Integration Rules Research Articles

A Practical Data Extraction, Cleaning, and Integration Method for Structural Condition Assessment of Highway Bridges

The success of regional bridge condition assessment, a crucial component of systematic maintenance strategies, relies heavily on comprehensive, well-structured regional bridge databases. This study proposes the data extraction, cleaning, and integration method for the construction of such databases. First, this research proposes an extraction method tailored for unstructured data often present in inspection reports. Additionally, this paper meticulously outlines a cleaning procedure designed to rectify two distinct categories of typical errors that are present within the inspection data. Subsequently, this study takes a holistic approach by establishing integration rules that harmonize data from various sources, including inspection records, monitoring data, traffic statistics, as well as design and construction blueprints. The architectural framework of the regional bridge information database is then meticulously laid out. To validate and demonstrate the effectiveness of the method, this study applies them to a set of representative highway bridges situated within Shandong Province. The results show that this approach can be used to successfully establish a functional regional bridge database. The database plays a pivotal role in harnessing the latent potential of an extensive range of multi-source information and propels the field of bridge condition assessment forward by providing a solid basis for informed decision making and strategic planning in the realm of infrastructure maintenance.

Unsupervised learning of stationary and switching dynamical system models from Poisson observations

Objective. Investigating neural population dynamics underlying behavior requires learning accurate models of the recorded spiking activity, which can be modeled with a Poisson observation distribution. Switching dynamical system models can offer both explanatory power and interpretability by piecing together successive regimes of simpler dynamics to capture more complex ones. However, in many cases, reliable regime labels are not available, thus demanding accurate unsupervised learning methods for Poisson observations. Existing learning methods, however, rely on inference of latent states in neural activity using the Laplace approximation, which may not capture the broader properties of densities and may lead to inaccurate learning. Thus, there is a need for new inference methods that can enable accurate model learning. Approach. To achieve accurate model learning, we derive a novel inference method based on deterministic sampling for Poisson observations called the Poisson Cubature Filter (PCF) and embed it in an unsupervised learning framework. This method takes a minimum mean squared error approach to estimation. Terms that are difficult to find analytically for Poisson observations are approximated in a novel way with deterministic sampling based on numerical integration and cubature rules. Main results. PCF enabled accurate unsupervised learning in both stationary and switching dynamical systems and largely outperformed prior Laplace approximation-based learning methods in both simulations and motor cortical spiking data recorded during a reaching task. These improvements were larger for smaller data sizes, showing that PCF-based learning was more data efficient and enabled more reliable regime identification. In experimental data and unsupervised with respect to behavior, PCF-based learning uncovered interpretable behavior-relevant regimes unlike prior learning methods. Significance. The developed unsupervised learning methods for switching dynamical systems can accurately uncover latent regimes and states in population spiking activity, with important applications in both basic neuroscience and neurotechnology.

Novel Definitions of α-Fractional Integral and Derivative of the Functions

An α-fractional integral and derivative of real function have been introduced in new definitions and then, they compared with the existing definitions. According to the properties of these definitions, the formulas demonstrate that they are most significant and suitable in fractional integrals and derivatives. The definitions of α-fractional derivative and integral coincide with the existing definitions for the polynomials for 0 ≤ α < 1. Furthermore, if α = 1, the proposed definitions and the usual definition of integer derivative and integral are identical. Some of the properties of the new definitions are discussed and proved, as well, we have introduced some applications in the α- fractional derivatives and integrals. Moreover, α-power series and α–rule of integration by parts have been proposed and implemented in this study.

Interpositional auxiliary components in the structure of a multi-topic scientific discourse

The article aims to study the presence/absence of references (interpositional auxiliary components) in the structure of a multi-topic scientific discourse. Today, the problem of compliance with the rules of academic integrity, which is caused by free access to a large amount of information and the often dishonesty of researchers, has become particularly noticeable. That is why it became necessary to control the presence of references to quotations and the author's ideas and the need to prepare them correctly. The purpose of the article is to analyze the presence of quotations as the main type of a reported speech in a scientific style, and to define the use of dominant methods of designing references to the sources. The goal determined the following task: to group randomly selected articles on various topics for analysis; to analyze the presence/absence of references in the texts; to characterize the methods of formatting the list of references; find out the productivity of different types of references; formulate conclusions and outline the research perspective. The article uses descriptive, comparative methods of contextual analysis and reception of quantitative calculations. The research material became 24 scientific articles, randomly selected from collections of scientific works published on the boundary of 2020 s, and conditionally divided into six blocks: "human sciences"; "sciences about the state"; "education sciences"; "sciences of nature"; "social sciences"; "technical sciences". It was found that the most productive model, according to which references to the paper of a certain author is formed in multidisciplinary scientific articles, is the construction «number of the work in the list of used literature» (261 fixations). It must be said that the construction can be seen in all blocks of research, and is more often traced in works on the technical sciences, state and social, episodically - in articles on the humanities.

