Works presented

Summary
This work addresses the analysis of deterministic inventory models in the context of cooperative game theory, exploring their application to cost distribution problems. The fundamental concepts necessary for the study are presented, including an introduction to cooperative game theory, transferable utility (TU) games, and their main solutions, such as the core, the Shapley value, and the Owen value. Within the framework of inventory models, different configurations of the EOQ (Economic Order Quantity) model are analyzed, starting with the basic deterministic model and extending to cases involving multiple items and agents. Two key variants are examined: models with exemptible costs, which include constraints allowing certain coalitions to be excluded from cost contributions, and models without exemptible costs, where all coalitions fully participate. Throughout the work, an illustrative example is studied to highlight the implications of the models and their solutions in practice. Additionally, the impact of different cost distribution rules on the allocation among agents or items is analyzed, considering both fairness and system efficiency.

Direction
GARCIA JURADO, IGNACIO (Tutorships)

Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Vidal Puga, Juan José (Chairman)
Oviedo de la Fuente, Manuel (Secretary)
PATEIRO LOPEZ, BEATRIZ (Member)

Summary
This Master's Thesis (TFM) explores game theory, with a focus on strategic games and matrix games, and their relationship with linear programming. Game theory, a mathematical discipline that models strategic decision-making among agents, is analyzed here from both theoretical and practical perspectives, emphasizing competitive and cooperative interactions. The study focuses on matrix games, a fundamental representation of strategic games where strategies and payoffs are organized in a matrix format. Through linear programming, optimization problems associated with these games are addressed, such as finding optimal mixed strategies that maximize players' gains or minimize their losses. The thesis includes practical examples, highlighting the resolution of a matrix-form game using the simplex method, a powerful tool in linear programming. Among the cases analyzed, a real-world problem related to decision-making under uncertainty is examined, demonstrating how game theory and linear programming provide efficient solutions.

Direction
GARCIA JURADO, IGNACIO (Tutorships)

Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Bergantiños Cid, Gustavo (Chairman)
GINZO VILLAMAYOR, MARIA JOSE (Secretary)
Darriba López, Diego (Member)

Summary
Over the years, the choice between public or private management of water resources has been, and continues to be, a subject of debate in many countries, regardless of the particular legislation of each one. There are arguments on both sides of the discussion, and we can divide them into three fundamental categories to choose which administration has a better performance: tariff price, water quality and management efficiency. In this dissertation, we will summarise some of the contributions of the existing literature on this subject, focusing on the ones which based their empirical analysis on Spain, since it will be similar for ours. Moreover, we will focus on the evaluation of the efficiency between both managements, using Data Envelopment Analysis. Thus, after a brief description of this technique and its main models, we will apply it to our particular case: a comparison between wastewater treatment plants' eficiency according to whether they are managed by public or private companies, we will focus on Viaqua Gestión Integral De Aguas De Galicia, S.A as our private business. Once we have these results, we will be able to compare the performance of WWTPs on the basis of an efficiency measure, so we will see which ones have a worse performance. Finally, we will perform a benchmarking analysis and a clustering technique, so we will be able to clasificate WWTPs in grups with similar characteristics and to study which ones are benchmarks for the others.

Direction
GINZO VILLAMAYOR, MARIA JOSE (Tutorships)
SAAVEDRA NIEVES, ALEJANDRO (Co-tutorships)

Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Vidal Puga, Juan José (Chairman)
Oviedo de la Fuente, Manuel (Secretary)
PATEIRO LOPEZ, BEATRIZ (Member)

