Hasil untuk "Applied mathematics. Quantitative methods"

Ahmad Mahmood, Paul W. Wiseman

Quantitatively mapping three-dimensional (3D) flow, diffusion, and particle density in crowded living cells remains challenging because most dynamic optical microscopy measurements are effectively planar and existing analysis methods struggle with dense, noisy volumetric data. We introduce volumetric spatio-temporal image correlation spectroscopy (vSTICS), a framework that recovers voxel-resolved flow, diffusion coefficients, and particle densities from 3D fluorescence time series. Growing Camellia japonica pollen tubes were imaged with field-synthesis lattice light-sheet microscopy, and localized 3D spatio-temporal correlation analysis was applied to overlapping volumetric samples to generate maps of velocity, diffusion, and density. Validation with synthetic flow-diffusion simulations showed accurate recovery of seeded transport parameters, including velocities near $3$ $μ$m s$^{-1}$ and diffusion near $10^{-3}$ $μ$m$^2$ s$^{-1}$. Fluorescent microsphere experiments verified particle number and point spread function readouts and measured diffusion coefficients of $0.3 \pm 0.1$ $μ$m$^2$ s$^{-1}$ in gel, consistent with imaging-FCS measurements of $0.5 \pm 0.2$ $μ$m$^2$ s$^{-1}$. Applied to mitochondria in pollen tubes, vSTICS resolved a bidirectional reverse-fountain pattern with slower anterograde transport ($0.1$-$1$ $μ$m s$^{-1}$) and faster retrograde motion peaking near $3$ $μ$m s$^{-1}$, plus a retrograde corridor about $2$ $μ$m wide. Density and diffusion maps indicated a denser, more advective core and higher peripheral diffusion. High-density sub-diffraction vesicle mapping produced similar velocity landscapes with about ten-fold higher particle densities. These results establish vSTICS as a practical method for quantitative 3D mapping of intracellular transport and refines the reverse-fountain model by revealing asymmetric, predominantly transverse circulation.

S. Billinge, I. Levin

S.A. Hosseini

This paper introduces a direct quadrature method for the numerical solution of Volterra integral equations of the first kind, utilizing a composite quadrature scheme based on the Floater–Hormann family of linear barycentric rational interpolants. The convergence of the proposed method is rigorously proved, and the order of convergence is explicitly derived in terms of the parameters of the method, thereby providing a clear theoretical framework for its performance. Several numerical experiments are provided to demonstrate both the efficiency and accuracy of the method, as well as to verify the excellent agreement between the implementation results and the theoretically predicted convergence rates.

Andrej Kolar-Požun, Gregor Kosec

The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis function interpolation. The resulting methods remain fully explicit and are convergent if properly chosen hyperviscosity terms are added to the update equations. We demonstrate that increasing the stencil size of the approximation has a desirable effect on numerical dispersion. Furthermore, our proposed methods can exhibit a decreased dispersion anisotropy compared to the finite difference time domain method.

Archana S. Morye

Origami is the art of paper folding, and it borrows its name from two Japanese words \emph{ori} and \emph{kami}. In Japanese, {ori} means folding, and the paper is called {kami}. While origami is just a hobby to most, there is a lot more to it. If you fold a square sheet of paper into any of the traditional origami model (for example the flapping bird) and unfold it, you can see crease patterns. These crease patterns tell us that there is a lot of geometry hidden behind the folds. In this article, we investigate the symbiotic relationship between mathematics and origami. The first part of this article explores the utility of origami in education. We will see how origami could become an effective way of teaching methods of geometry, mainly because of its experiential nature. Complex origami patterns cannot be created out of thin air. They usually involve understanding deep mathematical theories and the ability to apply them to paper folding. In the second part of the article, we attempt to provide a glimpse of this beautiful connection between origami and mathematics.

Leonardo S. G. Leite, Swarup Banerjee, Yihui Wei et al.

Graph theory has a long history in chemistry. Yet as the breadth and variety of chemical data is rapidly changing, so too do graph encoding methods and analyses that yield qualitative and quantitative insights. Using illustrative cases within a basic mathematical framework, we showcase modern chemical graph theory's utility in Chemists' analysis and model development toolkit. The encoding of both experimental and simulation data is discussed at various levels of granularity of information. This is followed by a discussion of the two major classes of graph theoretical analyses: identifying connectivity patterns and partitioning methods. Measures, metrics, descriptors, and topological indices are then introduced with an emphasis upon enhancing interpretability and incorporation into physical models. Challenging data cases are described that include strategies for studying time dependence. Throughout, we incorporate recent advancements in computer science and applied mathematics that are propelling chemical graph theory into new domains of chemical study.

