Special functions in solving partial differential equations
Authorship
C.F.S.
Double bachelor degree in Mathematics and Physics
C.F.S.
Double bachelor degree in Mathematics and Physics
Defense date
07.03.2025 10:00
07.03.2025 10:00
Summary
The solution by separation of variables of, for example, the wave equation in a circular spatial domain leads us to Bessel functions as the fundamental functions for obtaining series solutions. This final-year project is devoted to studying Bessel functions, along with other special functions, and demonstrating their applications in solving partial differential equations (PDEs) in circular or cylindrical spatial domains.
The solution by separation of variables of, for example, the wave equation in a circular spatial domain leads us to Bessel functions as the fundamental functions for obtaining series solutions. This final-year project is devoted to studying Bessel functions, along with other special functions, and demonstrating their applications in solving partial differential equations (PDEs) in circular or cylindrical spatial domains.
Direction
LOPEZ POUSO, RODRIGO (Tutorships)
LOPEZ POUSO, RODRIGO (Tutorships)
Court
QUINTELA ESTEVEZ, PEREGRINA (Chairman)
TRINCHET SORIA, ROSA Mª (Secretary)
DIAZ RAMOS, JOSE CARLOS (Member)
QUINTELA ESTEVEZ, PEREGRINA (Chairman)
TRINCHET SORIA, ROSA Mª (Secretary)
DIAZ RAMOS, JOSE CARLOS (Member)
Statistical Modeling of Sports Data
Authorship
A.G.A.
Double bachelor degree in Mathematics and Physics
A.G.A.
Double bachelor degree in Mathematics and Physics
Defense date
07.02.2025 12:45
07.02.2025 12:45
Summary
Throughout this work, an application of the supervised learning model Random Forest to sports data is presented. Specifically, data associated with NBA teams from recent seasons. In the first chapter, a brief introduction to supervised learning algorithms is provided, with a particular emphasis on the bias-variance tradeoff, a fundamental problem in this type of model. Next, a systematic description of decision trees is given. These are among the simplest supervised learning models but serve as essential components in more complex models such as Random Forest. In Chapter 3, the Random Forest model is introduced as defined by Leo Breiman in 2001. Additionally, key results related to its relative error reduction and variance are presented. Finally, in the last chapter, the Random Forest model is applied to advanced statistics of NBA teams. Both a classification case and a regression case will be analyzed. In each scenario, the dependence of the models on their hyperparameters will be studied, and the results will be compared with other commonly used models for this type of problem.
Throughout this work, an application of the supervised learning model Random Forest to sports data is presented. Specifically, data associated with NBA teams from recent seasons. In the first chapter, a brief introduction to supervised learning algorithms is provided, with a particular emphasis on the bias-variance tradeoff, a fundamental problem in this type of model. Next, a systematic description of decision trees is given. These are among the simplest supervised learning models but serve as essential components in more complex models such as Random Forest. In Chapter 3, the Random Forest model is introduced as defined by Leo Breiman in 2001. Additionally, key results related to its relative error reduction and variance are presented. Finally, in the last chapter, the Random Forest model is applied to advanced statistics of NBA teams. Both a classification case and a regression case will be analyzed. In each scenario, the dependence of the models on their hyperparameters will be studied, and the results will be compared with other commonly used models for this type of problem.
Direction
RODRIGUEZ CASAL, ALBERTO (Tutorships)
RODRIGUEZ CASAL, ALBERTO (Tutorships)
Court
CRUJEIRAS CASAIS, ROSA MARÍA (Chairman)
PENA BRAGE, FRANCISCO JOSE (Secretary)
DOMINGUEZ VAZQUEZ, MIGUEL (Member)
CRUJEIRAS CASAIS, ROSA MARÍA (Chairman)
PENA BRAGE, FRANCISCO JOSE (Secretary)
DOMINGUEZ VAZQUEZ, MIGUEL (Member)
L functions of elliptic curves and modular forms
Authorship
J.G.C.
Double bachelor degree in Mathematics and Physics
J.G.C.
