Abstract Beyond the practical experience and the intuition that could result from it, there is concrete evidence of Logic, particularly Mathematical Logic, it is a discipline that is difficult for students to grasp. Like all natural phenomena, it has a multidimensional character. In the present work, the authors, based on the specific results in three courses where this subject has been taught in the Discrete Mathematics subject for Cybersecurity at the University of Informatics Sciences, reveal the contents that have represented the greatest difficulty for the students and proposing, as a working hypothesis to be explored, proposals for the systemic and systematic structuring of the content, in order to contribute, from this dimension, to improving the instructional and educational results, particularly in the vision of the system, the development of deductive reasoning and the abstraction.

Resumen Más allá de la experiencia práctica y de la intuición que pudiera resultar de ella, existen evidencias concretas de la Lógica, en particular la Lógica matemática, es una disciplina que resulta difícil para su aprehensión por los estudiantes. Como todo fenómeno natural, tiene carácter multidimencional. En el presente trabajo los autores, sobre la base de los resultados específicos en tres cursos donde se ha impartido ese tema en la asignatura Matemática discreta para Ciberseguridad en la Universidad de las Ciencias Informáticas, develan los contenidos que mayor dificultad han representado para los estudiantes y adelantan, a modo de hipótesis de trabajo a explorar, propuestas de estructuración sistémica y sistemática del contenido, en aras de contribuir, desde esa dimensión, a mejorar los resultados instructivos y educativos, particularmente en la visión de sistema, el desarrollo del razonamiento deductivo y la abstracción.

Abstract: In this paper, we study the dragonfly algorithm, an optimization method derived from the observation of nature and mathematical modeled after the swarming behavior of dragonflies. Xin-She Yang devised this approach, which has been applied to various optimization challenges. [1]. The algorithm effectively explores the search space by imitating dragonfly behaviors like hunting for prey, fleeing from predators, and swarming. The method consists in apply Type-1 Fuzzy Logic to some of the parameters of the algorithm, in this case, W and Betha to analyze the results applied to the mathematical functions F1 through F10 included in this paper, once that we have applied the adaptation of parameters, we will review the results compared with the rest of the papers that implement the same mathematical functions, so we can have a general idea if this method can be reliable.

RESUMEN La investigación aborda la articulación del contexto empresarial con la práctica laboral de los estudiantes de ciencias contables. La lógica de la investigación tuvo en cuenta la utilización de métodos científicos del nivel teórico, empírico y estadísticos-matemáticos. La contribución práctica consiste en la articulación del sistema de relaciones que se establece entre los sujetos participantes y el contexto empresarial en el que se desarrolla la práctica laboral de los estudiantes de la carrera Licenciatura en Contabilidad y Finanzas. La implementación de un sistema de tareas docentes en la disciplina Práctica Laboral Contable y Financiera posibilitó las interrelaciones entre las dimensiones del contenido, las relaciones internas entre los componentes de la tarea docente y el vínculo de la teoría con la práctica de los estudiantes en la empresa desde la cooperación y subordinación entre los sujetos. Se reafirma que los estudiantes deben tener conocimientos técnico-profesionales, pero también ético-profesionales; se impone que se formen con respeto, profesionalidad, laboriosidad, honestidad y responsabilidad para dar respuesta a los principales problemas de su profesión y estén preparados para enfrentar y resolver las nuevas situaciones que se presenten en su futuro desempeño laboral.

ABSTRACT The research addresses the articulation of the business context with the work practice of accounting science students. The logic of the research took into account the use of scientific methods at the theoretical, empirical and statistical-mathematical level. The practical contribution consists of the articulation of the system of relationships that is established between the participating subjects and the business context in which the work practice of the students of the Bachelor's Degree in Accounting and Finance is developed. The implementation of a system of teaching tasks in the discipline of Accounting and Financial Labor Practice made possible the interrelationships between the dimensions of the content, the internal relationships between the components of the teaching task and the link of the theory with the practice of the students in the company. from cooperation and subordination between subjects. It is reaffirmed that students must have technical-professional knowledge, but also ethical-professional knowledge; It is essential that they be trained with respect, professionalism, hard work, honesty and responsibility to respond to the main problems of their profession and be prepared to face and resolve new situations that arise in their future work performance.

