Polynomial Function Research Articles

Implementasi Fungsi Polinomial pada Algoritma Gradient Boosting Regressor: Studi Regresi pada Dataset Obat-Obatan Kadaluarsa Sebagai Material Antikorosi

Corrosion is an electrochemical process between the metal surface and a corrosive environment that can lead to significant losses in various industries, especially in the oil and gas sector. Experimental studies are conducted to evaluate the performance of corrosion inhibitors and available resources. In this research, a machine learning (ML) approach is employed to assess the effectiveness of expired drug compounds as corrosion inhibitors. The primary challenge in machine learning is obtaining a highly accurate model to ensure that predictions are relevant to the properties of the tested materials. Therefore, the polynomial function is tested in the gradient-boosting regressor (GBR) algorithm to enhance the accuracy of the developed ML model. The results indicate that the implementation of the polynomial function in the GBR algorithm can improve the accuracy of the prediction model based on R2 and RMSE metrics.

Woven filter media used in wet filtration processes: investigation of pore size distribution, air and water permeability and finding correlations between them

Currently, methods for evaluating the performance of woven filter media used for filtration processes are mainly reduced to air permeability and filtration resistance. However, filtration processes are not limited to dry filtration only. Moreover, critical performance-related factors such as the pore size distribution and liquid permeability are studied but often omitted and ignored in the characterization process. The present study aims to investigate and analyze three characteristics, namely air and liquid permeability and pore size distribution, and to examine correlations between the studied characteristics. The results of the present study show that correlations between the studied characteristics do exist. Polynomial and exponential functions could describe the correlation between the mean flow pore diameter and permeability. At the same time, the dependency between air and water permeability is characterized by a logarithmic function. Consequently, the characterization and selection of filter cloths should be done by analyzing several different parameters simultaneously. These correlations could become the basis of a system of media indexing in the future.

Coronary stenosis quantification in cardiac computed tomography angiography: multi-factorial optimization of image quality and radiation dose.

The accuracy and variability of quantification in computed tomography angiography (CTA) are affected by the interplay of imaging parameters and patient attributes. The assessment of these combined effects has been an open engineering challenge. In this study, we developed a framework that optimizes imaging parameters for accurate and consistent coronary stenosis quantification in cardiac CTA while accounting for patient-specific variables. The framework utilizes a task-specific image quality index, the estimability index (), approximated by a surrogate estimability polynomial function (EPF) capable of finding the optimal protocol that (1)maximizes image quality with an upper bound for desired radiation dose or (2)minimizes the dose level with a lower bound of acceptable image quality. The optimization process was formulated with the decision variables being subject to a set of constraints. The methodology was verified using CTA data from a prior clinical trial (prospective multi-center imaging study for evaluation of chest pain) by assessing the concordance of its prediction with the trial results. Further, the framework was used to derive an optimum protocol for each case based on the patient attributes, gauging how much improvement would have been possible if the derived optimized protocol would have been deployed. The framework produced results consistent with imaging physics principles with approximated EPFs of 97% accuracy. The feature importance evaluation demonstrated a close match with earlier studies. The verification study found scores closely predicting the cardiologist scores to within 95% in terms of the area under the receiver operating characteristic curve and predicting potential for either an average of fourfold increase in within a targeted dose or a reduction in radiation dose by an average of 57% without reducing the image quality. The protocol optimization framework provides means to assess and optimize CTA in terms of either image quality or radiation dose objectives with its results predicting prior clinical trial findings.

Changes in Music Curriculum Education in Colleges and Universities Based on Cloud Classroom Assistive Technology

Abstract With the rapid development of science and technology, cloud classroom teaching has gradually become a trend. The cloud-based music teaching aid training system designed in this paper learns to map rhythmic and pitch features through music sequence generation technology. The onset detection algorithm of spectral flux detects the onset of the note. The Bezier curve is introduced into the melodic line feature generation algorithm to construct a polynomial function for interpolation between the first and the last endpoints, and the emotion is utilized to guide fractal music creation. Finally, the effectiveness of this auxiliary teaching system in college music teaching has been verified. The results show that the optimal Hamming distance of the system is 0.353 in the music melody generation experiment, which indicates that the system can quickly generate melody lines for students in music teaching and improve their learning efficiency. The system can significantly improve the rationality and efficiency of music skill training, which is worth promoting.

