Vector Of Variables Research Articles

Maximal operators along flat curves with one variable vector field

Abstract We study a maximal average along a family of curves $\{(t,m(x_1)\gamma(t)):t\in [-r,r]\}$ , where $\gamma|_{[0,\infty)}$ is a convex function and m is a measurable function. Under the assumption of the doubling property of $\gamma'$ and $1\leqslant m(x_1)\leqslant 2$ , we prove the $L^p(\mathbb{R}^2)$ boundedness of the maximal average. As a corollary, we obtain the pointwise convergence of the average in r > 0 without any size assumption for a measurable m.

Hotelling T2 control chart based on minimum vector variance for monitoring high‐dimensional correlated multivariate process

AbstractMultivariate control charts are practical tools that simultaneously monitor several correlated quality characteristics in a process. Monitoring high‐dimensional data structures is challenging because, in most cases, the process sample size for monitoring parameters is greater than the number of process characteristics. Many researchers have used the multivariate Hotelling's T2 chart to monitor high‐dimensional data using the maximum‐likelihood methods (MLM) to estimate the covariance matrices. However, the multivariate Hotelling's T2chart based on MLM suffers from low statistical performance. In this paper, we proposed a multivariate Hotelling's T2 chart based on the minimum vector variance (MVV) and some regularized methods for monitoring high‐dimensional data structures. The performance of the proposed chart is evaluated in terms of the average run length (ARL). The results reveal the superiority of the proposed MVV Hotelling's T2 chart over the existing Hotelling's T2 charts for high‐dimensional correlated processes.

On the accuracy of calculating invariants in centered rarefaction waves and in their influence area

We perform a comparative analysis of the accuracy of second-order TVD (Total Variation Diminishing), third-order RBM (Rusanov-Burstein-Mirin), and fifth-order in space and third-order in time A-WENO (Alternative Weighted Essentially Non-Oscillatory) difference schemes for solving a special Cauchy problem for shallow water equations with discontinuous initial data. The exact solution of this problem contains a centered rarefaction wave and does not contain a shock wave. It is shown that in the centered rarefaction wave and its influence area, the solutions of these three schemes with different orders converge to different invariants of the exact solution. This leads to a decrease in the accuracy of these schemes when calculating the vector of base variables of the considered Cauchy problem. The P-form of the first differential approximation of the difference schemes is used for the theoretical justification of these numerical results.

Rapid Classification of Milk Using a Cost-Effective Near Infrared Spectroscopy Device and Variable Cluster-Support Vector Machine (VC-SVM) Hybrid Models.

Removing fat from whole milk and adding water to milk to increase its volume are among the most common food fraud practices that alter the characteristics of milk. Usually, deviations from the expected fat content can indicate adulteration. Infrared spectroscopy is a commonly used technique for distinguishing pure milk from adulterated milk, even when it comes from different animal species. More recently, portable spectrometers have enabled in situ analysis with analytical performance comparable to that of benchtop instruments. Partial Least Square (PLS) analysis is the most popular tool for developing calibration models, although the increasing availability of portable near infrared spectroscopy (NIRS) has led to the use of alternative supervised techniques, including support vector machine (SVM). The aim of this study was to develop and implement a method based on the combination of a compact and low-cost Fourier Transform near infrared (FT-NIR) spectrometer and variable cluster-support vector machine (VC-SVM) hybrid model for the rapid classification of milk in accordance with EU Regulation EC No. 1308/2013 without any pre-treatment. The results obtained from the external validation of the VC-SVM hybrid model showed a perfect classification capacity (100% sensitivity, 100% specificity, MCC = 1) for the radial basis function (RBF) kernel when used to classify whole vs. not-whole and skimmed vs. not-skimmed milk samples. A strong classification capacity (94.4% sensitivity, 100% specificity, MCC = 0.95) was also achieved in discriminating semi-skimmed vs. not-semi-skimmed milk samples. This approach provides the dairy industry with a practical, simple and efficient solution to quickly identify skimmed, semi-skimmed and whole milk and detect potential fraud.

