Non-local differential equations with piecewise constant dependence
Authorship
P.C.F.
Master in Mathematics
P.C.F.
Master in Mathematics
Defense date
07.12.2024 12:00
07.12.2024 12:00
Summary
In this work, we study non-local differential equations with piecewise constant dependence, with a particular focus on those with reflection in their argument. The approach consists of obtaining the explicit expression of the solution to the linear problem through the construction of the corresponding Green’s function, as well as seeking a new formula to describe the set of parameters involved in the analyzed equations for which the Green’s function has a constant sign. We also prove the existence of solutions for nonlinear problems using various results from fixed-point theory. All of the above is specifically applied to the first-order linear problem with periodic conditions, demonstrating several existence results for the associated nonlinear problem and precisely delimiting the region where the Green’s function H(m,M) has a constant sign when T is in (0, 1]. The studied equations have potential applications in fields such as biomedicine or quantum mechanics. Moreover, this work represents a significant advancement as it is the first time that equations with involution and piecewise constant arguments have been jointly studied.
In this work, we study non-local differential equations with piecewise constant dependence, with a particular focus on those with reflection in their argument. The approach consists of obtaining the explicit expression of the solution to the linear problem through the construction of the corresponding Green’s function, as well as seeking a new formula to describe the set of parameters involved in the analyzed equations for which the Green’s function has a constant sign. We also prove the existence of solutions for nonlinear problems using various results from fixed-point theory. All of the above is specifically applied to the first-order linear problem with periodic conditions, demonstrating several existence results for the associated nonlinear problem and precisely delimiting the region where the Green’s function H(m,M) has a constant sign when T is in (0, 1]. The studied equations have potential applications in fields such as biomedicine or quantum mechanics. Moreover, this work represents a significant advancement as it is the first time that equations with involution and piecewise constant arguments have been jointly studied.
Direction
CABADA FERNANDEZ, ALBERTO (Tutorships)
CABADA FERNANDEZ, ALBERTO (Tutorships)
Court
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
Grothendieck duality
Authorship
G.S.M.F.
Master in Mathematics
G.S.M.F.
Master in Mathematics
Defense date
07.12.2024 13:00
07.12.2024 13:00
Summary
We study the foundations of Grothendieck duality theory for quasi-coherent sheaves on a scheme through the formal approach pioneered by Neeman. Through the use of the Brown representability theorem we define a functor fx as a right adjoint to Rf_* and we investigate its basic properties and relations with other functors defined on the derived category of complexes of sheaves with quasi-coherent cohomology. We prove a base change theorem for fx and use it to define a functor f!. We study conditions on f under which fx can be calculated.
We study the foundations of Grothendieck duality theory for quasi-coherent sheaves on a scheme through the formal approach pioneered by Neeman. Through the use of the Brown representability theorem we define a functor fx as a right adjoint to Rf_* and we investigate its basic properties and relations with other functors defined on the derived category of complexes of sheaves with quasi-coherent cohomology. We prove a base change theorem for fx and use it to define a functor f!. We study conditions on f under which fx can be calculated.
Direction
ALONSO TARRIO, LEOVIGILDO (Tutorships)
ALONSO TARRIO, LEOVIGILDO (Tutorships)
Court
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
Modular forms and Hida theory
Authorship
L.O.P.
Master in Mathematics
L.O.P.
Master in Mathematics
Defense date
07.12.2024 16:00
07.12.2024 16:00
Summary
This work aims to define and study modular forms in different contexts, as well as introducing Hida theory and presenting various applications of algebraic geometry in the study of modular forms. The work begins by defining classical modular forms in the context of the general linear group, which is the simplest setting in which they can be studied, and by defining Hecke operators on them. Then, these concepts are generalized to understand modular forms in the so-called congruence subgroups, and after this, various necessary tools for advancing to the more complex stages of the work are introduced, such as $p$-adic numbers or group cohomology. In the next stage, Serre's construction of $p$-adic modular forms is carried out, and the results presented up to that point are generalized, in addition to discussing new intrinsic results of this construction. In the final chapters of the document, Hida theory is introduced. This consists of packaging modular forms into families which satisfy good algebraic properties. We further discuss a geometric approach, which leads to Katz's construction of modular forms.
This work aims to define and study modular forms in different contexts, as well as introducing Hida theory and presenting various applications of algebraic geometry in the study of modular forms. The work begins by defining classical modular forms in the context of the general linear group, which is the simplest setting in which they can be studied, and by defining Hecke operators on them. Then, these concepts are generalized to understand modular forms in the so-called congruence subgroups, and after this, various necessary tools for advancing to the more complex stages of the work are introduced, such as $p$-adic numbers or group cohomology. In the next stage, Serre's construction of $p$-adic modular forms is carried out, and the results presented up to that point are generalized, in addition to discussing new intrinsic results of this construction. In the final chapters of the document, Hida theory is introduced. This consists of packaging modular forms into families which satisfy good algebraic properties. We further discuss a geometric approach, which leads to Katz's construction of modular forms.
Direction
RIVERO SALGADO, OSCAR (Tutorships)
RIVERO SALGADO, OSCAR (Tutorships)
Court
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
Curvature adapted hypersurfaces in symmetric spaces
Authorship
M.J.R.S.D.T.
Master in Mathematics
M.J.R.S.D.T.
Master in Mathematics
Defense date
07.12.2024 17:00
07.12.2024 17:00
Summary
The main aim of this work is to address the study of curvature adapted homogeneous hypersurfaces in symmetric spaces of non-compact type. In this line, we start by introducing some preliminary results concerning Riemannian Geometry in order to bring in symmetric spaces and analyze some of their fundamental properties. After that, we focus on symmetric spaces of non-compact type and we show that they can be described as solvable Lie groups endowed with a left-invariant metric. Finally, we present cohomogeneity one actions on symmetric spaces of non-compact type, paying special attention to those producing a Riemannian foliation. We finally proof that, in a wide class of symmetric spaces of non-compact type, homogeneous foliations of cohomogeneity one are curvature adapted.
The main aim of this work is to address the study of curvature adapted homogeneous hypersurfaces in symmetric spaces of non-compact type. In this line, we start by introducing some preliminary results concerning Riemannian Geometry in order to bring in symmetric spaces and analyze some of their fundamental properties. After that, we focus on symmetric spaces of non-compact type and we show that they can be described as solvable Lie groups endowed with a left-invariant metric. Finally, we present cohomogeneity one actions on symmetric spaces of non-compact type, paying special attention to those producing a Riemannian foliation. We finally proof that, in a wide class of symmetric spaces of non-compact type, homogeneous foliations of cohomogeneity one are curvature adapted.
Direction
SANMARTIN LOPEZ, VICTOR (Tutorships)
SANMARTIN LOPEZ, VICTOR (Tutorships)
Court
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
Imperfection modules and separable extensions
Authorship
A.S.R.
