Non-symmetric Distributions Research Articles

FRET calibration by symmetrization on the cell surface

Maximum position of Shannon-information of FRET frequency distribution represented as a function of the α (or G) calibrating factor as calculated in the framework of dual-laser flow cytometric FRET method – also called 3-cube FRET – gives a fairly good approximation of the real α, using only a single FRET sample. The estimation is accurate for completely symmetric FRET distributions like Gaussian and uniform. For non-symmetric distributions, the committed error has been found to depend on the direction and degree of deviation from the complete symmetry. The maximum information is characterized also by zero skewness, and minima in kurtosis and in the χ-value, defined as the “absolute deviation from the Gaussian”, as other α- functions characterizing shape. As to practice, information maximum of FRET distribution can be used to determine α, whenever symmetry can be assumed. In other cases, the goodness of estimation can be inferred from the information content and shape parameters (skewness, kurtosis and “χ-value”) of the primarily measured FRET parameter A′, based on their inverse correlations with their counterparts computed with the target FRET distribution. Above a threshold in FRET efficiency or its coefficient of variation, resonant peaks (“Ω-curves”) in FRET information appear on the α-scale, with their positions stabilized around α values with reduced fluctuations dictated by symmetry of the target FRET distribution. The phenomenon is explained by a FRET-induced broadening of the A′ distribution reaching the domain containing A′ = −α.

Microstructure and optical properties of Au:N doped diamond-like carbon films: Effect of working pressure

In recent years, the incorporation of impurities (metallic or non-metallic) into diamond-like carbon films for industrial and biological applications has garnered considerable attention from researchers. In this study, gold nanoparticles and nitrogen impurities were introduced into diamond-like carbon using a co-deposition method involving Radio Frequency Plasma-Enhanced Chemical Vapor Deposition (RF-PECVD) and Radio Frequency Sputtering (RF-sputtering),modifying the working pressure from 14.5 to 19.5 mTorr. X-ray Diffraction (XRD) patterns confirmed the presence of gold nanocrystals in the samples. The surface morphology of the films was analyzed using images obtained from Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM) subjected to statistical and fractal analyses. These investigations revealed non-symmetric Gaussian distributions of the grains, demonstrating a multifractal nature in all samples, as well as a complex relationship between film roughness and working pressure. Films prepared at working pressures of 16.5 and 18.5 mTorr exhibited the roughest and smoothest surfaces, respectively. Fast Fourier Infrared (FTIR) spectroscopy was used to identify functional groups and to estimate the sp2/sp3 ratio. Raman spectra show D and G bands associated with the disordered graphitic carbon of the DLC, with the intensity of the G band being higher than that of the D band, indicating a higher sp2 bonding content compared to sp3 bonding. Subsequently, the absorption UV–visible spectrum of the samples was examined, confirming the presence of gold nanoparticles in the films, as evidenced by the occurrence of a Localized Surface Plasmon Resonance peak, whose location dependent on the working pressure used during deposition. These observations are consistent with other microscopic and structural analyses.

Elastic analysis of functionally graded porous cylinders under uniform internal pressure by using shear deformation theory

This research aims to analyze cylindrical shells made of functionally graded porous materials, focusing on three types of monotonous, symmetric, and nonsymmetric porosity distributions. Material properties are defined for different porosity distributions, individually. Due to the slight variation of Poisson’s ratio, it is assumed to be constant throughout the thickness of the cylinder. The governing equations are derived using the first-order shear deformation theory and the virtual work principle. The governing equations are solved using the eigenvalue–eigenvector method for clamped–clamped boundary conditions. The solution’s accuracy and convergence are validated by conducting a comparative study. Finally, the numerical results include the components of displacement, axial displacement, radial displacement, circumferential stress, radial stress, and shear stress are reported according to porosity coefficient and different porosity distributions.

