Fourth Moment Research Articles

Chance-constrained stochastic optimal control of epidemic models: A fourth moment method-based reformulation

This work proposes a methodology for the reformulation of chance-constrained stochastic optimal control problems that ensures reliable uncertainty management of epidemic outbreaks. Specifically, the chance constraints are reformulated in terms of the first four moments of the stochastic state variables through the so-called fourth moment method for reliability. Moreover, a spectral technique is employed to obtain surrogate models of the stochastic state variables, which enables the efficient computation of the required statistics. The practical implementation of the proposed approach is demonstrated via the optimal control of two different stochastic mathematical models of the COVID-19 transmission. The numerical experiments confirm that, unlike those reformulations based on the Chebyshev–Cantelli’s inequality, the proposed method does not exhibit the undesired outcomes that are typically observed when a higher precision is required for the risk level associated to the given chance constraints.

Large sample correlation matrices with unbounded spectrum

In this paper, we demonstrate that the diagonal of a high-dimensional sample covariance matrix stemming from n independent observations of a p-dimensional time series with finite fourth moments can be approximated in spectral norm by the diagonal of the population covariance matrix regardless of the spectral norm of the population covariance matrix. Our assumptions involve p and n tending to infinity, with p/n tending to a constant which might be positive or zero. Consequently, we investigate the asymptotic properties of the sample correlation matrix with a divergent spectrum, and we explore its applications by deriving the limiting spectral distribution for its eigenvalues and analyzing the convergence of divergent and non-divergent spiked eigenvalues under a generalized spiked correlation framework.

Sign Changes of the Error Term in the Piltz Divisor Problem

Abstract We study the function $\Delta _{k}(x):=\sum _{n\leq x} d_{k}(n) - \mbox{Res}_{s=1} ( \zeta ^{k}(s) x^{s}/s )$, where $k\geq 3$ is an integer, $d_{k}(n)$ is the $k$-fold divisor function, and $\zeta (s)$ is the Riemann zeta-function. For a large parameter $X$, we show that if the Lindelöf hypothesis (LH) is true, then there exist at least $X^{\frac{1}{k(k-1)}-\varepsilon }$ disjoint subintervals of $[X,2X]$, each of length $X^{1-\frac{1}{k}-\varepsilon }$, such that $|\Delta _{k}(x)|\gg x^{\frac{1}{2}-\frac{1}{2k}}$ for all $x$ in the subinterval. In particular, $\Delta _{k}(x)$ does not change sign in any of these subintervals. If the Riemann hypothesis (RH) is true, then we can improve the length of the subintervals to $\gg X^{1-\frac{1}{k}} (\log X)^{-k^{2}-2}$. These results may be viewed as higher-degree analogues of theorems of Heath-Brown and Tsang, who studied the case $k=2$, and Cao, Tanigawa, and Zhai, who studied the case $k=3$. The first main ingredient of our proofs is a bound for the second moment of $\Delta _{k}(x+h)-\Delta _{k}(x)$. We prove this bound using a method of Selberg and a general lemma due to Saffari and Vaughan. The second main ingredient is a bound for the fourth moment of $\Delta _{k}(x)$, which we obtain by combining a method of Tsang with a technique of Lester.

Workflow Trace Profiling and Execution Time Analysis in Quantitative Verification

Workflows orchestrate a collection of computing tasks to form a complex workflow logic. Different from the traditional monolithic workflow management systems, modern workflow systems often manifest high throughput, concurrency and scalability. As service-based systems, execution time monitoring is an important part of maintaining the performance for those systems. We developed a trace profiling approach that leverages quantitative verification (also known as probabilistic model checking) to analyse complex time metrics for workflow traces. The strength of probabilistic model checking lies in the ability of expressing various temporal properties for a stochastic system model and performing automated quantitative verification. We employ semi-Makrov chains (SMCs) as the formal model and consider the first passage times (FPT) measures in the SMCs. Our approach maintains simple mergeable data summaries of the workflow executions and computes the moment parameters for FPT efficiently. We describe an application of our approach to AWS Step Functions, a notable workflow web service. An empirical evaluation shows that our approach is efficient for computer high-order FPT moments for sizeable workflows in practice. It can compute up to the fourth moment for a large workflow model with 10,000 states within 70 s.

Kilómetro 0: inicio de las trayectorias migratorias de trabajadoras domésticas en Chile

This study aims to describe how the migratory trajectories of migrant domestic workers begin in Chile and the role of migratory networks and emotional factors in their decisions. A qualitative analysis of six biographical narratives is employed to examine the complexities of their labor and migratory trajectories, influenced by intersecting factors such as gender, class, and ethnicity, within the context of global care chains. The results reveal five central moments when making the decision to migrate. The first moment is characterized by the fact that none of the cases had worked as domestic workersin their home countries. In the second moment, the need to change their circumstances in their home countries arises, often due to political crises, economic challenges, or gender-based violence. The third moment involves the existence of a migratory network of friends and family who assist in their journey.In the fourth moment, a significant emotional factor plays a central role in the decision to migrate, influencing the timing of the decision. Finally, in the fifth moment, the decision to migrate to Chile is made.

