Conference Agenda

This study proposes a socioeconomic vulnerability typology for Ecuadorian parishes based on official data from the 2022 Population and Housing Census. A total of 308 parishes are analyzed using 17 socioeconomic and basic services indicators, previously standardized. Hierarchical cluster analysis is applied using Ward’s method with Manhattan distance, evaluating multiple linkage criteria and distance metrics. The optimal number of clusters is determined through the agglomerative coefficient, silhouette width, and dendrogram inspection, resulting in a robust five-cluster solution. The validity of the classification is further assessed through a comparison with the K-means algorithm, achieving a 93% agreement between both clustering approaches. The resulting clusters reveal distinct territorial patterns in socioeconomic conditions and access to basic infrastructure, enabling the identification of priority areas for targeted public policy interventions. These findings demonstrate the usefulness of cluster analysis as a data-driven tool for territorial planning and decision-making, providing a reproducible and adaptable methodological framework applicable to other geographic and socioeconomic contexts.

This study aimed to determine the relationship between family problems and academic performance in mathematics among secondary school students from a private educational institution in Nuevo Chimbote (Peru), 2025. A quantitative approach was used, with a non-experimental, cross-sectional design and a descriptive–correlational scope. The sample comprised 65 ninth-grade students. Family problems were measured using a 12-item questionnaire (psychological, behavioral, and communication dimensions), and mathematics performance was obtained from official first-term grade records under a competency-based framework. Internal consistency was adequate (overall Cronbach’s α = 0.827; overall ordinal α = 0.84). Descriptively, mild family problems predominated (66.2%), and most students were at the “starting” achievement level in mathematics (53.8%). Bivariate normality tests rejected joint normality; therefore, Spearman’s rho was applied. No significant relationship was found between family problems and mathematics performance (ρ = −0.118; p = .350). It is concluded that, in this sample and time period, family problems were not statistically associated with mathematics achievement. Strengthening mathematics learning support and monitoring results across additional school periods are recommended.

We develop a mathematical framework connecting fuzzy
logic inference with deterministic nonlinear dynamics for
macroeconomic modeling. Starting from linguistic policy

variables encoded via continuous fuzzy membership func-
tions, we prove that the state space inherits a canonical

compact metrizable topology. Using Takagi-Sugeno fuzzy
inference, we construct a well-posed ordinary differential

equation and establish topological conjugacy with multidi-
mensional logistic dynamics. We characterize the stabil-
ity properties of fixed points and prove existence, unique-
ness, and continuous dependence of solutions. The frame-
work enables analytical treatment of qualitative economic

communications within dynamical systems theory, with
applications to inflation forecasting and policy design.

Abstract:
Feature extraction constitutes an essential stage in digital image processing, as it enables the transformation of high-dimensional visual information into compact and discriminative representations. This article presents a scientific study focused on the use of matrix calculus techniques for feature extraction in digital images, with particular emphasis on texture analysis and pattern recognition. Images are modeled as numerical matrices, which allows for the systematic application of linear algebra tools such as linear transformations, matrix decompositions, and eigenvalue-based statistical methods. Classical techniques are analyzed, including the Discrete Fourier Transform, the Discrete Cosine Transform, Singular Value Decomposition, and Principal Component Analysis, as well as statistical descriptors derived from co-occurrence matrices. The study highlights the relevance of these methods due to their mathematical interpretability, computational efficiency, and applicability in pattern recognition systems.

The research aimed to determine the relationship between the use of GeoGebra software and academic performance in linear
functions of students at the I.E. Evariste Galois, Ca˜ nete, in 2025. It was structured in eight parts. The first part presented the problem and objectives;
Part 2 addressed the theoretical framework with foundations on GeoGebra and academic performance. Part 3 formulated hypotheses
and variables, and Part 4 detailed the methodological design, sample, and instruments. Part 5 presented the descriptive and inferential results;
Part 6 discussed these results, highlighting a very strong positive correlation between the variables, with Spearman’s Rho coefficients between
0.900 and 1.000 and a p-value > 0.05. Finally, Part 7 presented the conclusions of the study, and Part 8 formulated recommendations aimed
at integrating technology into the teaching of linear functions.

The present research is aimed at studying the influence of the SageMath software on solving differential manifold problems among university students of Physical and Mathematical Sciences. The research design is pre-experimental. The sample consisted of 33 students of both sexes, selected through probabilistic sampling, to whom a pre-test and a post-test were applied. These instruments made it possible to collect information and measure the variable of differential manifold problem solving. The results were analyzed at both descriptive and inferential levels. The findings indicate that the SageMath software has a significant influence on solving differential manifold problems among university students of Physical and Mathematical Sciences, with a 95% level of statistical confidence. Evidence of this is the significant increase in the level of problem-solving performance (t(33) = 23.204, p < 0.05) between the pre-test scores (μ₁ = 8.6041) and the post-test scores (μ₂ = 13.9791). Likewise, the SageMath software significantly influences the planning, execution, and verification stages in solving differential manifold problems among university students of Physical and Mathematical Sciences.