Efficient Matching in Large DAE Models

This article presents a matching algorithm for bipartite graphs containing repetitive structures and represented by intension as Set-Based Graphs . Under certain conditions on the structure of the graphs, the computational cost of this novel algorithm is not affected by the cardinality of the sets of vertices and edges. The main application of the algorithm is that of matching large Equation-Based Models where provided that most equations are defined using for loop statements that iterate over vectors of unknown variables, the computational cost becomes independent of the growth of the vectors involved. Besides introducing the algorithm, the article describes its implementation in a Modelica compiler and studies its performance over different test models.

A novel variable selection algorithm based on neural network for near-infrared spectral modeling

BackgroundPartial least squares (PLS) is a widely used technique for modeling spectral data. Researchers have developed numerous PLS-based variable selection algorithms to enhance model predictive ability and interpretability. In recent years, as neural network technology has advanced, these algorithms have been increasingly applied to spectral data modeling. However, current research on neural network modeling tends to prioritize network structure over variable selection. ResultsOur study introduces a neural network-based variable selection algorithm called VSNN (Variable Selection based on Neural Network). By iteratively eliminating unimportant variables using an exponentially decreasing function (EDF), the algorithm achieves the selection of variables in spectral data. VSNN can easily integrate different types of neural networks. In this study, we analyzed the impact of neural network types, activation functions, and variable importance vectors on algorithm performance. We tested the algorithm on four datasets: corn moisture, corn oil, tablets, and meat. The results indicate that VSNN significantly enhances the predictive ability of the model compared to partial least squares (PLS), neural networks (NN), and Joint Mutual Information Maximisation (JMIM). Specifically, non-linear activation functions markedly improve performance on non-linear meat datasets. Compared to PLS, the Root Mean Square Error of Prediction (RMSEP) values for the four datasets—corn moisture, corn oil, tablets, and meat—decreased from 0.0409, 0.0728, 3.97, and 3.2 to 0.002, 0.0236, 3.12, and 0.36, respectively, after applying the VSNN variable selection algorithm. SignificanceVSNN can serve as a versatile framework to enhance variable selection, modeling, and predictive performance by adapting neural network types and variable importance evaluation indicators. As machine learning technology advances, the strength of VSNN is poised to increase. This study highlights the potential of VSNN as an effective algorithmic framework for variable selection in spectroscopy applications.

Maximization of strength–ductility balance of dual-phase steels using generative adversarial networks and Bayesian optimization

Dual-phase (DP) steels with a soft ferrite matrix and hard martensite islands exhibit an excellent combination of strength and ductility. However, further improvement of the strength–ductility balance is desirable for automotive applications, and the optimization of the DP microstructure is crucial for enhancing mechanical properties. This study aimed to maximize the strength–ductility balance of DP steel using an integrated computational framework comprised by generative adversarial networks (GAN), finite element method (FEM), and Bayesian optimization. GAN was trained on the microstructures of real DP steels to generate synthetic microstructure images randomly mapped from latent variable vectors, and the tensile properties of the generated microstructures were evaluated using FEM. Bayesian optimization was then employed to identify latent variables yielding microstructures with the highest tensile strength (TS), uniform elongation (uEL), or strength–ductility balance (TS × uEL). The optimized microstructures of DP steels were then quantitatively analyzed to elucidate the relationship between the microstructural morphology and tensile properties. The optimal synthetic DP microstructure exhibited a TS × uEL value higher by 4027 MPa% than the highest value shown by real DP steels. Thus, the proposed integrated optimization framework enables efficient computational design of various material microstructures for maximizing desired mechanical properties.

Advanced Defect Detection in Wrap Film Products: A Hybrid Approach with Convolutional Neural Networks and One-Class Support Vector Machines with Variational Autoencoder-Derived Covariance Vectors