Numerical analysis of temporal second‐order accurate scheme for the abstract Volterra integrodifferential equation

In this paper, a second‐order accurate scheme is considered for the temporal discretization of the abstract Volterra integrodifferential equation with a weakly singular kernel. The time discrete scheme is constructed by the Crank–Nicolson method for approximating the time derivative and product integration (PI) rule for approximating the integral term. The proposed scheme employs a graded mesh for time to compensate for the singular behavior of the exact solution at . Under the suitable assumptions, the stability and convergence are established by the energy argument, and the error is of order , where is the parameter for the time grids. Numerical experiments validate the theoretical estimate.

Gaussian rule for integrals involving Bessel functions

Gaussian rule for integrals involving Bessel functions

UNIVERSAL EDUCATIONAL EXISTENTIALS OF PAULO FREIRE: METHODOLOGICAL PRINCIPLES OF THE FORMATION OF ACADEMIC INTEGRITY

The issue of the formation of academic integrity is extremely relevant in the context of the integration of the national education system into the European educational space. However, the problem of the methodological principles of this process has not received sufficient attention in the domestic scientific literature. One of the important pedagogical theories that should be chosen to justify the theoretical foundation of cultivating the values of academic integrity is the critical pedagogy of the Brazilian educator Paulo Freire. That is why the purpose of this article is to analyze Paulo Freire’s pedagogical theory as a methodological basis for the formation of academic integrity of participants in the educational process. The analysis of Paulo Freire’s pedagogical ideas in the context of critical pedagogy shows that the highest and noblest goal of education is to liberate a person from injustice. Critical education should form a critical consciousness that constantly questions and doubts, that develops itself and encourages others to improve. Bearers of such consciousness are capable of transforming social reality, able to resist manipulative practices, and an important goal of the educational process is the formation of a personality capable of acquiring and producing new knowledge. Such a person can be educated only on the basis of respect, trust, humanity, subjectivity, dialogue and co-creation, using problem-based and person-oriented learning technologies. Young people with developed critical thinking, creative, inquisitive, who build their activities on the production of new things for the improving of people’s lives are based on the principles of trust and justice. They with a high probability will adhere to the principles, norms and rules of integrity, primarily academic, since education is a leading type of activity for pupils and student youth.

CECM: A continuous empirical cubature method with application to the dimensional hyperreduction of parameterized finite element models

We propose a method for finding optimal quadrature/cubature rules with positive weights for parameterized functions in 1D, 2D or 3D spatial domains. The method takes as starting point the values of the functions at the Gauss points of a finite element (FE) mesh of the spatial domain for a representative sample of input parameters, and then construct an elementwise continuous orthogonal basis for such functions using the truncated Singular Value Decomposition (SVD) along with element polynomial fitting. To avoid possible memory bottlenecks in computing the SVD, we propose a Sequential Randomized SVD (SRSVD) in which the matrix is provided in a column-partitioned format, and which uses randomization to accelerate the processing of each individual block. After computing the basis functions, the method determines an exact integration rule for such functions, featuring as many points as functions, and in which the points are selected among the Gauss points of the FE mesh. Finally, the desired optimal rule is obtained by an sparsification process in which the algorithm zeroes one weight at a time while readjusting the positions and weights of the remaining points so that the constraints of the problem are satisfied. We apply this methodology to multivariate polynomials in cartesian domains to demonstrate that the method is indeed able to produce optimal rules – i.e., Gauss product rules –, and to a 2-parameters, 3D sinusoidal–exponential function to illustrate the use of the SRSVD in scenarios in which the standard SVD cannot handle the operation because of memory limitations. Lastly, the fact that the method does not require the analytical expression of the integrand functions – just their values at the FE Gauss points – makes it suitable for dealing with the so-called hyperreduction of parameterized finite element models. We exemplify this by showing its performance in the derivation of low-dimensional surrogate models in the context of the multiscale FE method. The Matlab source codes of both the CECM and the SRSVD, along with the scripts for launching the numerical tests, are openly accessible in the public repository https://github.com/Rbravo555/CECM-continuous-empirical-cubature-method.

