Random Variables Research Articles

Electronic oral health surveillance system for Egyptian preschoolers using District Health Information System (DHIS2): design description and time motion study

BackgroundEarly childhood caries (ECC) is a major global health issue affecting millions of children. Mitigating this problem requires up-to-date information from reliable surveillance systems. This enables evidence-based decision-making to devise oral health policies. The World Health Organization (WHO) advocates the adoption of mobile technologies in oral disease surveillance because of their efficiency and ease of application. The study describes developing an electronic, oral health surveillance system (EOHSS) for preschoolers in Egypt, using the District Health Information System (DHIS2) open-source platform along with its Android App, and assesses its feasibility in data acquisition.MethodsThe DHIS2 Server was configured for the DHIS2 Tracker Android Capture App to allow individual-level data entry. The EOHSS indicators were selected in line with the WHO Action Plan 2030. Two modalities for the EOHSS were developed based on clinical data capture: face-to-face and tele/asynchronous. Eight dentists in the pilot team collected 214 events using modality-specific electronic devices. The pilot’s team's feedback was obtained regarding the EOHSS's feasibility in collecting data, and a time-motion study was conducted to assess workflow over two weeks. Independent t-test and Statistical Process Control techniques were used for data analysis.ResultsThe pilot team reported positive feedback on the structure of the EOHSS. Workflow adaptations were made to prioritize surveillance tasks by collecting data from caregivers before acquiring clinical data from children to improve work efficiency. A shorter data capture time was required during face-to-face modality (4.2 ± 0.7 min) compared to telemodality (5.1 ± 0.9 min), p < 0.001). The acquisition of clinical data accounted for 16.9% and 21.1% of the time needed for both modalities, respectively. The time required by the face-to-face modality showed random variation, and the tele-modality tasks showed a reduced time trend to perform tasks.ConclusionsThe DHIS2 provides a feasible solution for developing electronic, oral health surveillance systems. The one-minute difference in data capture time in telemodality compared to face-to-face indicates that despite being slightly more time-consuming, telemodality still shows promise for remote oral health assessments that is particularly valuable in areas with limited access to dental professionals, potentially expanding the reach of oral health screening programs.

A direct and analytical method for inverse problems under uncertainty in energy system design: combining inverse simulation and Polynomial Chaos theory

This article introduces and formalizes a novel stochastic method that combines inverse simulation with the theory of generalized Polynomial Chaos (gPC) to solve and study inverse problems under uncertainty in energy system design applications. The method is particularly relevant to design tasks where only a deterministic forward model of a physical system is available, in which a target design quantity is an input to the model that cannot be obtained directly, but can be quantified reversely via the outputs of the model. In this scenario, the proposed method offers an analytical and direct approach to invert such system models. The method puts emphasis on user-friendliness, as it enables its users to conduct the inverse simulation under uncertainty directly in the gPC domain by redefining basic algebra operations for computations. Moreover, the method incorporates an optimization-based approach to integrate supplementary constraints on stochastic quantities. This feature enables the solution of inverse problems bounding the statistical moments of stochastic system variables. The authors exemplify the application of the proposed method with proof-of-concept tests in energy system design, specifically performing uncertainty quantification and sensitivity analysis for a Multi-Energy System (MES). The findings demonstrate the high accuracy of the method as well as clear advantages over conventional sampling-based methods when dealing with a small number of stochastic variables in a system or model. However, the case studies also highlight the current limitations of the proposed method such as slow execution speed due to the optimization-based approach and the challenges associated with, for example, the curse of dimensionality in gPC.

Entropy Analysis of FPGA Interconnect and Switch Matrices for Physical Unclonable Functions

Random variations in microelectronic circuit structures represent the source of entropy for physical unclonable functions (PUFs). In this paper, we investigate delay variations that occur through the routing network and switch matrices of a field-programmable gate array (FPGA). The delay variations are isolated from other components of the programmable logic, e.g., look-up tables (LUTs), flip-flops (FFs), etc., using a feature of Xilinx FPGAs called dynamic partial reconfiguration (DPR). A set of partial designs is created to fix the placement of a time-to-digital converter (TDC) and supporting infrastructure to enable the path delays through the target interconnect and switch matrices to be extracted by subtracting out common-mode delay components. Delay variations are analyzed in the different levels of routing resources available within FPGAs, i.e., local routing and across-chip routing. Data are collected from a set of Xilinx Zynq 7010 devices, and a statistical analysis of within-die variations in delay through a set of the randomly-generated and hand-crafted interconnects is presented.