Physical-Unclonable-Function-Based Lightweight Three-Factor Authentication for Multiserver Architectures

To support more complex and robust online services, enterprise-class applications prefer to interconnect multiple servers as the pedestal to enhance the system’s interoperability. However, the multiserver architecture always struggles to reconcile the trade-off between convenience and security, leaving users exposed to a variety of network attack threats. Existing security authentication schemes based on the Chebyshev Chaotic Map for multiserver architectures cannot provide three-factor (including password, biometric feature, and smart card) security. Therefore, we propose a novel Physical-Unclonable-Function-based Lightweight Three-Factor Authentication (PUF-LTA) scheme, which can achieve three-factor security. The PUF-LTA scheme mainly includes two components: (1) PUF-assisted registration and (2) lightweight mutual authentication with one-time interaction. During the PUF-assisted registration process, to defend against side-channel attacks on smart cards, the login credentials of users are XORed with the unique identifier generated by the PUF so that the adversary cannot obtain these secret login credentials. During the lightweight mutual authentication process, we combine the Chebyshev polynomial map and symmetric encryption/decryption to negotiate the session key between users and servers, which only needs one interaction. The security performance of PUF-LTA is theoretically proved by leveraging the random oracle model. In contrast with relevant multiserver authentication schemes, PUF-LTA is more efficient and suitable for resource-constrained multiserver environments because it can ensure secure three-factor authentication and support flexible biometrics and password updates with less computation cost.

Cognitive Structure Trajectory in Developing Limit Concept Learning in Senior High School

The existing comprehension of the concept of limit is marked by a deficiency in prioritising the enhancement of students' cognitive frameworks. The aim of this study is to examine the formation of cognitive structures while acquiring the concept of limitations. This study utilises qualitative approaches, namely descriptive analysis, to examine the development of cognitive processes in the process of acquiring the concept of boundaries. This study investigates the investigation of cognitive structures to ascertain the process of drawing conclusions, with the aim of creating instructional materials that facilitate comprehension of the concept of constraints. The survey included students who were currently enrolled in the 2021/2022 academic year at three public senior high schools in Pontianak. The study aims to analyse the progression of students' cognitive structures during the acquisition of the concept of limitations. The results revealed that all 14 students showed competence in determining the limit of a continuous polynomial function, specifically in the context of a linear function and a quadratic function. Substitution is commonly used to determine the limit of a linear function and the limit of a quadratic function. Only a single student employs the attributes of the limit function and graph trajectory to solve these two categories of problems. Researchers can conduct further investigation to examine the misconceptions that students have regarding the limit of functions. These misconceptions can be detected by analysing problems that involve substitution and have solutions that are already known. In senior high school, it is advisable to use graphs and tables to teach the concept of limit function since they aid in facilitating the learning process.

PWSC: a novel clustering method based on polynomial weight-adjusted sparse clustering for sparse biomedical data and its application in cancer subtyping

BackgroundClustering analysis is widely used to interpret biomedical data and uncover new knowledge and patterns. However, conventional clustering methods are not effective when dealing with sparse biomedical data. To overcome this limitation, we propose a hierarchical clustering method called polynomial weight-adjusted sparse clustering (PWSC).ResultsThe PWSC algorithm adjusts feature weights using a polynomial function, redefines the distances between samples, and performs hierarchical clustering analysis based on these adjusted distances. Additionally, we incorporate a consensus clustering approach to determine the optimal number of classifications. This consensus approach utilizes relative change in the cumulative distribution function to identify the best number of clusters, resulting in more stable clustering results. Leveraging the PWSC algorithm, we successfully classified a cohort of gastric cancer patients, enabling categorization of patients carrying different types of altered genes. Further evaluation using Entropy showed a significant improvement (p = 2.905e−05), while using the Calinski–Harabasz index demonstrates a remarkable 100% improvement in the quality of the best classification compared to conventional algorithms. Similarly, significantly increased entropy (p = 0.0336) and comparable CHI, were observed when classifying another colorectal cancer cohort with microbial abundance. The above attempts in cancer subtyping demonstrate that PWSC is highly applicable to different types of biomedical data. To facilitate its application, we have developed a user-friendly tool that implements the PWSC algorithm, which canbe accessed at http://pwsc.aiyimed.com/.ConclusionsPWSC addresses the limitations of conventional approaches when clustering sparse biomedical data. By adjusting feature weights and employing consensus clustering, we achieve improved clustering results compared to conventional methods. The PWSC algorithm provides a valuable tool for researchers in the field, enabling more accurate and stable clustering analysis. Its application can enhance our understanding of complex biological systems and contribute to advancements in various biomedical disciplines.

