Process Variance Research Articles

Methods for estimating integrated variance: Jump robustness issues in high frequency time series

Integrated variance is a volatility measure of a process in continuous time, which is applicable in financial mathematics as a means to optimize a portfolio, project dynamics of a price of a financial asset. The consistency of an estimator for integrated variance of a random process is at the core of this article. A fundamental diffusion process is extended by adding a jump component as a means of improving the descriptive function of the process. It is activity of jumps that is a factor subject to which is the consistency of the estimator for integrated variance. Due to this fact, consistency is defined as an extent to which the estimator at hand is jump robust. Two main methods for estimating integrated variance are considered and the capacity of corresponding estimators to withstand the effect of jumps while converging is briefly analyzed. The arguments indicating a necessity for further research of the effect of jumps with reference to works of the authors who have established a ground for analysis of integrated variance and those works containing main asymptotic results for consistency of integrated variance estimators are elaborated. Based on this, avenue for further research and development of asymptotic theory for consistency of an estimator for integrated variance is identified.

Stochastic Resilience in Operations Management Using Ito Diffusion and Gamma Catastrophe Processes

This study introduces a novel Ito diffusion model for operations management, addressing the challenge of maintaining resilience in supply chains and production networks against unpredictable disruptions. The model incorporates a general catastrophe process with a low occurrence rate, using stochastic methods to represent disruption magnitudes as gamma distribution variables. It provides an analytical framework detailing the process's mean, variance, and sample path. Applying this model across various operational scenarios demonstrates its practical significance. By examining the impacts of disruptions on operational efficiency, the model offers insights into disruption dynamics, crucial for resilience planning and risk mitigation. The findings enhance logistics networks' resilience and efficiency, aiding decision-makers in navigating disruptions. This research presents a practical tool for decision-making in operations management and sets the stage for future research with complex variables and emerging technologies to enhance predictive strength in a dynamic environment.

Real estate for social purpose: varieties of entrepreneurialism in Toronto’s non-profit housing sector

Non-profit housing providers have faced ongoing pressure from neoliberal restructuring policies since the late twentieth century. In reaction to funding cuts and policies requiring them to become more business-like, housing organisations have become more hybrid, incorporating entrepreneurial logics and practices from the real estate sector. We expand on the concept of hybridity to argue that under certain institutional contexts, non-profits can apply real estate entrepreneurialism towards their social housing missions. Analysing development and acquisition practices of 13 non-profit housing providers in the Greater Toronto Area, we explore how non-profits balance entrepreneurial practices with their commitment to de-commodified housing. Three types of hybrid organisations are identified: large economy-of-scale organisations that prioritise growth and real estate professionalisation; service-focused organisations whose mission statement limits their growth aspirations; and newcomers, whose forays into housing development face both internal capacity limits and criticism from veteran organisations. The variances in hybridisation processes across and within institutional contexts, we find, require a more nuanced theorisation of the longer-term implications of neoliberalisation on social housing. Learning from Toronto’s budding social purpose real estate sector, we identify key resources for entrepreneurial housing non-profits: building sectoral assets, knowledge sharing, risk management, and a balance between organisational diversity and scale.

A Process Mean Shift Model Considering the Process Variance and Wear Function in Cutting Process

A Process Mean Shift Model Considering the Process Variance and Wear Function in Cutting Process

Design and analysis of a fault tolerance nano-scale code converter based on quantum-dots

Quantum-dot cellular automata (QCA), a nano-scale computer framework, is developing as a potential alternative to current transistor-based technologies. However, it is susceptible to a variety of fabrication-related errors and process variances because it is a novel technology. As a result, QCA-based circuits pose reliability-related problems since they are prone to faults. To address the dependability challenges, it is becoming increasingly necessary to create fault-tolerance QCA-based circuits. On the other hand, the applications of code converters in digital systems are essential for rapid signal processing. Using fault-tolerance XOR and multiplexer, this research suggests a nano-based binary-to-gray and gray-to-binary code converter circuit in a single layer to increase efficiency and reduce complexity. The fault-tolerance performance of the suggested circuits against cell omission, misalignment, displacement, and extra cell deposition faults has significantly improved. Concerning the generalized design metrics of QCA circuits, the fault-tolerance designs have been contrasted with the existing structures. The proposed fault-tolerance circuits' energy dissipation findings have been calculated using the precise QCADesigner-E power estimator tool. Using the QCADesigner-E program, the proposed circuits' functionality has been confirmed. The results implied the high efficiency and applicability of the proposed designs.

