1,222 research outputs found

    Big Data Analysis and Programming for Engineers

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    This text serves to cover critical programming, data analysis, statistical analysis, and mathematical skills for engineers. In particular fundamental programming skills are demonstrated using Mathematica specifically the importing of data sets, loop structures, plotting and statistically analyzing data, image analysis, and machine learning. Critical engineering topics such as solid mechanics, vibrations, and engineering problems which require solving ODEs and PDEs are covered.https://scholarlycommons.pacific.edu/open-textbooks/1026/thumbnail.jp

    The Long Search for Collatz Counterexamples

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    Despite decades of effort, the Collatz conjecture remains neither proved, nor refuted by a counterexample, nor formally shown to be undecidable. This note introduces the Collatz problem and probes its logical depth with a test question: can the search space for counterexamples be iteratively reduced, and when would it help

    Symbolic computation of solitary wave solutions and solitons through homogenization of degree

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    A simplified version of Hirota's method for the computation of solitary waves and solitons of nonlinear PDEs is presented. A change of dependent variable transforms the PDE into an equation that is homogeneous of degree. Solitons are then computed using a perturbation-like scheme involving linear and nonlinear operators in a finite number of steps. The method is applied to a class of fifth-order KdV equations due to Lax, Sawada-Kotera, and Kaup-Kupershmidt. The method works for non-quadratic homogeneous equations for which the bilinear form might not be known. Furthermore, homogenization of degree allows one to compute solitary wave solutions of nonlinear PDEs that do not have solitons. Examples include the Fisher and FitzHugh-Nagumo equations, and a combined KdV-Burgers equation. When applied to a wave equation with a cubic source term, one gets a bi-soliton solution describing the coalescence of two wavefronts. The method is largely algorithmic and is implemented in Mathematica.Comment: Proceedings Conference on Nonlinear and Modern Mathematical Physics (NMMP-2022) Springer Proceedings in Mathematics and Statistics, 60pp, Springer-Verlag, New York, 202

    Making Presentation Math Computable

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    This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book

    Rational Function Simplification for Integration-by-Parts Reduction and Beyond

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    We present FUEL (Fractional Universal Evaluation Library), a C++ library for performing rational function arithmetic with a flexible choice of third-party computer algebra systems as simplifiers. FUEL is an outgrowth of a C++ interface to Fermat which was originally part of the FIRE code for integration-by-parts (IBP) reduction for Feynman integrals, now promoted to be a standalone library and with access to simplifiers other than Fermat. We compare the performance of various simplifiers for standalone benchmark problems as well as IBP reduction runs with FIRE.Comment: 18 pages, 1 figure, 6 table

    Routines and Applications of Symbolic Algebra Software

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    Computing has become an essential resource in modern research and has found application across a wide range of scientific disciplines. Developments in symbolic algebra tools have been particularly valuable in physics where calculations in fields such as general relativity, quantum field theory and physics beyond the standard model are becoming increasing complex and unpractical to work with by hand. The computer algebra system Cadabra is a tensor-first approach to symbolic algebra based on the programming language Python which has been used extensively in research in these fields while also having a shallow learning curve making it an excellent way to introduce students to methods in computer algebra. The work in this thesis has been concentrated on developing Cadabra, which has involved looking at two different elements which make up a computer algebra program. Firstly, the implementation of algebraic routines is discussed. This has primarily been focused on the introduction of an algorithm for detecting the equivalence of tensorial expressions related by index permutation symmetries. The method employed differs considerably from traditional canonicalisation routines which are commonly used for this purpose by using Young projection operators to make such symmetries manifest. The other element of writing a computer algebra program which is covered is the infrastruc- ture and environment. The importance of this aspect of software design is often overlooked by funding committees and academic software users resulting in an anti-pattern of code not being shared and contributed to in the way in which research itself is published and promulgated. The focus in this area has been on implementing a packaging system for Cadabra which allows the writing of generic libraries which can be shared by the community, and interfacing with other scientific computing packages to increase the capabilities of Cadabra

    Технология комплексной поддержки жизненного цикла семантически совместимых интеллектуальных компьютерных систем нового поколения

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    В издании представлено описание текущей версии открытой технологии онтологического проектирования, производства и эксплуатации семантически совместимых гибридных интеллектуальных компьютерных систем (Технологии OSTIS). Предложена стандартизация интеллектуальных компьютерных систем, а также стандартизация методов и средств их проектирования, что является важнейшим фактором, обеспечивающим семантическую совместимость интеллектуальных компьютерных систем и их компонентов, что существенное снижение трудоемкости разработки таких систем. Книга предназначена всем, кто интересуется проблемами искусственного интеллекта, а также специалистам в области интеллектуальных компьютерных систем и инженерии знаний. Может быть использована студентами, магистрантами и аспирантами специальности «Искусственный интеллект». Табл. 8. Ил. 223. Библиогр.: 665 назв

    Implementación de un sistema experto para el diagnóstico de las cardiopatías más comunes en adultos utilizando lógica difusa