An efficient and robust method to estimate halo concentration based on the method of moments

ABSTRACT We propose an efficient and robust method to estimate the halo concentration based on the first moment of the density distribution, which is $R_1\equiv \int _0^{r_{\rm vir}}4\pi r^3\rho (r)\mathrm{ d}r/M_{\rm vir}/r_{\rm vir}$. We find that R1 has a monotonic relation with the concentration parameter of the Navarro–Frenk–White (NFW) profile, and that a cubic polynomial function can fit the relation with an error $\lesssim 3~{{\ \rm per\ cent}}$. Tests on ideal NFW haloes show that the conventional NFW profile fitting method and the Vmax/Vvir method produce biased halo concentration estimation by $\approx 10~{{\ \rm per\ cent}}$ and $\approx 30~{{\ \rm per\ cent}}$, respectively, for haloes with 100 particles. In contrast, the systematic error for our R1 method is smaller than 0.5 per cent even for haloes containing only 100 particles. Convergence tests on realistic haloes in N-body simulations show that the NFW profile fitting method underestimates the concentration parameter for haloes with ≲300 particles by $\gtrsim 20~{{\ \rm per\ cent}}$, while the error for the R1 method is $\lesssim 8~{{\ \rm per\ cent}}$. We also show other applications of R1, including estimating Vmax and the Einasto concentration ce ≡ rvir/r−2. The calculation of R1 is efficient and robust, and we recommend including it as one of the halo properties in halo catalogues of cosmological simulations.

MSGL+: Fast and Reliable Model Selection-Inspired Graph Metric Learning

The problem of learning graph-based data structures from data has attracted considerable attention in the past decade. Different types of data can be used to infer the graph structure, such as graphical Lasso, which is learned from multiple graph signals or graph metric learning based on node features. However, most existing methods that use node features to learn the graph face difficulties when the label signals of the data are incomplete. In particular, the pair-wise distance metric learning problem becomes intractable as the dimensionality of the node features increases. To address this challenge, we propose a novel method called MSGL+. MSGL+ is inspired from model selection, leverages recent advancements in graph spectral signal processing (GSP), and offers several key innovations: (1) Polynomial Interpretation: We use a polynomial function of a certain order on the graph Laplacian to represent the inverse covariance matrix of the graph nodes to rigorously formulate an optimization problem. (2) Convex Formulation: We formulate a convex optimization objective with a cone constraint that optimizes the coefficients of the polynomial, which makes our approach efficient. (3) Linear Constraints: We convert the cone constraint of the objective to a set of linear ones to further ensure the efficiency of our method. (4) Optimization Objective: We explore the properties of these linear constraints within the optimization objective, avoiding sub-optimal results by the removal of the box constraints on the optimization variables, and successfully further reduce the number of variables compared to our preliminary work, MSGL. (5) Efficient Solution: We solve the objective using the efficient linear-program-based Frank–Wolfe algorithm. Application examples, including binary classification, multi-class classification, binary image denoising, and time-series analysis, demonstrate that MSGL+ achieves competitive accuracy performance with a significant speed advantage compared to existing graphical Lasso and feature-based graph learning methods.