Master in Mathematics
A.S.R.
Master in Mathematics
Defense date
09.11.2024 16:00
09.11.2024 16:00
Summary
In this work the general properties of the differentials and imperfection modules of a commutative algebra are introduced and given, and a detailed study of these modules is made in the case where the considered algebra is a field extension, particulary in the case of separable extensions, which come to be characterized by the cancellation of the imperfection module. In Chapter 1 the general properties of differentials and imperfection modules are provided. In Chapter 2 the separable fiel extensions are studied, first in the algebraic case (completing what was given about them in the course 'Ecuaciones algebraicas' of the Degree program), and then in the general case, proving MacLane's separability criterion. In Chapter 3 the concept of p-base is introduced and the differentials and imperfection modules of field extensions are studied. Among other results, the Cartier equality is proved, which relates, in the finite case, the dimension of these modules with the transcendence degree of the extension. The Chapter ends by proving that arbitrary separable extensions are characterized by the cancellation of the imperfection module, which has the immediate consequence of characterizing separable extensions through extensions of derivations.
In this work the general properties of the differentials and imperfection modules of a commutative algebra are introduced and given, and a detailed study of these modules is made in the case where the considered algebra is a field extension, particulary in the case of separable extensions, which come to be characterized by the cancellation of the imperfection module. In Chapter 1 the general properties of differentials and imperfection modules are provided. In Chapter 2 the separable fiel extensions are studied, first in the algebraic case (completing what was given about them in the course 'Ecuaciones algebraicas' of the Degree program), and then in the general case, proving MacLane's separability criterion. In Chapter 3 the concept of p-base is introduced and the differentials and imperfection modules of field extensions are studied. Among other results, the Cartier equality is proved, which relates, in the finite case, the dimension of these modules with the transcendence degree of the extension. The Chapter ends by proving that arbitrary separable extensions are characterized by the cancellation of the imperfection module, which has the immediate consequence of characterizing separable extensions through extensions of derivations.
Direction
GARCIA RODICIO, ANTONIO (Tutorships)
GARCIA RODICIO, ANTONIO (Tutorships)
Court
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
Symmetric spaces
Authorship
D.T.B.
Master in Mathematics
D.T.B.
Master in Mathematics
Defense date
09.11.2024 16:45
09.11.2024 16:45
Summary
Riemannian symmetric spaces are Riemann manifolds where every element is an isolated fixed point of an involutive isometry, which makes them a particular case of homogenous space. They are of special interest because, as its name says, they have many symmetries, so its comprehension is easier. Indeed, they can be expressed as a Lie group quotient, so its study is closely related to Lie group and Lie algebra theory. That allows us to solve geometric problems using linear algebra tools. In this work, we set the basis for the study of Riemannian symmetric spaces. In particular, we show that there are three types of symmetric spaces: Euclidean, compact and non-compact. Every symmetric space can be decomposed as a product of spaces of one of these types. We also explain the duality between compact and non-compact type. Finally, we define the rank, an important geometric invariant, and we compute the rank of some symmetric spaces.
Riemannian symmetric spaces are Riemann manifolds where every element is an isolated fixed point of an involutive isometry, which makes them a particular case of homogenous space. They are of special interest because, as its name says, they have many symmetries, so its comprehension is easier. Indeed, they can be expressed as a Lie group quotient, so its study is closely related to Lie group and Lie algebra theory. That allows us to solve geometric problems using linear algebra tools. In this work, we set the basis for the study of Riemannian symmetric spaces. In particular, we show that there are three types of symmetric spaces: Euclidean, compact and non-compact. Every symmetric space can be decomposed as a product of spaces of one of these types. We also explain the duality between compact and non-compact type. Finally, we define the rank, an important geometric invariant, and we compute the rank of some symmetric spaces.
Direction
DIAZ RAMOS, JOSE CARLOS (Tutorships)
DIAZ RAMOS, JOSE CARLOS (Tutorships)
Court
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
ALCALDE CUESTA, FERNANDO (Chairman)
FERNANDEZ FERNANDEZ, FRANCISCO JAVIER (Secretary)
Jeremías López, Ana (Member)
Analysis and reconstruction of the membranous labyrinth in humans and its implications in Benign Paroxysmal Positional Vertigo
Authorship
J.A.S.
Master in Industrial Mathematics
J.A.S.
Master in Industrial Mathematics
Defense date
02.07.2024 10:30
02.07.2024 10:30
Summary
Benign Paroxysmal Positional Vertigo (VPPB) is a condition that disrupts balance and occurs when fragments of calcium carbonate become free within a patient's vestibular system. The treatment involves repositioning these fragments through a series of maneuvers on the patient's head. This work supports a national health project within the framework of personalized medicine, aiming to adapt these maneuvers to the specific anatomy of each patient. To achieve this, a method has been developed for the computational acquisition of the centerlines of the bony and membranous labyrinths of the vestibular system, an indispensable step for generating precise spatial models that facilitate the personalization for each case. The developed process, its implementation, and the statistical and numerical validation of the results obtained on real geometries will be addressed.
Benign Paroxysmal Positional Vertigo (VPPB) is a condition that disrupts balance and occurs when fragments of calcium carbonate become free within a patient's vestibular system. The treatment involves repositioning these fragments through a series of maneuvers on the patient's head. This work supports a national health project within the framework of personalized medicine, aiming to adapt these maneuvers to the specific anatomy of each patient. To achieve this, a method has been developed for the computational acquisition of the centerlines of the bony and membranous labyrinths of the vestibular system, an indispensable step for generating precise spatial models that facilitate the personalization for each case. The developed process, its implementation, and the statistical and numerical validation of the results obtained on real geometries will be addressed.
Direction
VAZQUEZ CENDON, MARIA ELENA (Tutorships)
VAZQUEZ CENDON, MARIA ELENA (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Busto Ulloa, Saray (Secretary)
Cendán Verdes, José Jesús (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Busto Ulloa, Saray (Secretary)
Cendán Verdes, José Jesús (Member)
Adaptation of Lagrangian model for simulating Early Life Stages (ELS) of anchovy
Authorship
S.G.P.
Master in Industrial Mathematics
S.G.P.
Master in Industrial Mathematics
Defense date
02.07.2024 11:00
02.07.2024 11:00
Summary
In recent years, the use of Early Life Stages (ELS) models of fish species for simulating eggs and larvae as Lagrangian particles forced by an oceanographic model coupled to an ecological one has become widespread in oceanography. At the Spanish Institute of Oceanography (IEO), a code has been developed to simulate the early life stages of the Iberian sardine (Sardina pilchardus), including both the physical processes to which they are subjected and the biological ones that characterize this pelagic species and giving it an individual-based approach (IBM). From the IEO, it is proposed to adapt the IBM model available for the Iberian sardine to another species of commercial interest in Galicia: the European anchovy (Engraulis encrasicolus). This species is a small pelagic with similarities with the sardine in its ELS, so the same type of model is used. A revision of the models will be presented, in order to be able to propose and implement in the software OpenDrift a model to simulate the ELS of the anchovy. Once this code is obtained, different analyses of the ELS model components and sensitivity studies will be shown to analyze which parts of the model are determinant for the description of the two species with this IBM model approach.