A Monte Carlo resampling framework for implementing goodness‐of‐fit tests in spatial capture‐recapture models

Abstract Spatial capture‐recapture (SCR) models provide estimates of animal density from spatially referenced encounter data and has become the most widely adopted approach for estimating density. Despite the rapid growth in the development and application of spatial capture‐recapture methods, approaches for assessing model fit have received very little attention when compared to other classes of hierarchical models in ecology. Here, we develop an approach for testing goodness‐of‐fit (GoF) for frequentist SCR models using Monte Carlo simulations. We derive probability distributions of activity centres from the fitted model. From these, we calculate the expected encounters in the capture history based on the SCR parameter estimates, propagating the uncertainty of the estimates and the activity centre locations via Monte Carlo simulations. Aggregating these test statistics result in count data, allowing us to test fit with Freeman‐Tukey tests. These tests are based on summary statistics of the total encounters of each individual at each trap (FT‐ind‐trap), total encounters of each individual (FT‐individuals) and total encounters at each trap (FT‐traps). We assess the ability of these GoF tests to diagnose lack of fit under a range of assumption violating scenarios. FT‐traps had the strongest response to unmodelled spatial and trap heterogeneity in detection probability (power = 0.53–0.56), while FT‐ind‐traps had the strongest responses to random individual variation in detectability (power = 0.88) and non‐spatial discrete variation in (power = 0.35). The tests, designed to diagnose poor fit in the detection parameters, were insensitive to unmodelled heterogeneity in density (power = &lt;0.001). They also demonstrated low false positive rates (&lt;0.001) when the correct models were fitted; therefore, it is very unlikely that they will provide false indications of poor model fit. We demonstrate that these GoF tests are capable of detecting lack‐of‐fit when unmodelled heterogeneity is present in the detection sub‐model. When used jointly, the combinations of test results are also able to infer the type of lack‐of‐fit in certain cases. Our Monte Carlo sampling methods may be extended to a wider range of GoF tests, thereby providing a platform for developing more GoF methods for SCR.

A Class of Polynomial Recurrences Resulting in $$({\text {n}}/{\text {log}}\,\,{\text {n}}, {\text {n}}/{\text {log}}^2{\text {n}})$$–Asymptotic Normality

AbstractWe consider sequences of polynomials that satisfy differential–difference recurrences. Polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete mathematics. It is, therefore, of interest to understand the properties of such polynomials and their probabilistic consequences. We identify a class of polynomial recurrences that lead to a normal law with the expected value and the variance proportional to $$n/\log ~n$$ n / log n and $$n/\log ^2n$$ n / log 2 n , respectively. Examples include Stirling numbers of the second kind and other polynomials concerning set partitions as well as polynomials related to Whitney numbers of Dowling lattices.

Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencils

The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the staircase form and then applying a standard solver, such as the QZ algorithm, to that regular part. Recently, several novel approaches have been proposed to transform the singular pencil into a regular pencil by relatively simple randomized modifications. In this work, we analyze three such methods by Hochstenbach, Mehl, and Plestenjak that modify, project, or augment the pencil using random matrices. All three methods rely on the normal rank and do not alter the finite eigenvalues of the original pencil. We show that the eigenvalue condition numbers of the transformed pencils are unlikely to be much larger than the δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}-weak eigenvalue condition numbers, introduced by Lotz and Noferini, of the original pencil. This not only indicates favorable numerical stability but also reconfirms that these condition numbers are a reliable criterion for detecting simple finite eigenvalues. We also provide evidence that, from a numerical stability perspective, the use of complex instead of real random matrices is preferable even for real singular matrix pencils and real eigenvalues. As a side result, we provide sharp left tail bounds for a product of two independent random variables distributed with the generalized beta distribution of the first kind or Kumaraswamy distribution.