Trajectory-shaping guidance based on optimality formulation for cooperative attack of multiple interceptors

In this study, we present an optimal guidance structure that achieves impact angle and time constraints for the salvo attack of multiple missiles. As the first step in deriving a guidance law, we define a desired profile of the look angle that satisfies the impact angle and time constraints using a polynomial function of the relative range. The guidance command is configured based on the optimality formulation that achieves the desired profile of the look angle while minimizing the usage of the normal acceleration. The resulting trajectory under the proposed law is expressed as a polynomial form whose exponents can be selected to satisfy the desired constraints with the impact courses of various curvatures. In addition, the proposed law can achieve a wide range of terminal constraints since the time-to-go, which is difficult to estimate for a trajectory with a small radius of curvature, is not required for implementation. The numerical simulation results show that the proposed law achieves precise interception under various terminal conditions, validating the proposed law.

A new study for dynamical characteristics of double-variable-edge and variable thickness plates made of open-cell porous metal

This article explores the dynamic characteristics of a specific plate known as 'double-variable-edge' (DVE) plate with varying thickness, constructed from functionally graded porous material. The edge profiles of the plate and its thickness variation are defined by optional mathematical functions (polynomial and arc functions are chosen in this paper). The nonlinear dynamics of the double-variable-edge and variable thickness (DVEVT) plate, encompassing periodic and chaotic behaviors, have been investigated utilizing classical plate theory, incorporating the Von Karman-Donnell geometrical nonlinearity assumption, and employing Galerkin's method. Furthermore, this paper examines the linear characteristics by assessing fundamental frequencies. To establish the reliability of this approach, the linear frequencies and nonlinear curves are validated against prior literature and finite element analysis (FEA). Additionally, the study reveals the emergence of chaotic phenomena, as evidenced by the phase plane and Poincaré map, which become increasingly pronounced as the external load approaches the critical load. This critical load point signifies the juncture at which the structural behaviors transitions into a state of chaos. This research is anticipated to unlock significant potential within the aerospace, mechanical, and construction engineering, particularly for structures characterized by intricate profiles and varying thicknesses.

The case for the curve: Parametric regression with second- and third-order polynomial functions of predictors should be routine.

The case for the curve: Parametric regression with second- and third-order polynomial functions of predictors should be routine.

First-year university students’ understanding of function concepts encountered in Grade 12 Mathematics: a case study

This article focuses on first-year university students’ understanding of concepts related to third-degree polynomial and trigonometric functions that they encountered during their study of Grade 12 mathematics. In this study three online questions from two firstyear mathematics quizzes at the University of KwaZulu-Natal were analysed. The first question focused on the characteristics of a polynomial function, while the second and third questions focused on the characteristics of trigonometric functions. The characteristics included calculus-related concepts, for example, intervals of increase or decrease, concavity and local extrema. It was found that about a fifth of the participants (n = 557), science students who studied the core mathematics module Introduction to Calculus, had difficulties in answering those calculus-related questions compared to determining the general non-calculus characteristics, for example, the range and domain. The study also found that about a quarter of the participants lacked relational understanding with regard to calculus-related concepts. This study recommends that lecturers need to spend more time on calculus-related concepts of a function that focus on relational understanding.

A three-dimensional constitutive equation for shape memory polymer composites considering energy dissipation under single loading–unloading condition

Shape memory polymer composites (SMPCs), composed of shape memory polymers (SMPs) and fabrics, can recover their deformed shapes to initial configurations by changing temperature. The shape recovery energy of the SMPs and the elastic energy of the fabrics are regarded as key points to predict the restored configuration of the SMPCs. In this research, a three-dimensional constitutive equation for SMPCs is newly developed, considering the energy dissipation of fabrics under a single loading–unloading condition. The constitutive equation is derived from Mooney–Rivlin, viscoelastic, and stored strain energy models for SMPs, as well as polynomial functions for fabrics. The Mooney–Rivlin and viscoelastic models describe the time- and temperature-dependent hyperelastic properties, and the stored strain energy model can explain the shape recovery. The polynomial functions are newly proposed to take into account the dissipated energy of fabrics, such as residual deformation and hysteresis effect. Because the elastic energy of fabrics considerably influences the shape recovery of SMPCs, the proposed constitutive equation can accurately predict the recovered configuration. Analyses of SMPCs are conducted using the finite element method and validated by comparing them with the results obtained from experiments. The constitutive equation is used to analyze the shape recovery behaviors of an SMPC skin. The skin can be largely stretched, and the deformed shape can be restored to its initial shape by applying electricity. The SMPC skin is applied to a morphing flap, and its shape-changing behaviors are demonstrated experimentally.