Correlation analysis of degrading systems based on bivariate Wiener processes under imperfect maintenance

AbstractThis article focuses on the correlation between the degradation levels of the two components that form a system. The degradation evolution of each component is modeled using Wiener processes. Both components are dependent and this dependence is described using the trivariate reduction method. To reduce the degradation and extend the system lifetime, preventive maintenance actions are periodically performed. These preventive maintenance actions are imperfect and they are modeled by using an arithmetic reduction of degradation of infinite order model with a determined maintenance efficiency parameter. The evolution of the maintained system is analysed by assessing the expectation and variance of both degradation processes at successive maintenance times. The novelty of this work is the analysis of the Pearson correlation coefficient between the degradation levels of the two components. Different properties of the monotonicity of the Pearson correlation coefficient between the two degradation paths are obtained by considering equal maintenance efficiency and equal general time scales functions for the two Wiener degradation processes associated to each degrading component.

Present, Past, and Future of Lean Six Sigma Applications: From Evolution to the Era of Artificial Intelligence

Background: Lean Six Sigma is a fact-based, data-driven approach that avoids mistakes to improve quality and efficiency. Artificial intelligence (AI) is now evident in lean six sigma applications. AI waste elimination solutions can eliminate large amounts of waste that LSS could not. In lean six sigma, six sigma tackles process variance, whereas lean reduces waste to improve process quality and efficiency. Objective: To describe new pieces, trends, and the adoption and implementation of new technologies like AI by examining the current literature across multiple aspects for a more instructive and piquant viewpoint. Methods: This study is a combination of systematic and bibliometric review, where the systematic review was based on a class framework by selecting 97 articles from reputed journal databases, and the bibliometric review was conducted using a VOS viewer and web of science database for a period of 15 years (2007-2022). Results: By describing LSS's historical evolution, major concerns, prevalent research approaches, and application areas, the study helps practitioners and academics understand its present state for robust research. AI and other cutting-edge technologies help discover non-value-added operations that are difficult to recognize manually. Conclusion: This study has revealed the critical success factors for deploying LSS in numerous businesses. The motivations, barriers, and limits in the direction of the application of LSS are also discussed. The research trends in implementing modern technologies like AI showed a green wave. Future research may emphasize and dominate LSS implementation issues with modern technologies like AI.

Credibility Theory for Variance Premium Principle

The method of credibility theory plays a critical role in various research areas of actuarial science. Among others, the hypothetical mean and process variance are two quantities that convey crucial information to insurance companies when determining premiums for the insureds. The classical credibility model charges premiums by applying a linear combination of the mean of past claims and the population mean, and the corresponding estimator is proved to be the best estimator of the hypothetical mean under the mean squared loss criterion. Enlightened by the prestigious variance premium principle, we propose a credibility approach to estimate the linear combination of hypothetical mean and process variance under the quadratic loss function. Our proposed estimator consists of the linear form of observations and their quadratic terms, as well as some quantities representing population information. Meanwhile, a spin-off result is found and utilized to compare with the classical credibility model and the q-credibility model. The nonparametric estimators of structural quantities are also provided for ease of practical usage. Several numerical illustrations are carried out to demonstrate the performance of the estimator. A real dataset from a Swiss insurance company is also analyzed for the practical application of our results, where a data-driven procedure is proposed for determining the safety loading.

Quantum-assisted Hilbert-space Gaussian process regression

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture prior information on the statistics of noise, smoothness of the functions, and training data uncertainty. However, their computational complexity quickly becomes intractable as the size of the data set grows. We propose a Hilbert-space approximation-based quantum algorithm for Gaussian process regression to overcome this limitation. Our method consists of a combination of classical basis function expansion with quantum computing techniques of quantum principal component analysis, conditional rotations, and Hadamard and tests. The quantum principal component analysis is used to estimate the eigenvalues, while the conditional rotations and the Hadamard and tests are employed to evaluate the posterior mean and variance of the Gaussian process. Our method provides polynomial computational complexity reduction over the classical method. Published by the American Physical Society 2024

Stochastic processes and mean square calculus on fractal curves

Abstract In this paper, random and stochastic processes are defined on fractal curves. Fractal calculus is used to define the cumulative distribution function, probability density function, moments, variance, and correlation function of stochastic processes on fractal curves. A new framework, which is a generalization of mean square calculus, is formulated. The sequence of random variables on the fractal curve, fractal mean square continuity, mean square F α {F^{\alpha}} -derivative, and fractal mean square integral are discussed. The mean square solution of a fractal stochastic equation is derived and plotted to illustrate the details.

