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We evaluate depletion forces in molecular dynamics simulation of a binary mixture of spheres (depleted particles) and rods (depletant particles) for a wide range of densities for both species. This evaluation was carried out using a recently proposed least squares fitting algorithm. We found that the restriction of the rods' rotational degrees of freedom, when the distance between two spheres is less than the rods length, creates a shallow, and apparently linear, attractive force ramp. For intersphere distances smaller than the rods' diameter, a much stronger attractive force is found, and a large repulsive barrier appears between these aforementioned regimes, roughly at the distance of the rods' thickness. The evaluated forces are validated via a comparison of the pairwise correlation functions obtained from molecular dynamics simulation of a mono-disperse sphere fluid, using the evaluated effective forces, against the original (full system) pairwise correlation functions. Agreement is excellent. We also record the angular pairwise correlation function, using the P2(x) Legendre polynomial, and find that for high densities of both species, a local nematic ordering starts to appear. This nematic order may be a factor in the small differences found between original and effective pairwise correlation functions at high densities of rods. [ABSTRACT FROM AUTHOR]

We propose an approach to represent the second-quantized electronic Hamiltonian in a compact sum-of-products (SOP) form. The approach is based on the canonical polyadic decomposition of the original Hamiltonian projected onto the sub-Fock spaces formed by groups of spin–orbitals. The algorithm for obtaining the canonical polyadic form starts from an exact sum-of-products, which is then optimally compactified using an alternating least squares procedure. We discuss the relation of this specific SOP with related forms, namely the Tucker format and the matrix product operator often used in conjunction with matrix product states. We benchmark the method on the electronic dynamics of an excited water molecule, trans-polyenes, and the charge migration in glycine upon inner-valence ionization. The quantum dynamics are performed with the multilayer multiconfiguration time-dependent Hartree method in second quantization representation. Other methods based on tree-tensor Ansätze may profit from this general approach. [ABSTRACT FROM AUTHOR]

Geomagnetic navigation has become a hot spot in current research because of its characteristics of passiveness and good concealment. However, the magnetic interference from various ferromagnetic substances, electronic equipment, etc., of the carrier will be superimposed on the geomagnetic field, causing magnetometer measurement errors, thus affecting navigation accuracy. In practice, due to the limited maneuverability of the carrier, sufficient geomagnetic observation data cannot be obtained, resulting in the observation equation used for carrier magnetic interference compensation to be seriously pathological. To achieve the compensation of carrier magnetic interference, this paper proposes the total least squares method based on the ridge regression using the L curve to solve ridge parameters. This method can effectively suppress the measurement noise that exists on both sides of the observation equation, and is suitable for alleviating the pathological effects of carrier magnetic interference compensation. Experimental results show that the compensated magnetometer measurement error is reduced to 3% of the carrier magnetic interference by using the method proposed in this paper, which obtains more stable and accurate parameter estimates. [ABSTRACT FROM AUTHOR]

Urban environments, characterized by bustling mass transit systems and high population density, host a complex web of microorganisms that impact microbial interactions. These urban microbiomes, influenced by diverse demographics and constant human movement, are vital for understanding microbial dynamics. We explore urban metagenomics, utilizing an extensive dataset from the Metagenomics & Metadesign of Subways & Urban Biomes (MetaSUB) consortium, and investigate antimicrobial resistance (AMR) patterns. In this pioneering research, we delve into the role of bacteriophages, or "phages"–viruses that prey on bacteria and can facilitate the exchange of antibiotic resistance genes (ARGs) through mechanisms like horizontal gene transfer (HGT). Despite their potential significance, existing literature lacks a consensus on their significance in ARG dissemination. We argue that they are an important consideration. We uncover that environmental variables, such as those on climate, demographics, and landscape, can obscure phage‐resistome relationships. We adjust for these potential confounders and clarify these relationships across specific and overall antibiotic classes with precision, identifying several key phages. Leveraging machine learning tools and validating findings through clinical literature, we uncover novel associations, adding valuable insights to our comprehension of AMR development. [ABSTRACT FROM AUTHOR]

BACKGROUND: Cassava utilization for food and/or industrial products depends on inherent properties of root dry matter content (DMC) and the starch fraction of amylose content (AC). Accordingly, in the present study, near‐infrared reflectance spectroscopy (NIRS) models were developed to aid breeding and selection of DMC and AC as critical industrial traits taking care of root sample preparation and cassava germplasm diversity available in Uganda. RESULTS: Upon undertaking calibrations and cross‐validations, best models were adopted for validation. DMC in calibration samples ranged from 20 to 45 g 100g−1, whereas, for amylose content, it ranged from 14 to 33 g 100g−1. In the validation set, average DMC was 29.5 g 100g−1, whereas, for amylose content, it was 24.64 g 100g−1. For DMC, a modified partial least square regression model had regression coefficients (R2) of 0.98 and 0.96, respectively, in the calibration and validation set. These were also associated with low bias (−0.018) and ratio of performance deviation that ranged from 4.7 to 5.0. In addition, standard error of prediction values ranged from 0.9 g 100g−1 to 1.06 g 100g−1. For AC, the regression coefficient was 0.91 for the calibration set and 0.94 for the validation set. A bias equivalent to −0.03 and a ratio of performance deviation of 4.23 were observed. CONCLUSION: These findings confirm the robustness of NIRS in the estimation of dry matter content and amylose content in cassava roots and thus justify its use in routine cassava breeding operations. © 2023 The Authors. Journal of The Science of Food and Agriculture published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to focus on the transient flow and heat transfer of a non-newtonian fluid (Casson fluid) between parallel disks in the presence of an external magnetic field. The bottom disk is considered to be porous and fixed, whereas the upper disk moves down. Also, the influence of the heat source/sink and viscous dissipation is taken into account. The conservative partial differential equations have been transformed into dimensionless ones and are solved semi-analytically using Least Square Method. Besides, applying a numerical solution, the accuracy of analytical results is verified using the fourth-order Runge–Kutta method. The effects of various physical parameters such as suction/injection, heat source/sink, Prandtl number, magnetic field, slip condition, and Casson fluid parameter on velocity and temperature distribution as well as skin-friction coefficient and Nusselt number are examined and discussed. The results have shown that higher values of the Casson fluid parameter decrease the Nusselt number and shear stress. Also, it is observed that the Hartmann number augmentation decreases the heat transfer rate. What is more, it is shown that the intensity of injection/suction affects how streamlines behave against the central vertical axis. [ABSTRACT FROM AUTHOR]

