Process Variance Research Articles

New EWMA charts for process variance

AbstractThe EWMA chart is effective in detecting small shifts in the process mean or process variance. Numerous EWMA charts for the process variance have been suggested in the literature. In this article, new one‐sided and two‐sided EWMA charts are developed for monitoring the variance of a normal process. In developing these new EWMA charts, first, new unbiased estimators of the process variance are developed, followed by incorporating the developed estimators into the new EWMA charts' statistics. The Monte Carlo simulation method is adopted to evaluate the zero‐state and steady‐state run‐length performances of the proposed EWMA variance charts, in comparison with that of three existing EWMA variance charts and the weighted adaptive CUSUM variance chart. The findings reveal that the proposed charts generally perform better than the existing charts. An example of application is given to show the implementation of the proposed and existing charts in detecting increases or decreases in the process variance.

A heavy-traffic perspective on departure process variability

This paper studies the departure process from a single-server queue in heavy-traffic over time scales that are of diffusion time scale, and over time scales that are both shorter and longer than diffusion time scale. In addition, the paper shows how one can compute the variance of such Brownian departure processes using stochastic calculus methods. Furthermore, the paper studies the implications of these results for downstream queues that are fed by such departure processes, and shows that downstream equilibrium congestion depends on upstream departure variability over the downstream queue’s characteristic heavy traffic time scale. These results also shed further light on the discontinuity in departure process asymptotic variability that is known as the BRAVO effect.

Evaluation of integrals with fractional Brownian motion for different Hurst indices

In this paper, we will evaluate integrals that define the conditional expectation, variance and characteristic function of stochastic processes with respect to fractional Brownian motion (fBm) for all relevant Hurst indices, i.e. . Particularly, the fractional Ornstein–Uhlenbeck (fOU) process gives rise to highly nontrivial integration formulas that need careful analysis when considering the whole range of Hurst indices. We will show that the classical technique of analytic continuation, from complex analysis, provides a way of extending the domain of validity of an integral from to the larger domain . Numerical experiments for different Hurst indices confirm the robustness and efficiency of the integral formulations presented. Moreover, we provide accurate and highly efficient financial option pricing results for processes that are related to the fOU process, with the help of Fourier cosine expansions.

Sigmoidal dynamics of macro-financial leverage

<abstract> <p>Logistic sigmoids due to their flexibility seem to be natural candidates for modelling macrofinancial leverage behavior. The sigmoidal leverage transition towards its stationary value, which was driven by the yield spreads, could have replicated the dynamics of macrofinancial assets, debt and capital. The leverage transition, in its turn, has been a major factor in better balancing macrofinancial liabilities and assets. The sigmoidal leverage trajectories including their inflections and different phases were identified by a nonlinear transition function providing information necessary for steering the process towards its stable state. Solving the stationary Kolmogorov-Fokker-Plank logistic equation revealed that random leverage realizations might follow the gamma distribution. Parameters of its stationary probability density function, as well as the expected and the modal leverage, were dependent on the process variance and the yield spreads. Thus, the stochastic leverage behaviour reproduced a sequence of stylized phases similar to the observed in the US Treasuries market meltdown in 2020. In particular, larger yield spreads and smaller modal leverage signalled a "defensive" market response to sudden volatility increases. In addition, it was shown that the logistic leverage modelling could be helpful in the analysis of debt and money dynamics including some consequences of "minting a one trillion dollars coin".</p> </abstract>

Multi-objective robust optimization of profit for a naphtha cracking furnace considering uncertainties in the feed composition