The Neutron Skin-Thickness of 208Pb Determined by Electron and Proton Scattering

Abstract Electron as well as proton elastic scattering is not able to determine the point proton and point neutron densities, $\rho _\tau (r), (\tau =p,n)$, separately. If both scatterings are analyzed consistently, those densities would be determined uniquely, since the two densities are observed by different combinations from each other. Previous experiments have not provided $\rho _\tau (r)$ uniquely, but the values of the mean square radii of $\rho _p(r)$, $\langle \, r^2\, \rangle _p$, and of $\rho _n(r)$, $\langle \, r^2\, \rangle _n$, are shown to be determined consistently through the fourth moment of the observed charge density, $\langle \, r^4\, \rangle _c$, in 208Pb. The previous analyses of $(\gamma , \pi ^0)$ and $\bar{p}$-nucleus obtained a similar value of $\langle \, r^2\, \rangle _n$, but they do not yield the experimental value of $\langle \, r^4\, \rangle _c$ observed in electron scattering.

The Berry–Esseen bound in de Jong’s CLT

We prove a Berry–Esseen bound in de Jong’s classical CLT for normalized, completely degenerate U-statistics, which says that the convergence of the fourth moment sequence to three and a Lindeberg–Feller type negligibility condition are sufficient for asymptotic normality. Our bound is of the same optimal order as the bound on the Wasserstein distance to normality that has recently been proved by Döbler and Peccati (2017).

Central limit theorem in disordered Monomer‐Dimer model

AbstractWe consider the disordered monomer‐dimer model on general finite graphs with bounded degrees. Under the finite fourth moment assumption on the weight distributions, we prove a Gaussian central limit theorem for the free energy of the associated Gibbs measure with a rate of convergence. The central limit theorem continues to hold under a nearly optimal finite ‐moment assumption on the weight distributions if the underlying graphs are further assumed to have a uniformly subexponential volume growth. This generalizes a recent result by Dey and Krishnan who showed a Gaussian central limit theorem in the disordered monomer‐dimer model on cylinder graphs. Our proof relies on the idea that the disordered monomer‐dimer model exhibits a decay of correlation with high probability. We also establish a central limit theorem for the Gibbs average of the number of dimers where the underlying graph has subexponential volume growth and the edge weights are Gaussians.

Persistence of large-scale coherent structures in a turbulent pipe flow through an improved lattice Boltzmann approach

We simulated a turbulent pipe flow within the lattice Boltzmann method using a multiple-relaxation-time collision operator with Maxwell–Boltzmann equilibrium distribution expanded, for the sake of a more accurate description, up to the sixth order in Hermite polynomials. The moderately turbulent flow (Reτ≈181.3) is able to reproduce up to the fourth statistical moment with great accuracy compared with other numerical schemes and with experimental data. A coherent structure identification was performed based on the most energetic streamwise turbulent mode, which revealed a surprising memory effect related to the large-scale forcing scheme that triggered the pipe's turbulent state. We observe that the existence of large-scale motions that are out of the pipe's stationary regime does not affect the flow's detailed single-point statistical features. Furthermore, the transitions between the coherent structures of different topological modes were analyzed as a stochastic process. We find that for finely resolved data, the transitions are effectively Markovian, but for larger decimation time lags, due to topological mode degeneracy, non-Markovian behavior emerges, in agreement with previous experimental studies.

Development of higher order deterministic approaches of forward and inverse uncertainty quantification for nonlinear engineering systems

This paper introduces an innovative numerical scheme that may accurately quantify the parameter and response distributions with minimal computational costs, with specific applications to the numerical computation of multiphase flows under various fluid conditions. The probabilistic approach of uncertainty quantification, e.g., the Monte Carlo simulation, although known to be effective in estimating the parameter/response distribution for highly nonlinear problems, is usually not applicable to multi-physics and multi-scale integrated systems due to its high computational cost. The objective of this study is first, to reduce the computing demand for complex physical system calculations and, at the same time, to accurately predict actual probability distributions by developing a higher order deterministic approach to uncertainty quantification. To achieve this, instead of executing simulation codes multiple times to estimate the probability distribution, the first to fourth moments of the probability density function are derived directly by employing a second order Taylor expansion form of the responses along with Bayesian statistics. This characterizes the parameter and response distributions computed by inverse and forward uncertainty quantification based on their mean value, mode, covariance, skewness, and kurtosis. The parameter distribution is estimated by the numerically calculated higher moments of the parameters with a posteriori probability density function being derived by Bayesian inference. The parameter distribution is then mapped into the second order approximated response function to compute the characteristics of the response distribution through both analytical calculation and numerical approximation of the moments of the responses. The proposed approach is numerically demonstrated through simulations of two benchmark problems: MIT pressurizer and FEBA tests. The prediction of the responses is improved by inverse uncertainty quantification as numerical calculations with the a posteriori model parameters are in better agreement with the measured data over a wide range of transient periods. Additionally, the response distribution estimated by the proposed approach of forward uncertainty quantification accurately predicts the distribution computed by the Monte Carlo simulation.