In recent years, the use of Early Life Stages (ELS) models of fish species for simulating eggs and larvae as Lagrangian particles forced by an oceanographic model coupled to an ecological one has become widespread in oceanography. At the Spanish Institute of Oceanography (IEO), a code has been developed to simulate the early life stages of the Iberian sardine (Sardina pilchardus), including both the physical processes to which they are subjected and the biological ones that characterize this pelagic species and giving it an individual-based approach (IBM). From the IEO, it is proposed to adapt the IBM model available for the Iberian sardine to another species of commercial interest in Galicia: the European anchovy (Engraulis encrasicolus). This species is a small pelagic with similarities with the sardine in its ELS, so the same type of model is used. A revision of the models will be presented, in order to be able to propose and implement in the software OpenDrift a model to simulate the ELS of the anchovy. Once this code is obtained, different analyses of the ELS model components and sensitivity studies will be shown to analyze which parts of the model are determinant for the description of the two species with this IBM model approach.
Direction
Rodríguez Seijo, José Manuel (Tutorships)
Rodríguez Seijo, José Manuel (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Busto Ulloa, Saray (Secretary)
Cendán Verdes, José Jesús (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Busto Ulloa, Saray (Secretary)
Cendán Verdes, José Jesús (Member)
Mathematical Modeling of Microbial Community Dynamics
Authorship
A.P.V.
Master in Industrial Mathematics
A.P.V.
Master in Industrial Mathematics
Defense date
02.07.2024 12:00
02.07.2024 12:00
Summary
This study considers the dynamic modeling of microbial communities. A microbial community is a complex, interdependent network of microorganisms living together and interacting with each other. Our objective is to illustrate how mathematical modeling enables a systematic and quantitative study of these biological systems, facilitating a deeper understanding, and enabling the creation of “in silico” experiments that emulate the real behavior of the community. To achieve this goal, we begin by introducing a selection of different microbial models of increasing complexity (Chapter 2) using deterministic nonlinear ordinary differential equations (ODEs). These models often depend on a number of unknown unmeasurable parameters that may be identified or estimated from experimental data. Next, we illustrate the importance of examining identifiability properties. In particular, structural identifiability is often disregarded due to its complexity, but as we will show, it is one of the main steps in the model calibration process. Chapter 3 analyzes the structural identifiability of the selected models, discussing the available methodologies and software. We proceed to solve the model calibration problem and its practical identifiability in Chapter 4. Finally, we highlight the main pitfalls and challenges encountered, emphasising under and over-fitting scenarios and suggesting ways to surmount these difficulties.
This study considers the dynamic modeling of microbial communities. A microbial community is a complex, interdependent network of microorganisms living together and interacting with each other. Our objective is to illustrate how mathematical modeling enables a systematic and quantitative study of these biological systems, facilitating a deeper understanding, and enabling the creation of “in silico” experiments that emulate the real behavior of the community. To achieve this goal, we begin by introducing a selection of different microbial models of increasing complexity (Chapter 2) using deterministic nonlinear ordinary differential equations (ODEs). These models often depend on a number of unknown unmeasurable parameters that may be identified or estimated from experimental data. Next, we illustrate the importance of examining identifiability properties. In particular, structural identifiability is often disregarded due to its complexity, but as we will show, it is one of the main steps in the model calibration process. Chapter 3 analyzes the structural identifiability of the selected models, discussing the available methodologies and software. We proceed to solve the model calibration problem and its practical identifiability in Chapter 4. Finally, we highlight the main pitfalls and challenges encountered, emphasising under and over-fitting scenarios and suggesting ways to surmount these difficulties.
Direction
Balsa Canto, Eva María (Tutorships)
Balsa Canto, Eva María (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Busto Ulloa, Saray (Secretary)
Cendán Verdes, José Jesús (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Busto Ulloa, Saray (Secretary)
Cendán Verdes, José Jesús (Member)
Numerical implementation of strain gauges for dynamic reconstructions of ITER components
Authorship
A.S.F.
Master in Industrial Mathematics
A.S.F.
Master in Industrial Mathematics
Defense date
02.07.2024 12:30
02.07.2024 12:30
Summary
ESTEYCO is developing the Tokamak reactor Monitoring System (TSM) for ITER. The TSM will be responsible for providing an interpretation of the mechanical behavior of the reactor based on the thousands of signals acquired by the sensors (temperature, deformation, acceleration, etc.) that will be integrated into the reactor. This interpretation will be made using reconstruction algorithms generally based on the numerical simulation of the different systems. In the specific case of strain gauges, the numerical simulation of this measurement technique in a precise and automated manner is not evident. For example, numerical simulation can provide point deformation values, whereas the gauges essentially obtain relative displacements between two points along the adhesion surface of it. In addition, due to the very high number of sensors to implement, and the need to make modifications in them throughout the different stages of development of the TSM, its numerical implementation is necessary in an automated way for any type of finite element used in these models (beams and solids, mainly). The objective of this Master's thesis will be the development of the methodology of numerical simulation of the measurement of a real deformation sensor. In addition, once the theoretical work has been done, the experimental validation of the tool developed will be carried out using a prototype of an ITER component for which ESTEYCO plans to implement an experimental campaign in the coming months.
ESTEYCO is developing the Tokamak reactor Monitoring System (TSM) for ITER. The TSM will be responsible for providing an interpretation of the mechanical behavior of the reactor based on the thousands of signals acquired by the sensors (temperature, deformation, acceleration, etc.) that will be integrated into the reactor. This interpretation will be made using reconstruction algorithms generally based on the numerical simulation of the different systems. In the specific case of strain gauges, the numerical simulation of this measurement technique in a precise and automated manner is not evident. For example, numerical simulation can provide point deformation values, whereas the gauges essentially obtain relative displacements between two points along the adhesion surface of it. In addition, due to the very high number of sensors to implement, and the need to make modifications in them throughout the different stages of development of the TSM, its numerical implementation is necessary in an automated way for any type of finite element used in these models (beams and solids, mainly). The objective of this Master's thesis will be the development of the methodology of numerical simulation of the measurement of a real deformation sensor. In addition, once the theoretical work has been done, the experimental validation of the tool developed will be carried out using a prototype of an ITER component for which ESTEYCO plans to implement an experimental campaign in the coming months.