A cracking furnace is the primary unit of a naphtha cracking center (NCC) to produce ethylene (EL) and propylene (PL); the yields of EL and PL depend on the naphtha composition of the NCC feedstock. However, the naphtha composition typically fluctuates depending on the feedstock suppliers, and the consequent uncertainties in the composition causes investment risks associated with the net profit. However, owing to the high dimensional uncertainties of the naphtha, conventional sampling (e.g. Monte Carlo method) based robust optimization is infeasible option due to high computational cost. In this study, we adopt the polynomial chaos expansion (PCE) to surrogate the system considering the uncertainty. Owing to the orthogonality of the PCE, the statistical moment of the PCE can be directly calculated without uncertainty sampling and iterative simulation. In this study, the PCE-based profit optimization model of the NCC furnace is developed as follows: Initially, we infer probability density functions (PDF) using industrial data to consider the uncertainty in the naphtha composition. Using the inferred PDF, we extract training dataset samples with coil outlet temperature (COT), product price, feed composition, and the net profit. Subsequently, using the training dataset, we develop a polynomial chaos expansion (PCE)-based surrogate model to predict the moments of the net profit, namely, the mean, variance, and skewness. Owing to the orthogonality of the model, the moments can be parameterized with only decision variables instead of computing the uncertainty. Finally, we incorporate the developed PCE-based model into a genetic algorithm to simultaneously optimize two conflicting objectives: maximizing the mean profit and minimizing the variance. The optimization results reveal the trade-off relationship between the mean profit and investment risk (variance and skewness) of the NCC process under feed uncertainty. Owing to the orthogonality, the optimal decision point can be provided with low computation time and high prediction accuracy compared with the sampling based optimization method. Considering the application of the proposed optimization model, we conduct case studies for two different scenarios of the product price. The optimal COTs for maximum mean profit with minimum variance of profit in the first and second scenarios range from 723 to 833 and 734 to 898 ℃, respectively. Therefore, the proposed model can quantitatively predict the mean profit with investment risk and help decision-makers select optimal operating conditions considering both the investment tendency and uncertainty in the naphtha composition.

Disentangling global and domain-level adaptive behavior trajectories among children with autism spectrum disorder.

Heterogeneity in adaptive behavior abilities among people with autism spectrum disorder (ASD) is expressed not only as uneven levels of impairment across domains, but also in the developmental trajectories of adaptive skills. We studied the question of whether, after accounting for global adaptive behavior development, we find evidence of heterogeneity in the trajectories of specific domains of adaptive behavior. A sample of 504 children with ASD was obtained by combining data from two independent natural history studies conducted in North America. We used a factor of curves model to explain growth between 36 and 138 months in Vineland Adaptive Behavior Scales, Second Edition (VABS) age equivalents as a function of domain-specific and global growth processes. The domain-specific trajectories in all three domains (Communication, Daily Living Skills, and Socialization) reflected impairment relative to age expectations as well as slower-than-expected growth with age, and the parameters of these trajectories were moderately-to-strongly correlated across domains. The global adaptive behavior trajectory had an initial (36-41 months of age) developmental level of about 22 age-equivalent months, and eventually slowed after initially increasing by about 6months each year. The global trajectory accounted for the majority of variance in the domain-level processes; however, additional variance remained (14%-38%) in the domain-level intercepts, slopes, and quadratic processes. These results extend existing theoretical and empirical support for the hierarchical structure of adaptive behavior to include its development over time in clinical samples of children with ASD. A latent global trajectory may be sufficient to describe the growth of adaptive behavior in children with ASD; however, the remaining domain-specific variability after accounting for global adaptive behavior development allows for the possibility that differential effects of intervention on specific domains may be possible and detectable.

Lattice-based model for pricing contingent claims under mixed fractional Brownian motion

We propose a lattice-based model to approximate the dynamics of an asset with diffusion driven by a mixed fractional Brownian motion. Being it defined as the sum of a fractional Brownian motion and an independent Brownian motion, the method starts by discretizing separately the two processes. For the first process, we develop a binomial approach that is able to replicate the process variance at each discrete epoch, while a recombining binomial lattice is used to discretize the Brownian motion. Given the fractional Brownian motion path-dependency, the binomial approach is not recombining. Hence, to reduce the computational complexity, we establish a grid of representative values whose elements cover the range of possible asset values at each time slice. For each value of the grid, the algorithm identifies four successors in a bivariate environment. The successors may not appear among the generated asset values at the next epoch. In such cases, interpolation techniques are needed when solving backward to compute the initial value of the contingent claim. The proposed discretization allows to evaluate both European and American derivatives and numerical experiments confirm its accuracy and efficiency.

Constructing an indices system for evaluating the ecological integrity of forests in western Sichuan, China based on structural equation modeling