Random Dynamic Responses of Two Parallel Interfacial Cracks Between A Functionally Graded Material Strip And Two Dissimilar Elastic Strips

Abstract An analytical approach is presented in this article for the random dynamic study of two parallel interfacial cracks in a functionally graded material (FGM) strip that is bonded between two distinct elastic strips. One of the parallel cracks is placed at the interface of the elastic strip I and the FGM strip, and another is at the interface of the FGM strip and elastic strip II. A stationary stochastic process of time is used to model the dynamic loadings that are applied to the crack faces. To find the solution, the FGM strip is splited into a number of sub-strips, and using an average method, the material properties of each sub-strip are reduced to random variables. A fundamental problem is formulated to find the solution. The boundary conditions are reduced to a set of singular integral equations employing the Fourier sine, Fourier cosine, and Laplace transforms, which are solved by using the Collocation method. Further, the analytical expressions of dynamic stress intensity factors (DSIFs) about the crack tips in the time domain are obtained with the help of the Improved Dubner and Abate's method. Finally, the Monte Carlo method is used to obtain the mathematical expectation and standard deviation of DSIFs. The outcomes of the present study are also verified. The unique aspect of this study is the pictorial illustration of mathematical expectation and standard deviation as functions of the number of sub-strips, functionally graded parameter, thickness of the strips, and length of parallel interfacial cracks.

Stabilisation of the swing pattern of an anisotropic simple pendulum

Abstract The suppression of the effects of anisotropy on a pendulum by use of a rotating mount was initially envisaged by Léon Foucault, based on his observations of the vibrations of a rod clamped in a lathe. However, the method seems to never have been tried due to the practical difficulties involved. We report a computational study of the stabilisation of the swing pattern of a simple pendulum, showing anisotropic behaviour in a static configuration, by rotation of the system mount. When the mount is static, for most initial conditions the swing patterns quickly evolves into unstable, complex Lissajous-like patterns. When the pendulum mount is rotated faster than the pendulum frequency effects of anisotropy are suppressed, and the swing pattern stabilises to that of an isotropic 3D simple pendulum. Suppression of mount anisotropy influence occurs for relatively low rotation rates. We also study swing evolution in the presence of random variations in the orientation of the mount principal axes. The use of computational techniques confirms Foucault’s original observations and hypothesis and provides an interesting avenue for students to engage meaningfully with this historically important and inspiring experiment in a novel and challenging manner.

CNN-based prediction of microstructure-derived random property fields of composite materials

The simulation of random spatial variation in the mechanical properties of composite materials using random fields derived from their microstructure can be computationally demanding, since it often requires numerical homogenization of a large number of stochastic volume elements (SVEs). These SVEs are usually extracted from an initial image of the composite microstructure by using a moving window technique and their homogenized properties constitute the discrete data points of the random field at the centroid of each SVE. By replacing the expensive and highly repetitive homogenization procedure with a convolutional neural network (CNN), it is possible to perform nearly instant computations of random property fields. In this work, a CNN is proposed, that takes as input an SVE image and returns its apparent mechanical properties, and can therefore be applied along with the moving window technique. Training is performed on randomly generated SVEs with varying volume fractions and inclusion positions, which are representative of the SVEs obtained during processing of the initial large composite image. It is shown that the proposed CNN can accurately predict the mechanical properties of SVEs and it is subsequently applied for the prediction of random property fields derived from computer simulated and real microstructure images. Results show that, with the proposed methodology, it is possible to make accurate predictions of random fields within a few seconds, a procedure which could potentially require hours of computation time with the finite element based approach.

Neuroimaging meta regression for coordinate based meta analysis data with a spatial model.

Coordinate-based meta-analysis combines evidence from a collection of neuroimaging studies to estimate brain activation. In such analyses, a key practical challenge is to find a computationally efficient approach with good statistical interpretability to model the locations of activation foci. In this article, we propose a generative coordinate-based meta-regression (CBMR) framework to approximate a smooth activation intensity function and investigate the effect of study-level covariates (e.g. year of publication, sample size). We employ a spline parameterization to model the spatial structure of brain activation and consider four stochastic models for modeling the random variation in foci. To examine the validity of CBMR, we estimate brain activation on 20 meta-analytic datasets, conduct spatial homogeneity tests at the voxel level, and compare the results to those generated by existing kernel-based and model-based approaches. Keywords: generalized linear models; meta-analysis; spatial statistics; statistical modeling.

Testing independence based on Spearman’s footrule in high dimensions

. Spearman’s footrule is a widely used tool to discover the relationship between two continuous random variables, mainly because of its robustness, natural interpretation, and simplicity of calculation. In this article, we propose a new test statistic based on the sum of squares of pairwise Spearman’s footrule, to test the mutual independence of a high dimensional random vector. The large sample properties of the proposed test method are established. Simulation results show that the new test has higher power than existing test methods under some circumstances. An example with real life data is discussed to illustrate the usefulness and effectiveness of the proposed test statistic.