With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of total least squares problems, i.e., solving min E , r ‖ [ E , r ] ‖ F subject to (A + E) x = b + r , arises in numerous applications. Solving this problem requires finding the smallest singular value and corresponding right singular vector of [ A , b ] , which is challenging when A is large and sparse. An efficient algorithm for this case due to Björck et al. (SIAM J. Matrix Anal. Appl. 22(2), 413–429 2000), called RQI-PCGTLS, is based on Rayleigh quotient iteration coupled with the preconditioned conjugate gradient method. We develop a mixed precision variant of this algorithm, RQI-PCGTLS-MP, in which up to three different precisions can be used. We assume that the lowest precision is used in the computation of the preconditioner and give theoretical constraints on how this precision must be chosen to ensure stability. In contrast to standard least squares, for total least squares, the resulting constraint depends not only on the matrix A , but also on the right-hand side b . We perform a number of numerical experiments on model total least squares problems used in the literature, which demonstrate that our algorithm can attain the same accuracy as RQI-PCGTLS albeit with a potential convergence delay due to the use of low precision. Performance modeling shows that the mixed precision approach can achieve up to a 4 × speedup depending on the size of the matrix and the number of Rayleigh quotient iterations performed. [ABSTRACT FROM AUTHOR]

We study a two-dimensional coordinate descent method to solve large linear least squares problems expanding on the method presented by Leventhal and Lewis. For an overdetermined system with full column rank, they proved its convergence in expectation, regardless of its consistency. In our work, we present a block version of the same. We also present an update on the extension done by Ma et al. to address non-full rank linear systems or underdetermined linear systems. Convergence is analyzed for the stated methods, and numerical experiments are provided to demonstrate their efficiency. [ABSTRACT FROM AUTHOR]

High pressure circular dichroism (HP-CD) spectroscopy below 200 MPa, especially in the near-ultraviolet region, has long been expected to probe the protein self-association phenomena. However, its experimental difficulties have hampered obtaining the data available for quantitative analyses. In this paper, near-ultraviolet CD spectra measurements under various temperatures and pressures were demonstrated on nitrilase from Rhodococcus rhodochrous J1 (J1-NTase), which thermally self-associates from inactive protomer to active oligomer at atmospheric pressure. The exploration of instrumental conditions and simple raw data correction enabled us to complete the spectra in a temperature-pressure plane. The quality of data was checked by multivariate curve resolution with the alternating least squares method (MCR-ALS), which gave model-free decomposition into component spectra and their concentration profiles. The resultant two components pointed out that the obtained data were self-consistent and appeared to reflect free and bound protomers. [ABSTRACT FROM AUTHOR]

This paper analyses the effect of export diversification on income inequality in Central Africa through the employment channel. The sample consists of 9 countries over the period 2000–2019. A quadratic regression is applied to a panel data model using the random effect and the two stages least squares methods. The results show that export diversification increases income inequality in Central Africa. However, this effect is non-linear with the form of an inverted U. Increasing the number of wage workers reduces the marginal effect of export diversification on income inequality while increasing the number of unpaid workers increases this effect. Moreover, diversification is less likely to reduce income inequality when it increases male employment than when it increases female employment. The effect of diversification on income inequality remains non-linear in an inverted U-shape for CEMAC countries' members (CEMAC: Economic and Monetary Community of Central African States) and oil-producing countries, while it is non-linear in a U-shape for non-CEMAC countries and non-oil-producing countries. We recommend that Central African countries promote the diversification of exports while encouraging new productive activities to generate more paid jobs and to favor female employment. [ABSTRACT FROM AUTHOR]

This study examines the relationship between financial inclusion, renewable energy, and CO2 emissions using data from 11 Middle East and North Africa (MENA) countries from 2004 to 2019. Evidence from fixed effects-ordinary least squares (FE-OLS), dynamic ordinary least squares (DOLS), fully modified ordinary least squares (FMOLS), and canonical correlation regression (CRR) showed that financial inclusion contributes significantly to decarbonization. Country-specific analysis indicated that financial inclusion is associated with mitigating CO2 emissions in Egypt, Israel, Qatar, and Tunisia while significantly spurring CO2 emissions in Algeria, Lebanon, and Saudi Arabia. In addition, renewable energy contributes significantly to decarbonization in MENA, especially in Algeria, Lebanon, Tunisia, and Turkey. We recommend that policies promoting financial inclusion and renewable energy usage would contribute to the attainment of the carbon-neutrality goal by MENA countries. [ABSTRACT FROM AUTHOR]

Existing methods for fitting spatial autoregressive models have various strengths and weaknesses. For example, the maximum likelihood estimation (MLE) approach yields efficient estimates but is computationally burdensome. Computationally efficient methods, such as generalized method of moments (GMMs) and spatial two‐stage least squares (2SLS), typically require exogenous covariates to be significant, a restrictive assumption that may fail in practice. We propose a new estimating equation approach, termed combined moment equation (COME), which combines the first moment with covariance conditions on the residual terms. The proposed estimator is less computationally demanding than MLE and does not need the restrictive exogenous conditions as required by GMM and 2SLS. We show that the proposed estimator is consistent and establish its asymptotic distribution. Extensive simulations demonstrate that the proposed method outperforms the competitors in terms of bias, efficiency, and computation. We apply the proposed method to analyze an air pollution study, and obtain some interesting results about the spatial distribution of PM2.5 concentrations in Beijing. [ABSTRACT FROM AUTHOR]