Abstract This article focuses on the educator's mission, which must be to meet students within the realm of the natural logic of everyday language and guide them toward mathematical logic, the underlying set theory that forms the foundation of 20th-century mathematics. We examine the identity A=A, critiqued Hegelian theory as a fundamental law of thought and adopted in the psychoanalysis field as the gateway into mathematical discourse. We discuss Russell's paradox and its resolution by distinguishing between class and set. Special attention is given to the introduction of the empty set, unordered pairs, and singleton sets in the ZFC set theory. Following Lacanian guidelines, we illustrate how the mathematical discourse on arithmetic is not only subject to the contradiction of self-reference but is also inevitably influenced by the unconscious of the subject attempting to articulate a discourse without subject. In Lacanian theory, this influence is located in the Platonic conception and shows how it is present in the concept of One. We provide an introduction to Intuitionistic Logic, which is more attuned to natural language. We conclude by cautioning mathematics educators about the presence of the unconscious in the institutional relationship between teacher and student and justify our invitation for them to join us in embracing the motto: Teach by listening, learn by speaking . educator s mission 20thcentury thcentury 20th century th AA A A=A Russells Russell pairs guidelines selfreference self reference One Logic motto listening

Resumo Este artigo foca a prática educativa do professor que, em meio às vicissitudes que caracterizam o movimento da sala de aula, tem por desafio encontrar seus alunos no âmbito da lógica natural da linguagem diária e conduzi-los ao âmbito da lógica matemática subjacente à teoria dos conjuntos que fundamenta a matemática do século 20. Consideramos a identidade A=A, criticada pela teoria hegeliana como lei fundamental do pensamento e adotada no campo da psicanálise como portal de entrada no discurso matemático. Discutimos um paradoxo importante na matemática e sua solução, distinguindo classe de conjunto. Damos especial atenção à introdução do conjunto vazio, dos pares não ordenados e dos conjuntos unitários na teoria de conjuntos ZFC. Seguindo as diretrizes lacanianas, mostramos como o discurso matemático sobre a aritmética, não só fica sujeito à contradição da autorreferência, mas sofre inevitável influência do inconsciente do sujeito que pretende enunciar um discurso sem sujeito. Na teoria lacaniana é localizada essa influência na concepção platônica e mostrada como está presente no conceito de Um. Fornecemos uma introdução à Lógica Intuicionista a partir da lógica mais adaptada à linguagem natural. Concluímos alertando os professores de matemática sobre a presença do inconsciente na relação institucional professor/aluno e justificamos o convite que lhes fazemos, para adotarem conosco o lema: ensina-se ouvindo, aprende-se falando . aula conduzilos conduzi los 20 AA A A=A solução vazio ZFC lacanianas aritmética autorreferência Um professoraluno aluno fazemos lema ensinase ensina se ouvindo aprendese aprende 2

Abstract In this paper we present novel conceptions of identity arising in and motivated by a recently emerged branch of mathematical logic, namely, Homotopy Type theory (HoTT). We consider an established 2013 version of HoTT as well as its more recent generalised version called Directed HoTT or Directed Type theory (DTT), which at the time of writing remains a work in progress. In HoTT, and in particular in DTT, identity is not just a relation but a mathematical structure which admits for an interpretation in terms of Homotopy theory (directed Homotopy theory in the case of DTT), which in its turn is supported by common intuitions concerning identity of material objects through time, change and locomotion. The DDTbased conception of identity presented in the paper is nonsymmetric: here identity is “directed” or has a “sense”. We compare the HoTT-based conceptions of identity with standard theories of identity based on the Classical Predicate calculus, and show how the HoTT-based identity helps to treat traditional logical and philosophical problems related to identity and time. In the concluding part of the paper we explore some ontological implications of the HoTT-based identity and show how HoTT and DTT can serve for designing formal process ontologies. The paper is self-contained and comprises expositions and informal explanations of all relevant philosophical, logical and mathematical contents. logic namely HoTT. . (HoTT) 201 , (DTT) progress directed DTT) locomotion nonsymmetric “directed sense. sense “sense” HoTTbased calculus ontologies selfcontained self contained contents (HoTT 20 (DTT “sense 2

