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We present a Bayesian nonparametric system reliability model which scales well and provides a great deal of flexibility in modeling. The Bayesian approach naturally handles the disparate amounts of component and subsystem data that may exist. However, traditional Bayesian reliability models are quite computationally complex, relying on MCMC techniques. Our approach utilizes the conjugate properties of the beta-Stacy process, which is the fundamental building block of our model. These individual models are linked together using a method of moments estimation approach. This model is computationally fast, allows for right-censored data, and is used for estimating and predicting system reliability. [ABSTRACT FROM AUTHOR]

AbstractBefore implementing a new microbiological test method in pharmaceutical industry, it is required to assess whether it matches or surpasses the detection of microorganisms of the current microbiological method. The United Stated Pharmacopoeia Chapter 1223 (USP < 1223>) proposes two statistical approaches for testing non-inferiority of two qualitative microbiological methods when they can both test the same samples (paired design). The first approach compares the positive rates of the two methods. The non-inferiority test is not influenced by the performance of the methods alone, it is also affected by the spiked bacterial density. The second approach compares most probable numbers (MPNs) between the two methods, but the MPN assumes that the microbiological methods are perfect. To address the two abovementioned flaws, a generalized MPN (gMPN) approach is being proposed. Estimators for the accuracy, detection proportion, and bacterial density parameter are being derived using the method of moments. It will be shown that estimation of the accuracy and detection proportion has limited to no bias, but the bias for the bacterial density can become substantial. A test statistic for non-inferiority of accuracy, along with a sample size formula, is presented, showing nominal type I error and appropriate power. The proposed approach is demonstrated using real data. [ABSTRACT FROM AUTHOR]

The wide‐angle electromagnetic scattering problems can be rapidly solved by using the method of moments in conjunction with compressive sensing theory. The method mainly has two computational parts: measurement and recovery. To further enhance the performance, an improved orthogonal matching pursuit algorithm with a randomised atom selection process is proposed, significantly reducing the computational complexity of the recovery part. Additionally, a restart mechanism is designed to eliminate possible errors that might occur during the random process, ensuring the accuracy of recovery results. Numerical experiments with objects of different shapes validate the effectiveness and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

This research paper deals with an extension of the non-central Wishart introduced in 1944 by Anderson and Girshick, that is the non-central Riesz distribution when the scale parameter is derived from a discrete vector. It is related to the matrix of normal samples with monotonous missing data. We characterize this distribution by means of its Laplace transform and we give an algorithm for generating it. Then we investigate, based on the method of the moment, the estimation of the parameters of the proposed model. The performance of the proposed estimators is evaluated by a numerical study. [ABSTRACT FROM AUTHOR]

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This work represents a natural coalescence of two important lines of work — learning mixtures of Gaussians and algorithmic robust statistics. In particular, we give the first provably robust algorithm for learning mixtures of any constant number of Gaussians. We require only mild assumptions on the mixing weights and that the total variation distance between components is bounded away from zero. At the heart of our algorithm is a new method for proving a type of dimension-independent polynomial identifiability — which we call robust identifiability — through applying a carefully chosen sequence of differential operations to certain generating functions that not only encode the parameters we would like to learn but also the system of polynomial equations we would like to solve. We show how the symbolic identities we derive can be directly used to analyze a natural sum-of-squares relaxation. [ABSTRACT FROM AUTHOR]

Predicting the timing of phenological events is important in agriculture, especially high-revenue products. A project sponsored by USDA-ARS had the objective of adapting a previously developed model for estimating proportions of insects in different development stages as a function of temperature (degree) and time (days) for predicting bloom in almond orchards. Data for the model normally form a two-way table of counts, with rows corresponding to sample percentages of different development stages and columns to sampling times. In this study, we report a technique developed to estimate sample sizes of multinomial and product multinomial models using a method of moments and determine the empirical coverage of sample size. This study aims to determine an appropriate sample size for data collection. This involves establishing a sampling distribution for the Pearson statistic, defined as the product of the sample size and the deviance of empirical proportions from population proportions. The intended outcome is to predict the optimal timing for harvesting crops at desired development stages when coupled with the phenology model, for which variability of the maximum likelihood estimates of the phenology model depends on sample size. [ABSTRACT FROM AUTHOR]

Nowadays, due to their characteristics of high efficiency and energy saving, frequency converters are used in coal mine excavation machines and ventilation machines. They can cause serious electromagnetic radiation interference with the surrounding monitoring, sensing and other equipment. Therefore, it is necessary to explore the electromagnetic interference characteristics of mining converters. By choosing a ZJT-75/660SF mine frequency converter as the research object, an antenna model was established, and the method of moments was used to solve the problem. The electromagnetic radiation characteristics of the frequency converter were analyzed, and a field experiment was conducted to verify the effectiveness of the model by comparing the simulation and experimental data. According to the analysis of the electromagnetic intensity distribution characteristics of the near field and far field, the near-field intensity is concentrated in the inner part of the converter, but the far-field intensity has obvious directional characteristics, which are found to provide a reference value for the location of the underground mining converter. Finally, a method is proposed to improve electromagnetic radiation disturbance by changing the structure of the converter's heat dissipation hole, and the feasibility of this method is verified. [ABSTRACT FROM AUTHOR]

