Hasil untuk "Applied mathematics. Quantitative methods"

Jale Tezcan, Claudia Marin-Artieda

Analyzing and measuring the similarity between two signals is a common task in many vibration-based structural health monitoring applications. Coherence between input and response signals serves as a convenient indicator of damage, based on the premise that nonlinearity due to damage in a linear system manifests as a loss of coherence in specific frequency bands. Because input excitations in civil structures are difficult to measure, damage indicators based on the coherence between two response signals have been developed. These indicators have shown promise in detecting nonlinear behavior in structures that were initially linear. This paper proposes a new damage indicator based on Mutual Information, a nonlinear extension of the squared correlation coefficient, to quantify the similarity between two signals without making assumptions about the nature of their interactions or the underlying dynamics of the system. Mutual Information is distinguished from other nonlinear similarity metrics due to its ability to capture all types of nonlinear dependencies, its high computational efficiency, and its invariance to invertible transformations, such as scaling. The proposed approach is demonstrated using a standard dataset containing experimental data from a three-story aluminum frame structure under 17 different damage states. The results show that the proposed metric can detect deviations from the baseline state due to changes in mass, stiffness, or newly induced nonlinear behavior, suggesting its potential for monitoring changes in the structural system.

Adewale Samuel Hassan

This study investigated the asymmetric impact of natural resource exploitation on climate change in resource-rich African countries, based on panel data from 1980 to 2022. The dynamic common correlated effect (DCCE) and dynamic seemingly unrelated regression (DSUR) econometric techniques were employed to evaluate the long-term effects of positive shocks and negative shocks to natural resource exploitation. The findings revealed a positive relationship between both positive and negative shocks to natural resource exploitation and temperature, with increases in natural resource exploitation exerting a more intensified impact on temperature than decreases. In contrast, both positive and negative changes in natural resource exploitation are negatively related to precipitation, with an increased exploitation intensity having a more pronounced effect on rainfall patterns. The study also highlights the critical role of control variables such as GDP per capita, urban population, and total energy consumption in altering temperature and precipitation patterns. The findings underscore the importance of adopting sustainable natural resource extraction practices, integrating green technologies, and promoting collaboration across natural resource exploitation and renewable energy value chains to mitigate the negative impacts of natural resource exploitation.

S. Arfaoui, Ben Mabrouk

In the present paper, we precisely conduct a quantum calculus method for the numerical solutions of PDEs. A nonlinear Schrödinger equation is considered. Instead of the known classical discretization methods based on the finite difference scheme, Adomian method, and third modified ver-sions, we consider a discretization scheme leading to subdomains according to q-calculus and provide an approximate solution due to a specific value of the parameter q. Error estimates show that q-calculus may produce effi-cient numerical solutions for PDEs. The q-discretization leads effectively to higher orders of convergence provided with faster algorithms. The numer-ical tests are applied to both propagation and interaction of soliton-type solutions.

Laila Taourirte, Abderrahim Charkaoui, Nour Eddine Alaa

We analyze the existence of solutions for a class of quasilinear parabolic equations with critical growth nonlinearities, nonlinear boundary conditions, and \(L^1\) data. We formulate our problems in an abstract form, then using some techniques of functional analysis, such as Leray-Schauder's topological degree associated with the truncation method and very interesting compactness results, we establish the existence of weak solutions to the proposed models.

Gilson D. Honvoh, Roger S. Zoh, Anand Gupta et al.