ABSTRACT. Tomato is a demanding crop in terms of handling, mainly because irrigation has a strong influence on fruit production and quality. Salinity changes the absorption, transport, assimilation, and distribution of nutrients in the plant. In general, such effects are analyzed using statistical tests. However, fuzzy models allow simulations between points that are not verified in agricultural experimentation. Currently, systems with artificial intelligence have excelled in the field of applied sciences, particularly fuzzy systems applied to mathematical modeling. The objective of this research was to use fuzzy modeling to analyze the biometric variables during the development of hybrid tomatoes under two different conditions: the first concerning different water tensions in the soil and the second concerning different salinity doses in irrigation. To this end, two models were developed based on an experiment carried out at São Paulo State University (UNESP), School of Agriculture, Botucatu, São Paulo State, Brazil. Both models sought to estimate the values of biometric variables of the tomato crop. Thus, two models were developed: Model 1 regarded water tensions and days after sowing (DAS), while Model 2 featured salinity and DAS. Fuzzy models provided results that verified the effects of irrigation and salinity layers. Two Fuzzy Rule-Based Systems (FRBS), an input processor with two variables, a set of linguistic rules defined from statistical procedures with percentiles, the Mamdani fuzzy inference method, and the center of gravity method to defuzzification were elaborated for this purpose. The range between −25 and −10 kPa (for Model 1) and between 0.08 and 3 dS m−1 (for Model 2) provided the development within the ideal parameters for the complete development of the plant cycle. The use of fuzzy logic has shown effectiveness in evaluating the development of tomato crops, thus showing potential for use in agricultural sciences. Moreover, the created fuzzy models showed the same characteristics of the experiment, allowing their use as an automatic technique to estimate ideal parameters for the complete development of the plant cycle. The development of applications (software) that provide the results generated by the artificial intelligence models of the present study is the aim of future research. ABSTRACT handling quality absorption transport assimilation general tests However experimentation Currently sciences conditions end UNESP, UNESP , (UNESP) Agriculture Botucatu Brazil Thus DAS, DAS (DAS) layers RuleBased Rule Based FRBS, FRBS (FRBS) percentiles purpose 25 −2 10 −1 008 0 08 0.0 m1 m m− cycle crops Moreover software (software (UNESP (DAS (FRBS − 00 0.

ABSTRACT One of the didactic components of the Mathematics subject in 8th grade is the resolution of mathematical problems, since it allows students to develop a logic of thought, acquire security and rigor in their reasoning. For this reason, teachers must encourage learning styles that facilitate novel ways of acquiring knowledge effectively. The work strategies must become effective didactic tools that contribute to improving the acquisition and development of the necessary skills in students with academic potential in this subject. Hence, the objective of the research presented in the article is: to socialize some didactic alternatives applied to promote the resolution of mathematical problems in 8th grade students of the Hermanos Martínez Tamayo Vocational Pre-University Institute, from a developer teaching. The investigation required the use of the methods: documentary analysis, analytical-synthetic, inductive-deductive and modeling. The proposed didactic alternatives stimulate the cognitive psychic processes in order to improve the quality of the Mathematics teaching-learning process and to favor the appropriation and conscious application of the contents that contribute to the development of talent from the potential offered by the subject.

RESUMEN Uno de los componentes didácticos de la asignatura Matemática en 8vo grado lo constituye la resolución de problemas matemáticos, ya que permite a los estudiantes desarrollar una lógica de pensamiento, adquirir seguridad y rigor en sus razonamientos. Por esta razón, los profesores deben estimular los estilos de aprendizaje que faciliten novedosas formas de adquirir el conocimiento de manera efectiva. Las estrategias de trabajo deben convertirse en herramientas didácticas eficaces que contribuyan a mejorar la adquisición y desarrollo de las habilidades necesarias en los estudiantes con potencialidades académicas en esta asignatura. De ahí que el objetivo de la investigación que presenta el artículo sea: socializar algunas alternativas didácticas aplicadas para promover la resolución de problemas matemáticos en los estudiantes de 8vo grado del Instituto Preuniversitario Vocacional Hermanos Martínez Tamayo, desde una enseñanza desarrolladora. La investigación requirió el uso de los métodos: análisis documental, analítico-sintético, inductivo-deductivo y modelación. Las alternativas didácticas propuestas estimulan los procesos psíquicos cognoscitivos en función de mejorar la calidad del proceso de enseñanza-aprendizaje de la Matemática y de favorecer la apropiación y aplicación consciente de los contenidos que contribuyan al desarrollo del talento desde las potencialidades que ofrece la asignatura.

ABSTRACT The present investigation was developed in the Water and Sanitation Business Group, with the objective of proposing a mathematical model based on compensatory fuzzy logic and a checklist for the evaluation of organizational communication variables to improve the level of integration of the management system of the companies integrated into the Water and Sanitation Business Group; for this, two companies were taken as samples: Western Hydraulic Works Maintenance Company (EMAROHO) and Aguas de La Habana. Thanks to the help of specialists in Social Communication, four variables with their indicators were proposed, which are essential for the design of an organizational communication model. To meet the objective, techniques were applied to obtain and analyze information such as: direct observation, interviews, consultation of standards and records, Ishikawa diagrams, checklist, analysis of indicators in terms of Compensatory Fuzzy Logic, 360° technique, among others; obtaining that the most deficient variable was internal communication and the one with the best performance was the communication skills of the workers.