When the conjugate gradient (CG) method for solving linear algebraic systems was formulated about 70 years ago by Lanczos, Hestenes, and Stiefel, it was considered an iterative process possessing a mathematical finite termination property. With the deep insight of the original authors, CG was placed into a very rich mathematical context, including links with Gauss quadrature and continued fractions. The optimality property of CG was described via a normalized weighted polynomial least squares approximation to zero. This highly nonlinear problem explains the adaptation of CG iterates to the given data. Karush and Hayes immediately considered CG in infinite dimensional Hilbert spaces and investigated its superlinear convergence. Since then, the view of CG, as well as other Krylov subspace methods developed in the meantime, has changed. Today these methods are considered primarily as computational tools, and their behavior is typically characterized using linear upper bounds, or heuristics based on clustering of eigenvalues. Such simplifications limit the mathematical understanding of Krylov subspace methods, and also negatively affect their practical application. This paper offers a different perspective. Focusing on CG and the generalized minimal residual (GMRES) method, it presents mathematically important as well as practically relevant phenomena that uncover their behavior through a discussion of computed examples. These examples provide an easily accessible approach that enables understanding of the methods, while pointers to more detailed analyses in the literature are given. This approach allows readers to choose the level of depth and thoroughness appropriate for their intentions. Some of the points made in this paper illustrate well known facts. Others challenge mainstream views and explain existing misunderstandings. Several points refer to recent results leading to open problems. We consider CG and GMRES crucially important for the mathematical understanding, further development, and practical applications also of other Krylov subspace methods. The paper additionally addresses the motivation of preconditioning. [ABSTRACT FROM AUTHOR]

This paper presents a new formulation of the second-order fourth-moment method (sometimes referred to as second-order perturbation method or second-order method of moments). The method allows to efficiently predict the stochastic moments of a response function and is therefore often used within robust design optimization. The new approach allows a non-intrusive implementation at the same cost as existing, highly intrusive formulations. Therefore, the new approach can be applied to any objective function without significant implementation effort. It is based on a few finite difference steps into special directions and hence is dependent on the corresponding step sizes. An automatic step size procedure is supplied beside a detailed convergence analysis. The advantages of the new formulation are demonstrated by robust design optimizations of a 2D and a 3D example using the geometrically nonlinear finite element method. [ABSTRACT FROM AUTHOR]

The stochastic actor oriented model (SAOM) is a method for modelling social interactions and social behaviour over time. It can be used to model drivers of dynamic interactions using both exogenous covariates and endogenous network configurations, but also the co-evolution of behaviour and social interactions. In its standard implementations, it assumes that all individual have the same interaction evaluation function. This lack of heterogeneity is one of its limitations. The aim of this paper is to extend the inference framework for the SAOM to include random effects, so that the heterogeneity of individuals can be modelled more accurately. We decompose the linear evaluation function that models the probability of forming or removing a tie from the network, in a homogeneous fixed part and a random, individual-specific part. We extend the algorithm so that the variance of the random parameters can be estimated with method of moments. Our method is applicable for the general random effect formulations. We illustrate the method with a random out-degree model and show the parameter estimation of the random components, significance tests and model evaluation. We apply the method to the Kapferer's Tailor shop study. It is shown that a random out-degree constitutes a serious alternative to including transitivity and higher-order dependency effects. • The paper allows effects to be individual-specific to model heterogeneity accurately. • The method of moments is generalized to estimate random effects in the SAOM. • The model evaluation procedure based on the score-test is also been developed. • We identify interesting random effects in the Kapferer's Tailor-shop dataset. [ABSTRACT FROM AUTHOR]

We study the cycle structure of words in several random permutations. We assume that the permutations are independent and that their distribution is conjugation invariant, with a good control on their short cycles. If, after successive cyclic simplifications, the word w$$ w $$ still contains at least two different letters, then we get a universal limiting joint law for short cycles for the word in these permutations. These results can be seen as an extension of our previous work (Kammoun and Maïda. Electron. Commun. Probab. 2020;25:1‐14.) from the product of permutations to any non‐trivial word in the permutations and also as an extension of the results of Nica (Random Struct. Algorithms1994;5:703‐730.) from uniform permutations to general conjugation invariant random permutations. In particular, we get optimal assumptions in the case of the commutator of two such random permutations. [ABSTRACT FROM AUTHOR]

While reverse time migration (RTM) algorithm is commonly used in geophysical explorations, this paper addresses the RTM imaging procedure for reconstructing of lossy dielectric discontinuities in a planar waveguide using electromagnetic waves at a single frequency. The direct problem of the related configuration is solved via method of moments (MoM) to produce the synthetic scattered data to be used in RTM. The achievements of the method are examined and verified by including different numerical examples. It is shown that the RTM approach can be used as an alternative imaging methodology in parallel plate waveguide problems. [ABSTRACT FROM AUTHOR]