Double bachelor degree in Mathematics and Physics
Defense date
07.02.2025 17:45
07.02.2025 17:45
Summary
L functions are functions defined in the complex plane that allow us to obtain arithmetic information from analytic properties such as the location of their zeros, poles or the fulfillment of a certain functional equation. Moreover, they allow us to connect objects of different nature like elliptic curves, of geometric nature, and modular forms, of analytic nature, through the modularity theorem that establishes a correspondence between them through its associated L functions. In this work, we will focus on the study of L functions associated to generalizations of modular forms, the so-called automorphic forms, and Galois representations. In particular, we will begin by introducing Galois representations and their connections with elliptic curves and modular forms. Then, we will study automorphic forms and representations in the case of GL2 where Tate's thesis techniques to establish functional equations of its L functions will be introduced. In the next two chapters these concepts will be generalised to the general case of an arbitrary reductive algebraic group. All this will be studied placing it within the Langlands program that generalises the connection between elliptic curves and modular forms to a more general context.
L functions are functions defined in the complex plane that allow us to obtain arithmetic information from analytic properties such as the location of their zeros, poles or the fulfillment of a certain functional equation. Moreover, they allow us to connect objects of different nature like elliptic curves, of geometric nature, and modular forms, of analytic nature, through the modularity theorem that establishes a correspondence between them through its associated L functions. In this work, we will focus on the study of L functions associated to generalizations of modular forms, the so-called automorphic forms, and Galois representations. In particular, we will begin by introducing Galois representations and their connections with elliptic curves and modular forms. Then, we will study automorphic forms and representations in the case of GL2 where Tate's thesis techniques to establish functional equations of its L functions will be introduced. In the next two chapters these concepts will be generalised to the general case of an arbitrary reductive algebraic group. All this will be studied placing it within the Langlands program that generalises the connection between elliptic curves and modular forms to a more general context.
Direction
RIVERO SALGADO, OSCAR (Tutorships)
RIVERO SALGADO, OSCAR (Tutorships)
Court
GARCIA RODICIO, ANTONIO (Chairman)
CAO LABORA, DANIEL (Secretary)
Gómez Tato, Antonio M. (Member)
GARCIA RODICIO, ANTONIO (Chairman)
CAO LABORA, DANIEL (Secretary)
Gómez Tato, Antonio M. (Member)
Quarkonium and its relation to high-density and high-temperature matter
Authorship
C.P.L.C.
Bachelor of Physics
C.P.L.C.
Bachelor of Physics
Defense date
02.18.2025 11:00
02.18.2025 11:00
Summary
The objective of this work will be the study of matter at high density and temperature through mesons formed by heavy quarks and antiquarks, known as quarkonium. To reach this objective we will begin with an introduction of quantum chromodynamics (QCD) from its origins to the formation of the quark-gluon plasma in current experiments. Among the signals proposed for the study of plasma, particles formed by quark antiquark c occupy a very relevant place based on the modification of their properties depending on the density and temperature of the medium, as we will show in this work.
The objective of this work will be the study of matter at high density and temperature through mesons formed by heavy quarks and antiquarks, known as quarkonium. To reach this objective we will begin with an introduction of quantum chromodynamics (QCD) from its origins to the formation of the quark-gluon plasma in current experiments. Among the signals proposed for the study of plasma, particles formed by quark antiquark c occupy a very relevant place based on the modification of their properties depending on the density and temperature of the medium, as we will show in this work.
Direction
GONZALEZ FERREIRO, ELENA (Tutorships)
GONZALEZ FERREIRO, ELENA (Tutorships)
Court
ARES PENA, FRANCISCO JOSE (Chairman)
FERNANDEZ DOMINGUEZ, BEATRIZ (Secretary)
GONZALEZ ALEMANY, MANUEL MARIA (Member)
ARES PENA, FRANCISCO JOSE (Chairman)
FERNANDEZ DOMINGUEZ, BEATRIZ (Secretary)
GONZALEZ ALEMANY, MANUEL MARIA (Member)
Detection of fission fragments in an optical TPC
Authorship
D.P.C.
Bachelor of Physics
D.P.C.