Direction
BARRAL RODIÑO, PATRICIA (Tutorships)
BARRAL RODIÑO, PATRICIA (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Busto Ulloa, Saray (Secretary)
Cendán Verdes, José Jesús (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Varas Mérida, Fernando (Chairman)
Busto Ulloa, Saray (Secretary)
Cendán Verdes, José Jesús (Member)
Artificial Intelligence algorithms for automatic segmentation of the coronary tree.
Authorship
S.D.P.M.
Master in Industrial Mathematics
S.D.P.M.
Master in Industrial Mathematics
Defense date
02.08.2024 12:00
02.08.2024 12:00
Summary
The following work introduces a new procedure based on Artificial Intelligence to segment coronary trees in patients with possible coronary artery diseases. The aim of the project is to replace the current surgical gold standard, called FFR catheterization, with a non-invasive test. From a CT image we will reconstruct the 3D geometry of the patient’s coronary arteries using computer vision techniques, a procedure that until now could only be done manually. We include in the work a section on fluid simulation and the capabilities that this allows to obtain a multitude of parameters of medical interest.The implemented model is compared with the previous methodology, showing notable improvements. In addition, to ensure the quality of the segmentation, we also compare the results of the fluid simulations of the segmentations made by an expert against those made by the AI.
The following work introduces a new procedure based on Artificial Intelligence to segment coronary trees in patients with possible coronary artery diseases. The aim of the project is to replace the current surgical gold standard, called FFR catheterization, with a non-invasive test. From a CT image we will reconstruct the 3D geometry of the patient’s coronary arteries using computer vision techniques, a procedure that until now could only be done manually. We include in the work a section on fluid simulation and the capabilities that this allows to obtain a multitude of parameters of medical interest.The implemented model is compared with the previous methodology, showing notable improvements. In addition, to ensure the quality of the segmentation, we also compare the results of the fluid simulations of the segmentations made by an expert against those made by the AI.
Direction
Busto Ulloa, Saray (Tutorships)
Busto Ulloa, Saray (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Perales Perales, José Manuel (Chairman)
ALVAREZ DIOS, JOSE ANTONIO (Secretary)
Carretero Cerrajero, Manuel (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Perales Perales, José Manuel (Chairman)
ALVAREZ DIOS, JOSE ANTONIO (Secretary)
Carretero Cerrajero, Manuel (Member)
Thermomechanical modelling of the behaviour of a blast furnace through
Authorship
D.P.O.
Master in Industrial Mathematics
D.P.O.
Master in Industrial Mathematics
Defense date
09.24.2024 10:00
09.24.2024 10:00
Summary
The blast furnace trough is a fundamental part of the steelmaking process, since it is responsible for separating the pig iron (liquid-state metal) from the rest of the byproducts of the process. This Master's Thesis has been proposed by the Departamento de Matemática Aplicada of the Universidade de Santiago de Compostela, in the framework of one of its research lines in the mathematical modelling of steel production. Our aim is to perform the numerical simulation of the thermomechanical problem associated with this process, as well as to study the possibility of implementing reduced plate and beam models for thinner structures.
The blast furnace trough is a fundamental part of the steelmaking process, since it is responsible for separating the pig iron (liquid-state metal) from the rest of the byproducts of the process. This Master's Thesis has been proposed by the Departamento de Matemática Aplicada of the Universidade de Santiago de Compostela, in the framework of one of its research lines in the mathematical modelling of steel production. Our aim is to perform the numerical simulation of the thermomechanical problem associated with this process, as well as to study the possibility of implementing reduced plate and beam models for thinner structures.
Direction
BARRAL RODIÑO, PATRICIA (Tutorships)
BARRAL RODIÑO, PATRICIA (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Velazquez Lopez, Angel (Chairman)
Terragni , Filippo (Secretary)
ARREGUI ALVAREZ, IÑIGO (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Velazquez Lopez, Angel (Chairman)
Terragni , Filippo (Secretary)
ARREGUI ALVAREZ, IÑIGO (Member)
Design and validation of a virtual wind tunnel for prediction of drone operations in urban environments
Authorship
M.G.M.
Master in Industrial Mathematics
M.G.M.
Master in Industrial Mathematics
Defense date
07.11.2024 11:30
07.11.2024 11:30
Summary
The popularity of drones has increased notably in recent decades. Beyond their military origin, the applications of this type of aircraft are multiplying, extending their presence to very diverse fields such as agriculture, infrastructure inspection or rescue operations. Within this range of possibilities, one situation that may be occurring with increasing frequency is the performance of drone operations in urban environments. Given the nume- rous sources of complexity that may come into play, the design and validation of a virtual wind tunnel is proposed with the aim of predicting the feasibility of drone operations in these situations.
The popularity of drones has increased notably in recent decades. Beyond their military origin, the applications of this type of aircraft are multiplying, extending their presence to very diverse fields such as agriculture, infrastructure inspection or rescue operations. Within this range of possibilities, one situation that may be occurring with increasing frequency is the performance of drone operations in urban environments. Given the nume- rous sources of complexity that may come into play, the design and validation of a virtual wind tunnel is proposed with the aim of predicting the feasibility of drone operations in these situations.
Direction
Ferrín González, José Luis (Tutorships)
Ferrín González, José Luis (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Rodríguez Seijo, José Manuel (Chairman)
SALGADO RODRIGUEZ, MARIA DEL PILAR (Secretary)
Torrente Orihuela, Ester Aurora (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Rodríguez Seijo, José Manuel (Chairman)
SALGADO RODRIGUEZ, MARIA DEL PILAR (Secretary)
Torrente Orihuela, Ester Aurora (Member)
Direct Aero/Acoustic Modeling with Non-Homogeneous Atmospheric Conditions
Authorship
J.M.P.L.
Master in Industrial Mathematics
J.M.P.L.
Master in Industrial Mathematics
Defense date
07.11.2024 11:00
07.11.2024 11:00
Summary
Outdoor acoustic propagation in a non-homogeneous medium is analyzed, where temperature and wind are considered to be dependent on height. The main objective is to obtain the acoustic trajectory in a computationally optimal way. The range of distance is high, so classic numerical methods such as FEM are not suitable. Numerical resolution methods based on the Eikonal equation, Fast Marching and Fast Sweeping, are analyzed, obtaining good results for test cases. An algorithm is implemented that allows dividing the trajectory into straight segments, so that it is optimized based on the position of the intersection between segments, also with computationally acceptable results. Two methods are proposed for the resolution of outdoor acoustic propagation, spatial and temporal gradient method, obtaining good results in both. After comparing the advantages and disadvantages of each implementation, the temporal gradient method is valued as the most suitable method aligned with the objectives of the project. A critical sensitivity analysis with respect to different physical parameters that affect the system is carried out. From this analysis it is deduced that the wind is the factor that leads to more variations in the emission angles and hence introducing large errors if they are not modelled correctly.