This study proposes a novel approach that utilizes Convolutional Neural Networks (CNNs) and Support Vector Machines (SVMs) to tackle a critical challenge: detecting defects in wrapped film products. With their delicate and reflective film wound around a core material, these products present formidable hurdles for conventional visual inspection systems. The complex task of identifying defects, such as unwound or protruding areas, remains a daunting endeavor. Despite the power of commercial image recognition systems, they struggle to capture anomalies within wrap film products. Our research methodology achieved a 90% defect detection accuracy, establishing its practical significance compared with existing methods. We introduce a pioneering methodology centered on covariance vectors extracted from latent variables, a product of a Variational Autoencoder (VAE). These covariance vectors serve as feature vectors for training a specialized One-Class SVM (OCSVM), a key component of our approach. Unlike conventional practices, our OCSVM does not require images containing defects for training; it uses defect-free images, thus circumventing the challenge of acquiring sufficient defect samples. We compare our methodology against feature vectors derived from the fully connected layers of established CNN models, AlexNet and VGG19, offering a comprehensive benchmarking perspective. Our research represents a significant advancement in defect detection technology. By harnessing the latent variable covariance vectors from a VAE encoder, our approach provides a unique solution to the challenges faced by commercial image recognition systems. These advancements in our study have the potential to revolutionize quality control mechanisms within manufacturing industries, offering a brighter future for product integrity and customer satisfaction.

Constraining hybrid potential scalar field cosmological model in Lyra’s geometry with recent observational data

In this study, we investigate a scalar field cosmological model with Lyra’s geometry to explain the present cosmic expansion in a homogeneous and isotropic flat FRW universe. In Einstein’s field equations, we presupposed a variable displacement vector as an element of Lyra’s geometry. In the context of the conventional theory of gravity, we suggest a suitable parametrization of the scalar field’s dark energy density in the hybrid function of redshift [Formula: see text], confirming the essential transition behavior of the universe from a decelerating era to the present accelerated scenario. We present constraints on model parameters using the most recent observational datasets from OHD, BAO/CMB and Pantheon, taking Markov Chain Monte Carlo (MCMC) analysis into account. For the proposed model, the best estimated values of parameters for the combined dataset (OHD, BAO/CMB and Pantheon) are [Formula: see text][Formula: see text]km/s/Mpc, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. The model exhibits a flipping nature, and the redshift transition occurs at [Formula: see text]. The current value of the decelerated parameter for the proposed model is calculated as [Formula: see text] for the combined dataset. Some dynamical properties of the model like energy density ([Formula: see text]), scalar field pressure ([Formula: see text]), EoS parameter of scalar field ([Formula: see text]), and effective EoS parameter ([Formula: see text]) are analyzed and presented. Further, we have also examined the statefinder diagnosis and jerk parameters of the derived model. The total density parameter for the derived model is found to be unity which is in nice agreement with recent standard findings.

Enhancing Precision in Population Variance Vector Estimation: A Two-Phase Sampling Approach with Multi-Auxiliary Information

To enhance precision in estimating unknown population parameters, an auxiliary variable is often used. However, in scenarios where required information on an auxiliary variable is partially or fully unavailable, two-phase sampling is commonly employed. The challenge of estimating the variance vector using multi-auxiliary variables is a less explored area in current literature. This paper addresses the estimation of vector of unknown population variances for multiple study variables by using an estimated vector of variances derived from multi-auxiliary information. This approach is particularly relevant when population variances for the multi-auxiliary variables are not known prior to the survey. The paper introduces a generalized variance and a vector of biases for the proposed multivariate estimator. Special cases of the proposed multivariate variance estimator are provided, accompanied by expressions for mean square errors. Theoretical mathematical conditions are discussed to guide the preference for the proposed estimator. Through the analysis of real-world application-based data, the applicability and efficiency of the proposed multivariate variance estimator are demonstrated, outperforming modified versions of multivariate variance estimators. Additionally, a simulation study validates the superior performance of the proposed estimator compared to its modified estimators.

A PROJECTION-BASED ERROR ANALYSIS OF HDG METHODS FOR A NONLINEAR SYSTEM: COUPLED IN BOTH DIRECTIONS

A technique for the error analysis of hybrid discontinuous Galerkin methods (HDG) is applied to a coupled problem. The technique relies on the use of a projection whose design is inspired by the numerical traces of the methods. When this technique appeared in the literature (Cockburn et al., 2010), the authors performed an analysis for an elliptical problem. In this work, we will analyze two coupled elliptical subproblems. The main idea is to apply this projection technique, defined based on the shape of the numerical traces, in the numerical analysis of the HDG method for the coupled problem to verify whether this numerical analysis technique still maintains its main characteristics, such as simplicity and consistency, even with this coupling. The analysis of the coupled problem in two directions was carried out following the strategy of first analyzing the partially coupled problem (De Oliveira, 2024), and then the coupled problem in both directions. The differences between both problems were the analytical development of the coupling and the computation of the approximate solution, which in the problem treated here requires a fixed point algorithm. We expect that the orders of convergence for the approximate solutions correspond to theoretical expectations with the approximation spaces used, which are made up of natural polynomials, that is, order k for vector variables and k+1 for scalar variables. All theoretical and and experimental objectives were achieved, i.e., the convergence in the HDG simulations corresponded to what was theoretically expected.