Purpose: This study forecasts the government expenditure components in Nigeria, including recurrent and capital expenditures for 2021 and 2022, based on data from 1981 to 2020. Design/methodology/approach: The study employs statistical/econometric problems using the Feasible Quasi Generalized Least Squares approach. Expenditure forecasts involve three simulation scenarios: (1) do nothing where the economy follows its natural path; (2) an optimistic scenario, where the economy grows by specific percentages and (3) a pessimistic scenario that defines specific economic contractions. Findings: The estimation model is informed by Wagner's law specifying a positive link between economic activities and public spending. Model estimation affirms the expected positive relationship and is relevant for generating forecasts. The out-of-sample results show that a higher proportion of the total government expenditure (7.6% in 2021 and 15.6% in 2022) is required to achieve a predefined growth target (5%). Originality/value: This study offers empirical evidence that specifically requires Nigeria to invest a ratio of 3 to 1 or more in capital expenditure to recurrent expenditure for the economy to be guided on growth. [ABSTRACT FROM AUTHOR]

This article considers the parameter identification problems of stochastic systems which described by the finite impulse response moving average model. Since the system is disturbed by colored noise, we introduce the data filtering technique from a view point of improving the parameter estimation accuracy. The data filtering technique is to use a filter to filter the input and output data of the system disturbed by colored noise so as to improve the identification accuracy. By using the data filtering technique, this article proposes a filtering‐based recursive extended least squares (F‐RELS) algorithm. The convergence analysis indicates that the parameter estimates can converge to their true values. Compared with the recursive extended least squares algorithm, the proposed F‐RELS algorithm can obtain more accurate parameter estimation. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

A biomechanical model often requires parameter estimation and selection in a known but complicated nonlinear function. Motivated by observing that the data from a head-neck position tracking system, one of biomechanical models, show multiplicative time-dependent errors, we develop a modified penalized weighted least squares estimator. The proposed method can be also applied to a model with possible non-zero mean time-dependent additive errors. Asymptotic properties of the proposed estimator are investigated under mild conditions on a weight matrix and the error process. A simulation study demonstrates that the proposed estimation works well in both parameter estimation and selection with time-dependent error. The analysis and comparison with an existing method for head-neck position tracking data show better performance of the proposed method in terms of the variance accounted for. [ABSTRACT FROM AUTHOR]

The antiplane deformation of a two layered model consisting of a homogeneous, elastically isotropic (HEI) stratum of finite thickness lying on a HEI substratum occurring from a buried inclined strike-slip fault (ISF) situated in the stratum has been studied. The stratum is in welded contact with the substratum having different rigidity. The integral expressions for the deformation field occurring from a long strike-slip line dislocation for the antiplane strain case have been obtained using Fourier transform approach. The integrals have been solved analytically by expanding the denominator into a finite sum of exponential terms (FSET) using least square method. Further, the deformation is obtained for a long buried ISF of finite width via integrating over the width of line dislocation. The variation of the displacement has been computed graphically with respect to the epicentral distance as well as with depth. [ABSTRACT FROM AUTHOR]

This study assessed the viability of using hyperspectral imaging (HSI) technology for nondestructive detection of moisture content in oilseed rape leaves. Besides, a method (IVISSA-iPLS) coupling interval variable iterative space shrinkage approach (IVISSA) with interval partial least square (iPLS) was introduced to identify characteristic wavelengths. The IVISSA-iPLS algorithm changed the selection target from wavelength points to spectral intervals, reducing the computational burden while increasing the continuity between the selected wavelengths. Subsequently, the characteristic wavelengths selected by the IVISSA-iPLS were used as the input of the least square support vector regression (LSSVR) model to predict the moisture content of oilseed rape leaves. Additionally, the competitive adaptive reweighted sampling (CARS), the successive projections algorithm (SPA), the IVISSA, and the iPLS were investigated as wavelength selection algorithms for comparison. The results indicated that the LSSVR models based on the characteristic wavelengths acquired from the IVISSA-iPLS using divided wavelength intervals of 30, demonstrated the highest performance, with R p 2 of 0.9555, RMSEP of 0.0065, and RPD of 4.715. Finally, the optimal prediction model was used to visualize the moisture content of oilseed rape leaves, which offered a more intuitive and effective method for the evaluation of moisture content. The results ascertained the significant possibility of combining HSI with combinatorial algorithms in detecting, quantifying, and visualizing the moisture content of oilseed rape leaves. [ABSTRACT FROM AUTHOR]

This article studies the two-step conditional least squares (CLS) estimation for the bivariate Z -valued INAR(1) model with bivariate Skellam innovations. For readers' convenience, we first give a brief review of the bivariate Skellam distribution, bivariate signed thinning operator and the definition of the bivariate Z -valued INAR(1) model with bivariate Skellam innovations (denoted as the BSK-BINARS(1) model). Then, we discuss the stationarity and ergodicity of the BSK-BINARS(1) model, give some stochastic properties. Second, we discuss the two-step CLS estimate of the parameters and establish their large-sample properties. Third, we conduct a simulation study to illustrate the finite sample performances of the two-step CLS estimators, which are compared with those obtained by the plug-in method. Last but not least, we apply the BSK-BINARS(1) model on the zonal annual means temperature (*100). [ABSTRACT FROM AUTHOR]

We examine some bounded perturbations resilient iterative methods for addressing (constrained) consistent linear systems of equations and (constrained) least squares problems. We introduce multiple frameworks rooted in the operator of the Landweber iteration, adapting the operators to facilitate the minimization of absolute errors or residuals. We demonstrate that our operator-based methods exhibit comparable speed to powerful methods like CGLS, and we establish that the computational cost of our methods is nearly equal to that of CGLS. Furthermore, our methods possess the capability to handle constraints (e.g. non-negativity) and control the semi-convergence phenomenon. In addition, we provide convergence analysis of the methods when the current iterations are perturbed by summable vectors. This allows us to utilize these iterative methods for the superiorization methodology. We showcase their performance using examples drawn from tomographic imaging and compare them with CGLS, superiorized conjugate gradient (S-CG), and the non-negative flexible CGLS (NN-FCGLS) methods. [ABSTRACT FROM AUTHOR]