Outdoor acoustic propagation in a non-homogeneous medium is analyzed, where temperature and wind are considered to be dependent on height. The main objective is to obtain the acoustic trajectory in a computationally optimal way. The range of distance is high, so classic numerical methods such as FEM are not suitable. Numerical resolution methods based on the Eikonal equation, Fast Marching and Fast Sweeping, are analyzed, obtaining good results for test cases. An algorithm is implemented that allows dividing the trajectory into straight segments, so that it is optimized based on the position of the intersection between segments, also with computationally acceptable results. Two methods are proposed for the resolution of outdoor acoustic propagation, spatial and temporal gradient method, obtaining good results in both. After comparing the advantages and disadvantages of each implementation, the temporal gradient method is valued as the most suitable method aligned with the objectives of the project. A critical sensitivity analysis with respect to different physical parameters that affect the system is carried out. From this analysis it is deduced that the wind is the factor that leads to more variations in the emission angles and hence introducing large errors if they are not modelled correctly.
Direction
PRIETO ANEIROS, ANDRES (Tutorships)
PRIETO ANEIROS, ANDRES (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Rodríguez Seijo, José Manuel (Chairman)
SALGADO RODRIGUEZ, MARIA DEL PILAR (Secretary)
Torrente Orihuela, Ester Aurora (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Rodríguez Seijo, José Manuel (Chairman)
SALGADO RODRIGUEZ, MARIA DEL PILAR (Secretary)
Torrente Orihuela, Ester Aurora (Member)
Comparison between Weighted Monte Carlo and Generalized Weighted Monte Carlo methods
Authorship
P.P.P.
Master in Industrial Mathematics
P.P.P.
Master in Industrial Mathematics
Defense date
07.16.2024 10:30
07.16.2024 10:30
Summary
In this work we performed a study comparing the pricing methodologies of the Weighted Monte Carlo (WMC) and Generalized Weighted Monte Carlo (GWMC) methods on call and put options of 3 different underlying assets. First, we introduce the methodologies explaining their differences. Next, we show how to calibrate and apply them. Finally, we compare their performance by means of two tests, from which we conclude that the GWMC has a better chance of reproducing the option prices due to the improved distribution of prior weights that holds more information than the uniform one used in WMC.
In this work we performed a study comparing the pricing methodologies of the Weighted Monte Carlo (WMC) and Generalized Weighted Monte Carlo (GWMC) methods on call and put options of 3 different underlying assets. First, we introduce the methodologies explaining their differences. Next, we show how to calibrate and apply them. Finally, we compare their performance by means of two tests, from which we conclude that the GWMC has a better chance of reproducing the option prices due to the improved distribution of prior weights that holds more information than the uniform one used in WMC.
Direction
Vázquez Cendón, Carlos (Tutorships)
Vázquez Cendón, Carlos (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Perales Perales, José Manuel (Chairman)
Ferrín González, José Luis (Secretary)
Durany Castrillo, José (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Perales Perales, José Manuel (Chairman)
Ferrín González, José Luis (Secretary)
Durany Castrillo, José (Member)
Treatment of contacts between materials for the simulation of dental implants
Authorship
J.O.L.
Master in Industrial Mathematics
J.O.L.
Master in Industrial Mathematics
Defense date
07.17.2024 10:00
07.17.2024 10:00
Summary
In this master's thesis, the main objetive is the numerical simulation of the biomechanics of the lower jaw and analyze the behavior of dental implants, thus achieving a comparison of the type of contacts and models that characterize the implants materials that go deeper than the different research found. To do this, it is used the software Ansys. Before performing the simulations, it is necessary to define the anatomy of the lower jaw and the geometry treatment to be used to understand the decisions made during the simulation. Once this is defined, a brief description of the algorithms and models used during the simulation is made, continuing with the analysis of the results obtained. The simulations carried out can be divided into two parts: the simulation of the dental implants to study the behavior of the type of contact used and the simulation of the periodontal ligament (PDL) to study his behavior using different models to characterize the material. In the first part of the study, the tensions reached in an implant are analyzed varying the type of contact. Once a conclusion about the best type of contact has been reached, three more implants are tested in different positions. The second part focuses on the treatment of the PDL, using three differents types of models to characterizes it: isotropic linear elasticity, hyperelasticity and viscoelasticity. In addition, the linear model is deepened by varying its modulus of elasticity to check its behavior. Throughout the project, the different secondary investigations that would be interesting to carry out to improve the results obtained are commented on.
In this master's thesis, the main objetive is the numerical simulation of the biomechanics of the lower jaw and analyze the behavior of dental implants, thus achieving a comparison of the type of contacts and models that characterize the implants materials that go deeper than the different research found. To do this, it is used the software Ansys. Before performing the simulations, it is necessary to define the anatomy of the lower jaw and the geometry treatment to be used to understand the decisions made during the simulation. Once this is defined, a brief description of the algorithms and models used during the simulation is made, continuing with the analysis of the results obtained. The simulations carried out can be divided into two parts: the simulation of the dental implants to study the behavior of the type of contact used and the simulation of the periodontal ligament (PDL) to study his behavior using different models to characterize the material. In the first part of the study, the tensions reached in an implant are analyzed varying the type of contact. Once a conclusion about the best type of contact has been reached, three more implants are tested in different positions. The second part focuses on the treatment of the PDL, using three differents types of models to characterizes it: isotropic linear elasticity, hyperelasticity and viscoelasticity. In addition, the linear model is deepened by varying its modulus of elasticity to check its behavior. Throughout the project, the different secondary investigations that would be interesting to carry out to improve the results obtained are commented on.
Direction
Fernández García, José Ramón (Tutorships)
Fernández García, José Ramón (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Fernández Manin, Generosa (Chairman)
Varas Mérida, Fernando (Secretary)
BARRAL RODIÑO, PATRICIA (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Fernández Manin, Generosa (Chairman)
Varas Mérida, Fernando (Secretary)
BARRAL RODIÑO, PATRICIA (Member)
Analysis and characterization of pressure equipment using finite elements.
Authorship
J.R.L.A.
Master in Industrial Mathematics
J.R.L.A.
Master in Industrial Mathematics
Defense date
07.17.2024 10:30
07.17.2024 10:30
Summary
The objective of this project is to conduct a structural study of a pressure water filter model in collaboration with the company Espina, which specializes in the integral water cycle and civil engineering. For this study, a CAD model of each of the main components of the filter was created using SolidWorks software, based on the plans provided by the company. The generated components were assembled using SolidWorks tools. Subsequently, a detailed study of the boundary conditions and loads to be applied was carried out, according to the working conditions of the device. Additionally, different mathematical models of linear elastodynamics in 3D, 2D (plates), and 1D (bars and beams) were applied to each of the filter components. Finally, a finite element analysis was performed in COMSOL Multiphysics on the CAD model, with the purpose of analyzing the distribution of stresses generated by the working conditions of the filter and the displacements affecting each component.