Antonio Trejo-Morales, Hugo Jimenez-Hernandez

In this research, a proposed model aims to automatically identify patterns of spatial and temporal behavior of moving objects in video sequences. The moving objects are analyzed and characterized based on their shape and observable attributes in displacement. To quantify the moving objects over time and form a homogeneous database, a set of shape descriptors is introduced. Geometric measurements of shape, contrast, and connectedness are used to represent each moving object. The proposal uses Granger’s theory to find causal relationships from the history of each moving object stored in a database. The model is tested in two scenarios; the first is a public database, and the second scenario uses a proprietary database from a real scenario. The results show an average accuracy value of 78% in the detection of atypical behaviors in positive and negative dependence relationships.

Július Czap

Let \(G\) be a plane graph. Two edges of \(G\) are facially adjacent if they are consecutive on the boundary walk of a face of \(G\). A facial edge coloring of \(G\) is an edge coloring such that any two facially adjacent edges receive different colors. A facial graceful \(k\)-coloring of \(G\) is a proper vertex coloring \(c:V(G)\rightarrow\{1,2,\dots,k\}\) such that the induced edge coloring \(c^{\prime}:E(G)\rightarrow\{1,2,\dots,k-1\}\) defined by \(c^{\prime(uv)}=|c(u)-c(v)|\) is a facial edge coloring. The minimum integer \(k\) for which \(G\) has a facial graceful \(k\)-coloring is denoted by \(\chi_{fg}(G)\). In this paper we prove that \(\chi_{fg}(G)\leq 14\) for every plane graph \(G\) and \(\chi_{fg}(H)\leq 9\) for every outerplane graph \(H\). Moreover, we give exact bounds for cacti and trees.

Rodrigo Rodríguez-Gutiérrez, Francisco Hernandez-Cabrera, Francisco Javier Almaguer-Martínez et al.

B.I. Andrew, A. Anuradha

Hydrocarbons are one of the subclasses of organic compounds that comprise exactly of hydrogen and carbon. Alkanes are one of the types of hydrocarbons that have chemical formula CnH2n+2. Isomers are molecules with identical chemical formula but different structural arrangements, leading to variations in their spectral properties as their corresponding molecular graphs also differ in structure. This exploration is motivated by the understanding that variations in structural configurations manifest as differences in spectral properties, as evidenced by alterations in their respective molecular graphs. Alkanes with ten carbon atoms are called decanes. Our study employs a multifaceted approach, encompassing the determination of spectral properties and the calculation of eigenvalue-based entropy for the C10H22 decane isomers. This analysis is undertaken with the goal of unravelling the intricate relationships between structural variations and corresponding spectral bounds. Notably, our investigation extends beyond the realm of molecular structures to draw connections with physico-chemical properties. Through meticulous comparison of the obtained spectral data with the known characteristics of C10H22 isomers, we unveil interesting correlations among the characteristics. We establish that the spectral gap, a key parameter in our study, intriguingly exhibits a maximal correlation with the refractive index of the isomers. This finding not only enhances our understanding of the spectral intricacies of decane isomers but also underscores the practical implications of such research. The correlation between spectral gap and refractive index opens avenues for predicting and manipulating the optical properties of hydrocarbons, offering potential applications in diverse fields, from materials science to optics. In essence, this study bridges the gap between molecular structure and macroscopic properties, shedding light on the intricate interplay between isomeric variations and their consequential effects on spectral characteristics.

Shusen Yang, Fangyuan Zhao, Zihao Zhou et al.

Federated Learning (FL) has been becoming a popular interdisciplinary research area in both applied mathematics and information sciences. Mathematically, FL aims to collaboratively optimize aggregate objective functions over distributed datasets while satisfying a variety of privacy and system constraints.Different from conventional distributed optimization methods, FL needs to address several specific issues (e.g., non-i.i.d. data distributions and differential private noises), which pose a set of new challenges in the problem formulation, algorithm design, and convergence analysis. In this paper, we will systematically review existing FL optimization research including their assumptions, formulations, methods, and theoretical results. Potential future directions are also discussed.

Valentina Pederzoli, Mattia Corti, Davide Riccobelli et al.

The aim of this paper is to introduce, analyse and test in practice a new mathematical model describing the interplay between biological tissue atrophy driven by pathogen diffusion, with applications to neurodegenerative disorders. This study introduces a novel mathematical and computational model comprising a Fisher-Kolmogorov equation for species diffusion coupled with an elasticity equation governing mass loss. These equations intertwine through a logistic law dictating the reduction of the medium's mass. One potential application of this model lies in understanding the onset and development of Alzheimer's disease. Here, the equations can describe the propagation of misfolded tau-proteins and the ensuing brain atrophy characteristic of the disease. To address numerically the inherited complexities, we propose a Polygonal Discontinuous Galerkin method on polygonal/polyhedral grids for spatial discretization, while time integration relies on the theta-method. We present the mathematical model, delving into its characteristics and propose discretization applied. Furthermore, convergence results are presented to validate the model, accompanied by simulations illustrating the application scenario of the onset of Alzheimer's disease.