Impedance Variation in a Coaxial Coil Encircling a Metal Tube Adapter.

The impedance change in an induction coil surrounding a metal tube adapter is investigated using the truncated region eigenfunction expansion (TREE) method. The conventional TREE method is inapplicable to this problem as a consequence of the numerical overflow of the eigenfunctions of the air-metal multi-subdomain regions. The difficulty is surmounted by a normalization procedure for the numerical eigenfunctions obtained from the 1D finite element method (FEM). An efficient algorithm is devised by the Clenshaw-Curtis quadrature rule for integrals involving the numerical eigenfunctions. The numerical results of the TREE and FEM simulation coincide very well in all cases, and the efficiency of the proposed method is also confirmed.

Incorporating fractional operators into interaction dynamics of a chaotic biological model

In the exploration of mathematical models in biology, the traditional use of integer-order calculus may fall short in adequately capturing elements such as randomness and memory. As a viable alternative, fractional calculus has been embraced by mathematicians, extending derivatives and integrals to non-integer orders to provide more appropriate tools for managing complexity. In this research, we investigate the effectiveness of two well-known fractional operators, namely the Caputo–Fabrizio and Atangana–Baleanu derivatives, in studying the dynamics of a nonlinear food chain model consisting of three populations. This specific biological system exhibits highly chaotic behavior driven by its sensitivity to various parameters. To approximate solutions, we employ two implicit numerical approaches based on Lagrange interpolation and product integration rules. Furthermore, we analyze the equilibrium points of the system and evaluate their stability characteristics, offering insights into the long-term behavior of the model. To verify the presence of chaotic patterns across different parameter values, we employ two chaos detection techniques—the smaller alignment index and the 0-1 test. By incorporating fractional calculus operators into the dynamic equations, we are able to obtain a more precise representation of such biological systems. Future research endeavors should focus on leveraging additional fractional operators to further enhance the accuracy of modeling nonlinear systems in the field of biology.

MPM vs. CEL: Numerical modelling of penetration processes

MPM vs. CEL: Numerical modelling of penetration processes

Kernel method for estimating overlapping coefficient using numerical integration methods

In this paper, we proposed three nonparametric kernel estimators for the overlapping Weitzman measure Δ. Due to the difficulty of finding a general expression for Δ when the nonparametric kernel method is adopted, we suggest using the numerical integration method as the first stage of our estimation process. In particular, three numerical integration rules are considered, which are known as, trapezoidal and Simpson rules. The statistical properties of the resulting estimators are studied and investigated by using the simulation technique and their performances are also compared with some existing nonparametric kernel estimators developed by Eidous and Al-Talafhah (2020). The numerical results demonstrated the superiority and usefulness of the proposed technique over that suggested by Eidous and Al-Talafhah in estimating the overlapping measure Δ.

Some basic theorems and formulas for building fractal nonlinear wave models

As a tool to deal with the phenomenon in layered or porous media, many theoretical problems need to be improved urgently. In this paper, the definitions of two kinds of fractal derivatives based on scale transformation are developed from the perspective of mathematics, and the four operation rules, chain rules, Rolle theorem, mean value theorem, Taylor formula, variable upper limit integral derivation rule, definite integral basic principle, partial integral formula and double partial integral formula of the fractal version are given. Better still, we derive the fractal Euler-Lagrangian equation by using the variational method, and demonstrate the steps and effectiveness of deriving the fractal nonlinear wave equation based on the fractal Euler-Lagrangian equation through the example of the functionally graded beam.

Analysis of the Australian Stock Market: Organization, Players, Challenges, and Opportunities

The Australian stock market is discussed in this report because of its importance as a financial hub. In Australia, the primary market operator is the Australian Securities Exchange Ltd (ASX), which is increasingly utilizing technology to develop novel approaches to maximizing shareholder value. Several aspects of the Australian stock market and its participants are discussed using the existing literature as a basis for this paper. The report provides context for ASX's technology deployment. Secondly, it draws attention to the ASX's significant participants. The article's third section discusses the opportunities and threats that participants in the Australian stock market face. Problems have arisen in the regulation and operations of the Australian stock market due to recent changes, such as the transfer of regulatory authority to ASIC, the introduction of new rules regarding the disclosure of information regarding securities lending and short sales, and the introduction of novel market integrity rules. Investing in Australia's financial markets makes sense for several reasons, including the country's rapidly growing domestic market, sophisticated corporate infrastructure, pension-friendly government, and highly educated, multilingual workforce.