Single-use anion-exchange resins can reduce hazardous chromates to safe levels in drinking water. However, since most process control strategies monitor effluent concentrations, detection of any chromate leakage leads to premature resin replacement. Furthermore, variations in the inlet chromate concentration and other process conditions make process control a challenging step. In this work, we capture the uncertainty of the process conditions by applying the Ito process of Brownian motion with a drift into a stochastic optimal control strategy. The ion-exchange process is modeled using the method of moments, which helps capture the process dynamics, later formulated into mathematical objectives representing desired chromate removal. We then solved our developed models as an optimal control problem via Pontryagin's maximum principle. The objectives enabled a successful control via flow rate adjustments leading to higher chromate extraction. Such an approach maximizes the capacity of the resin and column efficiency to remove toxic compounds from water while capturing deviations in the process conditions. When dealing with highly toxic compounds like chromium, it is critical that its concentration in drinking water is kept at a low, safe level. As single-use ion-exchange resins are used to extract the hazardous chemical, changes in inlet concentrations can lead to premature leakage. Hence, an optimal control strategy is needed for the purification system while monitoring the inlet concentration rather than the outlet concentration to avoid a process control delay. For a successful optimization, predicting the output concentration based on the inlet conditions becomes necessary to maximize the performance of the extraction process. In this work, predictive modeling while capturing the uncertainties of the system maximized the chromate removal in less time than running the process at a constant flow rate. The results demonstrate that changing the flow rate with time is an improved strategy to achieve such performance. The flow rate change is a unique approach to an industry that designs its processes around a constant flow rate and reacts too late when system deviations have already occurred. Therefore, applying the approach described in this work will maximize the utilization of the purification process resulting in less waste produced and safer drinking water. [ABSTRACT FROM AUTHOR]

This paper provides two specification tests for the system of spatial autoregressive model of order m. We derive the theoretical limit distributions and show in a detailed Monte Carlo simulation study that the tests result in reasonable sized testing procedures with large power. In the empirical application, we analyze Euro Stoxx 50 returns in two different time spans, looking for insights how well models with different specifications of the spatial weighting matrices (local, country, industry and country-industry specific dependencies including interaction effects) fit to the data. The analyzes also demonstrate the ability of the tests to detect inaccurate Value-at-Risk forecasts. [ABSTRACT FROM AUTHOR]

Abstract In this article, a modified scheme of the fast dipole method (FDM) is proposed based on the Cartesian tensor. To achieve separation between the field and the source, the Taylor series used in the FDM is an incomplete second‐order expansion, which limits computational accuracy and flexibility. To address this issue, a Cartesian tensor is employed to expand the interactions between the far‐group pairs. This approach allows for a complete expansion of any order and offers flexibility in precision control, enabling a balance between computational efficiency and accuracy requirements across different application scenarios. Moreover, the computational accuracy of the proposed method can be improved without a substantial increase in time and memory requirements compared to the FDM. The validity and accuracy of the proposed method are demonstrated with numerical examples.

In this article, a modified scheme of the fast dipole method (FDM) is proposed based on the Cartesian tensor. To achieve separation between the field and the source, the Taylor series used in the FDM is an incomplete second‐order expansion, which limits computational accuracy and flexibility. To address this issue, a Cartesian tensor is employed to expand the interactions between the far‐group pairs. This approach allows for a complete expansion of any order and offers flexibility in precision control, enabling a balance between computational efficiency and accuracy requirements across different application scenarios. Moreover, the computational accuracy of the proposed method can be improved without a substantial increase in time and memory requirements compared to the FDM. The validity and accuracy of the proposed method are demonstrated with numerical examples. [ABSTRACT FROM AUTHOR]

Abstract In open networks, the geometric deformation and common image processing are common image manipulation modes, which pose a great challenge in robust watermarking. To improve the robustness of GRHFM‐based watermarking, a watermarking algorithm based on the fast GRHFM calculation method and ant colony optimization (ACO) based fractional parameter selection method is proposed. With the similarity between the discrete Fourier transform and GRHFM moment calculation, the algorithm utilizes fast Fourier transform to improve the GRHFM calculation accuracy and speed. To select the optimal GRHFM fractional parameter for watermarking algorithm, ACO is introduced to the fractional parameter adaptive selection method. Here, the fast Fourier transform‐based calculation method is combined with the adaptive parameter selection method to maximize the invisibility and robustness of watermarking. The experimental results indicate that the algorithm achieves higher robustness with the same payload and invisibility compared with other existing watermarking methods.

Abstract An approximation scheme that combines approximate solutions with error estimators to accelerate the adaptive h‐refinement of the RWG‐based method of moments (MoM) with the electric field integral equation (EFIE) is presented. The scheme is effectively implemented by using the near‐field matrix to solve the approximate solution. Several conventional error estimators incorporated with the scheme are investigated. Compared to using the full MoM system, it significantly reduces the computational cost while maintaining the refinement effect. Numerical results indicate that the scheme could accelerate the adaptive refinement, yielding significant reductions in computational time and memory requirements.

