https://repositorio.ufu.br/handle/123456789/5155 Fri, 02 Oct 2026 16:05:14 GMT 2026-10-02T16:05:14Z https://repositorio.ufu.br:443/retrieve/3d344d47-9a9e-4588-b62f-969a9f400189/IME-removebg-preview.png https://repositorio.ufu.br/handle/123456789/5155 https://repositorio.ufu.br/handle/123456789/50513 Title: Comparação entre modelos de redes neurais U-Net e U-Net Fuzzy para mensurar regiões de imagens de ultrassonografia bovina Abstract: Beef cattle production is one of the fundamental pillars of the Brazilian economy. Carcass ultrasonography enables the in vivo measurement of the Longissimus Muscle Area (LMA) and the Backfat Thickness (BFT) and Rump Fat Thickness (RFT), traits associated with mus- cularity and early development in cattle. However, obtaining these measurements still relies predominantly on manual delineation and interpretation performed by specialists, making the process subjective, time-consuming, and susceptible to inter-observer variability. The objec- tive of this study is to develop and compare two models for the automatic segmentation and measurement of these indicators in ultrasound images from two cattle breeds. The first model is a multitask U-Net convolutional neural network, while the second, termed Fuzzy U-Net, in- tegrates a U-Net architecture with an Adaptive Neuro-Fuzzy Inference System (ANFIS). The images were obtained from live animals at the Advanced Center for Beef Cattle Research and Development of the Institute of Animal Science (SAA-SP), located in Sertãozinho, São Paulo, Brazil. A total of 135 images were collected, including 108 from the Nelore breed and 27 from the Caracu breed. The dataset was expanded through data augmentation techniques, such as the inclusion of images with increased and decreased brightness. The segmentation masks used as reference, known as ground truth masks, were manually created with the assistance of a specialist. These masks consisted of binary images used to isolate specific regions within the ultrasound images, serving as references for model training and evaluation. Model performance was assessed using metrics such as accuracy, Mean Absolute Error (MAE), and the Dice coeffi- cient, which quantifies the similarity between the segmentation generated by the model and the reference masks produced by the specialist. The results indicate that the Fuzzy U-Net model outperforms the Multitask U-Net model in measuring the LMA and BFT indicators across all evaluation metrics, achieving accuracies of 95.15% for LMA and 99.95% for BFT. In contrast, both the Multitask U-Net and Fuzzy U-Net models exhibited similar performance for the RFT indicator. Finally, a computational application was developed to automatically detect specific regions and measure the indicators of interest in bovine ultrasound images using both models. This tool has the potential to assist in cattle selection and herd management. Tue, 28 Jul 2026 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/50513 2026-07-28T00:00:00Z https://repositorio.ufu.br/handle/123456789/50476 Title: Educação financeira e empreendedorismo no ensino fundamental Abstract: This study presents the development, implementation, and evaluation of a didactic sequence designed to teach Financial Mathematics through entrepreneurship to sixth-grade students in Basic Education. The proposal emerged from the need to connect mathematical content to students’ everyday experiences, promoting more meaningful learning and helping to overcome the widespread perception that school mathematics is detached from real-life situations. Grounded in the principles of Critical Mathematics Education, contextualized teaching, and Financial Education, the didactic sequence consisted of eight lessons and two educational games covering topics such as entrepreneurship, cash flow, percentages, costs, expenses, fixed capital, working capital, pricing, investments, and planning. The research adopted a qualitative approach supported by quantitative data and was conducted with three sixth-grade classes at Escola Municipal Professora Carlota de Andrade Marquez, located in Uberlândia, Minas Gerais, Brazil, with a total of 83 students, including 29 students in sixth grade A, 27 in sixth grade B, and 27 in sixth grade C. To evaluate the effectiveness of the proposal, a diagnostic assessment was administered before the intervention and reapplied at its conclusion, allowing for a comparison of students’ performance. The results showed improvements in students’ understanding of the mathematical concepts addressed, increased classroom participation, and greater engagement in the proposed activities. In addition to the quantitative evidence obtained from the assessments, classroom observations indicated positive changes in students’ attitudes toward Mathematics, reflected in their increased interest, participation, and ability to relate mathematical concepts to everyday situations. It is concluded that the proposed didactic sequence contributed to making Financial Mathematics more meaningful to students and resulted in an educational product that can be adapted and used by Basic Education teachers interested in teaching Financial Mathematics through contextualized learning experiences. Fri, 04 Sep 2026 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/50476 2026-09-04T00:00:00Z https://repositorio.ufu.br/handle/123456789/50413 Title: O grafo funcional de uma família de polinômios sobre uma extensão quadrática de um corpo finito Abstract: Let $X$ be a finite set and $f: X \rightarrow X$ an arbitrary function. The iteration of $f$ over $X$ yields a dynamical system that can be represented as a graph. In fact, the functional graph of $f$ is the directed graph $\mathscr{G}(f)=(\mathcal{V}, \mathcal{E})$, where $\mathcal{V}=X$ and $\mathcal{E}=\{\langle x, f(x)\rangle \mid x \in X\}$. The obtained dynamical system has applications in many areas such as cryptography, communications and physics. Let $\mathbb{F}_q$ be a finite field with $q$ elements of odd characteristic. In this work, we will fully describe the dynamics of the function $f(X)=c\left(X^{q+1} \pm a X^2\right)$ over the finite field $\mathbb{F}_{q^2}$, for $a \in\{ \pm 1\}$ and $c \in \mathbb{F}_q^*$. We will also provide partial results for $a \in \mathbb{F}_q^* \backslash\{ \pm 1\}$. Mon, 30 Jun 2025 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/50413 2025-06-30T00:00:00Z https://repositorio.ufu.br/handle/123456789/50379 Title: Redes neurais artifciais: uma abordagem didática e aplicações em problemas de matemática aplicada Abstract: This work presents an introductory study on arti cial neural networks, with emphasis on the mathematical foundations that support their structure and learning process. The main objective was to understand how these models operate from a mathematical perspective, especially highlighting the role of linear combination and gradient in the construction and training of neural networks. To this end, concepts from linear algebra, di erential calculus, and analytic geometry were revisited, establishing an appropriate theoretical basis for the interpretation of the arti cial neuron, activation functions, the cost function, and the backpropagation algorithm. Initially, the modeling of the arti cial neuron was discussed based on the linear combination of inputs, weights, and bias, emphasizing its relationship with lines, hyperplanes, and decision boundaries. Next, some of the main activation functions used in neural networks were presented, highlighting the importance of nonlinearity for the representational capacity of the model. Subsequently, the cost function, gradient, and chain rule were addressed, showing how these elements are articulated in the backpropagation process and in the updating of parameters through the gradient descent method. As a way of concretely illustrating the concepts studied, two computational applications were developed in Python. The rst consisted of a linear tting problem involving temperatures in degrees Celsius and Fahrenheit, in which the network successfully learned the expected relationship between input and output. The second involved a nonlinear classi cation problem in the plane, in which the network had to distinguish points located inside and outside a circle. In this case, the importance of the hidden layer and nonlinear activation functions for learning a decision boundary more compatible with the geometry of the problem was observed. In both applications, the matrix formulation proved particularly useful for organizing the calculations and supporting the computational implementation. Thus, it is concluded that the study of neural networks may constitute a relevant opportunity to connect Mathematics with contemporary topics in computing, contributing to a more grounded understanding of these models and opening possibilities for future developments in more general architectures and new applications. Fri, 20 Mar 2026 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/50379 2026-03-20T00:00:00Z