Цифровая идентичность и гуманистическая модель цифровой образовательной среды

The article is devoted to the problems of subjective and personal self-determination of students in the situation of contact with the infocommunication environment, in particular, to the analysis of “digital identity”, symbolizing the emergence of a new modality of individual identification in virtual space. The methodological basis of the study was philosophical, axiological and systemic approaches. In addition, the possibilities of the method of existential analytics are used, which make it possible to explore not only ontological, but also the value-semantic contexts of the formation of personal identity, allowing us to consider the essence of “I” in the unique unity of its personal qualities, as well as content analysis as the optimal diagnostic tool network identity. The article conceptualizes the concept of “digital identity”. It is shown that the representation of the life of young people in a virtual environment, as one of the forms of successful socialization, as well as the possibility of constructing a virtual personality and its self-presentation in the external environment with the help of ideal self-images, determine the projective nature of digital identity, which is, ultimately, a set of projections of real identity, translated using digital technologies into a sign-symbolic context. Based on examples of the reverse influence of online identity on the real one, a conclusion is made about the emergence of a tendency to blur the lines between them, marking the beginning of the process of merging digital and real identities. The result of the study is a humanistic model of the digital educational environment (DEL), which sets the main variable vectors for its development and implementation, taking into account the creative potential of a particular teacher, the conditions of the educational organization, the socio-pedagogical and socio-psychological specifics of students.

Robust Kalman filters based on the sub-Gaussian [formula omitted]-stable distribution

Motivated by filtering tasks under a linear system with non-Gaussian heavy-tailed noise, various robust Kalman filters (RKFs) based on different heavy-tailed distributions have been proposed. Although the sub-Gaussian α-stable (SGαS) distribution captures heavy tails well and is applicable in various scenarios, its potential has not yet been explored for RKFs. The main hindrance is that there is no closed-form expression of its mixing density. This paper proposes a novel RKF framework, RKF-SGαS, where the process noise is assumed to be Gaussian and the heavy-tailed measurement noise is modelled by the SGαS distribution. The corresponding joint posterior distribution of the state vector and auxiliary random variables is approximated by the Variational Bayesian approach. Also, four different minimum mean square error (MMSE) estimators of the scale function are presented. The first two methods are based on the Importance Sampling (IS) and Gauss–Laguerre quadrature (GLQ), respectively. In contrast, the last two estimators combine a proposed Gamma series (GS) based method with the IS and GLQ estimators and hence are called GSIS and GSGL. Besides, the RKF-SGαS is compared with the state-of-the-art RKFs under three kinds of heavy-tailed measurement noises, and the simulation results demonstrate its estimation accuracy and efficiency.

Fixed Point of α-Modular Nonexpanive Mappings in Modular Vector Spaces 𝓁p(·)

Let C denote a convex subset within the vector space 𝓁p(·), and let T represent a mapping from C onto itself. Assume α=(α1,⋯,αn) is a multi-index in [0,1]n such that ∑i=1nαi=1, where α1>0 and αn>0. We define Tα:C→C as Tα=∑i=1nαiTi, known as the mean average of the mapping T. While every fixed point of T remains fixed for Tα, the reverse is not always true. This paper examines necessary and sufficient conditions for the existence of fixed points for T, relating them to the existence of fixed points for Tα and the behavior of T-orbits of points in T’s domain. The primary approach involves a detailed analysis of recurrent sequences in R. Our focus then shifts to variable exponent modular vector spaces 𝓁p(·), where we explore the essential conditions that guarantee the existence of fixed points for these mappings. This investigation marks the first instance of such results in this framework.