The availability of vast amounts of longitudinal data from electronic health records (EHRs) and personal wearable devices opens the door to numerous new research questions. In many studies, individual variability of a longitudinal outcome is as important as the mean. Blood pressure fluctuations, glycemic variations, and mood swings are prime examples where it is critical to identify factors that affect the within-individual variability. We propose a scalable method, within-subject variance estimator by robust regression (WiSER), for the estimation and inference of the effects of both time-varying and time-invariant predictors on within-subject variance. It is robust against the misspecification of the conditional distribution of responses or the distribution of random effects. It shows similar performance as the correctly specified likelihood methods but is 103 ∼ 105 times faster. The estimation algorithm scales linearly in the total number of observations, making it applicable to massive longitudinal data sets. The effectiveness of WiSER is evaluated in extensive simulation studies. Its broad applicability is illustrated using the accelerometry data from the Women's Health Study and a clinical trial for longitudinal diabetes care.

Sample selection is one of the most important factors in estimating the unknown parameters of distributions, as it saves time, saves effort, and gives the best results. One of the challenges is deciding on a suitable distribution estimate technique and adequate sample selection to provide the best results in comparison with earlier research. The method of moments (MOM) was decided on to estimate the unknown parameters of the Gumbel distribution, but with four changes in the sample selection, which were simple random sample (SRS), ranked set sampling (RSS), maximum ranked set sampling (MRSS), and ordered maximum ranked set sampling (OMRSS) techniques, due to small sample sizes. The MOM is a traditional method for estimation, but it is difficult to use when dealing with RSS modification. RSS modification techniques were used to improve the efficiency of the estimators based on a small sample size compared with the usual SRS estimator. A Monte Carlo simulation study was carried out to compare the estimates based on different sampling. Finally, two datasets were used to demonstrate the adaptability of the Gumbel distribution based on the different sampling techniques. [ABSTRACT FROM AUTHOR]

In open networks, the geometric deformation and common image processing are common image manipulation modes, which pose a great challenge in robust watermarking. To improve the robustness of GRHFM‐based watermarking, a watermarking algorithm based on the fast GRHFM calculation method and ant colony optimization (ACO) based fractional parameter selection method is proposed. With the similarity between the discrete Fourier transform and GRHFM moment calculation, the algorithm utilizes fast Fourier transform to improve the GRHFM calculation accuracy and speed. To select the optimal GRHFM fractional parameter for watermarking algorithm, ACO is introduced to the fractional parameter adaptive selection method. Here, the fast Fourier transform‐based calculation method is combined with the adaptive parameter selection method to maximize the invisibility and robustness of watermarking. The experimental results indicate that the algorithm achieves higher robustness with the same payload and invisibility compared with other existing watermarking methods. [ABSTRACT FROM AUTHOR]

This paper presents a full-wave method, based on the method of moments (MoM), to calculate the S ¯ matrix from a two-dimensional complex sample in millimeter and submillimeter W and J bands. From the surface currents obtained by inverting the impedance matrix and from the Huygens principle, the reflection and transmission coefficients are computed. This allows us to obtain the four elements of the S ¯ matrix. Firstly, the method is validated from canonical samples (a dielectric slab and a stack of two dielectric slabs) by applying the well-known Fresnel coefficients. Secondly, for the W (75 to 110 GHz) and J (220 to 330 GHz) bands, a PVC slab covered by water drops is considered, for which the S ¯ matrix is compared with measurements made in quasi-optical free space. A satisfactory agreement is obtained between the measurements and the model. [ABSTRACT FROM AUTHOR]

In this paper, the general framework for contact-constrained topology optimization of Strömberg and Klarbring (2010) is extended to robust topology optimization. In doing so, a linear elastic design domain is considered and the augmented Lagrangian approach is used to model the unilateral contact. For topology optimization, the design space is parametrized with the SIMP-approach and the Sigmund's filter is applied. Additionally, the robust framework considers uncertainties at the contact support such as deviations of the geometry of the contact surface and the friction coefficient. Both uncertainties are described by the first-order second-moment method which leads to minimal additional costs. In fact, only two additional linear equations must be solved to obtain the robust objective and its gradient with respect to the design variables. Having both the objective and the gradient, the design update is computed with the method of moving asymptotes. The robust framework is applied to 2D and 3D examples to prove its scalability for real-world applications. [ABSTRACT FROM AUTHOR]

In this work, we present a straightforward and simple method of moments (MOM) solution procedure, with minimum mathematical manipulations, to solve the coupled integral equations for multiple, homogeneous and inhomogeneous, dielectric bodies of arbitrary shape directly in the time domain. The standard surface and volume integral equation formulations are used for homogeneous and inhomogeneous bodies, respectively. The numerical solution procedure does not involve a time-marching process as is usually adopted for time domain problems and seems to be one of the primary reasons for the late-time instabilities as a result of error accumulation. The present solution method is stable for a very long time as evidenced by several representative numerical examples presented for validation. [ABSTRACT FROM AUTHOR]

An approximation scheme that combines approximate solutions with error estimators to accelerate the adaptive h‐refinement of the RWG‐based method of moments (MoM) with the electric field integral equation (EFIE) is presented. The scheme is effectively implemented by using the near‐field matrix to solve the approximate solution. Several conventional error estimators incorporated with the scheme are investigated. Compared to using the full MoM system, it significantly reduces the computational cost while maintaining the refinement effect. Numerical results indicate that the scheme could accelerate the adaptive refinement, yielding significant reductions in computational time and memory requirements. [ABSTRACT FROM AUTHOR]