Molly Lynch, Michael Weselcouch

In this article we will use Minecraft to experimentally approximate the values of four different mathematical constants. The mathematical constants that we will approximate are $\sqrt{2}, π$, Euler's number $e$, and Apéry's constant $ζ(3)$. We will begin each section with a brief history of the number being approximated and describe where it appears in mathematics. We then explain how we used Minecraft mechanics to approximate the constant. At the end of each section, we provide some ideas for how to apply our techniques to the approximation of other mathematical constants in Minecraft or elsewhere. This article is a proof of concept that Minecraft can be used in higher education. We should note that the goal of this article is not to have the most accurate approximations possible, the goal is to inspire people to have fun while learning about various mathematical topics. We hope you learn something new in this article and feel inspired to try some of these techniques on your own.

Saulo Cézar Seiffert Santos, Malena Albuquerque Oliveira, Mirlane Maria Moura Matos

A Amazônia é conhecida por sua biodiversidade, formas culturais e tecnológicas, em exposições científico-culturais as audiências urbanas, turísticas e autóctones. Há instituições de Ciência e Tecnologia amazônicas que realizam atividade de divulgação científica das suas próprias pesquisas e tecnologias. O objetivo desse trabalho é conhecer a proposta comunicativa da Revista de Divulgação Científica (RDC) de uma instituição de Ciência e Tecnologia, o Instituto Nacional de Pesquisa da Amazônia – INPA, o seu Discurso de Divulgação Científica (DDC). Para isso, analisaremos 12 volumes publicados em cerca de seis anos, pela Pró-Reitoria de Extensão/INPA, a partir do aporte da leitura do Círculo de Bakhtin, visando construir uma interpretação fundamentada na Análise Discursiva. Nossos resultados - foram levantados 129 textos em 12 números de RDC, no qual se destacaram temas de desenvolvimento, pesquisa, educação, saúde, entre outros. Percebeu-se uma distinção entre o discurso da divulgação científica (65%) e divulgação institucional científica (34%) dos textos selecionados. Desse último grupo, selecionou-se dois textos na área de Educação Ambiental para análise detalhada, e percebeu-se uma perspectiva institucional de apresentação de projeto extensionista voltada ao público escolar, utilizou-se dos objetos de pesquisa biológica para ser atrativo para divulgação científico-ambiental com proposito de conservação da Amazônia.

Harun Pirim, Morteza Nagahi, Oumaima Larif et al.

Abstract Systems Thinking (ST) has become essential for practitioners and experts when dealing with turbulent and complex environments. Twitter medium harbors social capital including systems thinkers, however there are limited studies available in the extant literature that investigate how experts' systems thinking skills, if possible at all, can be revealed within Twitter analysis. This study aims to reveal systems thinking levels of experts from their Twitter accounts represented as a network. Unraveling of latent Twitter network clusters ensues the centrality analysis of their follower networks inferred in terms of systems thinking dimensions. COVID-19 emerges as a relevant case study to investigate the relationship between COVID-19 experts’ Twitter network and their systems thinking capabilities. A sample of 55 trusted expert Twitter accounts related to COVID-19 has been selected for the current study based on the lists from Forbes, Fortune, and Bustle. The Twitter network has been constructed based on the features extracted from their Twitter accounts. Community detection reveals three distinct groups of experts. In order to relate system thinking qualities to each group, systems thinking dimensions are matched with the follower network characteristics such as node-level metrics and centrality measures including degree, betweenness, closeness and Eigen centrality. Comparison of the 55 expert follower network characteristics elucidates three clusters with significant differences in centrality scores and node-level metrics. The clusters with a higher, medium, lower scores can be classified as Twitter accounts of Holistic thinkers, Middle thinkers, and Reductionist thinkers, respectfully. In conclusion, systems thinking capabilities are traced through unique network patterns in relation to the follower network characteristics associated with systems thinking dimensions.