Quantitative anatomy of the primary ossification center of the squamous part of temporal bone in the human fetus

Detailed numerical data about the development of primary ossification centers in human fetuses may influence both better evaluation and early detection of skeletal dysplasias, which are associated with delayed development and mineralization of ossification centers. To the best of our knowledge, this is the first report in the medical literature to morphometrically analyze the primary ossification center of the squamous part of temporal bone in human fetuses based on computed tomography imaging. The present study offers a precise quantitative foundation for ossification of the squamous part of temporal bone that may contribute to enhanced prenatal care and improved outcomes for fetuses with inherited cranial defects and skeletodysplasias. The examinations were carried out on 37 human fetuses of both sexes (16 males and 21 females) aged 18–30 weeks of gestation, which had been preserved in 10% neutral formalin solution. Using CT, digital image analysis software, 3D reconstruction and statistical methods, the size of the primary ossification center of the squamous part of temporal bone was evaluated. With neither sex nor laterality differences, the best-fit growth patterns for the primary ossification center of the squamous part of temporal bone was modelled by the linear function: y = −0.7270 + 0.7682 × age ± 1.256 for its vertical diameter, and the four-degree polynomial functions: y = 5.434 + 0.000019 × (age)4 ± 1.617 for its sagittal diameter, y = −4.086 + 0.00029 × (age)4 ± 2.230 for its projection surface area and y = −25.213 + 0.0004 × (age)4 ± 3.563 for its volume. The CT-based numerical data and growth patterns of the primary ossification center of the squamous part of temporal bone may serve as age-specific normative intervals of relevance for gynecologists, obstetricians, pediatricians and radiologists during screening ultrasound scans of fetuses. Our findings for the growing primary ossification center of the squamous part of temporal bone may be conducive in daily clinical practice, while ultrasonically monitoring normal fetal growth and screening for inherited cranial faults and skeletodysplasias.

An Iterative Curve-Fitting Baseline Correction Method for Raman Spectra Driven by Neural Network.

Baseline correction is a vital part of spectral preprocessing, especially for Raman spectra. Iterative polynomial fitting is an easy but less accurate way to find baselines compared to other methods such as wavelet transform and penalized least squares (PLS) methods. The polynomial fitting methods can also get distorted results in certain conditions. In this paper, a neural network model for detecting the trend of the baseline was proposed to improve the correction accuracy of the fitting methods. The model selects the function basis according to the baseline trend instead of using a fixed polynomial function to match the baseline for a more precise fit. We also propose a way to generate simulation data, these data can be used to train the neural network model. The model provides reliable results for real spectral data with noise. Our method provides a new idea to correct the baseline with a strange shape. In addition, we examine the limitations of conventional iterative polynomial fitting, adaptive iteratively reweighted PLS and explain why our approach surpasses these methods.

Free vibration and sound radiation of ABH-type functionally graded sandwich plates under elastic boundary restraints

Based on the first-order shear deformation theory, the free vibration and sound radiation of ABH-type functionally graded sandwich plates (ABH-type FG sandwich plate) under elastic boundary restraints are studied. The displacement field of the plate is described as an improved form of double Fourier cosine series and several closed-form auxiliary polynomial functions. The dynamic equation is solved by using the Rayleigh-Ritz method. The accuracy of the present method is validated and the effects of thickness variation coefficients and elastic boundary restraints on the vibr-acoustic characteristics are discussed. The research can provide an idea for the design of sandwich structures.