The coordinate-transformation-based differential method developed by Chandezon et al. is recognized as one of the simplest and most versatile approaches for modeling surface-relief gratings. In this study, we present a novel numerical solution using Legendre polynomial expansion, enabling us to deal efficiently with faceted gratings. Additionally, we introduce an oblique coordinate transformation to analyze overhanging faceted gratings. Notably, the C-method with polynomial expansion (CPE) demonstrates a dramatic improvement in convergence speed compared to the Fourier Modal Method (FMM). [ABSTRACT FROM AUTHOR]

A wide variety of methods are available to estimate the between‐study variance under the univariate random‐effects model for meta‐analysis. Some, but not all, of these estimators have been extended so that they can be used in the multivariate setting. We begin by extending the univariate generalised method of moments, which immediately provides a wider class of multivariate methods than was previously available. However, our main proposal is to use this new type of estimator to derive multivariate multistep estimators of the between‐study covariance matrix. We then use the connection between the univariate multistep and Paule–Mandel estimators to motivate taking the limit, where the number of steps tends toward infinity. We illustrate our methodology using two contrasting examples and investigate its properties in a simulation study. We conclude that the proposed methodology is a fully viable alternative to existing estimation methods, is well suited to sensitivity analyses that explore the use of alternative estimators, and should be used instead of the existing DerSimonian and Laird‐type moments based estimator in application areas where data are expected to be heterogeneous. However, multistep estimators do not seem to outperform the existing estimators when the data are more homogeneous. Advantages of the new multivariate multistep estimator include its semi‐parametric nature and that it is computationally feasible in high dimensions. Our proposed estimation methods are also applicable for multivariate random‐effects meta‐regression, where study‐level covariates are included in the model. [ABSTRACT FROM AUTHOR]

A challenge for high‐impact polystyrene (HIPS) production and design is the more accurate and low computational cost prediction of the phase separation and phase inversion conversion, the first conversion determining the onset of the two‐phase system and the second conversion defining the pathway toward a complex, for example, salami‐like morphology. In this work, a two‐phase deterministic method of moments (MoM) model running in several minutes is therefore developed in the intermediate styrene conversion range (up to around 30%), considering for simplicity only diffusional limitations on termination on an average basis. It is showcased that the phase separation conversion can be taken as 2 m%, and the phase inversion conversion should be calculated by algebraic means. Interestingly, the latter conversion varies with the initial reaction conditions either on a time basis (e.g., variation of initial radical concentration) or both a time and conversion basis (e.g., relative contribution of rubber and St partitioning coefficient). A comparison with the commonly used pseudo‐homogeneous MoM model reveals that by accounting for mass transfer in a more representative two‐phase model, the amount of monomer consumed is slightly reduced, the grafting efficiency decreases with increasing conversion instead of increasing, and the styrene composition in the graft copolymer decreases. The current work additionally puts forward two‐phase MoM data to facilitate future benchmarking with other (stochastic) modeling approaches and enables kinetic insights into heterogeneous grafting polymerization, further promoting the production of multiphase industrial polymer products. [ABSTRACT FROM AUTHOR]

Predicting the timing of phenological events is important in agriculture, especially high-revenue products. A project sponsored by USDA-ARS had the objective of adapting a previously developed model for estimating proportions of insects in different development stages as a function of temperature (degree) and time (days) for predicting bloom in almond orchards. Data for the model normally form a two-way table of counts, with rows corresponding to sample percentages of different development stages and columns to sampling times. In this study, we report a technique developed to estimate sample sizes of multinomial and product multinomial models using a method of moments and determine the empirical coverage of sample size. This study aims to determine an appropriate sample size for data collection. This involves establishing a sampling distribution for the Pearson statistic, defined as the product of the sample size and the deviance of empirical proportions from population proportions. The intended outcome is to predict the optimal timing for harvesting crops at desired development stages when coupled with the phenology model, for which variability of the maximum likelihood estimates of the phenology model depends on sample size.

One application of the compressive sensing (CS) technique in the method of moments involves restructuring matrix equations into a CS model to enhance computational efficiency. However, this compressive sensing-based method of moments (CS-MoM) model that has been reported is restricted to single excitation electromagnetic scattering contributions, as its iterative solver does not facilitate multiple excitation problems. In this paper, a direct solution scheme for CS-MoM is proposed to address wide-angle electromagnetic scattering challenges. The method is developed on overdetermined equation-based CS-MoM and utilizes the characteristic modes to construct the sparse transformation matrix. By converting the overdetermined equation into a normal matrix equation, the CS-MoM model is transformed into a reduced matrix equation with a smaller size, thus facilitating the solution using a direct solver such as lower-upper (LU) decomposition. For right-hand sides with varying incident angles, the reduced impedance matrix is LU-decomposed once in advance, and the decomposition factors are repeatedly used to derive the current coefficients. Moreover, the proposed method introduces the adaptive cross-approximation algorithm for filling mutual impedance. It not only enhances time performance but also significantly reduces memory consumption. Compared with the traditional characteristic mode basis function method, the proposed method exhibits superior time and memory performance, with the total time reduced by 71%, 51% and 35%, respectively, and the memory consumption reduced by about 85% in the given simulation results.