The objective of this project is to conduct a structural study of a pressure water filter model in collaboration with the company Espina, which specializes in the integral water cycle and civil engineering. For this study, a CAD model of each of the main components of the filter was created using SolidWorks software, based on the plans provided by the company. The generated components were assembled using SolidWorks tools. Subsequently, a detailed study of the boundary conditions and loads to be applied was carried out, according to the working conditions of the device. Additionally, different mathematical models of linear elastodynamics in 3D, 2D (plates), and 1D (bars and beams) were applied to each of the filter components. Finally, a finite element analysis was performed in COMSOL Multiphysics on the CAD model, with the purpose of analyzing the distribution of stresses generated by the working conditions of the filter and the displacements affecting each component.
Direction
QUINTELA ESTEVEZ, PEREGRINA (Tutorships)
QUINTELA ESTEVEZ, PEREGRINA (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Fernández Manin, Generosa (Chairman)
Varas Mérida, Fernando (Secretary)
BARRAL RODIÑO, PATRICIA (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Fernández Manin, Generosa (Chairman)
Varas Mérida, Fernando (Secretary)
BARRAL RODIÑO, PATRICIA (Member)
Modeling of radon dispersion in indoor spaces
Authorship
V.S.G.
Master in Industrial Mathematics
V.S.G.
Master in Industrial Mathematics
Defense date
07.17.2024 12:00
07.17.2024 12:00
Summary
Air pollution due to radon gas is a pressing issue because of its direct link to lung cancer. In areas such as Galicia, the concentration of radon gas in homes and workplaces can far exceed the legal level established by current legislation, putting the health of inhabitants and workers at risk. For this reason, it is particularly important to develop a system to reduce the concentration in inhabited areas quickly and efficiently. To this end, Computational Fluid Mechanics (CFD) will be used to develop a numerical model to predict the radon concentration in rooms as a function of the opening time of doors, windows or other sources of natural ventilation. From previously collected experimental data, a radon gas generation rate will be obtained which, together with the study of the prevailing climatic conditions depending on the time of year, will allow modelling the variation of the concentration as a function of time.
Air pollution due to radon gas is a pressing issue because of its direct link to lung cancer. In areas such as Galicia, the concentration of radon gas in homes and workplaces can far exceed the legal level established by current legislation, putting the health of inhabitants and workers at risk. For this reason, it is particularly important to develop a system to reduce the concentration in inhabited areas quickly and efficiently. To this end, Computational Fluid Mechanics (CFD) will be used to develop a numerical model to predict the radon concentration in rooms as a function of the opening time of doors, windows or other sources of natural ventilation. From previously collected experimental data, a radon gas generation rate will be obtained which, together with the study of the prevailing climatic conditions depending on the time of year, will allow modelling the variation of the concentration as a function of time.
Direction
VAZQUEZ CENDON, MARIA ELENA (Tutorships)
VAZQUEZ CENDON, MARIA ELENA (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Fernández Manin, Generosa (Chairman)
Varas Mérida, Fernando (Secretary)
BARRAL RODIÑO, PATRICIA (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Fernández Manin, Generosa (Chairman)
Varas Mérida, Fernando (Secretary)
BARRAL RODIÑO, PATRICIA (Member)
Simulating NMR spectra with a quantum computer
Authorship
A.R.C.
Master in Industrial Mathematics
A.R.C.
Master in Industrial Mathematics
Defense date
07.17.2024 12:30
07.17.2024 12:30
Summary
The process of simulating NMR spectra is limited by the computational cost of diagonalizing a Hamiltonian matrix associated with the spin system of the molecule whose spectrum is to be simulated. This matrix grows exponentially with the size of the spin system, and thus is not possible to simulate in an efficient and exact way the spectra of large molecules. In this work we explore the possibilities of quantum computing to perform exacts simulations, in the current context of quantum hardware becoming a reality and a growing interest on quantum technologies.
The process of simulating NMR spectra is limited by the computational cost of diagonalizing a Hamiltonian matrix associated with the spin system of the molecule whose spectrum is to be simulated. This matrix grows exponentially with the size of the spin system, and thus is not possible to simulate in an efficient and exact way the spectra of large molecules. In this work we explore the possibilities of quantum computing to perform exacts simulations, in the current context of quantum hardware becoming a reality and a growing interest on quantum technologies.
Direction
PENA BRAGE, FRANCISCO JOSE (Tutorships)
PENA BRAGE, FRANCISCO JOSE (Tutorships)
Court
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Fernández Manin, Generosa (Chairman)
Varas Mérida, Fernando (Secretary)
BARRAL RODIÑO, PATRICIA (Member)
VAZQUEZ CENDON, MARIA ELENA (Coordinator)
Fernández Manin, Generosa (Chairman)
Varas Mérida, Fernando (Secretary)
BARRAL RODIÑO, PATRICIA (Member)
Study of the duration of hospitalization for breast cancer patients in Spain
Authorship
S.B.H.
Master in Statistical Techniques
S.B.H.
Master in Statistical Techniques
Defense date
09.09.2024 12:15
09.09.2024 12:15
Summary
Breast cancer is one of the most common oncologic diseases and represents a major concern for public health globally. According to Sociedad Española de Oncología Médica (SEOM), it is the most diagnosed type of cancer in women, with an estimated incidence of 132 cases per 100000 inhabitants. This underlines the need for effective hospital management, and the duration of hospitalization is a crucial indicator of the efficiency of a health system. The aim of this project is to analyze the duration of hospitalization for patients with breast cancer in public hospitals in Spain between 2016 and 2021. Different types of regression models with count response are adjusted, taking into account the hierarchical structure of the data, as it is grouped by provinces, and also considering non-parametric effects of some covariates. With that been said, the aim of this project is to study and predict the duration of hospitalization using a generalized, hierarchical and additive regression model. In Chapter 1, an exploratory analysis of the entire database is carried out. In Chapter 2, the theoretical basis of the regression models mentioned above is presented, which will be applied to the available data in Chapter 3, with the support of the statistical software R. Finally, in Chapter 4, the main conclusions of this project are presented.
Breast cancer is one of the most common oncologic diseases and represents a major concern for public health globally. According to Sociedad Española de Oncología Médica (SEOM), it is the most diagnosed type of cancer in women, with an estimated incidence of 132 cases per 100000 inhabitants. This underlines the need for effective hospital management, and the duration of hospitalization is a crucial indicator of the efficiency of a health system. The aim of this project is to analyze the duration of hospitalization for patients with breast cancer in public hospitals in Spain between 2016 and 2021. Different types of regression models with count response are adjusted, taking into account the hierarchical structure of the data, as it is grouped by provinces, and also considering non-parametric effects of some covariates. With that been said, the aim of this project is to study and predict the duration of hospitalization using a generalized, hierarchical and additive regression model. In Chapter 1, an exploratory analysis of the entire database is carried out. In Chapter 2, the theoretical basis of the regression models mentioned above is presented, which will be applied to the available data in Chapter 3, with the support of the statistical software R. Finally, in Chapter 4, the main conclusions of this project are presented.