Sensitivity Analysis for Dynamic Control of PSTNs with Skewed Distributions

Probabilistic Simple Temporal Networks (PSTN) facilitate solving many interesting scheduling problems by characterizing uncertain task durations with unbounded probabilistic distributions. However, most current approaches assess PSTN performance using normal or uniform distributions of temporal uncertainty. This paper explores how well such approaches extend to families of non-symmetric distributions shown to better represent the temporal uncertainty introduced by, e.g., human teammates by building new PSTN benchmarks. We also build probability-aware variations of current approaches that are more reactive to the shape of the underlying distributions. We empirically evaluate the original and modified approaches over well-established PSTN datasets. Our results demonstrate that alignment between the planning model and reality significantly impacts performance. While our ideas for augmenting existing algorithms to better account for human-style uncertainty yield only marginal gains, our results surprisingly demonstrate that existing methods handle positively-skewed temporal uncertainty better.

On the descriptive and predictive capabilities of two model approaches considering the collagen fiber dispersion in healthy and aneurysmal arteries

Most constitutive models aim to describe the arterial macroscopic mechanical behavior via an elastin-rich ground substance reinforced by spatially dispersed collagen fibers. Two approaches are frequently considered for modeling collagen fiber dispersion, one is based on the generalized structure tensor (GST), and the other uses the angular integration (AI) method. Recently, both approaches have been reviewed for non-symmetric fiber distributions. It was concluded that both model ‘predictions’ fit very well with experimental data, solely based on the ability to ‘describe’ the same uniaxial or equibiaxial data set used for parameter estimation by not addressing any ‘predictive’ aspects. Therefore, this study systematically analyzes the ‘descriptive’ and ‘predictive’ capabilities of the GST and AI approaches by fitting their parameters to multiratio biaxial tensile test data of healthy and aneurysmal abdominal arteries. Subsequently, both model responses are investigated under realistic in vivo loading conditions, considering residual stresses, an axial in vivo stretch, and physiological blood pressure levels. In summary, no statistically significant difference in the ‘descriptive’ features of the two modeling approaches was identified. The pressure-radius relationship, the transmural stress distributions, and the axial force predicted by both models were analyzed for the healthy and diseased arterial ring, showing minor deviations based on fitting limitations.

Real-Time Rock-Properties Estimation for Geosteering: Statistical Rock-Physics-Driven Inversion of Seismic Acoustic Impedance and LWD Ultradeep Azimuthal Resistivity

Summary This work describes a statistical rock-physics-driven inversion of seismic acoustic impedance (AI) and ultradeep azimuthal resistivity (UDAR) log data, acquired while drilling, to estimate porosity, water saturation, and facies classes around the wellbore. Despite their limited resolution, seismic data integrated with electromagnetic resistivity log measurements improve the description of rock properties by considering the coupled effects of pore space and fluid saturation in the joint acoustic and electrical domains. The proposed inversion does not explicitly use a forward model, rather the correlation between the petrophysical properties and the resulting geophysical responses is inferred probabilistically from a training data set. The training set is generated by combining available borehole information with a statistical rock-physics modeling approach. In the inversion process, given colocated measurements of seismic AI and logging-while-drilling (LWD) electromagnetic resistivity data, the pointwise probability distribution of rock properties is derived directly from the training data set by applying the kernel density estimation (KDE) algorithm. A nonparametric statistical approach is used to approximate nonsymmetric volumetric distributions of petrophysical properties and to consider the characteristic nonlinear relationship linking water saturation with resistivity. Given an a priori facies classification template for the samples in the training set, it is possible to model the multimodal, facies-dependent behavior of the petrophysical properties, together with their distinctive correlation patterns. A facies-dependent parameterization allows the effect of lithology on acoustic and resistivity responses to be implicitly considered, even though the target properties of inversion are only porosity and saturation. To provide a realistic uncertainty quantification of the estimated rock properties, a plain Bayesian framework is described to account for rock-physics modeling error and to propagate seismic and resistivity data uncertainties to the inversion results. In this respect, the uncertainty related to the scale difference among the well-log data and seismic is addressed by adopting a scale reconciliation strategy. The main feature of the described inversion lies in its fast implementation based on a look-up table that allows rock properties, with their associated uncertainty, to be estimated in real time following the acquisition and inversion of UDAR data. This gives a robust, straightforward, and fast approach that can be effortlessly integrated into existing workflows to support geosteering operations. The inversion is validated on a clastic oil-bearing reservoir, where geosteering was used to guide the placement of a horizontal appraisal well in a complex structural setting. The results show that the proposed methodology provides realistic estimates of the rock-property distributions around the wellbore to depths of investigation of 50 m. These constitute useful information to drive geosteering decisions and can also be used, post-drilling, to update or optimize existing reservoir models.