The compressive sensing technique can significantly improve the efficiency of the method of moments in solving the monostatic electromagnetic scattering problem by compressing the number of incident sources. However, in the case of extensive and dense angle sampling, the computational burden arising from the large size of the incident excitation matrix becomes a concern. In this paper, a dual-layer compressive sensing scheme incorporating the adaptive cross approximation (ACA) algorithm is proposed to further improve the efficiency of the compressive sensing-based method of moments (CS-MoM) for solving the monostatic electromagnetic scattering problem of three-dimensional objects. The proposed scheme is derived from hybridizing the new incident source-based CS-MoM and the overdetermined equation-based CS-MoM. Firstly, in the outer layer, the original incident sources are recombined to construct new incident sources. Then, in the inner layer, the overdetermined equation-based CS-MoM model is constructed to obtain the current coefficients for each new incident source. Finally, the current coefficients under the new incident sources are taken as measurement values for constructing an undetermined system in the outer layer, thus reconstructing the original current coefficients. In the proposed method, the original excitation matrix is extracted and then quickly filled into two smaller matrices by the ACA algorithm, which dramatically improves the efficiency of filling the excitation matrix. The proposed method significantly improves the computational efficiency, especially in filling the excitation matrix, compared to the unitary new incident source-based CS-MoM. Some simulation results are given to demonstrate the effectiveness and efficiency of the proposed method.

The zero-suppressed binary decision diagram (ZDD) is a compact data structure widely used for the efficient representation of families of sparse subsets. Its inherent recursive structure also facilitates easy diagram manipulation and family operations. Practical applications generally fall under discrete optimization, such as combinatorial problems and graph theory. Given its utility, summarizing the subsets represented in the diagram using key metrics is of great value as this provides valuable insights into the characteristics of the family. The paper proposes a recursive algorithm to extract information on moments from families represented as a ZDD. Given a value for every element in the universe, the value of a subset is first formulated as the sum of the values of its elements. The moments of a family are then calculated as the mean of the exponentiated subset values, akin to the method of moments. Leveraging the structure of the ZDD, the proposed algorithm recursively traverses a given diagram for efficient moments evaluation via multinomial expansion. Its utility is then demonstrated with three classical problems—power sets, the knapsack problem, and paths in graphs—offering orders of magnitude increase in computational efficiency relative to conventional method. Overall, the proposed algorithm enhances the functionality of the ZDD by introducing an efficient family operation to uncover the distribution of subset values in a represented family.

This paper presents an exact series solution for fields radiated from a magnetic-frill source that is valid everywhere above the plane of the magnetic-frill. The derivation of the field expressions is based on Lommel expansions and direct integration of the vector potential. The field expressions presented in this study were in excellent agreement with the corresponding fields available in the literature. The known expressions for fields radiated from the magnetic-frill on its axis and those radiated from magnetic current rings are obtained as special cases from the field expressions presented in this study. These expressions can be used to accurately compute the tangential component of the incident electric field on the surface of an antenna needed in the MoM solution for a thick as well as a thin antenna input impedance computation, in addition to the analysis of the characteristics of coaxial wave-guides, cables, antennas mounted on ground planes, and in the analysis of electromagnetic compatibility problems and assistance in estimating human exposure to radiation from the apertures of coaxial cables.

Open-source software has been highly influential on software development in many fields, and also has a history within computational electromagnetics. With large amounts of open-source code available, both from within computational electromagnetics and from other fields, new combinations can be made by using already existing code packages. This can be especially beneficial to developers who do not otherwise have access to a substantial codebase. In this article we describe how a finite element-boundary integral code using the adaptive cross approximation was developed by combining different existing open-source software packages with new code in Python. We provide a brief overview of the numerical methods used, but our focus is on the implementation and insights that might be useful to others who could benefit from using open-source software in their work. Three numerical examples are also presented to demonstrate accuracy, performance and use of complex materials. Our code is provided at github.com/nwingren/fe2ms both to demonstrate how the open-source packages were combined in practice, but also for those who wish to test the code themselves.

The analysis of a single source in the vicinity of periodic structures is a very challenging task since the aperiodic source forbids a direct application of a periodic analysis method to the problem. Full wave methods addressing these problems involve infinite summations and double integrations which make the analysis cumbersome. Homogenization based methods reduce this complexity but at the expense of a loss of accuracy and flexibility in handling different kinds of structures. Moreover, the resulting Green’s functions still need integrations as opposed to being in closed-form. In this paper, a novel approach is proposed to obtain closed-form expressions for the Green’s functions of single sources over periodic structures which makes the analysis of these problems efficient while offering more accuracy and flexibility compared to existing homogenization methods in the literature. To compute the fields scattered by the periodic structure, the reflection coefficients are numerically computed for TE and TM polarized incident plane waves with different angles of incidence and they are approximated by complex exponentials. Approximated reflection coefficients are used in conjunction with the plane wave expansion of the fields radiated by the dipole so that the scattered fields can be expressed in closed-form by utilizing Bessel integral identities.

