of the pipeline is enhanced by a time factor 103 without sacrificing precision, making it possible to reduce the error associated with the surrogate modeling to below 10-2 percent which is compatible with the precision required for current stage IV experiments such as DESI. We find Ω m = 0.286±0.009, H 0 = 68.8±1.2 kms-1Mpc-1 and A s × 109 = 2.09 +0.25 -0.29. Our results on public BOSS data are in good agreement with BOSS official results and compatible with other independent full modeling analyses. We explore relaxing the prior on ωb and varying ns , without significant changes in the mean values of the cosmological parameters posterior distributions, but enlarging their widths. Finally, we explore the information content of the multipoles when constraining cosmological parameters.