RESUMEN La presente investigación se desarrolló en el Grupo Empresarial Agua y Saneamiento, con el objetivo de proponer un modelo matemático basado en la lógica difusa compensatoria y lista de chequeo para la evaluación de variables de comunicación organizacional para la mejora del nivel de integración del sistema de dirección de las empresas integradas al Grupo Empresarial Agua y Saneamiento; para ello se tomaron como muestras dos empresas: Empresa de Mantenimiento de Obras Hidráulicas de Occidente (EMAROHO) y Aguas de La Habana. Gracias a la ayuda de especialistas en Comunicación Social, fueron propuestas cuatro variables con sus indicadores, que resultan imprescindibles para el diseño de un modelo de comunicación organizacional. Para cumplir con el objetivo se aplicaron técnicas para la obtención y análisis de la información tales como: observación directa, entrevistas, consultas a normas y registros, diagramas Ishikawa, lista de chequeo, análisis de indicadores en términos de Lógica Difusa Compensatoria, técnica 360°, entre otros; obteniéndose que la variable más deficiente fue la comunicación interna y la de mejor desempeño las competencias comunicativas de los trabajadores.

ABSTRACT The development of this research had the objective of obtaining a mathematical model called La Pitia that addresses the management capacity of construction companies so that they can respond: Why are the delivery dates of the works not being met? Why is the quality pre-established in the regulations not being met? Why is industrial safety not complied with? Why are they exceeding planned costs? Why does construction management become a factor that generates pathologies? It is part of a job in the area of construction prognosis, whose scope is to predict success. In this search, functions were obtained that model the company's ability to reduce the risks that it will face during the execution process, which have been called Expertise, which indicates how far or close it could be to the desired success in the execution of the work. The vast majority of construction companies in Venezuela do not receive feedback on the results obtained from their works, nor do they have a formal data arrangement system that allows reliable forecasts to be made, which is why the mathematical development of this work was based on concepts of Approximate Reasoning and Fuzzy Logic.

RESUMEN El desarrollo de esta investigación ha tenido como objetivo obtener un modelo matemático denominado La Pitia que aborde la capacidad de gestión de las empresas constructoras con la finalidad de que puedan responder ¿Por qué no se cumplen las fechas de entrega de las obras? ¿Por qué no se cumple con la calidad preestablecidas en las normativas? ¿Por qué no se cumple con la seguridad industrial? ¿Por qué se exceden en los costos planificados? ¿Por qué la gestión de obra se transforma en un factor generador de patologías? Es parte de un trabajo en el área de la prognosis en la construcción, cuyo alcance es predecir el éxito. En esa búsqueda, se obtuvieron funciones que modelan la capacidad de la empresa en reducir los riesgos que confrontará durante el proceso de ejecución, a las que se les ha denominado Experticia, la cual indica, cuán lejos o cerca se podría estar del éxito deseado en la ejecución de la obra. La gran mayoría de las empresas constructoras en Venezuela no se retroalimentan de los resultados obtenidos de sus obras, ni tienen un sistema de arreglo formal de data que permita realizar pronósticos confiables, razón por la cual, el desarrollo matemático de este trabajo se apoyó en conceptos del Razonamiento Aproximado y de la Lógica Difusa.

Resumen Los juegos de aprendizaje en línea representan una importante alternativa en la formación de nociones lógico-matemática en el contexto de la educación inicial. En correspondencia, el presente estudio tiene por objetivo determinar la relación de los juegos de aprendizaje en línea con la formación de las nociones lógico-matemática en los niños y niñas de tres a cuatro años de Educación. La metodología tiene un enfoque cuantitativo, el tipo de investigación es cuasi experimental y correlacional. La muestra estuvo conformada por 28 niños del Subnivel Inicial de la escuela Gabriela Mistral de una población de 56 niños y niñas de 3 a 4 años. El proceso de muestreo fue no probabilístico de tipo censal. La observación se aplicó como técnica de la investigación y como instrumento la ficha de observación. El análisis de datos se ejecutó con el software estadístico SPSS versión 26 en español, aplicando una prueba de normalidad con el test de Kolmogorov-Smirnov para la estadística inferencial y calculando el Rho de Spearman, para determinar la correlación de las variables juegos de aprendizaje en línea y formación de nociones lógico-matemática. Es importante destacar el aumento de la cantidad de niños que alcanzaron la cualidad óptima en la variable si se observa, la cual refleja el 93% de mejora posterior a la aplicación de los juegos en línea. Concluyéndose que existe una relación positiva y preponderante entre las variables de estudio, constituyendo un aporte significativo en términos de la Educación Inicial, lo cual destaca la relevancia de la utilización de los juegos de aprendizaje en línea para la formación de las nociones lógico-matemática.