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    El presente trabajo de tesis fue desarrollado para proporcionar un diagnóstico temprano de las cardiopatías que causan más mortalidad en las personas adultas. En los últimos años las cardiopatías que causaron mayor mortalidad en esta población fueron la cardiopatía isquémica y la hipertensión arterial según diversas organizaciones especializadas en la salud como la Organización Mundial de Salud (2020), la Organización Panamericana de la Salud (2020), y también según el Ministerio de Salud del Perú. En este trabajo se ha implementado un sistema experto para el diagnóstico de cardiopatías más comunes en adultos como son la hipertensión arterial y la isquemia cardíaca. Esto se ha hecho utilizando la lógica difusa como herramienta matemática para el análisis y fuzificación o representación de la ambigüedad de las variables de entrada como edad, índice de masa corporal, presión arterial, colesterol, triglicéridos, tabaquismo y angina de pecho, y para obtener el valor de salida que es el nivel de riesgo de la cardiopatía se ha utilizado el método de defuzificación Centro de Gravedad (COG). Se ha construido la base de conocimiento que consta de 486 reglas, basado en los conocimientos del experto humano y la información recopilada; y para el análisis de las reglas se ha utilizado el motor de inferencia Mamdani. Para la construcción del sistema experto se ha utilizado la metodología de Buchanan. El sistema experto que ha sido desarrollado en el lenguaje PHP y la interfaz con el framework front-end Bootstrap, es solo un prototipo

    Ensino de matemática no período da pandemia : a emergência do uso de tecnologias digitais

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    Em fevereiro de 2020, foi confirmado no Brasil o primeiro caso de covid-19. A pandemia mudou tudo na vida da população mundial, a maneira como trabalhamos, fazemos compras e estudamos. Para evitar o contágio, as aulas foram suspensas a fim de evitar aglomerações. Iniciou-se então o Ensino Remoto Emergencial. Professores migraram suas atividades presenciais para atividades remotas. As tecnologias digitais foram um importante aliado para manter a educação durante a pandemia. A presente pesquisa tem como objetivo analisar as contribuições das tecnologias digitais, que foram utilizadas nas aulas de matemática no período da pandemia. Para isso foram realizadas entrevistas semiestruturadas com três professores de escolas públicas, que atuaram nos Ensinos Fundamental e Ensino Médio, no período entre os anos de 2019 e 2022. As entrevistas foram analisadas para tentar identificar como as tecnologias digitais foram usadas por esses educadores, observando as dificuldades, aprendizagens e reflexões que eles tiveram nesse período. Buscamos identificar se foi oferecido algum curso para esses professores ministrarem atividades remotas. Além disso, a pesquisa busca compreender como ocorreu o Ensino Remoto Emergencial, se houve ou não um padrão nas escolas em que esses entrevistados atuam. A partir da análise destes dados, foi possível constatar que durante o ERE, não houve um padrão nas escolas, algumas escolas tiveram atividades online, algumas tiveram só envio de materiais por plataformas educacionais ou era fornecido atividades impressas pela escola, para os alunos sem acesso a internet. Outro dado importante revelado pela pesquisa é a desigualdade social, afinal nem todos os alunos têm acesso à internet e não conseguiram acompanhar as atividades.In February 2020, the first case of covid-19 was confirmed in Brazil. The pandemic has changed everything in the lives of the world's population, the way we do, shop and study. To avoid contagion, classes were suspended to avoid agglomerations. Then, Emergency Remote Teaching began. Teachers migrated their face-to-face activities to remote activities. Digital technologies were an important ally to maintain education during the pandemic. The present digital research aims to analyze the contributions of technologies, which were used in mathematics classes during the pandemic. For this, semi-structured interviews were carried out, which worked with elementary and high school teachers, in the period between the years 2022. the difficulties, learning and that they had in this period. We are looking for teachers if offered any courses for these remote administrative activities. In addition, the research understands how Remote Learning Emerges, whether or not a standard in schools, which they believed to be dissociated. From the analysis of these data, it was possible to verify that during a pattern, some schools had online activities, only materials were sent by educational strategies or only printed activities were sent by the school, students without access to the internet. Another data from the research is social inequality, after all, not all students have access to the internet and are not revealed as activities

    Estudio teórico del Aprendizaje por Refuerzo y su aplicación práctica al posicionamiento de un dron cuadricóptero

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    El propósito de este proyecto es la aplicación de técnicas de Aprendizaje por Refuerzo a un problema robótico. En particular, al control de la posición de un dron cuadricóptero. Por un lado, estas técnicas forman parte de la Inteligencia Artificial. Por ello, lo primero será conocer un poco este campo, concretamente de la rama del Aprendizaje Automático, y hacer hincapié en el Aprendizaje por Refuerzo. Este consiste en aprender de la interacción con el entorno, es decir, de la experiencia, gracias a la obtención de una serie de recompensas en función de las acciones que se lleven a cabo y las observaciones que se reciban. Por otro lado, se hará una introducción a los drones y se indagará más en el dron cuadricóptero, explicando sus movimientos y las ecuaciones físicas que lo gobiernan. Finalmente, se pondrán en conjunto ambos bloques de conocimiento para realizar una simulación en el software Matlab-Simulink del control de la altitud de un cuadricóptero y evaluar sus resultados
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