On nonlinear stability analysis of saturated embedded porous nanobeams

In this work, the nonlinear stability behaviors of the saturated porous nanobeams embedded in an elastic foundation are investigated. The restrained nanobeam is modeled using geometrical nonlinear equations in conjunction with the constitutive law of saturation. Three patterns for saturation along the thickness of the nanobeam are considered as porous/monotonous, porous/nonlinear symmetric, and porous/nonlinear non-symmetric distributions. The infinite terms of the power series are discretized thanks to Stokes' transformation and trigonometric series. Then, the effects of saturation and nonlinearity on buckling loads are studied by considering the restrained boundary conditions. Moreover, the nonlinear results are validated with the saturated nanobeam with the rigid supporting conditions.

On designing new mixed modified exponentially weighted moving average - exponentially weighted moving average control chart

Control charts are an extremely valuable tool in statistical process control (SPC) for processing information from a system or procedure over time and displaying statistically significant changes in data while also showing how a system or process is changing. The modified exponentially weighted moving average - exponentially weighted moving average control chart (MEME) is proposed as a new mixed control chart for monitoring and quickly detecting moderate to small shifts in the mean process. Average and median run lengths are instruments for assessing efficiency through Monte Carlo simulations based on symmetric and nonsymmetric distributions. The performance comparison showed that the proposed chart outperformed alternatives control chart in simulation and in two real-data applications by lowering the out-of-control average run length.

Minimizing total tardiness in a two-machine flowshop with uncertain and bounded processing times

The two-machine flowshop scheduling problem with the performance measure of total tardiness is addressed. This performance measure is essential since meeting deadlines is a crucial part of scheduling and a major concern for some manufacturing systems. The processing times on both machines are uncertain variables and within some lower and upper bounds. This is due to uncertainty being an integral part of some manufacturing settings, making it impossible to predict processing times in advance. To the best of the author’s knowledge, this problem is addressed for the first time in this paper. A dominance relation is established and nineteen algorithms are proposed. These algorithms are extensively evaluated through randomly generated data for different numbers of jobs and four different distributions, representing both symmetric and non-symmetric distributions. Computational experiments show that the presented algorithms perform extremely well when compared with a random solution. In particular, the best of the considered 19 algorithms reduces the error of the random solution by 99.99% and the error of the worst algorithm (among the 19 algorithms) by 99.96%. The results are confirmed by a test of hypothesis and this algorithm is recommended.

Non-symmetric distributions of solids deposition for solid-water stratified flow in deviated tubing strings