Методи обґрунтування запасів запасних частин у системі управління транспортним процесом

The article formulates directions and analyzes the possibilities of substantiating and choosing the most optimal variant of applying mathematical models for forecasting the number and range of spare parts. The provided recommendations allow to take into account the multi-brand fleets of motor transport enterprises and trends for extrapolation in the short term, identified by the results of observations in real operating conditions. The main reasons for the occurrence of prolonged vehicle downtime due to technical malfunctions are considered. Traditional methods of planning spare parts inventories based on the use of reliability theory and results of mileage forecasting, standard time to failure; inventory management theory and statistical methods for forecasting random processes; methods of operations research; economic and mathematical methods; stochastic methods of transformation of random variables are analyzed. The article formalizes the grouping of factors that affect the size of stocks and the range of spare parts in the operation of rolling stock of enterprises, depending on the state of the system of organization of work of services for maintenance and repair of vehicles; structure of the fleet and technical characteristics of vehicles; level of development of the production base; availability, interest and qualification of personnel; operating conditions of automotive equipment. It is proposed to improve the logistics of spare parts inventory management and to formulate measures to improve the performance of carriers based on an assessment of the total costs incurred by the enterprise to maintain the reliability of rolling stock in operation and taking into account the amount of lost profit due to vehicle downtime in the technical service units. At the same time, it is recommended to use the mathematical apparatus of fuzzy set theory for decision-making, which allows formalizing the parameters of vaguely defined expectations of consumers of motor transport services and reducing the subjectivity of decision-making when solving problems of optimizing spare parts stocks in the transport process management system based on the analysis of the structure of consumer properties and service quality indicators.

Probabilistic Degenerate Fubini Polynomials Associated with Random Variables

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order r, namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of Y, we treat the gamma random variable with parameters α,β>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha ,\\beta > 0$$\\end{document}, the Poisson random variable with parameter α>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha > 0$$\\end{document}, and the Bernoulli random variable with probability of success p.

Probabilistic Degenerate Fubini Polynomials Associated with Random Variables

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order r, namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of Y, we treat the gamma random variable with parameters α,β>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha ,\\beta > 0$$\\end{document}, the Poisson random variable with parameter α>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha > 0$$\\end{document}, and the Bernoulli random variable with probability of success p.

A framework to analyse the probability of accidental hull girder failure considering advanced corrosion degradation for risk-based ship design

Ship’s hull girder failure could result from maritime accident that can cause human life loss, environmental disaster, and major economic impacts. In risk-based ship design paradigm, accounting for rare phenomena (e.g. ship-ship collision or grounding) is important to provide safe and durable structure. In-service corrosion-induced hull degradation should be considered at the design stage, as it can significantly affect structural strength. The current study presents a novel framework to estimate the probability of ship hull girder failure, accounting for novel corrosion modelling techniques and accidental damage. The associated uncertainties are considered using statistical sampling from evidence-based distributions. A state-of-the-art deterministic model for ultimate strength calculation is applied using Monte Carlo simulation approach, resulting in the probability of hull failure through a reliability assessment. Wave and still-water bending moments are considered random variables. Two case studies of tanker ships with varying sizes are executed to show the applicability of the proposed framework. The results indicate that proper consideration of corrosion is of high importance, as ageing can significantly increase the probability of failure if accidental damage happens. Therefore, whereas future research and model refinement are discussed, the presented framework can serve for risk-based ship design tool and assess existing structures’ safety.

Modelling the lymphatic metastatic progression pathways of OPSCC from multi-institutional datasets