Using continuous relative phase and modified vector coding analyses to quantify spinal coordination and coordinative variability for healthy and chronic low back pain patients: An exploratory comparative analysis

Differences in coordination and coordinative variability are common in people with low back pain. While differences may relate to the different analyses used to quantify these metrics, the preferred approach remains unclear. We aimed to compare coordination and coordinative variability, in people with and without low back pain performing a lifting/lowering task, using continuous relative phase and vector coding procedures, and to identify which technique better detects group differences. Upper lumbar (T12-L3), lower lumbar (L3-S1), and hip angular kinematics were measured using electromagnetic motion capture during 10 crate lifting/lowering repetitions from adults with (n = 47) and without (n = 17) low back pain. Coordination and coordinative variability for the Hip-Lower Lumbar and Lower Lumbar-Upper Lumbar joint pairs were quantified using mean absolute relative phase and deviation phase (continuous relative phase), and coupling angle and coupling angle variability (vector coding), respectively. T-tests examined group differences in coordination and variability. Cohen’s d bootstrapping analyses identified the more sensitive technique for detecting group differences. Less in-phase and more variable behavior was observed in the low back pain group, mostly independent of joint pair and analytical technique (P < 0.05, Cohen’s d range = 0.61 to 1.33). Qualitatively, the low back group limited motion at the lower lumbar spine during lifting/lowering. Continuous relative phase was more sensitive in detecting group differences in coordinative variability, while vector coding was more sensitive towards differences in coordination. These procedures convey distinct information and have their respective merits. Researchers should consider the choice of analytical techniques based on their study objectives.

Asynchronous switching and sparse discretization with time scaling for control vector parameterization optimal control

This work introduces a novel approach for solving open-loop Optimal Control Problems (OCPs) using multiple time grids, sparse discretization and a time scaling transformation. Control Vector Parameterization (CVP) method parameterizes control variables to create a finite-dimensional problem. The Variable Time Nodes Control Vector Parameterization (VTNCVP) discretization strategy allows each control component an independent time grid, offering enhanced input design flexibility and potentially yielding improved outcomes. A novel time scaling technique for OCPs with multiple time grids is presented that is easier to comprehend than existing methods and can circumvent some numerical difficulties. Additionally, Multiple Grid (MG)–Sparse Variable Time Nodes (MG-SVTN) is presented. This novel discretization strategy employs asynchronous switching with user-specified numbers of subdivisions for input controls, potentially yielding comparable objective function values to VTNCVP while reducing the dimensionality of decision variables. Two example problems with path constraints are solved using the methods.

Когнитивное моделирование процессов адаптивного обучения

An approach to modeling adaptive learning processes using signed and weighted directed graphs (digraphs) is exam-ined. The vertices of the digraphs represent the characteristics of educational activities. The orientation, signs, and weights of the digraph arcs define the mutual influence of these characteristics. The dynamics of adaptive learning are modeled within digraphs using a specific impulse process algorithm. An external disturbance is introduced into a partic-ular vertex of the digraph, and the propagation of this impulse is analyzed, enabling the prediction of values at other vertices of the digraph. The problem of optimizing the weights of digraph arcs is formulated, and an algorithm for solv-ing it is proposed to achieve stability in the impulse process. Computational experiments on a digraph revealed that the objective function for optimizing the arcs of a weighted digraph is multiextremal. The occurrence of a local minimum is determined by the initial values of the vector of design variables (weights of digraph arcs) and constraints on these var-iables. Consequently, the qualifications of the developer of the adaptive learning model who assigns these values are crucial. Cognitive models of adaptive learning can be classified as prescriptive and descriptive. Prescriptive models out-line what the adaptive learning process should be, while descriptive models depict existing adaptive learning processes and can be utilized to study their effectiveness. The developed methodology for cognitive modeling of adaptive learn-ing processes allows for the prediction of learning outcomes and can be employed in the research, design, and imple-mentation of adaptation mechanisms and intelligent control in e-learning systems, as well as in the didactic training of teachers in the field of e-learning.