Impact of torque on active Brownian particle: exact moments in two and three dimensions

Abstract In this work, we investigate the effects of torque, accounting for translational diffusion, on active Brownian particles (ABPs) in two (2d) and three (3d) dimensions. The torque is equivalent to chirality in 2d, well known as chiral active Brownian particles (cABPs), whereas in 3d, this is introduced as an external torque on the ABPs. Despite the inherent complexity in solving the Fokker–Planck equation, we demonstrate a Laplace transform method to precisely calculate the temporal evolution of various dynamic moments. Our analysis yields explicit expressions for multiple moments, such as the second and fourth moments of displacement, revealing the impact of persistence and chirality/torque. These moments exhibit oscillatory behavior, and excess kurtosis indicates deviations from the Gaussian distribution during intermediate time intervals.

Landslide type inference based on statistical analysis of a high-resolution digital elevation model in Gorce National Park, Poland

High-resolution digital elevation models are commonly utilized for detecting and classifying landslides. In this study, we aim to refine landslide detection and classification by analyzing the geometry of landslides using slope and aspect, coupled with descriptive statistics up to the fourth central moment (kurtosis). Employing the Monte Carlo method for creating terrain topography probability distributions and ANOVA tests for statistical validation, we analyzed 364 landslides in Gorce National Park, Poland, revealing significant kurtosis differences across landslide types and lithologies. This methodology offers a novel approach to landslide classification based on surface geometry, with implications for enhancing scientific research and improving landslide risk management strategies.

On the sieve M-estimation for a special bilinear time series model with time-functional variance noises

. The bilinear model has been frequently used in fields like control theory and economics to model seismic data. In this article, time-functional variance (TFV) noises are embedded into a specific bilinear model. We propose a generalized autoregressive conditional heteroskedasticity-type maximum likelihood estimator (GMLE) with a sieve method and then provide various inferential techniques based on this GMLE. It is shown that under the finite fourth moment of errors, the GMLE is consistent and asymptotically normally distributed. A simulation study and analysis of real data are additionally carried out to evaluate GMLE’s finite sample performance.

The Second and Fourth Moments of Discrete Gaussian Distributions over Lattices

Let Λ be an n-dimensional lattice. For any n-dimensional vector c and positive real number s, let Ds,c and DΛ,s,c denote the continuous Gaussian distribution and the discrete Gaussian distribution over Λ, respectively. In this paper, we establish the exact relationship between the second and fourth moments centered around c of the discrete Gaussian distribution DΛ,s,c and those of the continuous Gaussian distribution Ds,c, respectively. This provides a quantization form of the result obtained by Micciancio and Regev on the second and fourth moments of discrete Gaussian distribution. Using the relationship, we also derive an uncertainty principle for Gaussian functions, which extend the result of Zheng, Zhao, and Xu. Our proof is based on combination of the idea of Micciancio and Regev and the idea of Zheng, Zhao, and Xu, where the main tool is high-dimensional Fourier transform.

Maps, Apps and Race: The Market as a Theoretical Machine

AbstractMy commentary situates Desiree Fields' lecture within a long‐standing movement that, paying attention to real estate data and techniques of property, turned the housing market into a theoretical machine. I understand her intervention as a fourth and pivotal conceptual moment in the study of housing markets and inequalities for the discipline of geography, for it brings racial capitalism and settler colonialism as theoretical starting points to analyse the political economy of housing in the era of digital property technologies. As such, her lecture opens up a welcome, ambitious, yet also uncertain terrain to advance global urban theory under platform capitalism and stimulate relational approaches in housing studies. Discussing the regularities through which race, technology and property shape housing and wealth inequalities across variegated sites of market‐making provides a conceptual horizontality that acknowledges the United States as a testing ground, rather than a ground truth, for the production of geographical knowledge.