Direction
CONDE AMBOAGE, MERCEDES (Tutorships)
Reyes Santías, Francisco (Co-tutorships)
CONDE AMBOAGE, MERCEDES (Tutorships)
Reyes Santías, Francisco (Co-tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
Robust route optimization with cross-docking
Authorship
T.C.C.
Master in Statistical Techniques
T.C.C.
Master in Statistical Techniques
Defense date
09.09.2024 13:00
09.09.2024 13:00
Summary
In this work, a linear programming problem has been modeled based on a real case study from the company Inditex. It is a vehicle routing problem (VRP) with the existence of certain nodes called {\it cross-docks} where goods could be exchanged between trucks. A matheuristic has also been designed to scale the problem to realistic-sized instances and its performance has been compared with direct resolution. The results obtained show that the matheuristic is capable of finding quality solutions in reasonable times, making it a useful tool for route planning in the company.
In this work, a linear programming problem has been modeled based on a real case study from the company Inditex. It is a vehicle routing problem (VRP) with the existence of certain nodes called {\it cross-docks} where goods could be exchanged between trucks. A matheuristic has also been designed to scale the problem to realistic-sized instances and its performance has been compared with direct resolution. The results obtained show that the matheuristic is capable of finding quality solutions in reasonable times, making it a useful tool for route planning in the company.
Direction
GONZALEZ DIAZ, JULIO (Tutorships)
GONZALEZ DIAZ, JULIO (Tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
Beaching probability study of drift objects in the ocean
Authorship
D.G.G.
Master in Statistical Techniques
D.G.G.
Master in Statistical Techniques
Defense date
09.05.2024 13:00
09.05.2024 13:00
Summary
In the context of fishing, it is of particular interest to be able to predict the location of drifting objects in advance, in order to ensure that they do not end up on the coast. An increasing number of sailors are incorporating technological devices into their daily routines to assist them in their angling activities. Marine Instruments is a prominent entity within this domain, specialising in the fabrication of satellite buoys that enhance the efficacy of tuna fishing operations. It is therefore of significant interest to ascertain the optimal locations for the deployment of these objects, with the aim of preventing them from becoming stranded on the coast. By understanding the potential routes these objects might take, probability maps can be created to identify the optimal locations for placing them at sea. In this study, statistical spatial data techniques are employed to estimate the probability of these objects becoming stranded on the coast. Consequently, techniques such as kriging can be Used to generate geographic layers or maps that represent the areas in which an object should be placed to avoid being stranded on the coast within a specified time frame.
In the context of fishing, it is of particular interest to be able to predict the location of drifting objects in advance, in order to ensure that they do not end up on the coast. An increasing number of sailors are incorporating technological devices into their daily routines to assist them in their angling activities. Marine Instruments is a prominent entity within this domain, specialising in the fabrication of satellite buoys that enhance the efficacy of tuna fishing operations. It is therefore of significant interest to ascertain the optimal locations for the deployment of these objects, with the aim of preventing them from becoming stranded on the coast. By understanding the potential routes these objects might take, probability maps can be created to identify the optimal locations for placing them at sea. In this study, statistical spatial data techniques are employed to estimate the probability of these objects becoming stranded on the coast. Consequently, techniques such as kriging can be Used to generate geographic layers or maps that represent the areas in which an object should be placed to avoid being stranded on the coast within a specified time frame.
Direction
RODRIGUEZ CASAL, ALBERTO (Tutorships)
RODRIGUEZ CASAL, ALBERTO (Tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
Functional data analysis for classification with spectroscopy data
Authorship
M.D.D.L.F.B.
Master in Statistical Techniques
M.D.D.L.F.B.
Master in Statistical Techniques
Defense date
06.18.2024 09:00
06.18.2024 09:00
Summary
This work addresses breast and colon cancer detection as a binary classification problem. A database of infrared spectra of blood serum is provided, which gives information on the molecular composition of the sample. Due to their intrinsically functional nature, functional data analysis techniques will be applied. Once the problem has been motivated, the notions and tools of functional data analysis that are required for the study are presented. Then, an exploratory analysis of the database is performed, representing measures of central location, studying the existence of outliers and performing a functional principal component analysis. Finally, different types of classification models are fitted, being kNN the best performer in different evaluation metrics for the case of breast cancer against the reference group and quadratic discriminant analysis, QDA, in the case of colon cancer patients group against individuals from the reference group. In conclusion, promising results were obtained that establish a solid basis for the use of infrared spectroscopy in cancer detection. These underline the importance of expanding the database and exploring new analytical techniques to improve the scalability and generalisability of the results, which is essential for future research and clinical applications.
This work addresses breast and colon cancer detection as a binary classification problem. A database of infrared spectra of blood serum is provided, which gives information on the molecular composition of the sample. Due to their intrinsically functional nature, functional data analysis techniques will be applied. Once the problem has been motivated, the notions and tools of functional data analysis that are required for the study are presented. Then, an exploratory analysis of the database is performed, representing measures of central location, studying the existence of outliers and performing a functional principal component analysis. Finally, different types of classification models are fitted, being kNN the best performer in different evaluation metrics for the case of breast cancer against the reference group and quadratic discriminant analysis, QDA, in the case of colon cancer patients group against individuals from the reference group. In conclusion, promising results were obtained that establish a solid basis for the use of infrared spectroscopy in cancer detection. These underline the importance of expanding the database and exploring new analytical techniques to improve the scalability and generalisability of the results, which is essential for future research and clinical applications.
Direction
FEBRERO BANDE, MANUEL (Tutorships)
PATEIRO LOPEZ, BEATRIZ (Co-tutorships)
FEBRERO BANDE, MANUEL (Tutorships)
PATEIRO LOPEZ, BEATRIZ (Co-tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
Resampling techniques in semi-parametric time series forecasting models
Authorship
P.C.F.
Master in Statistical Techniques
P.C.F.
Master in Statistical Techniques
Defense date
06.18.2024 10:00
06.18.2024 10:00
Summary
Over the last 30 years, SO2 and NOx prediction models have been developed for the As Pontes Thermal Power Plant under different general regression methodological approaches. These models are, in general, of a semi-parametric type including in the non-parametric part trend estimations carried out with additive models, neural networks or functional data among others. This Master's thesis proposal aims to address the following objectives: 1) An updated general review of the models implemented for the aforementioned variables in the utility developed for the company. 2) A review of the resampling mechanisms developed in the various prediction techniques, with the aim of generating predictive confidence regions. 3) A comparative illustration of the different procedures with real environmental or simulated data.