Summary
Managing large volumes of documents presents a significant challenge for organizations, as manually classifying and processing them is inefficient and results in a waste of resources. While traditional approaches may be necessary in certain contexts, they limit the ability to quickly access and effectively utilize information. In response to this situation, various technological solutions are evolving to facilitate the efficient organization and access to documents. The first part of this work presents the development of a text classification model based on Transformers, an advanced natural language processing (NLP) architecture. The model automates the document classification process, which not only improves organizational efficiency but also enables faster and more effective use of the documents afterward. This approach, leveraging pre-trained models like BERT, takes advantage of their adaptability to specific tasks, making it possible to efficiently classify large volumes of data and enhance quick, accurate access to relevant information. In doing so, it contributes to resource optimization and better information management within the organization. To validate the model's effectiveness, it was compared to traditional classifiers such as kNN, Naïve Bayes, and Random Forest, using the same training data. In all cases, the BERT-based model demonstrated superior generalization capabilities, showing remarkable performance when classifying documents on topics none of the classifiers had encountered during training, and outperforming traditional techniques on the analyzed datasets. This highlights its advantage in adapting to new contexts and document types without requiring significant reconfiguration or adjustments. BERT's architecture allows it to understand the context and deep meaning of the text, providing flexibility in handling a wide variety of tasks, even when faced with data that does not perfectly align with the training examples. This adaptive capability makes BERT an ideal solution for environments where data and needs are constantly evolving, allowing for greater efficiency and accuracy in both document classification and information retrieval. The second part of this work is focused on developing a model for information retrieval and generation. This model serves as an initial proposal aimed at facilitating access to information from various sources, adding significant value to the organization's operational processes and optimizing the use of available data for decision-making. The model has been evaluated using a dataset extracted from the Huggingface platform. The results show that the generated responses achieved a cosine similarity of over 60% compared to the expected responses when the provided context was relevant to the question, suggesting a high degree of content alignment. This validates the model's ability to generate coherent and relevant responses in scenarios where context is key.

Direction
LÓPEZ TABOADA, GUILLERMO (Tutorships)

Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Vidal Puga, Juan José (Chairman)
Oviedo de la Fuente, Manuel (Secretary)
PATEIRO LOPEZ, BEATRIZ (Member)

Summary
Manifold estimation allows a non-linear and non-parametric dimension reduction when working with data in an euclidean space that are actually supported on (or close to) a lower dimension manifold, providing a better understanding on their underlying structure. In the particular case when the manifold is a curve, the problem is known as filament estimation. The aim of this work is to propose a new filament estimator that achieves the optimal rate in minimax sense of convergence in Hausdorff distance, up to logarithmic factor, when the ambient space is the plane. First, an introduction on concepts, shape conditions and estimators used in set estimation is presented. Next, the so-called EDT (Euclidean Distance Transform) estimator, in a filament estimation model with additive noise, is revised. A perpendicular noise model, in a more general manifold estimation context, in which the minimax rate is known, is also presented. Lastly, the new estimator, called the EDT estimator with r-convex hull, is proposed, and its convergence rate is obtained. We also study a possible choice on the shape parameter r from the data without affecting the convergence rate. The proposed estimator is applied to a tree stem cross section estimation problem in forest inventory.

Direction
PATEIRO LOPEZ, BEATRIZ (Tutorships)
RODRIGUEZ CASAL, ALBERTO (Co-tutorships)

Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Bergantiños Cid, Gustavo (Chairman)
GINZO VILLAMAYOR, MARIA JOSE (Secretary)
Darriba López, Diego (Member)

Summary
This study evaluates the performance of various global optimization methods for parameter estimation in biochemical networks, a critical task in Computational Systems Biology. Deterministic and stochastic algorithms are compared using a set of standard optimization problems and four benchmark challenges specific to Systems Biology (the BioPreDyn benchmark set). The goal is to identify the most effective and reliable methods for addressing the non-convex optimization problems that frequently arise in this field. The study’s most significant finding is that the “enhanced Scatter Search” (eSS) method demonstrated the highest reliability in solving Systems Biology optimization problems among the tested metaheuristics. While no single algorithm excelled in all cases, eSS consistently achieved the greatest reduction in the objective function value and demonstrated superior robustness overall. Deterministic methods proved unsuitable for large-scale problems, highlighting their limitations in such contexts. This study highlights the importance of selecting appropriate optimization algorithms for parameter estimation in modeling biochemical networks. It further emphasizes the efficacy of certain metaheuristics in addressing the complex optimization problems that arise in Systems Biology.

Direction
López Pouso, Óscar (Tutorships)

Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
VAZQUEZ CENDON, MARIA ELENA (Chairman)
Carretero Cerrajero, Manuel (Secretary)
ARREGUI ALVAREZ, IÑIGO (Member)