Birth outcomes and early growth patterns associated with age at adiposity rebound: the Ma’anshan birth cohort (MABC) study

ObjectiveEarly onset of adiposity rebound (AR) is considered an early indicator of obesity risk. Our objective was to investigate the association of birth outcomes and early physical growth patterns with early AR in children.MethodsStudy subjects (n = 2705) were enrolled from the Ma’anshan birth cohort (MABC). The body mass index (BMI), head circumference, waist circumference, and body fat were collected. Rapid weight gain (RWG) was defined by the change in weight standard-deviation score in the first two years of life. Group-based trajectory modeling (GBTM) was used to determine children’s physical growth trajectories. The age of AR was fitted using fractional polynomial function models.ResultsChildren with very high BMI trajectories (RR = 2.83; 95% CI 2.33 to 1.40), rising BMI trajectories (RR = 3.15; 95% CI 2.66 to 3.72), high waist circumference trajectories (RR = 4.17; 95% CI 3.43 to 5.06), and high body fat trajectories (RR = 3.01; 95% CI 2.62 to 3.46) before 72 months of age were at a greater risk of experiencing early AR. Low birth weight (LBW) (RR = 1.86; 95% CI 1.28 to 2.51), preterm birth (PTB) (RR = 1.50; 95% CI 1.17 to 1.93), and small for gestational age (SGA) (RR = 1.37; 95% CI 1.14 to 1.64) associated with increased risk of early AR. Moreover, infants experiencing RWG (RR = 1.59; 95% CI 1.40 to 1.83), low BMI trajectories (RR = 1.27; 95% CI 1.06 to 1.53) and rising BMI trajectories (RR = 1.50; 95% CI 1.22 to 1.84) in the first two years were at higher risk of developing early AR subsequently. Compared to the group with non-early AR, the BMI of children with early AR tended to be lower first (from birth to 6 months of age) and then higher (from 18 to 72 months of age).ConclusionsChildren with overall high BMI, high waist circumference, and high body fat before 72 months of age are more likely to experience early AR, but infants with low BMI trajectories, rising BMI trajectories and infants experiencing RWG in the first two years of life similarly increase the risk of early AR. These results can help to understand the early factors and processes that lead to metabolic risks.

Experimental and Numerical Evaluation of Solar Receiver Heat Losses of a Commercial 9 MWe Linear Fresnel Power Plant

Evaluating the heat losses of linear Fresnel concentrator (LFC) receivers is crucial for determining plant efficiency and managing the flow rate in solar lines. This becomes particularly significant when operating in direct steam generation to manage the steam quality at the line outlet. In general, the LFC receiver heat losses are determined experimentally on prototype systems to control the inlet condition or numerically using 3D computational fluid dynamics models or 1D mathematical models. The originality of this work is in reporting the study of heat losses of a commercial 9 MWe solar Fresnel power plant without impacting its electricity production. The experimentally measured receiver’s linear heat losses were found to be well represented by a second-degree polynomial function of the difference between the inlet/outlet fluid temperature average and the ambient temperature. Finally, to express the strong influence of wind speed on the receiver heat losses, a 1D single-phase model was developed and adapted to include the current receiver degradation. To conclude, the model was validated by comparing the experimental and theoretical results. Based on this comparison, it can be concluded that the model accurately predicts experimental heat losses with an acceptable uncertainty of ±30%, regardless of the wind velocity.

Transient probability density of nonlinear oscillator under parametric harmonic and external modulated stochastic excitations

In this study, the exponential-polynomial-closure (EPC) method is applied to determine and study the non-stationary probability density function (PDF) of the nonlinear system simultaneously stimulated by parametric harmonic and modulated stochastic excitations. The non-stationary probabilistic responses are represented as a time-related exponential polynomial function with unknown variables. Integrating the weighted residual error can result in a group of first-order differential equations. Those equations can be solved by numerical techniques to obtain the undefined variables. Four examples are given to show that the non-stationary behaviors of the presented oscillators can be addressed by the presented EPC procedure effectively, especially in the probabilistic tails which are of particular importance in reliability analysis. Moreover, the outcomes show that the response means equal to zero and the response PDFs are symmetrical with respect to the zero means. In particular, the presented EPC procedure can heavily decrease the running effort with no sacrifice to the solution correctness when compared with MCS.