Reduced-order modeling for time domain analysis of finite periodic structures with absorbing boundary conditions

A reduced-order model of finite periodic structures with absorbing boundary conditions (ABCs) and localized time-dependent excitations is proposed. 1D-periodic structures whose cells can represent any 2D or 3D arbitrary substructures are considered. The key steps for modeling an ABC in the time domain are: (i) expression of the impedance matrix with the wave finite element (WFE) method; (ii) partial rational decomposition of the impedance matrix; (iii) introduction of vectors of supplementary variables to describe the ABC in the time domain. In this paper, a model reduction approach is proposed to speed up the computation of the ABCs. The focus is on the reduction of the number of internal degrees of freedom of substructures, and the reduction of the number of degrees of freedom at the substructure interfaces. The approach allows the consideration of complex substructures with large FE models, and the computation of the time response of periodic structures at a low computational cost. Numerical experiments are carried out to highlight the relevance of the proposed approach. Specifically, the analysis of a metamaterial structure containing nonlinear resonant substructures is carried out with the proposed approach. Results show that, when compared to the linear case, band gaps in periodic structures with nonlinear substructures can be significantly improved.

Evaluation of walking activity and gait to identify physical and mental fatigue in neurodegenerative and immune disorders: preliminary insights from the IDEA-FAST feasibility study

BackgroundMany individuals with neurodegenerative (NDD) and immune-mediated inflammatory disorders (IMID) experience debilitating fatigue. Currently, assessments of fatigue rely on patient reported outcomes (PROs), which are subjective and prone to recall biases. Wearable devices, however, provide objective and reliable estimates of gait, an essential component of health, and may present objective evidence of fatigue. This study explored the relationships between gait characteristics derived from an inertial measurement unit (IMU) and patient-reported fatigue in the IDEA-FAST feasibility study.MethodsParticipants with IMIDs and NDDs (Parkinson's disease (PD), Huntington's disease (HD), rheumatoid arthritis (RA), systemic lupus erythematosus (SLE), primary Sjogren’s syndrome (PSS), and inflammatory bowel disease (IBD)) wore a lower-back IMU continuously for up to 10 days at home. Concurrently, participants completed PROs (physical fatigue (PF) and mental fatigue (MF)) up to four times a day. Macro (volume, variability, pattern, and acceleration vector magnitude) and micro (pace, rhythm, variability, asymmetry, and postural control) gait characteristics were extracted from the accelerometer data. The associations of these measures with the PROs were evaluated using a generalised linear mixed-effects model (GLMM) and binary classification with machine learning.ResultsData were recorded from 72 participants: PD = 13, HD = 9, RA = 12, SLE = 9, PSS = 14, IBD = 15. For the GLMM, the variability of the non-walking bouts length (in seconds) with PF returned the highest conditional R2, 0.165, and with MF the highest marginal R2, 0.0018. For the machine learning classifiers, the highest accuracy of the current analysis was returned by the micro gait characteristics with an intrasubject cross validation method and MF as 56.90% (precision = 43.9%, recall = 51.4%). Overall, the acceleration vector magnitude, bout length variation, postural control, and gait rhythm were the most interesting characteristics for future analysis.ConclusionsCounterintuitively, the outcomes indicate that there is a weak relationship between typical gait measures and abnormal fatigue. However, factors such as the COVID-19 pandemic may have impacted gait behaviours. Therefore, further investigations with a larger cohort are required to fully understand the relationship between gait and abnormal fatigue.

A structural after measurement approach to structural equation modeling.

In structural equation modeling (SEM), the measurement and structural parts of the model are usually estimated simultaneously. In this article, we revisit the long-standing idea that we should first estimate the measurement part, and then estimate the structural part. We call this the "structural-after-measurement" (SAM) approach to SEM. We describe a formal framework for the SAM approach under settings where the latent variables and their indicators are continuous. We review earlier SAM methods and establish how they are specific instances of the SAM framework. Decoupled estimation for the measurement and structural parts using SAM possesses three key advantages over simultaneous estimation in standard SEM. First, estimates are more robust against local model misspecifications. Second, estimation routines are less vulnerable to convergence issues in small samples. Third, estimates exhibit smaller finite sample biases under correctly specified models. We propose two variants of the SAM approach. "Local" SAM expresses the mean vector and variance-covariance matrix of the latent variables as a function of the observed summary statistics and the parameters of the measurement model. "Global" SAM holds the parameters of the measurement part fixed while estimating the parameters of the structural part. Our framework includes two-step corrected standard errors, and permits computing both local and global fit measures. Nonetheless, the SAM approach is an estimation strategy, and should not be regarded as a model-building tool. (PsycInfo Database Record (c) 2024 APA, all rights reserved).