Dynamic performance on solids flow with water in deviated tubing is essential for the reliability of pump and normal operation of horizontal and directional wells. Compared with coal-water flow in vertical tubing and sand-oil flow with high production in deviated tubing, solids deposition with water shows obvious non-symmetric distributions in deviated tubing from simulations and experiments. The mathematical model of two phase flow was developed under coupling conditions of deviated tubing, low flow rate and viscosity based on the kinetic theory of granular flow and first-order discrete scheme. The results show that solid-water stratified flow in deviated tubing can be divided into two zones of suspension bed and the moving bed throughout the flow field. The solid flowing velocity with water is negative and particles slide down at the bottom of moving bed zone. The process of solids flow with water in deviated tubing will produce pressure loss and consume the kinetic energy. The thickness of deposited layer and the flowing velocity of solids flow downward with water at the moving bed zone enhance with the decreased inlet flow rate and the increased particle size, tubing inside diameter (ID) and inclination angle. Solids are easier into suspension from the upper part of moving bed zone to suspension bed zone and more solid particles flow with water towards the tubing outlet with the increase of inlet flowing velocity. The decision is made to reduce the screen width, tubing ID and inclination angle to maintain to be greater than critical deposition velocity in order to prevent solids settling. And it provides the theoretical basis and technical reserves for solid control and offers an effective approach to enhance tubing cleaning in deviated strings.

Symmetric and Asymmetric Distributions: Theoretical Developments and Applications III

A summary of the eleven papers published in this special issue is presented here. This volume was the last in a series of special issues dealing with symmetric and non-symmetric continuous probability distributions. The works presented in this issue propose new probabilistic models and extend the properties of other existing models in the statistical literature.

Performance of new nonparametric Tukey modified exponentially weighted moving average-Moving average control chart.

Control charts are an amazing and essential statistical process control (SPC) instrument that is commonly used in monitoring systems to detect a specific defect in the procedure. The mixed Tukey modified exponentially weighted moving average - moving average control chart (MMEM-TCC) with motivation detection ability for fewer shifts in the process mean under symmetric and non-symmetric distributions is proposed in this paper. Average run length (ARL), standard deviation of run length (SDRL), and median run length (MRL) were used as efficiency criteria in the Monte Carlo simulation, and their efficiency was compared to existing control charts. Furthermore, the expected ARL (EARL) is a method for evaluating the performance of control charts beyond a specific range of shift sizes. The distinguishing feature of the proposed chart is that it performs efficiently in detecting small to moderate shifts. There are applications for PM 2.5 and PM 10 data that demonstrate the performance of the proposed chart.

Procedures and Guidelines for Inputting and Output Smoothening of Kinetic Monte Carlo Distributions

AbstractPopulation balance modeling is very popular in several branches of modern science, including (bio)chemical engineering, geography, and demography. A growing trend is the use of stochastic solvers (e.g., kinetic Monte Carlo), but care should be taken upon inputting and outputting distributed data for the populations involved. In the present contribution, several procedures and guidelines are formulated facilitating such data treatment. The solutions are exemplified through polymerization and polymer modification case studies, taking the molar mass or chain length as core stochastic variable. It is shown that rediscretization is often necessary, as experimentally measured distributions are not directly interpretable at the input side of stochastic solvers. This rediscretization should take place both for the abscissa and ordinate values of the distributions. As stochastic solvers often display noisy data as model output, attention is paid to the smoothening of the output distributions as well. It is highlighted that the kernel‐smoothening method is very promising, as it can reliably tackle postprocessing of nonsymmetric distributions. Guidelines are formulated regarding the correct interpretation of the distribution tail both for the input and output modifications.

Mixtures of Semi-Parametric Generalised Linear Models

The mixture of generalised linear models (MGLM) requires knowledge about each mixture component’s specific exponential family (EF) distribution. This assumption is relaxed and a mixture of semi-parametric generalised linear models (MSPGLM) approach is proposed, which allows for unknown distributions of the EF for each mixture component while much of the parametric structure of the traditional MGLM is retained. Such an approach inherently allows for both symmetric and non-symmetric component distributions, frequently leading to non-symmetrical response variable distributions. It is assumed that the random component of each mixture component follows an unknown distribution of the EF. The specific member can either be from the standard class of distributions or from the broader set of admissible distributions of the EF which is accessible through the semi-parametric procedure. Since the inverse link functions of the mixture components are unknown, the MSPGLM estimates each mixture component’s inverse link function using a kernel smoother. The MSPGLM algorithm alternates the estimation of the regression parameters with the estimation of the inverse link functions. The properties of the proposed MSPGLM are illustrated through a simulation study on the separable individual components. The MSPGLM procedure is also applied on two data sets.