Abstract Online learning games represent an important alternative in the formation of logical-mathematical notions in the context of initial education. Correspondingly, the present aims to determine the relationship of online learning games with the formation of logical-mathematical notions in children from three to four years of Education. The methodology has a quantitative approach, the type of research is quasi-experimental and correlational. The sample consisted of 28 children from the Initial Sublevel of the Gabriela Mistral school from a population of 56 boys and girls from 3 to 4 years old. The testing process was a non-probabilistic census type. Observation was applied as a research technique and the observation sheet as an instrument. The data analysis was carried out with the statistical software SPSS version 26 in Spanish, applying a normality test with the Kolmogorov-Smirnov test for inferential statistics and calculating Spearman's Rho, to determine the achievement of the learning game variables. line and formation of logical-mathematical notions. It is important to highlight the increase in the number of children who reached the optimal quality in the variable if observed, which reflects the 93% improvement after the application of online games. Concluding that there is a positive and preponderant relationship between the study variables, constituting a significant contribution in terms of Initial Education, which highlights the relevance of the use of online learning games for the formation of logical-mathematical notions.

Abstract The ISO/IEC 29110 standard is aimed explicitly at very small organizations as it adapts to the context and needs of this type of organization. After analyzing the structures of processes: activities, roles, tasks, and work products considered within the profile basic of the ISO/IEC 29110 standard, a lack of information was identified regarding the states of the work products that are necessary to carry out the tasks, which makes their proper implementation difficult. Therefore, this article presents proposals for tautologies of mathematical logic. As a result, proposals are presented to improve the establishment of states for work products that will aid in controlling the version of the work products and their associated documentation.

Resumen El estándar ISO/IEC 29110 está específicamente orientado a muy pequeñas organizaciones ya que se adapta al contexto y necesidades de este tipo de organizaciones. Tras haber analizado las estructuras de los procesos: actividades, roles, tareas, y productos de trabajo considerados dentro del estándar ISO/IEC 29110 en su perfil básico se identificó falta de información acerca de los estados de los productos de trabajo que son necesarios para desarrollar las tareas, lo que dificulta su correcta implementación. Para ayudar a resolver esta problemática este artículo presenta propuestas de tautologías de lógica matemática. Como resultado se presentan propuestas de mejora en el establecimiento de estados a productos de trabajo que ayudarán en el control de la versión de los productos de trabajo y su documentación asociada.

Resumo A substituição de equipamentos é uma relevante decisão de engenharia. O objetivo deste trabalho foi identificar e organizar as propostas de otimização matemática e as técnicas de busca de resultados que têm contribuído para a solução deste problema. Como resultado, classificamos os materiais bibliográficos identificados em sete tipos distintos de abordagens. O trabalho também fornece uma visão integradora do nível de complementaridade das categorias identificadas. A abordagem de visualização em rede representou cerca de 57% dos trabalhos selecionados e ainda está em uso. No entanto, desde 2000 outras abordagens, como lógica fuzzy, opções reais e aprendizado de máquina aumentaram 40% e se tornaram tendências atuais relevantes. engenharia problema resultado abordagens identificadas 57 uso entanto 200 fuzzy 40 relevantes 5 20 4 2

Abstract Equipment replacement is a definitive and relevant engineering decision. The aim of this work was to identify and organize the mathematical optimization proposals and solution search techniques that have contributed toward solving this problem. As a result, we classified the bibliographic materials we identified into seven distinct types of approaches. The work also provides an integrative overview of the level of complementarity of the categories we identified. The network visualization approach represented about 57% of the selected works and is still in use today. Nonetheless, since 2000 other approaches, such as fuzzy logic, real options, and machine learning have increased by 40% and become relevant current trends. decision problem result approaches 57 today Nonetheless 200 logic options 40 trends 5 20 4 2