Characterising X-ray variability in light curves with complex sampling patterns: Application to the eROSITA south ecliptic pole survey

Aims : During its all-sky survey phase, the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) X-ray telescope on board the Spectrum-Roentgen-Gamma (SRG) spacecraft scans through the ecliptic poles every 4 hours. This extensive data set of long-duration, frequent, and consistent observations of thousands of X-ray sources is ideal for a detailed long-term X-ray-variability analysis. However, individual observations are short, are separated by long but consistent gaps, and have varying exposure times. Therefore, the identification of variable sources and the characterisation and quantification of their variability requires a unique methodology. We aim to develop and evaluate variability analysis methods for eROSITA observations, focusing on sources close to the survey poles. We also aim to detect intrinsically variable sources at any count rate and quantify the variability of low-count-rate sources. Methods : We simulate eROSITA-like light curves to evaluate and quantify the effect of survey mode observations on the measured periodogram and normalised excess variance. We introduce a new method for estimating the normalised intrinsic variance of a source based on the Bayesian excess variance (bexvar) method. Results : We determine thresholds for identifying likely variable sources while minimising the false-positive rate, as a function of the number of bins, and the average count rate in the light curve. The bexvar normalised intrinsic variance estimate is significantly more accurate than the normalised excess variance method in the Poisson regime. At high count rates, the two methods are comparable. We quantify the scatter in the intrinsic variance of a stationary pink-noise process, and investigate how to reduce it. Finally, we determine a description of the excess noise in a periodogram caused by varying exposure times throughout a light curve. Although most of these methods were developed specifically for analysing variable active galactic nuclei in the eROSITA all-sky survey, they can also be used for the variability analysis of other datasets from other telescopes, with slight modifications.

The effect of process variability and data quality on performance of a state-space stock assessment model

State-space modeling is an emerging approach to age structured fisheries stock assessment that can accommodate multiple sources of variability in processes like recruitment, abundance, and selectivity. By maximizing the marginal likelihood by treating yearly deviations as random effects and then integrating them from the likelihood, these models can estimate multiple process variances. Several fisheries software packages have been developed that use a state-space framework with marginal likelihood, which has increased their popularity and usage across the U.S. Atlantic coast, Canada, and Europe. However, robust testing is still needed to gauge the applicability of these models and understand how they perform under a range of realistic variability in the process or observation error. Using an assessment model fit to Gulf of Maine Haddock as a baseline, we used a simulation-estimation procedure to test if state-space stock assessment models could produce approximately unbiased and precise estimates over a range of process variances that extended from zero to well above the levels estimated in the Gulf of Maine Haddock assessment, or when observations were noisier (i.e., more variable around their true value) than had been assumed in the assessment. We fit alternative estimation models that differed in which processes errors were included (of recruitment, expected survival, and fishery selectivity). State-space models which specify random effects in all three processes produced approximately unbiased and precise estimates of biomass and exploitation for most operating models and therefore are recommended except when variability in expected survival is absent (or very low), in which case the model is unlikely to converge. A conventional statistical-catch-at-age model with recruitment estimated as a fixed effect for each year, deterministic expected survival, and constant selectivity produced estimates that were comparable to the best state-space model, but do not provide internal estimates of process variances and did not perform well when recruitment was highly variable. This work will facilitate the use of state-space stock assessment models and choosing the parameterization that will produce the most accurate output to inform future predictions and management.