Second law analysis of aerodynamic characteristics with flow temperature variations of simple angle and compound angle full coverage film cooling

The present investigation employs entropy generation to quantify aerodynamic characteristics with flow temperature variations, and the associated second law losses, which are present within a film cooled boundary layer produced by a unique full-coverage compound angle hole configuration. With this arrangement, an alternating sign for the compound angle β is employed from one streamwise row of holes to another, such that compound angle β is +30° in one row of holes, followed by −30° in the next row of holes. Entropy change distributions, entropy generation distributions, and mass-averaged overall exergy destruction from this compound angle arrangement are compared to results from a simple angle arrangement with β = 0°. These quantities are determined from flow field measurements of local flow temperature variations, and local stagnation pressure variations with film cooling. Within the investigation, full-coverage film cooling blowing ratio values range from 2.9 to 6.0, mainstream Reynolds numbers Rems range from 127,000 to 142,000, and effusion flow Reynolds numbers range from about 7000 to approximately 13,000. Distributions of local entropy generation and mass-averaged overall exergy destruction (both relative to freestream flow) are determined using three analysis approaches, which account for local flow temperature variations only, local flow stagnation pressure variations only, and variations of stagnation pressure and local flow temperature together. Similar qualitative trends of local entropy generation for the three different types of data are observed, which mean that temperature and stagnation pressure within the flow experience similar rearrangements by secondary advection and diffusion phenomena for the two film cooling arrangements. From a quantitative perspective, values associated with flow temperature variations only, are consistently larger than values associated with stagnation pressure variations only. Important local variations of local entropy generation are observed for the compound angle arrangement, which are due to skewed and non-symmetric film distributions, along with the associated tilted horseshoe-shaped vortex, which forms around each film coolant concentration.

Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions

We study Bessel and Dunkl processes (Xt,k)t≥0 on RN with possibly multivariate coupling constants k≥0. These processes describe interacting particle systems of Calogero–Moser–Sutherland type with N particles. For the root systems AN−1 and BN these Bessel processes are related with β-Hermite and β-Laguerre ensembles. Moreover, for the frozen case k=∞, these processes degenerate to deterministic or pure jump processes.We use the generators for Bessel and Dunkl processes of types A and B and derive analogues of Wigner’s semicircle and Marchenko–Pastur limit laws for N→∞ for the empirical distributions of the particles with arbitrary initial empirical distributions by using free convolutions. In particular, for Dunkl processes of type B new non-symmetric semicircle-type limit distributions on R appear. Our results imply that the form of the limiting measures is already completely determined by the frozen processes. Moreover, in the frozen cases, our approach leads to a new simple proof of the semicircle and Marchenko–Pastur limit laws for the empirical measures of the zeros of Hermite and Laguerre polynomials respectively.

A New Goodness-of-Fit Test: Free Chi-Square (FCS)

This paper presents a new goodness-of-fit technique for testing the assumption of univariate distributions which is based on the theoretical distribution function of the hypothesized distribution. The existing methods are examined in two different categories: binning and binning-free. The most widely known binning test is the Chi-square test. The Kolmogorov-Smirnov, the Cramer-von Mises and the Anderson-Darling goodness-of-fit tests come to the forefront as the binning-free tests. When tests are evaluated in terms of distributions, it is examined in two different classes: the not distribution-free tests and the distribution-free tests. The desired goodness-of-fit test method for a researcher should be binning-free, distribution-free, more sensitivity, easy to use and fast. In this study, a test method is proposed which provides almost all the options that a researcher would want. The Monte-Carlo simulation methods are used to demonstrate the success of the proposed method. In these simulations, the normality test was applied for symmetric distributions whereas the lognormality test was applied for non-symmetric distributions. The proposed test method has demonstrated superiority in many aspects compared to other selected test methods on both simulations and three different real-life datasets.