This article investigates the security ensured state estimation problem for cyber‐physical system via a data‐driven method. First, based on the fact that different packets possess varying a degree of significance, that is, some packets play more important roles in the state estimation than others, a novel stochastic important‐data‐based (IDB) attack mechanism is constructed from the attacker's perspective, which can focus on attacking the important packets thus is expected to achieve more destructiveness. Second, as a countermeasure to the proposed IDB attack, a new data‐driven compensation method is proposed, for the first attempt, to compensate for the attack effect and enhance the estimation quality. The designed defense strategy has the following two advantages: (1) only system input and output data are utilized to establish the novel estimator, without knowing the actual system model knowledge, and (2) by constructing a data‐driven output predictor to compensate for the data loss, the accuracy of the state estimation can be efficiently improved. With the aid of the least squares technique and completing square technique, a minimum upper bound matrix for the estimation error covariance is obtained by properly designing the estimator gain. Finally, an illustrative example is given to highlight the destructiveness of the designed stochastic IDB attack and the effectiveness of the proposed novel data‐based compensation method. [ABSTRACT FROM AUTHOR]

This research addresses the tracking problem of least squares adaptive control for a class of nonlinear system with mismatched uncertainties. Different from most of existing solutions, modified predictive model is integrated into the proposed least squares adaptive control architecture. The significant role of modified predictive model in the adaptive control architecture is to achieve smooth transient by filtering out the high‐frequency oscillations, which cannot be canceled out by use of the hypothetical parameterized uncertainty models. Meanwhile, in order to guarantee tracking performance, a generalized restricted potential function (GRPF) is designed to constrain the weighted Euclidean norm of the predictive error of the modified predictive model to be less than a predefined scalar worst‐case bound. Finally, comparative simulations via the generic transport model (GTM) are conducted to examine the effectiveness of the proposed method. The results show that the transient performance and tracking performance of the controlled system can be improved simultaneously by the proposed method. [ABSTRACT FROM AUTHOR]

The chemical distribution on the lunar surface results from the combined effects of both endogenic and exogenic geological processes. Exploring global maps of chemical composition helps to gain insights into the compositional variation among three major geological units, unraveling the geological evolution of the Moon. The existing oxide abundance maps were obtained from spectral images of remote sensing and geochemical data from samples returned by Apollo and Luna, missing the chemical characteristics of the Moon's late critical period. In this study, by adding geochemical data from Chang'e (CE)-5 lunar samples, we construct inversion models between the Christiansen feature (CF) and oxide abundance of lunar samples using the particle swarm optimization–extreme gradient boosting (PSO-XGBoost) algorithm. Then, new global oxide maps (Al2O3, CaO, FeO, and MgO) and Mg# with the resolution of 32 pixels/degree (ppd) were produced, which reduced the space weathering effect to some extent. The PSO-XGBoost models were compared with partial least square regression (PLSR) models and four previous results, indicating that PSO-XGBoost models possess the capability to effectively describe nonlinear relationships between CF and oxide abundance. Furthermore, the average contents of our results and the Diviner results for 21 major maria demonstrate high correlations, with R2 of 0.95, 0.82, 0.95, and 0.86, respectively. In addition, a new Mg# map was generated, which reveals different magmatic evolutionary processes in the three geologic units. [ABSTRACT FROM AUTHOR]

Simulation is a crucial tool for the evaluation and comparison of statistical methods. How to design fair and neutral simulation studies is therefore of great interest for both researchers developing new methods and practitioners confronted with the choice of the most suitable method. The term simulation usually refers to parametric simulation, that is, computer experiments using artificial data made up of pseudo-random numbers. Plasmode simulation, that is, computer experiments using the combination of resampling feature data from a real-life dataset and generating the target variable with a known user-selected outcome-generating model, is an alternative that is often claimed to produce more realistic data. We compare parametric and Plasmode simulation for the example of estimating the mean squared error (MSE) of the least squares estimator (LSE) in linear regression. If the true underlying data-generating process (DGP) and the outcome-generating model (OGM) were known, parametric simulation would obviously be the best choice in terms of estimating the MSE well. However, in reality, both are usually unknown, so researchers have to make assumptions: in Plasmode simulation studies for the OGM, in parametric simulation for both DGP and OGM. Most likely, these assumptions do not exactly reflect the truth. Here, we aim to find out how assumptions deviating from the true DGP and the true OGM affect the performance of parametric and Plasmode simulations in the context of MSE estimation for the LSE and in which situations which simulation type is preferable. Our results suggest that the preferable simulation method depends on many factors, including the number of features, and on how and to what extent the assumptions of a parametric simulation differ from the true DGP. Also, the resampling strategy used for Plasmode influences the results. In particular, subsampling with a small sampling proportion can be recommended. [ABSTRACT FROM AUTHOR]

Linear mixed models provide a general and versatile approach for analyzing data collected in experiments, suitable for modeling repeated, longitudinal, or clustered observations. Important results for estimation can be obtained when subclasses of these mixed models are considered, based on some characteristics of their algebraic structure. The class of the models with commutative orthogonal block structure, for which least squares estimators are the best linear unbiased estimators, is of great interest. In an approach based on the algebraic structure of the models, and availing ourselves of U matrices, we study the possibility of extending a balanced mixed model, which could lead to a model with commutative orthogonal block structure. [ABSTRACT FROM AUTHOR]

With the breakthroughs made by physicists in high-dimensional mathematics, it has become possible to represent and solve a number of classical mathematical physics problems using the split quaternion algebra. In this paper, we study the least squares approximation of a class of Schrödinger equations in split quaternionic mechanics and propose two algebraic algorithms to the generalized right eigen-problem for an i-Hermitian split quaternion matrix pencil by using two isomorphic mappings. Numerical examples show the effectiveness of the proposed theories and algorithms. [ABSTRACT FROM AUTHOR]

Rice metabolomics is widely used for biomarker research in the fields of pharmacology. As a consequence, characterization of the variations of the pigmented and non-pigmented traditional rice varieties of Tamil Nadu is crucial. These varieties possess fatty acids, sugars, terpenoids, plant sterols, phenols, carotenoids and other compounds that plays a major role in achieving sustainable development goal 2 (SDG 2). Gas-chromatography coupled with mass spectrometry was used to profile complete untargeted metabolomics of Kullkar (red colour) and Milagu Samba (white colour) for the first time and a total of 168 metabolites were identified. The metabolite profiles were subjected to data mining processes, including principal component analysis (PCA), Orthogonal Partial Least Square Discrimination Analysis (OPLS-DA) and Heat map analysis. OPLS-DA identified 144 differential metabolites between the 2 rice groups, variable importance in projection (VIP) ≥ 1 and fold change (FC) ≥ 2 or FC ≤ 0.5. Volcano plot (64 down regulated, 80 up regulated) was used to illustrate the differential metabolites. OPLS-DA predictive model showed good fit (R2X = 0.687) and predictability (Q2 = 0.977). The pathway enrichment analysis revealed the presence of three distinct pathways that were enriched. These findings serve as a foundation for further investigation into the function and nutritional significance of both pigmented and non-pigmented rice grains thereby can achieve the SDG 2. [ABSTRACT FROM AUTHOR]

QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively simple but complete explanations about how to use QR decomposition for the least squares problem solution. Only basic knowledge of linear algebra and calculus are required. Both Givens rotations and Householder reflections usage for the linear least squares problem were considered. It was shown that the algorithm based on Givens rotations is even easier to program than explicit formation of the normal equations with subsequent usage of Gaussian elimination. [ABSTRACT FROM AUTHOR]

We introduce a novel enrichment technique for the element free Galerkin (EFG) method to capture the infinite stress field around the crack or notch tip. The singular enrichment bases are built through a weighted residual application of the governing partial differential equation. A special mapping is used to adapt the bases with the singularities. These bases are used in a moving least squares approximation to enrich the smooth polynomial bases of the EFG within the singularity-dominated zone in an intrinsic approach. The novelty of the method is that no a priori knowledge of the analytical singularity order is required to reproduce the singular bases, but they are automatically built during the solution procedure. The diffraction technique has been used to model the discontinuity of the notch tip. The effect of various parameters, including the enriched region size, enrichment factors, nodal distribution and irregularities, has been examined. Validation of the method using available analytical solutions or finite element modeling, revealed that the proposed enrichment is quite effective and accurate for displacement and stress components. [ABSTRACT FROM AUTHOR]

We consider adaptive least-squares finite element methods. First, we develop a guaranteed upper bound for the dual error in the L 2 norm, and this can be used as a stopping criterion for the adaptive procedures. Secondly, based on the a posteriori error estimates for the dual variable, we develop an error indicator that identifies the local area to refine, and establish the convergence of the adaptive procedures based on the Dörfler's marking strategy. Our convergence analysis is valid for the entire range of the bulk parameter 0 < Θ ≤ 1 and it shows the effect of bulk parameter and reduction factor of elements on the convergence rate. Confirming numerical experiments are provided. [ABSTRACT FROM AUTHOR]

Background: A Generalized Linear Mixed Model (GLMM) is recommended to meta-analyze diagnostic test accuracy studies (DTAs) based on aggregate or individual participant data. Since a GLMM does not have a closed-form likelihood function or parameter solutions, computational methods are conventionally used to approximate the likelihoods and obtain parameter estimates. The most commonly used computational methods are the Iteratively Reweighted Least Squares (IRLS), the Laplace approximation (LA), and the Adaptive Gauss-Hermite quadrature (AGHQ). Despite being widely used, it has not been clear how these computational methods compare and perform in the context of an aggregate data meta-analysis (ADMA) of DTAs. Methods: We compared and evaluated the performance of three commonly used computational methods for GLMM - the IRLS, the LA, and the AGHQ, via a comprehensive simulation study and real-life data examples, in the context of an ADMA of DTAs. By varying several parameters in our simulations, we assessed the performance of the three methods in terms of bias, root mean squared error, confidence interval (CI) width, coverage of the 95% CI, convergence rate, and computational speed. Results: For most of the scenarios, especially when the meta-analytic data were not sparse (i.e., there were no or negligible studies with perfect diagnosis), the three computational methods were comparable for the estimation of sensitivity and specificity. However, the LA had the largest bias and root mean squared error for pooled sensitivity and specificity when the meta-analytic data were sparse. Moreover, the AGHQ took a longer computational time to converge relative to the other two methods, although it had the best convergence rate. Conclusions: We recommend practitioners and researchers carefully choose an appropriate computational algorithm when fitting a GLMM to an ADMA of DTAs. We do not recommend the LA for sparse meta-analytic data sets. However, either the AGHQ or the IRLS can be used regardless of the characteristics of the meta-analytic data. [ABSTRACT FROM AUTHOR]

This study investigates the influences of air temperature (T), relative humidity (RH), wind speed (WS), clearance index (KT), particulate matter (PM) concentrations (PM10 and PM2.5), and aerosol optical depth (AOD) on ultraviolet (UV) radiation during clear skies in Riyadh, central Saudi Arabia. The observational dataset utilized in this study comprises global solar radiation (G), UVA radiation, AOD measurements, and PM concentrations. The data were collected from 2014 to 2015 at the King Abdulaziz City for Science and Technology (KACST) campus in Riyadh. Regression analyses were conducted to investigate the relationships between UV radiation and the considered variables. The methodology is based on the least square method and associated statistical tests. The findings of this study provide valuable insights into the impacts of meteorological variables and aerosols on UV radiation, contributing to the understanding of environmental and industrial applications in the Arabian Peninsula. The analyses showed that the strengths and magnitudes differed from one variable to another. No significant correlations between UVA radiation (315–400 nm) and hourly and daily values of PM2.5 were found. Moreover, no significant correlations were seen between daily values of the UVA radiation and RH and between the UVB (280–315 nm) and PM10. The rest of the correlations (between UV radiation and the PM10 and meteorological variables) were found to be significant. While WS, the ratio of the PM concentrations (PM2.5/PM10), KT, and T exhibited positive correlations with UV radiation, the rest of the variables had anti-correlations with UV radiation. The influences of T, WS, and RH on ambient PM concentrations during the considered period were taken into account, and it was found that the PM concentrations correlate, with different magnitudes and strengths, positively with T and negatively with RH and WS. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new three-parameter inverse Rayleigh distribution that extends the inverse Rayleigh distribution, constructed based on the generalized transmuted family of distributions proposed by Alizadeh, Merovci, and Hamedani. We explore statistical properties such as the quantile function, moments, harmonic mean, mean deviation, stress–strength reliability, and entropy. Parameter estimation is performed using various methods, including maximum likelihood, least squares, the method of the maximum product of spacings, and the method of Cramér–von Mises. The usefulness of the new three-parameter inverse Rayleigh distribution is illustrated by modeling a real dataset, demonstrating its superior fit compared to several other distributions. [ABSTRACT FROM AUTHOR]