BackgroundObesity has become an important threat to children’s health, with physical and psychological impacts that extend into adulthood. Limited physical activity and sedentary behavior are associated with increased obesity risk. Because children spend approximately 6 h each day in school, researchers increasingly study how obesity is influenced by school-day physical activity and energy expenditure (EE) patterns among school-aged children by using wearable devices that collect data at frequent intervals and generate complex, high-dimensional data. Although clinicians typically define obesity in children as having an age-and sex-adjusted body mass index (BMI) value in the high percentiles, the relationships between school-based physical activity interventions and BMI are analyzed using traditional linear regression models, which are designed to assess the effects of interventions among children with average BMI, limiting insight regarding the effects of interventions among children categorized as overweight or obese.MethodsWe investigate the association between wearable device–based EE measures and age-and sex-adjusted BMI values in data from a cluster-randomized, school-based study. We express and analyze EE levels as both a scalar-valued variable and as a continuous, high-dimensional, functional predictor variable. We investigate the relationship between school-day EE (SDEE) and BMI using four models: a linear mixed-effects model (LMEM), a quantile mixed-effects model (QMEM), a functional mixed-effects model (FMEM), and a functional quantile mixed-effects model (FQMEM). The LMEM and QMEM include SDEE as a summary measure, whereas the FMEM and FQMEM allow for the modeling of SDEE as a high-dimensional covariate. The FMEM and FQMEM allow the influence of the time of day at which physical activity is performed to be assessed, which is not possible using the LMEM or the QMEM. The FMEM assesses how frequently collected SDEE data influences mean BMI, whereas the FQMEM assesses the effects on quantile levels of BMI.ResultsThe LMEM and QMEM detected a statistically significant effect of overall mean SDEE on log (BMI) (the natural logarithm of BMI) after adjusting for intervention, age, race, and sex. The FMEM and FQMEM provided evidence for statistically significant associations between SDEE and log (BMI) for only a short time interval. Being a boy or being assigned a stand-biased desk is associated with a lower log (BMI) than being a girl or being assigned a traditional desk. Across our models, age was not a statistically significant covariate, and white students had significantly lower log (BMI) than non-white students in quantile models, but this significant effect was observed for only the 10th and 50th quantile levels of BMI. The functional regression models allow for additional interpretations of the influence of EE patterns on age-and sex-adjusted BMI, whereas the quantile regression models enable the influence of EE patterns to be assessed across the entire BMI distribution.ConclusionThe FQMEM is recommended when interest lies in assessing how device-monitored SDEE patterns affect children of all body types, as this model is robust and able to assess intervention effects across the full BMI distribution. However, the sample size must be sufficiently large to adequately power determinations of covariate effects across the entire BMI distribution, including the tails.

Hyoga Yamamoto, Shunki Anami, Ryo Matsuoka

Dynamic mode decomposition (DMD) is a powerful tool for separating the background and foreground in videos. This algorithm decomposes a video into dynamic modes, called DMD modes, to facilitate the extraction of the near-zero mode, which represents the stationary background. Simultaneously, it captures the evolving motion in the remaining modes, which correspond to the moving foreground components. However, when applied to noisy video, this separation leads to degradation of the background and foreground components, primarily due to the noise-induced degradation of the DMD mode. This paper introduces a novel noise removal method for the DMD mode in noisy videos. Specifically, we formulate a minimization problem that reduces the noise in the DMD mode and the reconstructed video. The proposed problem is solved using an algorithm based on the plug-and-play alternating direction method of multipliers (PnP-ADMM). We applied the proposed method to several video datasets with different levels of artificially added Gaussian noise in the experiment. Our method consistently yielded superior results in quantitative evaluations using peak-signal-to-noise ratio (PSNR) and structural similarity (SSIM) compared to naive noise removal methods. In addition, qualitative comparisons confirmed that our method can restore higher-quality videos than the naive methods.

Weifeng Xu, Xianku Zhang, Haoze Wang

Tank level control has some unavoidable factors such as disturbance, non-linearity, and time lag. This paper proposes a simple and robust control scheme with nice energy-saving effects and smooth output to improve the quality of the controller and meet real-world application requirements. A linear controller is first designed using a third-order closed-loop gain-shaping algorithm. We then use an arcsine function to modify the system with non-linear switching to reduce the effect of the non-linear modification on the dynamic performance of the control system. Furthermore, we use the Nyquist stability criterion to demonstrate the stability of the closed-loop system in the presence of time lag. The results of the final simulation experiment show that the controller not only has high control quality but also has the characteristics of energy saving and smooth output under the condition of lag and pump performance constraints. These features are necessary for extending the life of the pump and enhancing the applicability of the tank level controller.

