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
In this work, we present a globally optimal solution to a challenging and large-scale parameter estimation problem in dynamic systems. The proposed approach builds upon the methodology developed in our previous work, reported in the article Parameter estimation in ODEs: assessing the potential of local and global solvers (De Dios et al., 2025, accepted in Optimization and Engineering), and is applied to the resolution of the 3SP problem formulated by Moles et al. (2003). According to the literature reviewed, this problem has not previously been addressed through a complete formulation combined with a certified globally optimal solution. Our methodology is based on formulating the problem as a nonlinear programming (NLP) model, solved using mathematical optimization techniques implemented in AMPL and executed with deterministic global solvers. This approach makes it possible to obtain solutions with a global optimality guarantee in a context where heuristic methods have traditionally been used. The results show that it is feasible to tackle large-scale problems using global optimization techniques based on AMPL and current deterministic solvers. This challenges previously assumed limitations in the literature and opens the door to solving even more complex problems

Direction
GONZALEZ DIAZ, JULIO (Tutorships)

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

Summary
Fixed point theory has proven to be a branch of mathematics with great potential for solving multiple problems in nonlinear analysis, such as proving the existence, uniqueness, or multiplicity of solutions to both integral and differential equations. Specifically, Krasnoselskii’s fixed point theorem in cones of expansion-compression has been widely used in numerous research works to obtain nontrivial solutions to such problems. With the aim of obtaining existence results for systems of differential and integral equations with all components being nontrivial, different versions of this result have been developed, adapted to operators defined on product spaces. In this work, we introduce the fixed point index, a powerful tool with which we will prove the main results. Additionally, we propose a new version of Krasnoselskii’s theorem, in which the conditions on the operator are expressed in terms of the norms of the spaces forming the product space under consideration. This original result has motivated minor improvements to existing versions, which we also describe. Finally, we apply the most novel among these results to establish conditions that guarantee the existence of solutions with positive components for various systems of differential and integral equations.

Direction
Rodríguez López, Jorge (Tutorships)

Court
LADRA GONZALEZ, MANUEL EULOGIO (Chairman)
FERNANDEZ TOJO, FERNANDO ADRIAN (Secretary)
GARCIA RIO, EDUARDO (Member)

Summary
The objective of this Master's Thesis is to investigate the applicability of the rough Bergomi (rBergomi) model to pricing futures options on commodities. The rBergomi model is a stochastic volatility model driven by a fractional Brownian motion. It has been extensively studied in the context of equity markets, however, the literature on its application in commodity markets is scarce. We first review the mathematical foundations of asset pricing and the rBergomi model, analysing its advantages and disadvantages compared to classical stochastic volatility models. We then propose a novel model for pricing futures options on commodities that implements the rBergomi dynamics. Finally, we present an efficient numerical scheme for simulating the model and calibrate it to real market data on WTI Crude Oil.

Direction
Vázquez Cendón, Carlos (Tutorships)

Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Terragni , Filippo (Secretary)
López Pouso, Óscar (Member)

Summary
This paper explores the valuation of the exotic derivative product Callable Reverse Floater, a combination of a reverse floater and a call option. It establishes a theoretical foundation in stochastic calculus and financial theory. It introduces the SABR model for volatility and analyzes various stochastic models (Hull-White, Black-Karasinski, Linear Gaussian, and CIR) for valuation, with an emphasis on their implementation and calibration to market conditions. Finally, the valuation results obtained using the different models are presented and compared, analyzing their behavior and specific features.

Direction
Vázquez Cendón, Carlos (Tutorships)

Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Sanchez Villaseñor, Eduardo Jesús (Chairman)
RODRIGUEZ GARCIA, JERONIMO (Secretary)
Ferreiro Ferreiro, Ana María (Member)

Summary
The present work addresses the study of the isoperimetric problem, tracing its development from its most classical roots to its formulation in more advanced geometric contexts. This problem seeks to understand which regions within a given ambient space minimize the area of their boundary under a fixed volume constraint. In its classical formulation in the Euclidean plane R2, it is rigorously shown that among all Jordan curves, the one that encloses the greatest area is the circle a fact formalized through the isoperimetric inequality in the plane. Moreover, the isoperimetric problem is generalized to higher dimensions, showing that in Rn, the sphere is the unique compact and connected hypersurface that minimizes surface area for a given volume. This will be demonstrated by proving Alexandrov’s theorem and exploring the variational properties of hypersurfaces with constant mean curvature. This work further extends the study of the isoperimetric problem to the setting of Riemannian manifolds, where solving the isoperimetric problem proves to be significantly more challenging. In this context, the Cheeger isoperimetric constant is introduced, defined as the infimum of the ratios between boundary area and volume of regular domains. This constant also possesses deep analytical properties, as it provides a lower bound for the first eigenvalue of the Laplace Beltrami operator with Dirichlet boundary conditions. Furthermore, the present work provides a detailed study of the explicit computation of the Cheeger isoperimetric constant in a certain family of geometrically significant spaces, such as solvable, simply connected Lie groups equipped with a left invariant metric, where the constant can be expressed in terms of the trace of the adjoint representation of the Lie algebra. Finally, a particularly interesting case is analyzed: symmetric spaces of non compact type. Each of these spaces turns out to be isometric to a solvable, simply connected Lie group endowed with a left invariant metric, allowing for the computation of the Cheeger constant using struc tural tools such as the root space decomposition and the Iwasawa decomposition. Additionally, the explicit calculation of the Cheeger constant is presented for the specific cases of real and complex hyperbolic spaces.