Law Szee Huei, M. Yunus, H. Hashim

Science, Technology, Engineering, and Mathematics (STEM) education is being increasingly recognized as needing vital emphasis at a national level To enhance learning in Science and Mathematics, the repertoire of vocabularies plays a significant role As the coronavirus disease 2019 (COVID-19) continues its spread across the world, people’s vocabulary learning has been limited Responding to this situation with appropriate awareness, e-learning is being applied to teach the English language The intent of this study is to utilize Quizizz to enhance the vocabulary achievement among primary English as Second Language (ESL) pupils in rural schools The study’s research employed mixed methods with purposive sampling of 13 participants The research site was a rural school located 60km from the nearest town The data were collected both pre and post-test as designed by the researcher and Likert scale questionnaire The data was analyzed using appropriate quantitative analysis To shed more light on the implementation, a thematic analysis by use of a semi-structured interview was conducted The study finds that 10 out of 13 participants have shown an increase in their post-test of filling in the blank scoring test The data is strengthened by a moderately high mean score of a Likert scale questionnaire Furthermore, the participants highlighted that the Quizizz’s leaderboard matched their favored learning style In this way, this feature tends to evoke a positive learning atmosphere Thus, it can be concluded that Quizizz could enhance vocabulary achievement among primary English as Secondary Language (ESL) pupils in rural schools © 2021 by the authors;licensee Asian Online Journal Publishing Group

E. Gribanova

One of the key tools in an organization’s performance management is the goal tree, which is used for solving both direct and inverse problems. This research deals with goal setting based on a model of the future by presenting the goal and subgoal in the form of concrete quantitative and qualitative characteristics and stepwise formation of factors. A stepwise solution to a factor generation problem is considered on the basis of mathematical symmetry. This paper displays an algorithm for solving hierarchical inverse problems with constraints, which is based on recursively traversing the vertices that constitute the separate characteristics. Iterative methods, modified for the case of nonlinear models and the calculation of constraints, were used to generate solutions to the subproblems. To realize the algorithm, the object-oriented architecture, which simplifies the creation and modification of software, was elaborated. Computational experiments with five types of models were conducted, and the solution to a problem related to fast-food restaurant profit generation was reviewed. The metrics of remoteness from set values and t-statistics were calculated for the purpose of testing the received results, and solutions to the subproblems, with the help of a mathematical package using optimization models and a method of inverse calculations, were also provided. The results of computational experiments speak to the compliance of the received results with set constraints and the solution of separate subproblems with the usage of the mathematical package. The cases with the highest solution accuracy reached are specified.

Houssine Zine, Abderrahim El Adraoui, Delfim F. M. Torres

We propose a mathematical spatiotemporal epidemic SICA model with a control strategy. The spatial behavior is modeled by adding a diffusion term with the Laplace operator, which is justified and interpreted both mathematically and physically. By applying semigroup theory on the ordinary differential equations, we prove existence and uniqueness of the global positive spatiotemporal solution for our proposed system and some of its important characteristics. Some illustrative numerical simulations are carried out that motivate us to consider optimal control theory. A suitable optimal control problem is then posed and investigated. Using an effective method based on some properties within the weak topology, we prove existence of an optimal control and develop an appropriate set of necessary optimality conditions to find the optimal control pair that minimizes the density of infected individuals and the cost of the treatment program.

Hongzhang Xu, Rowena Ball

The old lie of mathematical inadequacy of Indigenous communities has been curiously persistent despite increasing evidence shows that many Indigenous communities practiced mathematics. Attempts to study and teach Indigenous mathematical knowledge have always been questioned and even denied validity. The Aboriginal and Torres Strait Islander Histories and Cultures cross-curriculum priority in the F-10 Australian schools curriculum, from 2022 onwards, includes content elaborations related to Indigenous mathematics, which have been developed and refined by expert Indigenous advisers. We celebrate this initiative, but experience also tells us to expect some resistance from sectors of the education communities who hold to an exclusively Anglo-European provenance of mathematics. Through this review article we seek to constructively forestall potential pushback and address concerns regarding the legitimacy and pedagogical value of Indigenous mathematics, by countering with evidence some published claims of mathematical inadequacies of Australian First Nations cultures.

Inês Angélica Andrade Freire, Janice Cassia Lando, Eliene Barbosa Lima

Na década de 1960, na Bahia, um grupo de professores de matemática tanto do ensino superior como da educação básica elaborou um programa curricular para o ensino de matemática no secundário, o qual foi viabilizado, em caráter experimental, por meio de apostilas e livros didáticos em sala de aula e, posteriormente, publicados e utilizados em maior escala. Assim, este artigo analisou historicamente a proposta do programa curricular de autoria do grupo de professores da Bahia, materializada na produção Coleção Matemática Moderna com saberes matemáticos e metodológicos norteados pelas recomendações internacionais do Movimento da Matemática Moderna, de forma local, historicamente situados e com uma dinâmica social que acomodou as diferentes concepções sobre os processos de ensino e de aprendizagem em matemática. A legitimidade, nesse período, de constituição de classes experimentais, possibilitou experimentações e avaliações desse programa curricular de matemática em escolas da educação básica, na cidade de Salvador, Bahia.