Bachelor of Physics
Defense date
02.18.2025 11:00
02.18.2025 11:00
Summary
We present the concept of optical TPC and its usefulness for the identification of high-energy particles. We review the existing literature on nuclear fission, with a particular focus on spontaneous fission, and show the need to develop a simple method for the identification of fission fragments in nuclei that would contribute to improving fission theory. In particular, we design an experiment for the reconstruction of the trajectories of Cf-252 fission fragments, taking into account the fact that each type of fragment will theoretically have a di!erent path within the TPC. We use several estimates and simulations to set the conditions of the experiment and carry it out with two di!erent detection technologies. We then successfully visualize the results and argue that the trajectories we obtain belong to fission fragments and not to alpha particles. Finally, we try, without success, to draw any conclusions about which specific nuclei we are detecting.
We present the concept of optical TPC and its usefulness for the identification of high-energy particles. We review the existing literature on nuclear fission, with a particular focus on spontaneous fission, and show the need to develop a simple method for the identification of fission fragments in nuclei that would contribute to improving fission theory. In particular, we design an experiment for the reconstruction of the trajectories of Cf-252 fission fragments, taking into account the fact that each type of fragment will theoretically have a di!erent path within the TPC. We use several estimates and simulations to set the conditions of the experiment and carry it out with two di!erent detection technologies. We then successfully visualize the results and argue that the trajectories we obtain belong to fission fragments and not to alpha particles. Finally, we try, without success, to draw any conclusions about which specific nuclei we are detecting.
Direction
CAAMAÑO FRESCO, MANUEL (Tutorships)
CABO LANDEIRA, CRISTINA (Co-tutorships)
CAAMAÑO FRESCO, MANUEL (Tutorships)
CABO LANDEIRA, CRISTINA (Co-tutorships)
Court
ARES PENA, FRANCISCO JOSE (Chairman)
FERNANDEZ DOMINGUEZ, BEATRIZ (Secretary)
GONZALEZ ALEMANY, MANUEL MARIA (Member)
ARES PENA, FRANCISCO JOSE (Chairman)
FERNANDEZ DOMINGUEZ, BEATRIZ (Secretary)
GONZALEZ ALEMANY, MANUEL MARIA (Member)
Exploring Dark Matter in the Universe
Authorship
B.R.M.
Bachelor of Physics
B.R.M.
Bachelor of Physics
Defense date
02.18.2025 11:00
02.18.2025 11:00
Summary
This work will cover the basic concepts regarding dark matter. Its structure is divided into three well-defined parts. The first part will discuss the current evidence that positions dark matter as one of the great frontiers of modern physics. Different phenomena are analyzed, such as galaxy rotation curves, the velocity of galaxies within clusters, gravitational lensing effects, the Lyman-alpha forest, and the bullet cluster. The second part aims to understand its nature. Here, the possible types of dark matter are introduced, along with its potential origin, how it may have evolved, and its implications for the history of the universe. Additionally, neutrinos and WIMPs are presented as candidates for dark matter. Finally, the two main approaches for detecting dark matter are discussed: direct and indirect detection, along with some of the major experiments in this field.
This work will cover the basic concepts regarding dark matter. Its structure is divided into three well-defined parts. The first part will discuss the current evidence that positions dark matter as one of the great frontiers of modern physics. Different phenomena are analyzed, such as galaxy rotation curves, the velocity of galaxies within clusters, gravitational lensing effects, the Lyman-alpha forest, and the bullet cluster. The second part aims to understand its nature. Here, the possible types of dark matter are introduced, along with its potential origin, how it may have evolved, and its implications for the history of the universe. Additionally, neutrinos and WIMPs are presented as candidates for dark matter. Finally, the two main approaches for detecting dark matter are discussed: direct and indirect detection, along with some of the major experiments in this field.
Direction
ALVAREZ MUÑIZ, JAIME (Tutorships)
ALVAREZ MUÑIZ, JAIME (Tutorships)
Court
ARES PENA, FRANCISCO JOSE (Chairman)
FERNANDEZ DOMINGUEZ, BEATRIZ (Secretary)
GONZALEZ ALEMANY, MANUEL MARIA (Member)
ARES PENA, FRANCISCO JOSE (Chairman)
FERNANDEZ DOMINGUEZ, BEATRIZ (Secretary)
GONZALEZ ALEMANY, MANUEL MARIA (Member)
Synthesis and caracterization of hollow gold nanoshells
Authorship
S.R.P.