Dissecting unique and common variance across body and brain health indicators using age prediction

AbstractAgeing is a heterogeneous multisystem process involving different rates of decline in physiological integrity across biological systems. The current study dissects the unique and common variance across body and brain health indicators and parses inter‐individual heterogeneity in the multisystem ageing process. Using machine‐learning regression models on the UK Biobank data set (N = 32,593, age range 44.6–82.3, mean age 64.1 years), we first estimated tissue‐specific brain age for white and gray matter based on diffusion and T1‐weighted magnetic resonance imaging (MRI) data, respectively. Next, bodily health traits, including cardiometabolic, anthropometric, and body composition measures of adipose and muscle tissue from bioimpedance and body MRI, were combined to predict ‘body age’. The results showed that the body age model demonstrated comparable age prediction accuracy to models trained solely on brain MRI data. The correlation between body age and brain age predictions was 0.62 for the T1 and 0.64 for the diffusion‐based model, indicating a degree of unique variance in brain and bodily ageing processes. Bayesian multilevel modelling carried out to quantify the associations between health traits and predicted age discrepancies showed that higher systolic blood pressure and higher muscle‐fat infiltration were related to older‐appearing body age compared to brain age. Conversely, higher hand‐grip strength and muscle volume were related to a younger‐appearing body age. Our findings corroborate the common notion of a close connection between somatic and brain health. However, they also suggest that health traits may differentially influence age predictions beyond what is captured by the brain imaging data, potentially contributing to heterogeneous ageing rates across biological systems and individuals.

Comprehensive Analysis and Experimental Validation of the Parkinson's Disease Lysosomal Gene ACP2 and Pan-cancer.

The pivotal role of lysosomal function in preserving neuronal homeostasis is recognized, with its dysfunction being implicated in neurodegenerative processes, notably in Parkinson's disease (PD). Yet, the molecular underpinnings of lysosome-related genes (LRGs) in the context of PD remain partially elucidated. We collected RNA-seq data from the brain substantia nigra of 30 PD patients and 20 normal subjects from the GEO database. We obtained molecular classification clusters from the screened lysosomal expression patterns. The lysosome-related diagnostic model of Parkinson's disease was constructed by XGBoost and Random Forest. And we validated the expression patterns of signature LRGs in the diagnostic model by constructing a PD rat model. Finally, the linkage between PD and cancer through signature genes was explored. The expression patterns of the 33 LRGs screened can be divided into two groups of PD samples, enabling exploration of the variance in biological processes and immune elements. Cluster A had a higher disease severity. Subsequently, critical genes were sieved through the application of machine learning methodologies culminating in the identification of two intersecting feature genes (ACP2 and LRP2). A PD risk prediction model was constructed grounded on these signature genes. The model's validity was assessed through nomogram evaluation, which demonstrated robust confidence validity. Then we analyzed the correlation analysis, immune in-filtration, biological function, and rat expression validation of the two genes with common pathogenic genes in Parkinson's disease, indicating that these two genes play an important role in the pathogenesis of PD. We then selected ACP2, which had a significant immune infiltration correlation, as the entry gene for the pan-cancer analysis. The pan-cancer analysis revealed that ACP2 has profound associations with prognostic indicators, immune infiltration, and tumor-related regulatory processes across various neoplasms, suggesting its potential as a therapeutic target in a range of human diseases, including PD and cancers. Our study comprehensively analyzed the molecular grouping of LRGs expression patterns in Parkinson's disease, and the disease progression was more severe in cluster A. And the PD diagnosis model related to LRGs is constructed. Finally, ACP2 is a potential target for the relationship between Parkinson's disease and tumor.

AF-OS-ELM-MVE: A new online sequential extreme learning machine of dam safety monitoring model for structure deformation estimation

Dam deformation monitoring is an important task in hydraulic engineering projects. Traditional statistical methods and machine learning algorithms have been widely applied in structural safety prediction due to the application’s convenience. However, most machine learning algorithms are offline models and are not suitable for simulating the complex dynamic process of dam displacement. In addition, dam safety monitoring should quantify the uncertainty of the time-dependent displacement and establish reliable prediction intervals. As a result, an online learning model that can qualify prediction intervals is necessary. In this paper, an online learning algorithm named AF-OS-ELM-MVE is proposed to solve the problems. It is based on the OS-ELM algorithm and optimized using the adaptive forgetting factor mechanism. Through selective forgetting for parameter tuning, it achieves self-adaptation to the underlying physical mechanism between the factors and the displacement data. Mean Variance Estimation (MVE) is also adapted to establish the new hybrid model. It can be used to estimate the variance of the prediction process, and the model can generate prediction intervals based on the minimum probability theory. The AF-OS-ELM-MVE model is verified using long-term monitoring data and the performance comparisons were made with a number of state-of-the-art models. The correlation coefficients of the proposed model in point prediction are above 0.99 for measuring points of different elevations, and at a 95% confidence level, it achieves 100% coverage of real displacements. The results demonstrate the effectiveness of the proposed model in predicting dam deformations and provide a more solid basis for dam safety analysis.