In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to performance degradation. After multiple iterations, divergence may occur. The traditional extended Kalman filter cannot accurately estimate the nonlinear model, and these errors still have an impact on the accuracy. To improve the filtering performance of the extended Kalman filter (EKF), this paper proposes a new extended Kalman filter (REKF) method that utilizes the statistical properties of the rounding error to enhance the estimation accuracy. After establishing the state model and measurement model, the residual term is used to replace the higher-order term in the Taylor expansion, and the least squares method is applied to identify the residual term step by step. Then, the iterative process of updating the extended Kalman filter is carried out. Within the Kalman filter framework, a higher-order rounding error-based extended Kalman filter (REKF) is designed for the joint estimation of rounding error and random variables, and the solution method for the rounding error is considered for the multilevel approximation of the original function. Through numerical simulations on a general nonlinear model, the higher-order rounding error-based extended Kalman filter (REKF) achieves better estimation results than the extended Kalman filter (EKF) and improves the filtering accuracy by utilizing the higher-order rounding error information, which also proves the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements. [ABSTRACT FROM AUTHOR]

In this paper, we consider the partial linear regression model yi = xiβ* + g(ti) + εi, i = 1, 2, ..., n, where (xi, ti) are known fixed design points, g(·) is an unknown function, and β* is an unknown parameter to be estimated, random errors εi are (α, β)-mixing random variables. The p-th (p > 1) mean consistency, strong consistency and complete consistency for least squares estimators of β* and g(·) are investigated under some mild conditions. In addition, a numerical simulation is carried out to study the finite sample performance of the theoretical results. Finally, a real data analysis is provided to further verify the effect of the model. [ABSTRACT FROM AUTHOR]

INTRODUCTION: This post hoc analysis evaluated the efficacy of tenapanor on abdominal symptoms in patients with irritable bowel syndrome with constipation. Abdominal symptoms assessed included pain, discomfort, bloating, cramping, and fullness. METHODS: The abdominal symptomdata were pooled from3 randomized controlled trials (NCT01923428, T3MPO- 1 [NCT02621892], and T3MPO-2 [NCT02686138]).Weekly scoreswere calculated for each abdominal symptom, and the Abdominal Score (AS) was derived as the average of weekly scores for abdominal pain, discomfort, and bloating. The overall change from baseline during the 12 weeks was assessed for each symptom weekly score and the AS. The AS 6/12-week and 9/12-week response rates (AS improvement of ‡2 points for ‡6/12- or ‡9/12-week) were also evaluated. The association of weekly AS response status (reduction of‡30%) withweekly complete spontaneous bowelmovement (CSBM)status (50and>0)was assessed. RESULTS: Among 1,372 patients (684 tenapanor [50 mg twice a day] and 688 placebo), the least squares mean change frombaseline in AS was22.66 for tenapanor vs22.09 for placebo (P < 0.0001). The 6/12-week AS response rate was 44.4% for tenapanor vs 32.4% for placebo (P < 0.0001), and for 9/12-week AS, 30.6%for tenapanor vs20.5%for placebo (P <0.0001).Asignificant association betweenweeklyCSBM status and weekly AS response status was observed each week (P < 0.0001), with a greater proportion achieving an AS reduction in patients with >0 CSBMs in a week. DISCUSSION: Tenapanor significantly reduced abdominal symptoms in patients with irritable bowel syndrome with constipation, particularly pain, discomfort, and bloating measured by AS, compared with placebo. [ABSTRACT FROM AUTHOR]

The use of renewable energy sources to achieve carbon neutrality is increasing. However, the uncertainty and volatility of renewable resources are causing problems in power systems. Flexible and low-carbon resources such as Energy Storage Systems (ESSs) are essential for solving the problems of power systems and achieving greenhouse gas reduction goals. However, ESSs are not being installed because of Korea's fuel-based electricity market. To address this issue, this paper presents a method for determining the optimal investment timing of Battery Energy Storage Systems (BESSs) using the Least Squares Monte Carlo (LSMC) method. A case study is conducted considering the System Marginal Price (SMP) and Capacity Payment (CP), which are electricity rates in Korea. Revenue is calculated through the arbitrage of a 10 MW/40 MWh lithium-ion BESS, and linear programming optimization is performed for ESS scheduling to maximize revenue. The ESS revenue with uncertainty is modeled as a stochastic process using Geometric Brownian Motion (GBM), and the optimal time to invest in an ESS is determined using an LSMC simulation considering investment costs. The proposed method can be used as a decision-making tool for ESS investors to provide information on facility investments in arbitrage situations. [ABSTRACT FROM AUTHOR]

The simplification of lines plays a crucial role in map generalization and multiscale representation; however, addressing inconsistent sidedness relationships between the simplified lines and their neighboring features poses a persistent challenge. In order to preserve correct and consistent sidedness relationships following simplification, this study introduces a novel line simplification method. This method incorporates topological constraints pertaining to left–right sidedness relationships, formulated as an optimization procedure based on the proposed partial total least squares method with constraints. The primary objective is to minimize the positional difference between the line features before and after simplification, with the sidedness relationship represented as an inequality constraint. Moreover, an optimization algorithm is derived to address the simplification problem effectively while adhering to the specified constraints. The proposed method is then applied to simplify the lines within three distinct datasets. Experimental results validate the efficacy of the proposed method in maintaining sidedness consistency across all tested datasets. In comparison to the Douglas–Peucker (DP) method, the proposed method exhibits minimal vertical displacement variance in the line feature points post‐simplification. Additionally, it achieves a smaller overall positional difference between the simplified and original lines compared to the DP method. These findings underscore the superior performance of the proposed method in maintaining sidedness relationships and minimizing positional differences during the line simplification process. [ABSTRACT FROM AUTHOR]