Comparison of risk factors for hemorrhagic stroke and ischemic stroke, a prospective long-term follow-up cohort study

Objective: To analyze and compare the risk factors for hemorrhagic stroke and ischemic stroke and understand the exposure levels in population. Methods: A cohort study of risk factors of stroke was conducted in a rural community in Fengxian District of Shanghai in 2003, and the common risk factors of stroke were investigated at baseline survey, the cerebrovascular hemodynamics indexes were detected, the cerebrovascular function score was calculated according to the unified integral rule, and the incidence of stroke was observed in follow up. The risk factors for hemorrhagic stroke and ischemic stroke were analyzed by cohort study. The risk factors for two subtypes of stroke were compared. Result: A total of 10 565 participants were included in the study, with a mean follow-up period of (11.15±2.26) years, and 103 hemorrhagic stroke cases and 268 ischemic stroke cases were observed during follow-up period. The independent risk factors of hemorrhagic stroke included decreased cerebrovascular function score [hazard ratio (HR)=1.56, 95%CI: 1.23-1.98], history of alcohol consumption (HR=2.46, 95%CI: 1.39-4.34), hypertension (HR=1.75, 95%CI: 1.00-3.07) and older age (HR=1.07, 95%CI: 1.04-1.10). The independent risk factors of ischemic stroke included decreased cerebrovascular function score (HR=1.43, 95%CI: 1.25-1.65), smoking history (HR=1.52, 95%CI: 1.13-2.05), hypertension (HR=1.51, 95%CI: 1.10-2.07), family history of stroke (HR=1.89, 95%CI: 1.13-3.15), left ventricular hypertrophy (HR=1.74, 95%CI: 1.07-2.81) and older age (HR=1.07, 95%CI: 1.05-1.08). Conclusions: Decreased cerebrovascular function score, hypertension, and older age were common independent risk factors of both types of stroke, alcohol consumption history was an independent risk factor of hemorrhagic stroke, and smoking history, and family history of stroke and left ventricular hypertrophy were independent risk factors of ischemic stroke.

Improved enrichments and numerical integrations in SGFEM for interface problems

Generalized/extended finite element methods (GFEM/XFEM) for an interface problem are generally enriched by a distance function to the interface to handle discontinuities across the interface. Evaluations of the distance function and its gradients are needed for assembling stiffness matrices, which requires certain computational geometry algorithms. The computational complexity grows if the number of integration points is increased. Besides, the mathematical analysis on the effect of numerical integration has not been established in the field of GFEM/XFEM yet. This study designs an improved enriched function for a stable GFEM (SGFEM, a stable version of GFEM) based on the distance function, which only requires evaluating the distance function at nodes of elements that interact the interface (the gradients of distance function are not needed). The optimal convergence order (in the energy norm) of the SGFEM with such an improved enriched function is proven. In turn, we propose a perturbed variational formula, which can be integrated exactly by simple Gaussian rules designed in this paper. We prove that the SGFEM based on the improved enriched function and the perturbed variational formula (exactly integrated by the numerical integration) achieves the optimal convergence order for the interface problem. Namely, we develop a numerical integration rule for the SGFEM such that the optimal convergence order of SGFEM is maintained for the interface problem. The theoretical achievements are verified by numerical experiments.

A Simultaneous Numerical Integration Routine for the Fast Calculation of Similar Integrations

In this paper, a fast and simultaneous integration routine that is tailored for obtaining the results of multiple numerical integrations is introduced. The routine uses the same nodes for multiple integrations defined for similar integrands. In the paper it is demonstrated by several examples that if the integrands of interest are similar on the integration path, then using the same nodes decreases the computational costs dramatically. The method is introduced by updating the popular Gauss-Kronrod quadrature rule, but the same steps given in the paper can be applied to any other numerical integration rule.