AbstractIn this note, we consider the performance of the classic method of moments for parameter estimation of symmetric variance-gamma (generalized Laplace) distributions. We do this through both theoretical analysis (multivariate delta method) and a comprehensive simulation study with comparison to maximum likelihood estimation, finding performance is often unsatisfactory. In addition, we modify the method of moments by taking absolute moments to improve efficiency; in particular, our simulation studies demonstrate that our modified estimators have significantly improved performance for parameter values typically encountered in financial modeling, and is also competitive with maximum likelihood estimation. [ABSTRACT FROM AUTHOR]

The streamlines of the energy flux (Poynting vectors) and chirality flux as well as the intensity of the electric field around various plasmonic nanostructures (nanocube, nanocuboid, nanotriangle, hexagonal nanoplate and bowtie nanoantenna) induced by a circularly polarized (CP) or linearly polarized (LP) light were studied theoretically. The boundary element method combined with the method of moment was used to solve a set of surface integral equations, based on the Stratton–Chu formulation, for analyzing the highly distorted electromagnetic (EM) field in the proximity of these nanostructures. We discovered that the winding behavior of these streamlines exhibits versatility for various modes of the surface plasmon resonance of different nanostructures. Recently, using plasmonic nanostructures to facilitate a photochemical reaction has gained significant attention, where the hot carriers (electrons) play important roles. Our findings reveal a connection between the flow pattern of energy flux and the morphology of the photochemical deposition around various plasmonic nanostructures irradiated by a CP light. For example, numerical results exhibit vertically helical streamlines of the Poynting vector around an Au nanocube and transversely twisted-roll streamlines around a nanocuboid. Additionally, the behaviors of the winding energy and chirality fluxes at the gap and corners of a plasmonic bowtie nanoantenna, implying a highly twisted EM field, depend on the polarization of the incident LP light. Our analysis of the streamlines of the Poynting vector and chirality flux offers an insight into the formation of plasmon-enhanced photocatalysis. [ABSTRACT FROM AUTHOR]

A comprehensive CFD model is developed to predict soot for a turbulent kerosene-air diffusion flame. The method of moments (MOM) soot model has better prediction capability with meaningful soot behavioral predictions than semi-empirical models. The coupled model is primarily validated with experimental measurements from the literature in the form of major species concentration, flame temperature, and soot volume fraction. A surrogate mix comprising 80% n-decane and 20% toluene on a liquid volume basis constitutes kerosene fuel. The 20% aromatic content is able to reproduce the sooting behavior with considerable accuracy. The model can replicate CO, CO2, CH4, C2H2, C2H4, and C6H6 concentrations, flame temperature, soot volume fraction, and soot aggregation parameters for a laminar JetA-1 flame at atmospheric pressure. The reproduction of flame temperature and major species concentrations for a laminar kerosene flame validates the applicability of the gas-phase kinetic mechanism and PAH formation pathway for the reacting flow system. The model also performs appreciably for measurements of a turbulent kerosene flame at higher operating pressures up to 6.44 bar. The peak soot volume fraction matches significantly well with the measurements for all the flames. The predicted peak soot volume fractions are 8.8, 27.3, 68, and 82 ppm compared to measured values of 9.3, 28.3, 63, and 67 ppm at pressures 1, 2.7, 4.81, and 6.44 bar, respectively. However, the location of the peak soot has a slight discrepancy at low pressures till 2.7 bar, showing the predicted peak earlier compared to a later appearance in the measurements. The simulated peak flame temperatures are 1377, 1393, 1412, and 1477 K as operating pressure increases from 1 to 2.7, 4.81, and 6.44 bar. The thermal absorbance from soot and species radiation plays a vital role in predicting the flame temperature. Soot radiation reduces flame temperature by ~ 500 K compared to gaseous radiation (CO2, H2O, CO, CH4, etc.), reducing approximately 100 K. The predictive soot number density, mean diameter, surface area, primary particle count in soot aggregates, and primary particle diameter carry a substantial dependency on the operating pressure. [ABSTRACT FROM AUTHOR]

We prove limit laws for the number of occurrences of a pattern on the fringe of a ranked tree-child network which is picked uniformly at random. Our results extend the limit law for cherries proved by Bienvenu et al. (Random Struct. Algoritm. 60 (2022), no. 4, 653–689). For patterns of height 1 and 2, we show that they either occur frequently (mean is asymptotically linear and limit law is normal) or sporadically (mean is asymptotically constant and limit law is Poisson) or not all (mean tends to 0 and limit law is degenerate). We expect that these are the only possible limit laws for any fringe pattern. [ABSTRACT FROM AUTHOR]