The elective clinical target volume (CTV-N) in oropharyngeal squamous cell carcinoma (OPSCC) is currently based mostly on the prevalence of lymph node metastases in different lymph node levels (LNLs) for a given primary tumor location. We present a probabilistic model for ipsilateral lymphatic spread that can quantify the microscopic nodal involvement risk based on an individual patient’s T-category and clinical involvement of LNLs at diagnosis. We extend a previously published hidden Markov model (HMM), which models the LNLs (I, II, III, IV, V, and VII) as hidden binary random variables (RVs). Each represents a patient’s true state of lymphatic involvement. Clinical involvement at diagnosis represents the observed binary RVs linked to the true state via sensitivity and specificity. The primary tumor and the hidden RVs are connected in a graph. Each edge represents the conditional probability of metastatic spread per abstract time-step, given disease at the edge’s starting node. To learn these probabilities, we draw Markov chain Monte Carlo samples from the likelihood of a dataset (686 OPSCC patients) from three institutions. We compute the model evidence using thermodynamic integration for different graphs to determine which describes the data best.The graph maximizing the model evidence connects the tumor to each LNL and the LNLs I through V in order. It predicts the risk of occult disease in level IV is below 5% if level III is clinically negative, and that the risk of occult disease in level V is below 5% except for advanced T-category (T3 and T4) patients with clinical involvement of levels II, III, and IV. The provided statistical model of nodal involvement in OPSCC patients trained on multi-institutional data may guide the design of clinical trials on volume-deescalated treatment of OPSCC and contribute to more personal guidelines on elective nodal treatment.

Uncertain statistics models for characterizing annual total energy production

In the field of annual total energy production, it is hard to determine whether the experimental data is linear or nonlinear growth characteristics. Therefore, different regression models are used to test the properties of the observed data. This article uses actual data to perform parameter estimation and residual analysis of linear and nonlinear regression models. In addition, uncertain nonlinear time series model is used to fit the experimental data in order to find a more suitable statistics model after obtaining the growth properties of the observed data. A test is introduced to prove that the disturbance terms presented in the regression and time series models are actually uncertain variables, not random variables. Moreover, the uncertain hypothesis tests show that the uncertain time series model is in better agreement with the real data of the annual total energy production.

Complete [formula omitted]th moment convergence of moving average processes for [formula omitted]-widely acceptable random variables under sub-linear expectations

In this article, we studied complete qth moment convergence of the moving average processes produced by m-widely acceptable (m-WA) random variables under sub-linear expectations. The results here extend those of the moving average processes generated by m-WOD random variables in probability.

Fuzzy random sensitivity analysis for the overall structure reliability of reinforced concrete freezing wellbores in deep alluvium based on hidden Markov model

To address the shortcomings of traditional reliability theory in characterizing the stability of deep underground structures, the advanced first order second moment of reliability was improved to obtain fuzzy random reliability, which is more consistent with the working conditions. The traditional sensitivity analysis model was optimized using fuzzy random optimization, and an analytical calculation model of the mean and standard deviation of the fuzzy random reliability sensitivity was established. A big data hidden Markov model and expectation-maximization algorithm were used to improve the digital characteristics of fuzzy random variables. The fuzzy random sensitivity optimization model was used to confirm the effect of concrete compressive strength, thick-diameter ratio, reinforcement ratio, uncertainty coefficient of calculation model, and soil depth on the overall structural reliability of a reinforced concrete double-layer wellbore in deep alluvial soil. Through numerical calculations, these characteristics were observed to be the main influencing factors. Furthermore, while the soil depth was negatively correlated, the other influencing factors were all positively correlated with the overall reliability. This study provides an effective reference for the safe construction of deep underground structures in the future.

Non-probabilistic reliability-based multi-scale topology optimization of thermo-mechanical continuum structures with stress constraints

A reliability-based non-probabilistic multiscale topology optimization (NRBMTO) method with stress constraints is proposed for thermo-mechanical continuous structures with uncontrollable stresses. The physical parameters, external loads and temperature values at the macro scale, are regarded as non-probabilistic uncertain parameters in the optimization of structural topologies with complex physical fields at multi-scale. The homogenization-based finite element method is employed to quantify thermo-mechanical structures with multi-scale uncertain parameters in the established multi-scale topology model. The ellipsoid model is applied to describe the uncertainty of non-probabilistic random variables, and the non-probabilistic reliability index is obtained by estimating the failure probability based on the first-order reliability method (FORM). The unit stresses are aggregated to the global maximum stresses with the normalized p-norm function, taking into account the mechanical and thermal stresses. The sensitivity information of the compliance and stress constraint to the macro- and micro-design variables and uncertain variables are derived simultaneously. The macro- and micro- design variables are solved by the method of moving asymptotes (MMA), respectively. Several numerical examples are given to verify the effectiveness and feasibility of the proposed NRBMTO method. The results demonstrate that the optimized structure based on the NRBMTO method provides better security with reliability index β=3 and minimum compliance (244.39) while stress is controlled below 235 MPa compared to the classical deterministic multiscale topology optimization (DMTO) method.