Comparison of numerical-integration-based methods for blood flow estimation in diffuse correlation spectroscopy

Background and ObjectiveDiffuse correlation spectroscopy (DCS) is an optical blood flow monitoring technology that has been utilized in various biomedical applications. In signal processing of DCS, nonlinear fitting of the experimental data and the theoretical model can be a hindrance in real-time blood flow monitoring. As one of the approaches to resolve the issue, INISg1, the inverse of numerical integration of squared g1 (a normalized electric field autocorrelation function), that could surpass the state-of-the-art technique at the time in terms of signal processing speed, has been introduced. While it is possible to implement INISg1 using various numerical integration methods, no relevant studies have been performed. Meanwhile, INISg1 was only tested within limited experimental conditions, which cannot guarantee the robustness of INISg1 in various experimental conditions. Thus, this study aims to introduce variants of INISg1 and perform a thorough comparison of the original INISg1 and its variants. MethodsIn this study, based on the right Riemann sum (RR) and trapezoid rule (TR) of numerical integration, INISg1_RR and INISg1_TR are suggested. They are thoroughly compared with the original INISg1 using model-based simulations that offer us control of most of the experimental conditions, including integration time, β, and photon count rate. ResultsExcept for some extreme cases, INISg1 performed more robustly than INISg1_RR and INISg1_TR. However, in extreme conditions, variants of INISg1 performed better than INISg1. With the same condition, the signal processing speed of INISg1 was 1.63 and 1.98 times faster than INISg1_RR and INISg1_TR, respectively. ConclusionThis study shows that INISg1 is robust in most cases and the study can be a guide for researchers using INISg1 and its variants in different types of DCS applications.

Modeling fracture in brittle materials by higher-order phase field method using C1 non-Sibsonian interpolants

PurposeThis study implements the fourth-order phase field method (PFM) for modeling fracture in brittle materials. The weak form of the fourth-order PFM requires C1 basis functions for the crack evolution scalar field in a finite element framework. To address this, non-Sibsonian type shape functions that are nonpolynomial types based on distance measures, are used in the context of natural neighbor shape functions. The capability and efficiency of this method are studied for modeling cracks.Design/methodology/approachThe weak form of the fourth-order PFM is derived from two governing equations for finite element modeling. C0 non-Sibsonian shape functions are derived using distance measures on a generalized quad element. Then these shape functions are degree elevated with Bernstein-Bezier (BB) patch to get higher-order continuity (C1) in the shape function. The quad element is divided into several background triangular elements to apply the Gauss-quadrature rule for numerical integration. Both fourth-order and second-order PFMs are implemented in a finite element framework. The efficiency of the interpolation function is studied in terms of convergence and accuracy for capturing crack topology in the fourth-order PFM.FindingsIt is observed that fourth-order PFM has higher accuracy and convergence than second-order PFM using non-Sibsonian type interpolants. The former predicts higher failure loads and failure displacements compared to the second-order model due to the addition of higher-order terms in the energy equation. The fracture pattern is realistic when only the tensile part of the strain energy is taken for fracture evolution. The fracture pattern is also observed in the compressive region when both tensile and compressive energy for crack evolution are taken into account, which is unrealistic. Length scale has a certain specific effect on the failure load of the specimen.Originality/valueFourth-order PFM is implemented using C1 non-Sibsonian type of shape functions. The derivation and implementation are carried out for both the second-order and fourth-order PFM. The length scale effect on both models is shown. The better accuracy and convergence rate of the fourth-order PFM over second-order PFM are studied using the current approach. The critical difference between the isotropic phase field and the hybrid phase field approach is also presented to showcase the importance of strain energy decomposition in PFM.

Magnetic Integration for Multiple Resonant Converters

A universal integration method for the magnetic components (MCs) of multiple resonant converters is proposed in this article. Two rules for integration of multiple independent MCs are summarized, one of which is to keep functional independent of MCs after integration, while the other is to achieve lower loss and volume through integration. Following the proposed rules and by dividing an MC into winding-part and nonwinding-part, integration is achieved by sharing the nonwinding-part of the MCs. An input-series output-parallel (ISOP) resonant converter is taken as an example to show how integration is accomplished step by step. It is shown that, both volume and loss of the magnetic cores are reduced after integration of all the high frequency transformers and inductors. Detailed theoretical analysis, finite element analysis simulations and comparisons have been presented. A 600 V–800 V input, 28 V/2000 W-output ISOP resonant converter was built. Experimental results have been provided to verify the effectiveness and feasibility of the proposed integration methods.