Dynamic reliability analysis of angular contact ball bearing based on maximum entropy quadratic fourth moment method*

ABSTRACT Bearing failure occurs when the dynamic contact stress exceeds the yield strength of the bearing material during operation. To minimise the risk of bearing failure, a new reliability theory method is proposed based on the stress-strength model of bearings, incorporating random input variables to analyse the reliability of angular contact ball bearings (ACBBs) and quantify their dynamic performance. The maximum entropy quadratic fourth moment method is used to calculate the probability distribution of maximum orthogonal shear stress-strength of bearing, and the maximum entropy principle is used to obtain the approximation of the minimum human error factors. Additionally, reliability-based sensitivity indices are derived to investigate the parametric significance of random input variables. Using B218 bearing as an example, the engineering application of this method in dynamic reliability and reliability-based sensitivity analysis is illustrated. Monte Carlo simulation is performed to verify the accuracy and effectiveness of the method to provide benchmark results. The results show that the Poisson’s ratio have a greater influence on the dynamic reliability of ACBBs than other parameters. Improving parameters such as ball diameter, raceway groove curvature radius and contact angle can also improve the reliability of bearings to some extent.

Log determinant of large correlation matrices under infinite fourth moment

Log determinant of large correlation matrices under infinite fourth moment

Conceptions of bibliographic managers in university teachers. An approach in Latin American.

Due to the accumulation of information generated by the information society, it is necessary to establish scientific criteria for its systematization. The objective of the research was to understand the implicit theories on the use of bibliographic managers in the organization of scientific information in university teachers in Latin American university teachers (Colombia, Ecuador and Peru). The interpretative paradigm, phenomenological method and qualitative approach were used. The key informants were defined by fifteen teachers with research experience. The technique was the semi-structured interview, and the instrument was the interview script. The study was based on four cyclical-recursive moments, the first was the natural attitude, where information was obtained from the key informants as a result of the interviews. The second moment allowed the epoche-eidetic reduction, consisting of the analysis of each interview. The third moment originated the transcendental epoche-reduction, analyzing each attribute and their consistency. The fourth moment revealed the constitution of the study, integrating in a semantic network the categories, subcategories, and attributes that emerged. Even when it is recognized from the cognitive conception about the concept of bibliographic managers, its applicability or use, it seems not to be so effective in scientific academic spaces and activities, because teachers are still anchored to the traditionalist vision of organizing information through "drive, folder or excel", reflecting the resistance to change. The imperative need for continuous training in the use of bibliographic managers in both students and teachers is asserted, reflected as a transversal strategy throughout all academic cycles and semesters and internalized as a research policy that leads to generate a new change in the conception of researching reliable scientific sources, optimizing time, organizing information and guaranteeing quality research.

Implementasi Five Moment Hand Hygiene Pada Perawat Di Ruang Rawat Medikal Bedah Rumah Sakit Santa Elisabeth Medan

The prevalence of nosocomial infections worldwide has become a serious concern for healthcare professionals, especially in hospitals. One contributing factor is the inadequate implementation of the five moments hand hygiene in handwashing procedures that do not conform to operational procedure standards. The aim of this research is to determine how the implementation of the five moments hand hygiene among nurses in the surgical medical care ward at Santa Elisabeth Hospital in Medan. This study utilized a descriptive cross-sectional approach, employing observation sheets. The sample size included 30 nurses in the Surgical Medical Care Ward at Santa Elisabeth Hospital in Medan, using total sampling technique. The measurement tool was an observation sheet, and the data analysis employed univariate analysis. The research findings revealed that, in the first moment before patient contact, 56.7% of nurses did not adhere to the practice, while 43.3% did. In the second moment, before aseptic procedures, 56.7% of nurses did not comply, and 43.3% did. In the third moment, after exposure to patient body fluids, all nurses (100%) adhered to the practice. In the fourth moment, after patient contact, all nurses (100%) complied. In the fifth moment, after contact with the patient's environment, all nurses (100%) followed the practice. It is hoped that nurses can consistently implement the five moments hand hygiene to prevent disease transmission and nosocomial infections, fostering a habit of incorporating these practices into nosocomial infection prevention.

Testing Many Zero Restrictions in a High Dimensional Linear Regression Setting

We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with k ≫ n regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension regression models with nuisance terms. The parsimoniously parametrized models identify whether the original parameter of interest is or is not zero. Estimating fixed low dimension sub-parameters ensures greater estimator accuracy, it does not require a sparsity assumption nor therefore a regularized estimator, it is computationally fast compared to, e.g., de-biased Lasso, and using only the largest in a sequence of weighted estimators reduces test statistic complexity and therefore estimation error. We provide a parametric wild bootstrap for p-value computation, and prove the test is consistent and has non-trivial n / { ln ( n ) M n } -local-to-null power where M n is the l ∞ covariate fourth moment.