ABSTRACT Objectives. To develop and test a framework to assess the potential of public health systems to maintain a resilient performance. Methods. Quantitative data from public databases and qualitative data from technical reports of Brazilian health authorities were used to develop the framework which was assessed and modified by experts. Fuzzy logic was used for the mathematical model to determine scores for four resilient abilities – monitoring, anticipation, learning, and response – and an aggregated coefficient of resilient potential in health care. The coefficient measures used data from before the coronavirus disease 2019 (COVID-19) pandemic. These were compared with measures of the actual performance of health systems in 10 cities in Brazil during the pandemic. Results. The coefficient of resilient potential in health care showed that the cities most affected by COVID-19 had lower potential for resilient performance before the pandemic. Some local health systems had adequate response capabilities, but other abilities were not well developed, which adversely affected the management of the spread of COVID-19. Conclusions. The coefficient of resilient potential in health care is useful to indicate important areas for resilient performance and the different types of resilience capacities that can be considered in different contexts and levels of public health systems. Regular assessment of the potential of health systems for resilient performance would help highlight opportunities for continuous improvement in health system functions during chronic stress situations, which could strengthen their ability to keep functioning in the face of sudden disturbances.

RESUMO Objetivos. Desenvolver e testar uma estrutura de avaliação do potencial dos sistemas de saúde pública de manter um desempenho resiliente. Métodos. Dados quantitativos de bancos de dados públicos e dados qualitativos de relatórios técnicos das autoridades sanitárias brasileiras foram utilizados para desenvolver a estrutura, que foi avaliada e modificada por especialistas. A lógica fuzzy foi utilizada na criação de um modelo matemático para determinar a pontuação em quatro capacidades de resiliência (monitoramento, antecipação, aprendizagem e resposta) e um coeficiente agregado do potencial de resiliência na atenção à saúde. O coeficiente foi calculado utilizando dados anteriores à pandemia da doença provocada pelo coronavírus de 2019 (COVID-19). Esses dados foram comparados com medidas do desempenho real dos sistemas de saúde em 10 cidades brasileiras durante a pandemia. Resultados. O coeficiente de potencial de resiliência na atenção à saúde revelou que as cidades mais afetadas pela COVID-19 tinham menor potencial de desempenho resiliente antes da pandemia. Alguns sistemas de saúde locais tinham capacidades de resposta adequadas, porém as outras capacidades não estavam bem desenvolvidas, o que prejudicou o gerenciamento da propagação da COVID-19. Conclusões. O coeficiente de potencial de resiliência na atenção à saúde é útil para indicar áreas importantes para um desempenho resiliente e os vários tipos de capacidade de resiliência que podem ser considerados em diferentes contextos e níveis dos sistemas de saúde pública. Uma avaliação periódica do potencial de desempenho resiliente dos sistemas de saúde ajudaria a assinalar oportunidades para melhorias contínuas das funções desses sistemas durante situações de estresse crônico, o que poderia aumentar sua capacidade de continuar funcionando diante de perturbações repentinas.

RESUMEN Objetivos. Elaborar y examinar un marco para evaluar el potencial de los sistemas de salud pública de mantener un desempeño resiliente. Métodos. Para elaborar el marco, se emplearon datos cuantitativos de bases de datos públicas y datos cualitativos de informes técnicos de las autoridades de salud brasileñas. A continuación, este marco fue evaluado y modificado por expertos. Se utilizó la lógica difusa en el modelo matemático empleado para determinar la puntuación de cuatro capacidades resilientes (seguimiento, anticipación, aprendizaje y respuesta) y un coeficiente agregado de potencial resiliente en la atención médica. Para las medidas del coeficiente se emplearon datos previos a la pandemia de la enfermedad por el coronavirus del 2019 (COVID-19), que se compararon con las medidas del desempeño real de los sistemas de salud en diez ciudades de Brasil durante la pandemia. Resultados. El coeficiente de potencial resiliente en la atención de salud indicó que las ciudades más afectadas por la COVID-19 presentaban un menor potencial de desempeño resiliente antes de la pandemia. En algunos sistemas de salud locales la capacidad de respuesta era adecuada pero otras capacidades no estaban suficientemente desarrolladas, lo que afectó de manera negativa el manejo de la propagación de la COVID-19. Conclusiones. El coeficiente de potencial resiliente en la atención de salud es útil para indicar aspectos importantes del desempeño resiliente y los diferentes tipos de capacidades de resiliencia que pueden considerarse en diferentes contextos y niveles de los sistemas de salud pública. La evaluación periódica del potencial de los sistemas de salud para tener un desempeño resiliente ayudaría a poner de relieve las oportunidades de mejora continua de las funciones del sistema de salud en situaciones de estrés crónico, lo que podría fortalecer su capacidad para seguir funcionando frente a perturbaciones repentinas.