Simulation modeling with memory-type control charts for monitoring the process variability

Memory-type control charts, renowned for their effectiveness in identifying small deviations in the process variance, are commonly used to monitor the process variability. In this article, we introduce a new tool, the Quadruple Exponentially Weighted Moving Average (QEWMA) chart, which is designed for the specific purpose of monitoring changes in the process variability. We refer to this chart as the -QEWMA chart. The performance of the -QEWMA chart is assessed through an extensive series of Monte-Carlo simulations, carefully considering the run-length distribution. Comparing it with other well-known memory-type charts, it becomes evident that the -QEWMA chart excels in its ability to effectively detect small shifts in the process dispersion. To illustrate the practical application of this chart, we provide an example.

A novel Bayesian Max-EWMA control chart for jointly monitoring the process mean and variance: an application to hard bake process

In this article, we introduce a novel Bayesian Max-EWMA control chart under various loss functions to concurrently monitor the mean and variance of a normally distributed process. The Bayesian Max-EWMA control chart exhibit strong overall performance in detecting shifts in both mean and dispersion across various magnitudes. To evaluate the performance of the proposed control chart, we employ Monte Carlo simulation methods to compute their run length characteristics. We conduct an extensive comparative analysis, contrasting the run length performance of our proposed charts with that of existing ones. Our findings highlight the heightened sensitivity of Bayesian Max-EWMA control chart to shifts of diverse magnitudes. Finally, to illustrate the efficacy of our Bayesian Max-EWMA control chart using various loss functions, we present a practical case study involving the hard-bake process in semiconductor manufacturing. Our results underscore the superior performance of the Bayesian Max-EWMA control chart in detecting out-of-control signals.

Statistical inference for mean and variance of oscillatory processes

When constructing confidence intervals for the mean and variance of a stationary continuous-time stochastic process, two approaches have been considered in the literature: one based on the so-called long-run variance of the process and its square, and the other based on the so-called self-normalization. These approaches are revisited here in the context of random oscillatory processes such as random (non-)linear oscillators and related models with particular attention to the problem of estimating the non-zero long-run variances of the processes. The case of the zero long-run variance, which has been studied and is quite different, is also considered. The approaches are extended to the situation where multiple independent records of the stochastic process are available, for example, by introducing an estimator of the long-run variance which improves on other natural candidate estimators. Finally, a simulation study is provided to assess the performance of the proposed methods in estimating the long-run variances and constructing confidence intervals, and a data example is considered.

Safe Machine-Learning-Supported Model Predictive Force and Motion Control in Robotics

Many robotic tasks, such as human-robot interactions or the handling of fragile objects, require tight control and limitation of appearing forces and moments alongside sensible motion control to achieve safe yet high-performance operation. We propose a learning-supported model predictive force and motion control scheme that provides stochastic safety guarantees while adapting to changing situations. Gaussian processes (GPs) are used to learn the uncertain relations that map the robot’s states to the forces and moments. The model predictive controller uses these Gaussian process models to achieve precise motion and force control under stochastic constraint satisfaction. As the uncertainty only occurs in the static model parts — the output equations — a computationally efficient stochastic MPC formulation is used. analysis of recursive feasibility of the optimal control problem and convergence of the closed loop system for the static uncertainty case are given. Chance constraint formulation and back-offs are constructed based on the variance of the Gaussian process to guarantee safe operation. The approach is illustrated on a lightweight robot in simulations and experiments.

Calculation of the Mean and Variance in the Birth-Death Immigration processes for M\M\1 Queueing Model

This paper, delineates how catastrophe affect the Birth-Death and Immigration Process (BDI). To find the general solution for the population size distribution, the Probability Generating Function (PGF) is used. When the rates of birth, death, immigration, and catastrophe are remain's constant, the accurate solution of mean and variance is also obtained. In addition, the mean and variance are time dependent. The system's behavior, a numerical example is presented for investigated.