In order to reconstruct the possible defects on the plate surface with arrays, a new wave tomography method based on the method of moments is established in this paper. According to the relationship between the probe number and grid amount, two algorithms, that is, the neural network and principal component analysis (PCA), are proposed and used to solve the ill-conditioned inversion equations. The neural network makes imaging feasible even if input data are not enough, and the PCA can greatly improve the computational efficiency via reducing the matrix dimension. Both numerical simulations and experimental measurements are conducted with the algorithm's correctness and high precision validated. After investigating the influence of probe number on imaging quality, it is demonstrated that the algorithm can exactly predict the defect location when the input scattering data is not enough or fewer probes are arranged. More probes are needed for reconstructing the specific shape and thickness, especially when multiple defects are included. The qualitative results and quantitative data are conducive to providing some reference for engineering applications in nondestructive testing and structural health monitoring. [ABSTRACT FROM AUTHOR]

The generalized Kaiser–Bessel window function is defined via the modified Bessel function of the first kind and arises frequently in tomographic image reconstruction. In this paper, we study in details the properties of the Kaiser–Bessel distribution, which we define via the symmetric form of the generalized Kaiser–Bessel window function. The Kaiser–Bessel distribution resembles to the Bessel distribution of McKay of the first type, it is a platykurtic or sub-Gaussian distribution, it is not infinitely divisible in the classical sense and it is an extension of the Wigner's semicircle, parabolic and n-sphere distributions, as well as of the ultra-spherical (or hyper-spherical) and power semicircle distributions. We deduce the moments and absolute moments of this distribution and we find its characteristic and moment generating function in two different ways. In addition, we find its cumulative distribution function in three different ways and we deduce a recurrence relation for the moments and absolute moments. Moreover, by using a formula of Ismail and May on quotient of modified Bessel functions of the first kind, we deduce a closed-form expression for the differential entropy. We also prove that the Kaiser–Bessel distribution belongs to the family of log-concave and geometrically concave distributions, and we study in details the monotonicity and convexity properties of the probability density function with respect to the argument and each of the parameters. In the study of the monotonicity with respect to one of the parameters we complement a known result of Gronwall concerning the logarithmic derivative of modified Bessel functions of the first kind. Finally, we also present a modified method of moments to estimate the parameters of the Kaiser–Bessel distribution, and by using the classical rejection method we present two algorithms for sampling independent continuous random variables of Kaiser–Bessel distribution. The paper is closed with conclusions and proposals for future works. [ABSTRACT FROM AUTHOR]

In modern wireless telecommunication systems, antenna arrays are widely used as elements of multiple – input multiple – output technology. In the fifth-generation systems, arrays are utilized to realize beamforming that forms the radiation pattern of the base station in the direction of the mobile user. This requires the utilization of many-element antenna arrays that are precisely controlled to achieve the required radiation properties. In this paper we apply the concept of deep neural network to model antenna array radiation properties. In this proof-of-concept research we aim at investigating to what extent it is possible to use deep neural networks for modeling antenna arrays. We consider a full-wave model of linear array with a reflector, which was controlled by the phase and amplitude of the signals feeding the elementary radiators. The applied method made it possible to solve the direct and inverse problems. The results that we obtained show that deep neural networks are able to model antenna array properties. [ABSTRACT FROM AUTHOR]

In today's competitive market, it is crucial to continually improve antenna manufacturing technologies to keep up with the increasing demands. Researchers can utilize numerical methods to create novel and highly effective antenna designs, pushing the boundaries of antenna engineering. This paper considers two approaches to efficiently model and design sparse wire-grid antennas. The main idea is to create an optimal wire structure that closely approximates the current paths in the antenna while maintaining its integrity with minimal mass. This structure can be used in further simulations with controlled characteristic accuracy and less resources. In this study, these approaches were applied to modelling horn, conical horn, and reflector antennas. The verification was conducted by comparing their results with those obtained from numerical and experimental tests for the same antenna designs. The findings demonstrated good agreement between the results. In addition, we investigated the impact of using these approaches on the antenna characteristics and found that they can enhance the performance of certain characteristics while reducing costs in manufacturing and modelling. [ABSTRACT FROM AUTHOR]

The reliability assessment of the project duration is essential for successful project management; this has prompted the development of various methods to assess whether a project will be completed within the target duration. In this study, an efficient and effective method for assessing the reliability of project duration based on the method of moments is proposed, which utilizes bivariate-dimension reduction technology and the third-moment reliability index. The proposed method can avoid the extensive calculations of various factors in the commonly used methods: the correlation coefficients between each pair of paths and the joint failure probability of each pair of representative paths. From two numerical examples, it can be concluded that the proposed method can obtain almost the same results as Monte Carlo simulations with less calculation. [ABSTRACT FROM AUTHOR]

Abstract Here, the multibranch linear–linear basis function (MB‐LL) is applied to the Poggio–Miller–Chang–Harrington–Wu–Tsai equation for calculating the scattering problem of multi‐scale dielectric targets. The MB‐LL basis function replaces the positive and negative triangles of the traditional linear–linear basis function (LL) with multiple branches, so it can be used at the junction of the meshes of different size. By using the MB‐LL basis function, we can easily divide the calculation region into several non‐overlapping regions, which is very suitable for the simulation of multiscale targets. At the same time, the MB‐LL basis function inherits the properties of the LL basis function, which is more accurate than the multibranch Rao–Wilton–Glisson (MB‐RWG) basis function. Numerical examples demonstrate the advantages of the proposed method.