Alexandr Oblizanov, Natalya Shevskaya, Anatoliy Kazak et al.

In recent years, artificial intelligence technologies have been developing more and more rapidly, and a lot of research is aimed at solving the problem of explainable artificial intelligence. Various XAI methods are being developed to allow the user to understand the logic of how machine learning models work, and in order to compare the methods, it is necessary to evaluate them. The paper analyzes various approaches to the evaluation of XAI methods, defines the requirements for the evaluation system and suggests metrics to determine the various technical characteristics of the methods. A study was conducted, using these metrics, which determined the degradation in the explanation quality of the SHAP and LIME methods with increasing correlation in the input data. Recommendations are also given for further research in the field of practical implementation of metrics, expanding the scope of their use.

Howard S. Cohl, Roberto S. Costas-Santos

AbstractOne may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the degree is allowed to be a complex number instead of a non-negative integer. These functions are referred to as Jacobi functions. In a similar fashion as associated Legendre functions, these break into two categories, functions which are analytically continued from the real line segment [Formula: see text] and those analytically continued from the real ray [Formula: see text] Using properties of Gauss hypergeometric functions, we derive multi-derivative and multi-integral representations for the Jacobi functions of the first and second kind.

V. Nesrstov'a, I. Wilms, J. Palarea‐Albaladejo et al.

High‐dimensional compositional data are commonplace in the modern omics sciences, among others. Analysis of compositional data requires the proper choice of a log‐ratio coordinate representation, since their relative nature is not compatible with the direct use of standard statistical methods. Principal balances, a particular class of orthonormal log‐ratio coordinates, are well suited to this context as they are constructed so that the first few coordinates capture most of the compositional variability of data set. Focusing on regression and classification problems in high dimensions, we propose a novel partial least squares (PLS) procedure to construct principal balances that maximize the explained variability of the response variable and notably ease interpretability when compared to the ordinary PLS formulation. The proposed PLS principal balance approach can be understood as a generalized version of common log‐contrast models since, instead of just one, multiple orthonormal log‐contrasts are estimated simultaneously. We demonstrate the performance of the proposed method using both simulated and empirical data sets.

Claudemir Miranda Barboza, Gladys Denise Wielewski

Este artigo apresenta um breve panorama da produção acadêmica que abarca as tecnologias digitais na perspectiva da formação inicial do professor de Matemática entre os anos de 2011 a 2021 e para isso buscou-se na Biblioteca Digital de teses e dissertações brasileira, usando o descritor “Tecnologias Digitais” AND “Formação Inicial do Professor de Matemática”. A pesquisa teve uma abordagem qualitativa por entender que esse tipo de pesquisa fornece informações mais descritivas. O trabalho buscou compreender como as tecnologias digitais contribuem para a formação inicial do professor de matemática, por meio de uma breve abordagem da utilização das tecnologias digitais na perspectiva dos conhecimentos do professor de Matemática. A discussão dos conhecimentos do professor de Matemática se respaldou nos aportes teóricos de Shulman (1986), Fiorentini (2003), Blanco (2003), Tardif (2014) e Carrillo (2014, 2018). Os resultados apontam para as potencialidades das tecnologias digitais na formação do professor e como suporte para evidenciar os conhecimentos de conteúdo matemático e os conhecimentos pedagógicos para o ensino da Matemática, a demonstram que o software GeoGebra está bem inserido nos debates de tecnologias em educação matemática, mostram também fragilidade na formação inicial do professor nesse aspecto.

Frank Phillipson, Peter Langenkamp, Reinder Wolthuis

Bayesian Belief Networks are used in many fields of application. Defining the conditional dependencies via conditional probability tables requires the elicitation of expert belief to fill these tables, which grow very large quickly. In this work, we propose two methods to prepare these tables based on a low number of input parameters using specific structures and one method to generate the table using probability tables of each relation of a child node with a certain parent. These tables can be used further as a starting point for elicitation.