Direction
DOMINGUEZ VAZQUEZ, MIGUEL (Tutorships)
RODRIGUEZ VAZQUEZ, ALBERTO (Co-tutorships)

Court
LADRA GONZALEZ, MANUEL EULOGIO (Chairman)
FERNANDEZ TOJO, FERNANDO ADRIAN (Secretary)
GARCIA RIO, EDUARDO (Member)

Summary
This master’s thesis focuses on the simulation of an innovative industrial process driven by the company Ferroglobe. The process takes place in a vacuum-operated reactor, where an electric field is applied to generate heat. This heating allows the necessary conditions to be reached for the reactants inside to produce a high-value metallurgical product. The product is formed in the gas phase, transported along the reactor, and condensed at the top, where a condenser is located. The main objective of the project is to understand and optimize this process using mathematical modeling and numerical simulation techniques. All simulations were carried out using ANSYS Fluent software, which is taught in the Master’s in Industrial Mathematics. With the reactor simulation, the company will gain a better understanding of its operation, facilitating the evaluation of geometric modifications, identification of zones at risk of condensation, and scaling of the process, thus reducing the need for experimental testing.

Direction
GOMEZ PEDREIRA, MARIA DOLORES (Tutorships)

Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Terragni , Filippo (Secretary)
López Pouso, Óscar (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
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
The unemployment rate is a key variable for analyzing the evolution of the labor market in Spain, but it is published quarterly with a lag of one and a half months after the end of the quarter in question. Therefore, the Strategic Planning and PMO Department of ABANCA proposes the construction of a leading indicator of the unemployment rate, estimated monthly from the data on Social Security affiliation and registered unemployment, available at the beginning of each month. To this end, using temporal disaggregation models, the data on employed and unemployed people are monthlyzed using the monthly series of affiliations and registered unemployment. From these estimates, a monthly unemployment rate is calculated, which is then converted to quarterly frequency, allowing its comparison with the official data from the Labor Force Survey (LFS). In addition, a methodology for correcting seasonality and calendar effects is incorporated, which is essential for the analysis of time series, since the official series are not corrected for the impact of these factors. Once these effects have been canceled, a more detailed analysis and comparisons are feasible, which, without this adjustment, would be inadequate.

Direction
Vilar Fernández, José Antonio (Tutorships)

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

Summary
The main goal of this dissertation is to introduce model categories and the homotopy category of a model category. In order to do that, we study two examples. The first one is in the context of topological spaces. The second one is purely algebraic, we study chain complexes. To accomplish our goal, we need also to introduce Quillen's small object argument.

Direction
Gómez Tato, Antonio M. (Tutorships)
MOSQUERA LOIS, DAVID (Co-tutorships)

Court
OTERO ESPINAR, MARIA VICTORIA (Chairman)
DOMINGUEZ VAZQUEZ, MIGUEL (Secretary)
ALONSO TARRIO, LEOVIGILDO (Member)

Summary
In this dissertation, we develop algebraic and combinatorial methods within the framework of topological robotics. More specifically, we study homotopy invariants related to the motion planning problem, such as the Lusternik-Schnirelmann category and topological complexity, through a unifying notion: homotopic distance. The techniques we use combine classical tools from algebraic topology, such as homotopy groups and (co)homology, with ideas from combinatorial and computational topology via simplicial complexes. This allows us to define new original invariants that strictly improve existing bounds and results in the literature, as well as to design algorithms which, through the implementation of symbolic computation programs, calculate these invariants for any triangulable space.