The main objective of this paper was to highlight the nexus between migrant remittances and energy transition in a panel of 45 African countries from 2000 to 2020. The study utilized several estimation techniques ranging from fixed and random effects to two‐stage least square. The empirical findings suggest that remittances reduce energy transition in African countries. However, the growth of remittances reverses this relationship. There is therefore an U‐shaped relationship between remittances and energy transition in Africa. Furthermore, when disaggregating countries by income level, the results reveal that in low‐income countries, remittances reduce energy transition, but this effect is reversed in low‐ and middle‐income countries. Remittances are therefore a determinant in the choice of households for the process of energy transition. Thus, in order to take advantage of this relationship, African countries need to emphasize policies that can increase the flow of remittances by improving their financial system. In addition, migrant remittances contribute to improving access to modern, reliable, and affordable energy services through income growth of remittance‐receiving households. [ABSTRACT FROM AUTHOR]

Red beet (Beta vulgaris) contains betalain, which comprises red-violet betacyanin and yellow betaxanthin with esthetic and health benefits. Betacyanin and betaxanthin are usually detected using common chemical analysis, which requires a long time, skilled analysts, and sample destruction. For fast and accurate measurement, this study utilized a portable low-cost Visible-Near Infrared Spectra (Vis-NIR) spectrometer at 350 - 1000 nm combined with partial least square regression to predict the betacyanin and betaxanthin contents of red beet powder. The best calibration models for betacyanin and betaxanthin had R² c of 0.89 and 0.919, respectively, and standard error of calibration SEC of 0.108 and 0.037 mg/g, respectively. The models were able to predict the contents of both pigments with R² p of 0.87, standard error of prediction SEP of 0.108 mg/g, and the ratio of prediction to deviation RPD of 2.52 for betacyanin and R² p of 0.84, SEP of 0.056 mg/g, and RPD of 2.47 for betaxanthin. When applied to external unknown data, the models predicted the contents of betacyanin and betaxanthin with R² of 0.98 and root mean square error of 0.107 and 0.055 mg/g. Moreover, the predicted values were not significantly different at 95 % confidence. [ABSTRACT FROM AUTHOR]

A nondestructive method for the analysis of pharmaceuticals (nonsteroidal anti-inflammatory drugs, fluoroquinolones, acetylsalicylic acid, vinpocetine, tetracyclines) via IR diffuse reflection recorded using a smartphone and a 3D-printed device is proposed. Diffuse reflection of IR radiation (850 nm) from tablet medications can be captured using a smartphone camera. Blister packaging and tablet coatings slightly decrease the intensity of the reflection signal at a wavelength of 850 nm, as confirmed by a comparative analysis of colorimetric measurements of the pharmaceutical samples inside packaging, outside packaging, and fractured tablets. A correlation between the analytical signal and the concentration of the active substance is observed regardless of the study of the tablet. The dataset was processed using principal component analysis (PCA), hierarchical cluster analysis (HCA), partial least squares regression (PLS), and the least squares method using the PhotoMetrix PRO® smartphone software. These algorithms can be used to identify medications by their manufacturer and determine the concentration of active substances. Colorimetric signals from tablets of the same manufacturer form distinct clusters in the dendrograms created using the HCA algorithm. The PCA data indicate the arrangement of signals from tablets of different manufacturers in separate quadrants, facilitating the identification of the pharmaceutical companies. The use of chemometric analysis for determining the concentration of the active substance is also considered. [ABSTRACT FROM AUTHOR]

Here, Raman spectroscopy is used to develop a univariate partial least squares (PLS) calibration capable of quantifying geochemistry in synthetic and natural silicate glass samples. The calibration yields eight oxide-specific models that allow predictions of silicon dioxide (SiO2), sodium oxide (Na2O), potassium oxide (K2O), calcium oxide (CaO), titanium dioxide (TiO2), aluminum oxide (Al2O3), ferrous oxide (FeOT), and magnesium oxide (MgO) (wt%) in glasses spanning a wide range of compositions, while also providing correlation-coefficient matrices that highlight the importance of specific Raman channels in the regression of a particular oxide. The PLS suite is trained on 48 of the 69 total glasses, and tested against 21 validation samples (i.e., held out of training). Trends in root mean square error of calibration (RMSEC), root mean square error of cross-validation (RMSECV), and root mean square error of prediction (RMSEP) model accuracy metrics are investigated to uncover the efficacy of utilizing multivariate analysis for such Raman data and are contextualized against recently produced strategies. The technique yields an average root mean of calibration (∼2.4 wt%), cross-validation (∼ 2.9 wt%), prediction (∼ 2.6 wt%), and normalized variance (∼ 28%). Raman band positional shifts are also mapped against underlying chemical variations; with major influences arising primarily as a function of overall oxidation state and silica concentration: via ferric cation (Fe3+)/ferrous cation (Fe2+) ratios and SiO2 (wt%). The algorithm is further validated preliminarily against a separate external set of 11 natural basaltic glasses to unravel the limitations of the synthetic models on natural samples, and to determine the suitability of "universal" Raman-model applications in scenarios where prior chemical contextualization of the target sample is possible. This study represents the first time Raman spectra of amorphous silicates have been paired with PLS, offering a foundation for future improvements utilizing these systems. [ABSTRACT FROM AUTHOR]

Aims: This study aimed to illuminate the neuropathological landscape of attention deficit hyperactivity disorder (ADHD) by a multiscale macro–micro‐molecular perspective from in vivo neuroimaging data. Methods: The "ADHD‐200 initiative" repository provided multi‐site high‐quality resting‐state functional connectivity (rsfc‐) neuroimaging for ADHD children and matched typically developing (TD) cohort. Diffusion mapping embedding model to derive the functional connectome gradient detecting biologically plausible neural pattern was built, and the multivariate partial least square method to uncover the enrichment of neurotransmitomic, cellular and chromosomal gradient‐transcriptional signatures of AHBA enrichment and meta‐analytic decoding. Results: Compared to TD, ADHD children presented connectopic cortical gradient perturbations in almost all the cognition‐involved brain macroscale networks (all pBH <0.001), but not in the brain global topology. As an intermediate phenotypic variant, such gradient perturbation was spatially enriched into distributions of GABAA/BZ and 5‐HT2A receptors (all pBH <0.01) and co‐varied with genetic transcriptional expressions (e.g. DYDC2, ATOH7, all pBH <0.01), associated with phenotypic variants in episodic memory and emotional regulations. Enrichment models demonstrated such gradient‐transcriptional variants indicated the risk of both cell‐specific and chromosome‐ dysfunctions, especially in enriched expression of oligodendrocyte precursors and endothelial cells (all pperm <0.05) as well enrichment into chromosome 18, 19 and X (pperm <0.05). Conclusions: Our findings bridged brain macroscale neuropathological patterns to microscale/cellular biological architectures for ADHD children, demonstrating the neurobiologically pathological mechanism of ADHD into the genetic and molecular variants in GABA and 5‐HT systems as well brain‐derived enrichment of specific cellular/chromosomal expressions. [ABSTRACT FROM AUTHOR]