Multivariate probabilistic rock-physics models using Kumaraswamy distributions

Rock-physics models are physical equations that map petrophysical properties into geophysical variables, such as elastic properties and density. These equations are generally used in quantitative log and seismic interpretation to estimate the properties of interest from measured well logs and seismic data. Such models are generally calibrated using core samples and well-log data and result in accurate predictions of the unknown properties. Because the input data are often affected by measurement errors, the model predictions are often uncertain. Instead of applying rock-physics models to deterministic measurements, I have applied the models to the probability density function (PDF) of the measurements. This approach has been previously adopted in the literature using Gaussian distributions, but for petrophysical properties of porous rocks, such as volumetric fractions of solid and fluid components, the standard probabilistic formulation based on Gaussian assumptions is not applicable due to the bounded nature of the properties, the multimodality, and the nonsymmetric behavior. The proposed approach is based on the Kumaraswamy PDF for continuous random variables, which allows modeling double-bounded nonsymmetric distributions and is analytically tractable, unlike beta or Dirichlet distributions. I have developed a probabilistic rock-physics model applied to double-bounded continuous random variables distributed according to a Kumaraswamy distribution and derived the analytical solution of the probability distribution of the rock-physics model predictions. The method is evaluated for three rock-physics models: Raymer’s equation, Dvorkin’s stiff sand model, and Kuster-Toksöz’s inclusion model.

Informational Measures of the Shape of the Amoroso Distributions for the Research of Dispersed Materials

For the particle size distribution function various forms of exponential models are used to construct models of the properties of dispersed substance. The most difficult stage of applied research is to determine the shape of the particle distribution model. For the particle size distribution function various forms of exponential models are used to construct models of the properties of dispersed substance. The most difficult stage of applied research is to determine the shape of the particle distribution model. The article proposes a uniform model for setting the interval of information uncertainty of non-symmetric particle size distributions. Based on the analysis of statistical and information uncertainty intervals, new shape coefficients of distribution models are constructed, these are the entropy coefficients for shifted and non shifted distributions of the Amoroso family. Graphics of dependence of entropy coefficients of non-symmetrical distributions show that distributions well-known are distinguish at small of the shapes parameters. Also it is illustrated for parameters of the form more than 2 that it is preferable to use the entropy coefficients for the unshifted distributions.The material contains also information measures for the well-known logarithmic normal distribution which is a limiting case of distribution Amorozo.

Wheel–rail impact loads and axle bending stress simulated for generic distributions and shapes of discrete wheel tread damage

Wheel–rail impact loads generated by discrete wheel tread irregularities may result in high dynamic bending stresses in the wheelset axle, leading to a decrease in component life and an elevated risk for fatigue failure. In this paper, a versatile and cost-efficient method to simulate the vertical dynamic interaction between a wheelset and railway track, accounting for generic distributions and shapes of wheel tread damage, is presented. The wheelset (comprising two wheels, axle and any attached equipment for braking and power transmission) and track with two discretely supported rails are described by three-dimensional finite element (FE) models. The coupling between the two wheel‒rail contacts (one on each wheel) via the wheelset axle and via the sleepers is considered. The simulation of dynamic vehicle–track interaction is carried out in the time domain using a convolution integral approach, while the non-linear wheel–rail normal contact is solved using Kalker's variational method. Wheelset designs that are non-symmetric with respect to the centre of the axle, track support conditions that are non-symmetric with respect to the centre of the track, as well as non-symmetric distributions of tread damage on the two wheels (or irregularities on the two rails) can be studied. Time-variant stresses are computed for the locations in the wheelset axle which are prone to fatigue. Based on Green's functions for stress established using the wheelset FE model, this is achieved in a post-processing step. An extensive parametric study has been performed where wheel–rail impact loads and axle stresses have been computed for different distributions and sizes of tread damage as well as for different train speeds.