Direction
Gómez Tato, Antonio M. (Tutorships)
MOSQUERA LOIS, DAVID (Co-tutorships)

Court
LADRA GONZALEZ, MANUEL EULOGIO (Chairman)
FERNANDEZ TOJO, FERNANDO ADRIAN (Secretary)
GARCIA RIO, EDUARDO (Member)

Summary
Accurate estimation of discards is essential for effective fish stock management, as discard data are part of the fishing mortality. Failure to do so could seriously compromise the long-term sustainability of fish stocks. However, the accuracy of discard estimates is affected by various factors, from sampling design of the sampling programs to the estimation process. Sampling experts have expressed concern about the paucity of data quality indicators in discard estimates, particularly when data from nonprobability survey methods need to be used as proxies for probability data. As a case study, we use data from observers on board the Spanish trawl fleet targeting demersal fish in ICES subarea 7. Sampling follows a multistage design, from vessel selection to the collection of the sample of discarded catch during each haul. To obtain the most accurate discard estimates, it is necessary to properly specify the successive methods for selecting sampling units, as well as to correctly parameterize the variance calculation at each sampling step. For this purpose, a two-stage sampling design was employed. In the first stage, fishing trips were selected using simple random sampling without replacement (SRSWOR), while in the second stage, fishing operations were selected using systematic sampling. Two complementary approaches were adopted to estimate the variance. First, the classical SRSWOR estimate was used, and for SYSS, the approximations obtained using the method of successive differences and the estimate based on the SRSWOR assumption were compared. Second, resampling techniques, particularly the bootstrap method, were implemented to assess uncertainty in a more flexible and robust manner.

Direction
Mosquera Rodríguez, Manuel Alfredo (Tutorships)

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

Summary
This work focuses on the simulation of nail penetration into a lithium-ion cell, a critical issue for the safety of lithium-ion batteries. Penetration of a metallic object can cause internal short circuits and local generation of excessive heat, leading to fire or explosion risks. To address this problem, a 2D axisymmetric model was developed that simulates the electrochemical and thermal interactions during nail penetration. Gmsh software was used for mesh generation, and FEniCSx together with Multiphenicsx was used to solve the differential equations describing the phenomena involved. In particular, special attention was paid to simulating different convection coefficients and cell states of charge to assess their effects.

Direction
Varas Mérida, Fernando (Tutorships)

Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Sanchez Villaseñor, Eduardo Jesús (Chairman)
RODRIGUEZ GARCIA, JERONIMO (Secretary)
Ferreiro Ferreiro, Ana María (Member)

Summary
This work aims to improve the efficiency of a warehouse sorter in the textile industry through the optimal assignment of tasks to its workers. Various garments are fed into the sorter from the warehouse, a process where two work roles are distinguished. Upon reaching a specific destination, the product falls into the box below it. Once they are full, the boxes are evacuated by humans, with two other possible work roles. The decision-making problem will consist of how many people will occupy each of the four work roles, in order to satisfy the demand, generated by the needs of a set of stores, in the shortest possible time. This text deeply describes the problem and formulates an integer linear programming model to solve it. After verifying that this model will not be able to solve realistic-sized instances, and observing that the total number of worker-role assignments is much lower than expected, a simulator is built that more faithfully recreates the sorter and evaluates the possible assignments, returning the best one as the optimal solution.

Direction
GONZALEZ DIAZ, JULIO (Tutorships)

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

Summary
This Master's Thesis addresses the study of the homotopy groups of spheres, one of the classic and fundamental topics in Algebraic Topology. First, some basic topological constructions are introduced, such as pointwise sum, suspensions (of spheres), and smash product, along with a brief introduction to category theory. Subsequently, we will develop the higher-order homotopy groups. We will analyze their definition through homotopy classes of maps of the type $Sn \longrightarrow X$, some of their main properties, and the notion of relative homotopy groups, which allows us to study a long exact sequence between these homotopy groups. Key tools such as the Excision Theorem and the Freudenthal Suspension Theorem are also presented, useful for calculating $\pi_n(Sn)$, among others. Finally, the concept of fibration is introduced, especially the Hopf fibration given by $S1 \longrightarrow S3 \overset{p}{\longrightarrow}S2$, which allows the study of the homotopy group $\pi_3(S2) = \mathbb{Z}$.

Direction
Gómez Tato, Antonio M. (Tutorships)

Court
OTERO ESPINAR, MARIA VICTORIA (Chairman)
DOMINGUEZ VAZQUEZ, MIGUEL (Secretary)
ALONSO TARRIO, LEOVIGILDO (Member)

Summary
Singular differential equations present some term tending to infinity at some point in their domain, which often occurs when dealing with problems in electromagnetism or mechanics. In this work, after presenting some useful techniques for the study of periodic boundary value problems, we will introduce the concept of singular differential equations through examples and we will comment the two most common classifications of singularities found in the literature. Afterwards, we will apply the mentioned techniques to prove the existence of positive periodic solutions for different families of second-order singular differential equations, distinguishing between those without damping, that is, those in which the first derivative does not appear, and those with damping.