With the concern for biodiversity conservation and ecological sustainability, the traditional method of assessing conservation management based on single elements such as timber production, stand structure, and forest area is no longer applicable. Especially for China, where the primary goal of national park conservation management is to “protect and maintain the authenticity and integrity of natural ecosystems”, it is necessary to construct a set of indicators that can comprehensively evaluate the effectiveness of natural ecosystem conservation management. Therefore, in this study, we take Jiuzhaigou and Giant Panda National Park, in Sichuan, China, as examples, and construct a set of ecological integrity evaluation indices system from the perspective of attributes of forest ecosystems. Initially, we screened the candidate indicators based on the coefficient of variation, distribution range, and redundancy analysis and identified 16 indicators as the evaluation indices of ecological integrity. Next, the model fit and the interrelationship of the components of the ecological integrity model were verified using a combination of structural equation modeling and actual data. The model validation results showed that: (1) CMIN/DF = 1.66, RMSEA = 0.058, GFI = 0.954, and other model fit metrics have reached the best reference standard, indicating that the ecological integrity model overall fit is high. (2) In the parameter estimation results of the model observed and latent variables, the ecological integrity model explained 96%, 85% and 89% of the variance in species composition, stand structure and ecological processes, respectively, indicating that the evaluation indices selected can effectively predict the ecological integrity of forests. In addition, we used the factor loadings in the structural equation model to calculate the weights of the indices and used the weighted sum to calculate the ecological integrity. A one-way ANOVA was conducted to compare the differences among the ecological integrity of forests of different origins, forest types and life forms. The relative importance and linear regression were used to elucidate the main factors affecting forest ecological integrity. The results showed that (1) except for the scrub community, the mean value of forest ecological integrity was >0.45, which was in the middle-to-upper level. (2) the ecological integrity of forests of different origins and different forest types showed a changing pattern: natural forest > plantation forest, mixed forest > pure forest. (3) Stand age and elevation strongly influenced the ecological integrity of forests, with relative contribution rates of 64.54% and 11.88%, respectively.

On the Low Degree of Entropy Implied by the Solutions of Modern Macroeconomic Models.

The non-causal ("forward-looking") solution used routinely in academic macroeconomics may represent a violation of a law of entropy, namely that the direction of time is one way (from the past and towards the present), and that the variance of economic processes increases with time. In order to re-establish a degree of compatibility with the law of entropy, so called hybrid forms are required add-ins to DSGE (Dynamic Stochastic General Equilibrium) models. However, the solution that uses hybrid forms is a particular special case of a causal solutions of autoregressive distributed lags, VARs and recursive and simultaneous equations models well known from empirical macro econometrics. Hence, hybrid forms of small scale DSGE models can be analysed and tested against competing model equations, using an econometric encompassing framework.

Kernel-based models for influence maximization on graphs based on Gaussian process variance minimization

The inference of novel knowledge, the discovery of hidden patterns, and the uncovering of insights from large amounts of data from a multitude of sources make data science to an art rather than just a mere scientific discipline. The study and design of mathematical models and signal processing tools able to analyze information represents a central research topic within data science. In this work, we introduce and investigate a model for influence maximization (IM) on graphs using ideas from kernel-based signal approximation, Gaussian process regression, and the minimization of a corresponding variance term. Data-driven approaches can be applied to determine proper kernels for this IM model and machine learning methodologies are adopted to tune the model parameters. Compared to stochastic models for influence maximization that rely on Monte-Carlo simulations, our kernel-based model allows for a simple and cost-efficient update strategy to compute optimal influencing nodes on a graph. In several numerical experiments, we show the properties and benefits of this model.

Statistical Analysis of Silicon Photomultiplier Output Signals

Silicon photomultipliers are relatively new devices designed as a matrix of single-photon avalanche detectors, which have become popular for their miniature dimensions and low operating voltage. Their superior sensitivity allows detecting low-photon-count optical pulses, e.g., in ranging and LIDAR applications. The output signal of the photomultiplier is a non-stationary stochastic process, from which a weak periodic pulse can be extracted by means of statistical processing. Using the double-exponential approximation of output avalanche pulses the paper presents a simple analytical solution to the mean and variance of the stochastic process. It is shown that even for an ideal square optical pulse the rising edge of the statistically detected signal is longer than the edge of individual avalanche pulses. The knowledge of the detected waveform can be used to design an optimum laser pulse waveform or algorithms for estimating the time of arrival. The experimental section demonstrates the proposed procedure.

Simultaneous optimization of inventory, maintenance, and quality for production systems subject to multiple mean and variance shifts

This article presents a general, integrated production, quality, and condition-based maintenance model for imperfect processes with multiple out-of-control operating states. The production system is subject to multiple quality disruptions, which affect both the process mean and variance, and failures. The quality of the production process output is monitored by a fully adaptive control scheme, and the state of deterioration is estimated through periodic sampling inspection. The proposed control scheme’s operation is modeled through a Markov chain, and the optimal quality control, maintenance, and inventory policy are defined based on an expected total cost minimization criterion. Finally, an illustrative example is employed to demonstrate the operation of the proposed model, sensitivity analysis is conducted to generate insights into how the process parameters misspecification affects the economic performance, and a comparative study is performed to evaluate the model’s superiority against the respective single quality shift model.

Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments

We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that generates realistic subexponential autocorrelation functions, and the “static” nature of the control originates from a realistic observability assumption in the system. The Markovian lift was effectively used to discretize the system into a finite-dimensional process, which is easier to analyze. The resolution of the problem is based on backward Kolmogorov equations and a quadratic solution ansatz. The control problem has a closed-form solution, and the variance has both strict upper and lower bounds, indicating that the variance cannot take an arbitrary value even when it is subject to a high control cost. The correspondence between the discretized system based on the Markovian lift and the original infinite-dimensional one is discussed. Then, a convergent Markovian lift is presented to approximate the infinite-dimensional system. Finally, the control problem was applied to real cases using available data for a river reach. An extended problem subject to an additional constraint on maintaining the flow variability was also analyzed without significantly degrading the tractability of the proposed framework.

Notes on ultraslow nonlocal telegraph evolution equations

This paper provides a refinement of the study of asymptotic behaviour for a class of nonlocal in time telegraph equations with positively singular kernels. Based on fundamental properties of relaxation functions and recent representation of the fundamental solution in [Nonlinear Anal. 193 (2020), 111411], we establish the asymptotic expansions of the variance of the stochastic process for both long-time and short-time, which sharply improves the main result in [Proc. Amer. Math. Soc. 149 (2021), 2067–2080] by removing their technical conditions on the regularly varying behaviours and reformulating the asymptotic expansion in a more natural form. By analysing a new noncommutative operation on a subclass of completely positive functions, we provide a new way to construct finitely many ultraslow subdiffusion processes that are rapidly slower than a given ultraslow kernel. Consequently, we show that for a given completely monotonic ultraslow kernel, there is an induced kernel whose corresponding mean square displacement is logarithmic.

R400: A novel gene signature for dose prediction in radiation exposure studies in humans

Radiation’s harmful effects on biological organisms have long been studied through mainly evaluating pathological changes in cells, tissues, or organs. Recently, there have been more accessible gene expression datasets relating to radiation exposure studies. This provides an opportunity to analyze responses at the molecular level toward revealing phenotypic differences. Biomarkers in toxicogenomics have been suggested as indicators of radiation exposure and seem to react differently to various dosages of radiation. This study proposes a predictive gene signature specific to radiation exposure and can be used in automatically diagnosing the exposure dose. In searching for a reliable gene set that will correctly identify the exposure dose, consideration needs to be given to the size of the set. For this reason, we experimented with the number of genes used for training and testing. Gene set sizes of 28, 100, 200, 300, 400, 500, 600, 700, 800, 900 and 1,000 were tested to find the size that provided the best accuracy across three datasets. Models were then trained and tested using multiple datasets in various ways, including an external validation. The dissimilarities between these datasets provide an analogy to real-world conditions where data from multiple sources are likely to have variances in format, settings, time parameters, participants, processes, and machine tolerances, so a robust training dataset from many heterogeneous samples should provide better predictability. All three datasets showed positive results with the correct classification of the radiation exposure dose. The average accuracy of all three models was 88% for gene sets of both 400 and 1,000 genes. R400 provided the best results when testing the three datasets used in this study. A literature validation of top selected genes shows high relevance of perturbations to adverse effects reported during cancer radiotherapy.

Metabolic control analysis enables rational improvement of E. colil-tryptophan producers but methylglyoxal formation limits glycerol-based production