Penalized structural equation models (PSEM) is a new powerful estimation technique that can be used to tackle a variety of difficult structural estimation problems that can not be handled with previously developed methods. In this paper we describe the PSEM framework and illustrate the quality of the method with simulation studies. Maximum-likelihood and weighted least squares PSEM estimation is discussed for SEM models with continuous and categorical variables. We show that traditional EFA, multiple group alignment (MGA), and Bayesian SEM (BSEM) are examples of PSEM. The PSEM framework also extends standard SEM models with the possibility to structurally align various model parameters. Exploratory latent growth models, also referred to as Tuckerized curve models, can also be estimated in the PSEM framework and are illustrated here with simulation studies and an empirical example. [ABSTRACT FROM AUTHOR]

Background: Fatigue is a debilitating symptom of myasthenia gravis (MG). The impact of fatigue on MG can be assessed by Quality of Life in Neurological Disorders (Neuro-QoL) Short Form Fatigue scale. Transformation of raw Neuro-QoL fatigue scores to T-scores is a known approach for facilitating clinical interpretation of clinically meaningful and fatigue severity thresholds. Methods: In the Phase 3, double-blind, placebo-controlled RAISE study (NCT04115293), adults with acetylcholine receptor autoantibody-positive generalised MG (MG Foundation of America Disease Class II–IV) were randomised 1:1 to daily subcutaneous zilucoplan 0.3 mg/kg or placebo for 12 weeks. Patients completing RAISE could opt to receive zilucoplan 0.3 mg/kg in an ongoing, open-label extension study, RAISE-XT (NCT04225871). In this post-hoc analysis, we evaluated the long-term effect of zilucoplan on fatigue in RAISE patients who entered RAISE-XT. We report change in Neuro-QoL Short Form Fatigue T-scores and fatigue severity levels from RAISE baseline to Week 60. Results: Mean Neuro-QoL Short Form Fatigue T-scores improved from baseline to Week 12 in the zilucoplan group (n = 86) with a clinically meaningful difference versus placebo (n = 88; least squares mean difference: − 3.61 (nominal p-value = 0.0060]), and these improvements continued further to Week 60. At Week 12, more patients on zilucoplan (n = 34, 47.2%) experienced improvements in ≥ 1 fatigue severity level from baseline versus placebo (n = 23, 28.4%; p = 0.017). At Week 60, most (n = 55, 65.5%) patients had mild fatigue or none. Conclusion: Treatment with zilucoplan demonstrated statistical and clinically meaningful improvements in fatigue scores and severity versus placebo during RAISE, which were sustained to Week 60 in RAISE-XT. [ABSTRACT FROM AUTHOR]

Using a straight-line generating mechanism for a walking robot leg has several advantages over traditional bio-inspired leg designs including energy efficiency and simplicity of control system. As a walking robot propeller, we proposed a six-link mechanism based on our design of lambda-type mechanism, with an output link, which performs a rectilinear and translational movement. This ensures an unlimited range of foot adaptation on irregularities of the supporting surface. A new analytical method of mechanism synthesis is developed based on least square approximation, and its numerical implementation is presented. Due to minimizing the deviation directly from the desired output motion, the method does not suffer from so-called "branching defect" and allows synthesis of the mechanism with desired transmission angle. Improving the transmission angle ensures higher efficiency (therefore, lower power consumption) of the mechanism. A walking robot was developed using the optimal leg design which has high accuracy, optimum motion transfer, and step-cycle parameter which were achieved by multicriteria optimization based on the proposed synthesis method. [ABSTRACT FROM AUTHOR]

Previous research has identified an unfilled gap between, on the one hand, mathematical prerequisites needed for a formal treatment of least squares and, on the other hand, only teaching procedural aspects of curve fitting. As a response to this, the present study explores students' suggestions of how they think a computer or calculator does curve fitting. The data evolve through observations of mathematics classroom group work and interviews during a physics laboratory group work of year 10 secondary school students in Sweden. The results show that these students seemed well equipped to, on their own, suggest relevant and mathematically founded strategies for formal curve fitting though not least squares. Specifically, the students were inventive in their group work in the sense that several of their suggestions for how curve fitting could work are the same as those that appear in mathematics history from early 1700 until contemporary methods, covering both algebra and statistics. As such, the mathematical content in the results contrasts previous research on informal fit, which often results in the students counting the number of points over and under the fitted line but with less articulated justifications for their fit. [ABSTRACT FROM AUTHOR]

Clustering and spatial representation methods are often used in combination, to analyse preference ratings when a large number of individuals and/or object is involved. When analysed under an unfolding model, row‐conditional linear transformations are usually most appropriate when the goal is to determine clusters of individuals with similar preferences. However, a significant problem with transformations that include both slope and intercept is the occurrence of degenerate solutions. In this paper, we propose a least squares unfolding method that performs clustering of individuals while simultaneously estimating the location of cluster centres and object locations in low‐dimensional space. The method is based on minimising the mean squared centred residuals of the preference ratings with respect to the distances between cluster centres and object locations. At the same time, the distances are row‐conditionally transformed with optimally estimated slope parameters. It is computationally efficient for large datasets, and does not suffer from the appearance of degenerate solutions. The performance of the method is analysed in an extensive Monte Carlo experiment. It is illustrated for a real data set and the results are compared with those obtained using a two‐step clustering and unfolding procedure. [ABSTRACT FROM AUTHOR]