Elizabeth Antonia Leonel de Moraes Martines, João Marcos Araújo Paz

Este trabalho tem como objetivo refletir sobre a importância da didática para o desenvolvimento profissional dos professores do ensino superior e sobre a constituição da identidade docente, a partir de uma pesquisa exploratória sobre a evolução da didática e das experiências docentes ao longo de vinte anos por parte de um dos autores. Os autores refletem sobre a importância da didática para a formação permanente dos docentes do ensino superior, entendendo que o problema se mostra relevante, já que o número de docentes deste nível de ensino em todo país vem crescendo com o aumento das instituições de ensino superior (IES) e junto a isso, existe a necessidade da formação destes para atuarem como docentes, visto que a maioria não teve formação didático-pedagógica para esta função. Os autores defendem a perspectiva de multidimensionalidade adotada por vários autores na contemporaneidade, ao entender que esta articula organicamente diversas dimensões da didática (humanista, técnica e política-cultural) e refletem sobre sua importância no desenvolvimento profissional do professor do ensino superior.

Lina Wang, Hang Zhang, Yaoyao Li et al.

The Luby transform code is a forward error correction code and was originally designed for the erasure channel. In this paper, the Luby transform codes over the Mars communication channel are investigated. To guarantee the reliable data transmission over the Mars communication channel which are usually affected by fading and noises, the progressive edge-growth algorithm is improved and used in for encoding the Luby transform codes. And then a partly systematic Luby transform code with an improved progressive edge-growth algorithm is designed to improve the error propagation phenomenon in Mars communications. Performance evaluations of the designed partly systematic Luby transform code based on the random graph, PEG and improved progressive edge-growth algorithms, respectively, are conducted through a series of simulations. Simulation results show that the performance of the partly systematic Luby transform code based on the improved progressive edge-growth algorithm outperforms those of the partly systematic Luby transform code based on two other algorithms and has the lower bit error rate and overhead.

F. Arzani, M.R. Peyghami

In this paper, we present a new derivative-free spectral residual method for solving large-scale systems of equations. Our algorithm is equipped with a dwindling multidimensional nonmonotone filter in which whose envelope is dwindling as the step-length of line search is decreasing. The proposed algorithm is also combined with a relaxed nonmonotone line search technique which allows the algorithm to enjoy the nonmonotone property from scratch. Under some standard assumptions, the global convergence property of the proposed algorithm is established. Numerical results on some test problems show the efficiency and effectiveness of the new algorithm in practice.

D. Torre, H. Kunze, Manuel Ruiz-Galán et al.

1Department of Applied Mathematics and Sciences, Khalifa University, Abu Dhabi 127788, UAE 2Department of Economics, Management, and Quantitative Methods, University of Milan, 20122 Milan, Italy 3Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada N1G 2W1 4Department of Applied Mathematics, University of Granada, 18071 Granada, Spain 5School of Accounting, Economics and Finance, University of Wollongong, Wollongong, NSW 2522, Australia

Makar Ghazaryan, Tatiana Sergeevna Yakushkina, David B. Saakian

Crow-Kimura model is one of the famous models of population genetics. Last decade models with low-dimensional fitness landscape have been investigated. We consider the Crow-Kimura model of evolutionary dynamics on multi-dimensional fitness landscape with a single peak. We deduce exact solution for the dynamics, confirmed well by the numerics.

Murat Yalman

Abstract The purpose of this study was to determine the views of preservice teacher about e-books and the level of their general knowledge about these kinds of technological tools. The subjects in this study consisted of 543 (310 females and 233 males) students. In line with the purpose of this study, both qualitative and quantitative methods were applied. The results demonstrated that the use of e-books increased in accordance with the students’ levels. It was found out that the general knowledge levels of the social sciences students about e-books were lower when compared to the students from the departments of Science, Mathematics and Foreign Languages. It was seen that 19,15% of the students did not make any preference between e-books and conventional printed books while 54,88% of them preferred printed books and 25,97% them e-books.

Eka Nella Kresma