BackgroundAlthough efficient l-tryptophan production using engineered Escherichia coli is established from glucose, the use of alternative carbon sources is still very limited. Through the application of glycerol as an alternate, a more sustainable substrate (by-product of biodiesel preparation), the well-studied intracellular glycolytic pathways are rerouted, resulting in the activity of different intracellular control sites and regulations, which are not fully understood in detail. Metabolic analysis was applied to well-known engineered E. coli cells with 10 genetic modifications. Cells were withdrawn from a fed-batch production process with glycerol as a carbon source, followed by metabolic control analysis (MCA). This resulted in the identification of several additional enzymes controlling the carbon flux to l-tryptophan.ResultsThese controlling enzyme activities were addressed stepwise by the targeted overexpression of 4 additional enzymes (trpC, trpB, serB, aroB). Their efficacy regarding l-tryptophan productivity was evaluated under consistent fed-batch cultivation conditions. Although process comparability was impeded by process variances related to a temporal, unpredictable break-off in l-tryptophan production, process improvements of up to 28% with respect to the l-tryptophan produced were observed using the new producer strains. The intracellular effects of these targeted genetic modifications were revealed by metabolic analysis in combination with MCA and expression analysis. Furthermore, it was discovered that the E. coli cells produced the highly toxic metabolite methylglyoxal (MGO) during the fed-batch process. A closer look at the MGO production and detoxification on the metabolome, fluxome, and transcriptome level of the engineered E. coli indicated that the highly toxic metabolite plays a critical role in the production of aromatic amino acids with glycerol as a carbon source.ConclusionsA detailed process analysis of a new l-tryptophan producer strain revealed that several of the 4 targeted genetic modifications of the E. colil-tryptophan producer strain proved to be effective, and, for others, new engineering approaches could be derived from the results. As a starting point for further strain and process optimization, the up-regulation of MGO detoxifying enzymes and a lowering of the feeding rate during the last third of the cultivation seems reasonable.

Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions.

For renewal-reward processes with a power-law decaying waiting time distribution, anomalously large probabilities are assigned to atypical values of the asymptotic processes. Previous works have revealed that this anomalous scaling causes a singularity in the corresponding large deviation function. In order to further understand this problem, we study in this article the scaling of variance in several renewal-reward processes: counting processes with two different power-law decaying waiting time distributions and a Knudsen gas (a heat conduction model). Through analytical and numerical analyses of these models, we find that the variances show an anomalous scaling when the exponent of the power law is -3. For a counting process with the power-law exponent smaller than -3, this anomalous scaling does not take place: this indicates that if we only consider the standard deviation from the expectation, any anomalous behavior will not be detected. In this case, we argue that anomalous scaling appears in higher order cumulants. Finally, many-body particles interacting through soft-core interactions with the boundary conditions employed in the Knudsen gas are studied using numerical simulations. We observe that the variance scaling becomes normal even though the power-law exponent in the boundary conditions is -3.

Using whole-brain diffusion tensor analysis to evaluate white matter structural correlates of delayed visuospatial memory and one-week motor skill retention in nondemented older adults: A preliminary study.

Skill retention is important for motor rehabilitation outcomes. Recent work has demonstrated that delayed visuospatial memory performance may predict motor skill retention in older and neuropathological populations. White matter integrity between parietal and frontal cortices may explain variance in upper-extremity motor learning tasks and visuospatial processes. We performed a whole-brain analysis to determine the white matter correlates of delayed visuospatial memory and one-week motor skill retention in nondemented older adults. We hypothesized that better frontoparietal tract integrity would be positively related to better behavioral performance. Nineteen participants (age>58) completed diffusion-weighted imaging, then a clinical test of delayed visuospatial memory and 50 training trials of an upper-extremity motor task; participants were retested on the motor task one week later. Principal component analysis was used to create a composite score for each participant’s behavioral data, i.e. shared variance between delayed visuospatial memory and motor skill retention, which was then entered into a voxel-based regression analysis. Behavioral results demonstrated that participants learned and retained their skill level after a week of no practice, and their delayed visuospatial memory score was positively related to the extent of skill retention. Consistent with previous work, neuroimaging results indicated that regions within bilateral anterior thalamic radiations, corticospinal tracts, and superior longitudinal fasciculi were related to better delayed visuospatial memory and skill retention. Results of this study suggest that the simple act of testing for specific cognitive impairments prior to therapy may identify older adults who will receive little to no benefit from the motor rehabilitation regimen, and that these neural regions may be potential targets for therapeutic intervention.

Variational Principles for Asymptotic Variance of General Markov Processes

A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get an upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and non-reversible diffusion processes.

Some bounds for the renewal function and the variance of the renewal process

Renewal equations are frequently encountered in several applications when regenerative arguments are used in modelling. Since, these equations usually do not have analytical solutions, bounds have a great practical importance. The aim of this paper is to present some new bounds for the renewal function and the variance of the renewal process. A general lower bound for the renewal function is given, which is a refinement of all known lower bounds and attains the well-known asymptotic result of Asmussen (2003). Also, some new tighter upper and lower bounds for the renewal function, which are based on several reliability classifications of the distribution of the inter-arrival times, are given. Improved upper and lower bounds for the variance of the renewal process are also presented. Finally, several numerical examples are given to illustrate the effectiveness of the proposed new bounds.