Bachelor of Physics
S.R.P.
Bachelor of Physics
Defense date
02.18.2025 11:00
02.18.2025 11:00
Summary
In recent years, gold nanoparticles have been subject to extensive research due to their phototermic properties, as well as their high biocompatibility and low toxicity. These characteristics make them useful both in medical and non medical applications. In this work we describe a detailed synthesis method of a specific nanoparticle morphology: nanoshells. Furthermore, we conduct a study on their phototermic properties, as well as a morphology study based on images obtained through TEM microscopy.
In recent years, gold nanoparticles have been subject to extensive research due to their phototermic properties, as well as their high biocompatibility and low toxicity. These characteristics make them useful both in medical and non medical applications. In this work we describe a detailed synthesis method of a specific nanoparticle morphology: nanoshells. Furthermore, we conduct a study on their phototermic properties, as well as a morphology study based on images obtained through TEM microscopy.
Direction
TOPETE CAMACHO, ANTONIO (Tutorships)
TOPETE CAMACHO, ANTONIO (Tutorships)
Court
ARES PENA, FRANCISCO JOSE (Chairman)
FERNANDEZ DOMINGUEZ, BEATRIZ (Secretary)
GONZALEZ ALEMANY, MANUEL MARIA (Member)
ARES PENA, FRANCISCO JOSE (Chairman)
FERNANDEZ DOMINGUEZ, BEATRIZ (Secretary)
GONZALEZ ALEMANY, MANUEL MARIA (Member)
Simulation of Artificial Intelligence Models with Electronic Devices
Authorship
M.S.Y.
Bachelor of Physics
M.S.Y.
Bachelor of Physics
Defense date
02.18.2025 11:00
02.18.2025 11:00
Summary
The objective of this bachelor’s thesis is to explore different simulation tools for artificial intelligence (AI) models using electronic devices, specifically studying phase-change memory (PCM). The motivation behind this work is the development of physical accelerators for AI models, aimed at reducing energy consumption and increasing computing speed. To achieve this, the implementation of computing-in-memory (CIM) architectures is analyzed, as they help reduce the burden associated with the classic Von Neumann architecture, which is no longer the most optimal for modern AI models. Both training and inference will be addressed using the AIHWKit tool, developed by IBM, which allows the simulation of neural networks while accounting for the non-idealities of emerging memory devices. Additionally, different model customization options will be explored to improve their accuracy and stability. The first part of this work focuses on introducing the limitations of current hardware and how analog computing can address these issues. Then, the physical properties of PCM will be explained, followed by an introduction to neural networks and a detailed discussion of AIHWKit. Finally, the performance of neural networks in different configurations will be compared.
The objective of this bachelor’s thesis is to explore different simulation tools for artificial intelligence (AI) models using electronic devices, specifically studying phase-change memory (PCM). The motivation behind this work is the development of physical accelerators for AI models, aimed at reducing energy consumption and increasing computing speed. To achieve this, the implementation of computing-in-memory (CIM) architectures is analyzed, as they help reduce the burden associated with the classic Von Neumann architecture, which is no longer the most optimal for modern AI models. Both training and inference will be addressed using the AIHWKit tool, developed by IBM, which allows the simulation of neural networks while accounting for the non-idealities of emerging memory devices. Additionally, different model customization options will be explored to improve their accuracy and stability. The first part of this work focuses on introducing the limitations of current hardware and how analog computing can address these issues. Then, the physical properties of PCM will be explained, followed by an introduction to neural networks and a detailed discussion of AIHWKit. Finally, the performance of neural networks in different configurations will be compared.
Direction
BREA SANCHEZ, VICTOR MANUEL (Tutorships)
BREA SANCHEZ, VICTOR MANUEL (Tutorships)
Court
ARES PENA, FRANCISCO JOSE (Chairman)
FERNANDEZ DOMINGUEZ, BEATRIZ (Secretary)
GONZALEZ ALEMANY, MANUEL MARIA (Member)
ARES PENA, FRANCISCO JOSE (Chairman)
FERNANDEZ DOMINGUEZ, BEATRIZ (Secretary)
GONZALEZ ALEMANY, MANUEL MARIA (Member)