Resumen El objetivo de este estudio es caracterizar el conocimiento de profesores de matemáticas en formación inicial en la Universidad Nacional de Costa Rica sobre aspectos lógico-sintácticos y matemáticos de la demostración, al evaluar argumentos matemáticos. La investigación se posiciona en el paradigma interpretativo y tiene un enfoque cualitativo. Consta de dos fases empíricas: en la primera, se aplicó un cuestionario sobre los aspectos lógico-sintácticos a 25 sujetos, durante los meses de setiembre y octubre de 2018 y, en la segunda, un cuestionario sobre los aspectos matemáticos a 19 sujetos, durante los meses de mayo y junio de 2019. Para el análisis de la información, se propusieron indicadores de conocimientos, entendidos como frases para determinar evidencias de conocimientos en las respuestas de los sujetos. Se apreció que la gran mayoría de los futuros profesores de matemáticas evidencian conocimiento para discriminar cuándo un argumento matemático corresponde o no a una demostración en virtud de los aspectos lógicos y sintácticos, y de elementos matemáticos asociados a proposiciones con la estructura de la implicación universal. En general, brindaron mayores evidencias de conocimiento sobre los aspectos lógico-sintácticos que sobre los aspectos matemáticos. Concretamente, evidenciaron que un caso particular o la prueba de la proposición recíproca no demuestra el resultado; asimismo, evidenciaron conocimiento sobre la demostración directa e indirecta de la implicación universal. En el caso de los aspectos matemáticos considerados como las hipótesis, los axiomas, las definiciones y los teoremas, se apreció que podrían tener diferentes niveles de dificultades para comprender una demostración.

Resumo Este estudo teve como objetivo caracterizar o conhecimento de professores de matemáticas em formação inicial na Universidade Nacional da Costa Rica sobre aspectos lógico-sintáticos e matemáticos da demonstração ao avaliar argumentos matemáticos. A pesquisa está posicionada no paradigma interpretativo e tem um enfoque qualitativo. Consiste em duas fases empíricas: na primeira foi aplicado um questionário sobre os aspectos lógico-sintáticos a 25 sujeitos, durante os meses de setembro e outubro de 2018 e, na segunda, um questionário sobre os aspectos matemáticos a 19 sujeitos, durante os meses de maio e junho de 2019. Para a análise das informações foram estabelecidos indicadores de conhecimentos, entendidos como frases para determinar evidências de conhecimentos nas respostas dos sujeitos. Constatou-se que a grande maioria dos futuros professores de matemáticas evidencia conhecimento para discriminar quando um argumento matemático corresponde ou não a uma demonstração em função dos aspectos lógicos e sintáticos, e de elementos matemáticos associados às proposições com a estrutura da implicação universal. Em geral, foram fornecidos maiores evidências de conhecimento sobre os aspectos lógico-sintáticos do que sobre os aspectos matemáticos. Concretamente, evidenciaram que um caso particular ou a prova da proposição recíproca não demonstra o resultado; da mesma forma, evidenciaram conhecimento sobre a demonstração direta e indireta da implicação universal. No caso dos aspectos matemáticos considerados como as hipóteses, os axiomas, as definições e os teoremas, percebe-se que poderiam ter diferentes níveis de dificuldades para compreender uma demonstração.

Abstract The objective of this study is to characterize the knowledge of mathematics teachers in initial training (MTITs) at the Universidad Nacional (Costa Rica) on the logic-syntactic and mathematical aspects involved in proving, when evaluating mathematical arguments. The research is positioned in the interpretive paradigm and has a qualitative approach. It consists of two empirical phases: in the first, a questionnaire regarding logic-syntactic aspects was applied to 25 subjects, during the months of September and October 2018 and; in the second phase, a second questionnaire covering mathematical aspects was applied to 19 subjects, during the months of May and June 2019. For the analysis of the information, knowledge indicators were proposed. Knowledge indicators are understood as phrases to determine evidence of knowledge in the responses of the subjects. It was appreciated that the vast majority of future mathematics teachers show knowledge to discriminate when a mathematical argument corresponds or not to a proof by virtue of the logic and syntactic aspects, and of mathematical elements associated with propositions with the structure of universal implication. In general, subjects displayed greater evidence of knowledge on the logic-syntactic aspects than on the mathematical aspects. Specifically, they evidenced that consideration of a particular case or the proof of the reciprocal proposition does not prove the result; likewise, subjects evidenced knowledge about the direct and indirect proof of the universal implication. In the case of the mathematical aspects considered as hypotheses, axioms, definitions and theorems, it was appreciated that subjects could have different levels of difficulties to understand a proof.