Direction
Rodríguez López, Rosana (Tutorships)

Court
OTERO ESPINAR, MARIA VICTORIA (Chairman)
DOMINGUEZ VAZQUEZ, MIGUEL (Secretary)
ALONSO TARRIO, LEOVIGILDO (Member)

Summary
Marine Instruments is a leading company in the design and manufacture of electronic equipment for marine environments. Its reputation is based on the high reliability of its products, ensured by a rigorous production process that concludes with exhaustive quality control. For buoys, this control includes an oven test: printed circuit boards (PCBs) are subjected to 60 degrees while running a standardized test program, and their power consumption is continuously recorded. Currently, validation is performed manually through visual inspection of the consumption curves to identify possible anomalies. This work proposes automating that classification phase by extracting and modeling characteristic fault features and designing a detection algorithm that combines data analytics and artificial intelligence techniques. The aim is to reduce inspection times, improve process traceability, and further increase the reliability of the final product.

Direction
VAZQUEZ CENDON, MARIA ELENA (Tutorships)

Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Terragni , Filippo (Secretary)
López Pouso, Óscar (Member)

Summary
This work aims to construct and study the p-adic L-function attached to a modular form. It begins by introducing the concepts of modular forms and modular symbols and their basic properties. Next, the construction of the L p-adic function is made, for which the L functions are introduced and some of the related properties and concepts are studied, proving the algebraicity of some of its concrete values and using Stevens' control theorem (whose proof is addressed later) to finally construct the p-adic L-function associated to a modular form and prove its interpolation property, under certain hypotheses. The last part focuses on studying what happens when the weight of the modular form varies and analyzing the critical and Eisenstein cases.

Direction
RIVERO SALGADO, OSCAR (Tutorships)

Court
LADRA GONZALEZ, MANUEL EULOGIO (Chairman)
FERNANDEZ TOJO, FERNANDO ADRIAN (Secretary)
GARCIA RIO, EDUARDO (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)

Summary
This work aims to provide an introduction to Iwasawa theory, beginning with the study of the structure of finitely generated modules over Zp[[T]], which can be understood as a generalization of the classification theorem for modules over a principal ideal domain. This, in turn, allows us to establish Iwasawa’s control theorem for the class number of cyclotomic fields. In the second part, we present more recent results that provide a better understanding of the algebraic structure of Zp-extensions, formulating Iwasawa’s main conjecture, which relates this algebraic structure to a purely analytic object: the p-adic zeta function. Finally, we explain the general strategy used in the proof of this result, and we conclude by illustrating some current research trends in the area.

Direction
RIVERO SALGADO, OSCAR (Tutorships)

Court
OTERO ESPINAR, MARIA VICTORIA (Chairman)
DOMINGUEZ VAZQUEZ, MIGUEL (Secretary)
ALONSO TARRIO, LEOVIGILDO (Member)

Summary
Efficient management of sales periods has become increasingly important in the commercial strategy of the textile sector, where balancing stock liquidity and profitability is essential. In this context, INDITEX has reinforced its leadership not only through its agile market response, but also through its control of inventory management and pricing during sales campaigns. Traditionally scheduled after periods of high demand, sales help free up space for new collections, but their optimal planning poses significant challenges. This creates the need to anticipate the impact that different discount levels may have on sales, especially in an environment where margins and customer perception are critical variables. This work addresses this challenge through an in-depth analysis of historical data and the development of predictive models capable of estimating sales performance under various pricing scenarios. The main goal is to provide INDITEX with a tool to support informed decision-making regarding discounts, thereby optimizing commercial performance during the sales period and strengthening its strategic position in the global fashion market.

Direction
AMEIJEIRAS ALONSO, JOSE (Tutorships)
GINZO VILLAMAYOR, MARIA JOSE (Co-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
In this work, we delve into the theoretical foundations of the well-known power series method and the lower and upper solutions method, subsequently combining them with Automatic Differentiation in order to to develop two programs in Python. The first program enables the construction of the Taylor polynomial of the desired degree for the solution of an initial value problem associated with an ordinary differential equation, under the assumption that the given function is analytic - a case in which the effectiveness of the power series method is ensured. The second program addresses a boundary value problem of Dirichlet type associated with an ODE with a continuous given function. This program does not aim to approximate the solution, but rather to prove its existence by constructing both a lower and an upper solution for the problem.

Direction
LOPEZ POUSO, RODRIGO (Tutorships)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Co-tutorships)

Court
LADRA GONZALEZ, MANUEL EULOGIO (Chairman)
FERNANDEZ TOJO, FERNANDO ADRIAN (Secretary)
GARCIA RIO, EDUARDO (Member)