Resumen El cáncer es una enfermedad genética compleja con opciones terapéuticas limitadas, debido a la heterogeneidad tumoral y a la aparición de multirresistencia a los fármacos. La vía metabólica de los esfingolípidos (SL) se caracteriza por ser capaz de integrar diferentes tipos de señales de estrés celular y definir la supervivencia celular. Por lo tanto, sugerimos estudiar las perturbaciones en la vía de los esfingolípidos (SLP) causadas por fármacos quimioterapéuticos utilizando un enfoque de biología de sistemas y evaluar su funcionalidad como sensor de respuesta a fármacos. Usamos un sensor de esfingomielina-BODIPY (SMBOD) para estudiar el metabolismo de SL mediante citometría de flujo e imágenes de células vivas en diferentes modelos de cáncer. Para decodificar la complejidad de la ruta, implementamos modelos de mezcla gaussianos, modelos de ecuaciones diferenciales ordinarias, algoritmos de clasificación no supervisados y un modelo de lógica difusa para evaluar su utilidad como sensor de respuesta a la quimioterapia. Nuestros resultados muestran que los fármacos quimioterapéuticos perturban la SLP de diferentes formas y de una manera específica de la línea celular. Además, encontramos que pocas características de fluorescencia de SM-BOD predicen la quimiosensibilidad con alta precisión. Finalmente, encontramos que la composición relativa de especies de SL parece contribuir a la citotoxicidad resultante de muchos tratamientos. Este informe ofrece un marco conceptual y matemático para desarrollar modelos matemáticos personalizados para predecir y mejorar la terapia del cáncer.

Resumo O câncer é uma doença genética complexa com opções terapêuticas limitadas, devido à heterogeneidade tumoral e ao aparecimento de multirresistência aos fármacos. A via metabólica dos esfingolipídeos (SP) é caracterizada por ser capaz de integrar diferentes tipos de sinais de estresse celular e definir a sobrevivência celular. Portanto, sugerimos estudar as perturbações na rota dos esfingolipídeos (SP) causadas por fármacos quimioterápicos usando uma abordagem de biologia de sistemas e avaliar sua funcionalidade como sensor de resposta a fármacos. Usamos um sensor de esfingomielina-BODIPY (SM-BOD) para estudar o metabolismo do SP por citometria de fluxo e imagens de células vivas em diferentes modelos de câncer. Para decodificar a complexidade do caminho, implementamos modelos de mistura gaussiana, modelos de equações diferenciais ordinárias, algoritmos de classificação não supervisionados e um modelo de lógica difusa para avaliar sua utilidade como sensor de resposta à quimioterapia. Nossos resultados mostram que os fármacos quimioterápicos perturbam a rota dos SP de diferentes maneiras e de maneira específica da linhagem celular. Além disso, descobrimos que poucas características de fluorescência do SM-BOD predizem a quimiossensibilidade com alta precisão. Finalmente, descobrimos que a composição relativa de espécies de SP parece contribuir para a citotoxicidade resultante de muitos tratamentos. Este relatório oferece uma estrutura conceitual e matemática para o desenvolvimento de modelos matemáticos personalizados para prever e melhorar a terapia do câncer.

Abstract Cancer is a complex genetic disease with reduced treatment alternatives due to tumor heterogeneity and drug multiresistance emergence. The sphingolipid (SL) metabolic pathway integrates different responses of cellular stress signals and defines cell survival. Therefore, we suggest studying the perturbations on the sphingolipid pathway (SLP) caused by chemotherapeutic drugs using a systems biology approach to evaluate its functionality as a drug response sensor. We used a sphingomyelin-BODIPY (SM-BOD) sensor to study SL metabolism by flow cytometry and live cell imaging in different cancer models. To decode pathway complexity, we implemented Gussian mixture models, ordinary differential equations models, unsupervised classification algorithms and a fuzzy logic approach to assess its utility as a chemotherapy response sensor. Our results show that chemotherapeutic drugs perturb the SLP in different ways in a cell line-specific manner. In addition, we found that few SM-BOD fluorescence features predict chemosensitivity with high accuracy. Finally, we found that the relative species composition of SL appears to contribute to the resulting cytotoxicity of many treatments. This report offers a conceptual and mathematical framework for developing personalized mathematical models to predict and improve cancer therapy.