Over the last 30 years, SO2 and NOx prediction models have been developed for the As Pontes Thermal Power Plant under different general regression methodological approaches. These models are, in general, of a semi-parametric type including in the non-parametric part trend estimations carried out with additive models, neural networks or functional data among others. This Master's thesis proposal aims to address the following objectives: 1) An updated general review of the models implemented for the aforementioned variables in the utility developed for the company. 2) A review of the resampling mechanisms developed in the various prediction techniques, with the aim of generating predictive confidence regions. 3) A comparative illustration of the different procedures with real environmental or simulated data.
Direction
FEBRERO BANDE, MANUEL (Tutorships)
GONZALEZ MANTEIGA, WENCESLAO (Co-tutorships)
FEBRERO BANDE, MANUEL (Tutorships)
GONZALEZ MANTEIGA, WENCESLAO (Co-tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
Survival Analysis for the detection and classification of anomalies in vehicles
Authorship
P.M.T.
Master in Statistical Techniques
P.M.T.
Master in Statistical Techniques
Defense date
06.18.2024 10:00
06.18.2024 10:00
Summary
This work illustrates the use of Survival Analysis techniques for the detection and classification of anomalies in vehicles. Its main objective is the development of algorithms that allow detecting intrusions in vehicles with high effectiveness and with a low rate of false alerts, as well as classifying them among possible known attacks, all with high statistical rigor. To do this, emphasis will be placed on how its parameters influence the distribution of the variables of interest and, therefore, the detection accuracies. An attempt will be made to model the problem with parameters that play a known role, thus allowing a full understanding of the nature of the results.
This work illustrates the use of Survival Analysis techniques for the detection and classification of anomalies in vehicles. Its main objective is the development of algorithms that allow detecting intrusions in vehicles with high effectiveness and with a low rate of false alerts, as well as classifying them among possible known attacks, all with high statistical rigor. To do this, emphasis will be placed on how its parameters influence the distribution of the variables of interest and, therefore, the detection accuracies. An attempt will be made to model the problem with parameters that play a known role, thus allowing a full understanding of the nature of the results.
Direction
Uña Álvarez, Jacobo de (Tutorships)
Uña Álvarez, Jacobo de (Tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
Development and Implementation of an Entirely SQL-Based Cloud ML System
Authorship
A.C.E.
Master in Statistical Techniques
A.C.E.
Master in Statistical Techniques
Defense date
06.19.2024 11:00
06.19.2024 11:00
Summary
This project illustrates the implementation of machine learning capabilities, especially through BigQuery ML, with the purpose of leveraging the accessibility of SQL interfaces for creating several models in BigQuery. The evaluated models are explained both theoretically and practically, compared to their Python equivalents, and range from multiple linear regression or logistic regression to ensemble methods, forecasting techniques, recommendation systems, and clustering. The comparison between BigQuery ML and Python is conducted by developing the respective models in both environments, using specific datasets to assess their performance and capabilities. The main objective of this study is to highlight and compare the skills of both platforms, aiming to provide a guide that facilitates a more suitable choice based on the specific needs of each data science project.
This project illustrates the implementation of machine learning capabilities, especially through BigQuery ML, with the purpose of leveraging the accessibility of SQL interfaces for creating several models in BigQuery. The evaluated models are explained both theoretically and practically, compared to their Python equivalents, and range from multiple linear regression or logistic regression to ensemble methods, forecasting techniques, recommendation systems, and clustering. The comparison between BigQuery ML and Python is conducted by developing the respective models in both environments, using specific datasets to assess their performance and capabilities. The main objective of this study is to highlight and compare the skills of both platforms, aiming to provide a guide that facilitates a more suitable choice based on the specific needs of each data science project.
Direction
CRUJEIRAS CASAIS, ROSA MARÍA (Tutorships)
CRUJEIRAS CASAIS, ROSA MARÍA (Tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
Branch and Bound Techniques in the Field of Polynomial Optimization
Authorship
M.A.R.
Master in Statistical Techniques
M.A.R.
Master in Statistical Techniques
Defense date
06.19.2024 11:45
06.19.2024 11:45
Summary
Optimization or Operations Research is a prominent area of mathematics known for its application in the real world, especially in business decision-making. To achieve this, it is necessary to create a mathematical model that describes, through the objective function, what we wish to maximize or minimize, adding the necessary constraints. In many situations, the function used in the formulation of the problem are polynomials, giving rise to an important class of problems: the polynomial optimization ones. In general, these problems tend to be nonlinear and non-convex, so obtaining a global solution can be a complex task. There are various theoretical methods among which the algorithm based on the Reformulation-Linearization Technique (RLT) stands out. RAPOSa is a recent global solver specially designed for polynomial optimization problems based on the RLT algorithm. In this work, we present and study the efficiency of a new variation of the RLT-based algorithm, developed during an internship at the CITMAga, with the support of the RAPOSa development team.
Optimization or Operations Research is a prominent area of mathematics known for its application in the real world, especially in business decision-making. To achieve this, it is necessary to create a mathematical model that describes, through the objective function, what we wish to maximize or minimize, adding the necessary constraints. In many situations, the function used in the formulation of the problem are polynomials, giving rise to an important class of problems: the polynomial optimization ones. In general, these problems tend to be nonlinear and non-convex, so obtaining a global solution can be a complex task. There are various theoretical methods among which the algorithm based on the Reformulation-Linearization Technique (RLT) stands out. RAPOSa is a recent global solver specially designed for polynomial optimization problems based on the RLT algorithm. In this work, we present and study the efficiency of a new variation of the RLT-based algorithm, developed during an internship at the CITMAga, with the support of the RAPOSa development team.
Direction
GONZALEZ RODRIGUEZ, BRAIS (Tutorships)
GONZALEZ DIAZ, JULIO (Co-tutorships)
GONZALEZ RODRIGUEZ, BRAIS (Tutorships)
GONZALEZ DIAZ, JULIO (Co-tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
Analysis of the excess of mortality in Galicia
Authorship
A.D.F.
Master in Statistical Techniques
A.D.F.
Master in Statistical Techniques
Defense date
06.19.2024 12:30
06.19.2024 12:30
Summary
This work has been developed under modality B of the final projects for the Master's in Statistical Techniques, through an internship carried out at the Epidemiology Service of the Dirección Xeral de Saúde Pública (DXSP) of the Consellería de Sanidade. The main objective of this report is to identify the excess or deficit of deaths in a specific year, based on deaths that occurred in previous years. The secondary objective is to identify the causes that contribute to the observed variations. This analysis was justified by a notable increase in excess deaths in Galicia for the year 2022, detected by the MoMo system (daily mortality monitoring for all causes), which prompted a more in-depth study by the DXSP. First, a bibliographic review was conducted on the existing analysis methods for predicting expected deaths, to determine the difference between observed and expected deaths. Second, the most appropriate techniques for achieving the best possible prediction were identified, including generalized linear models and mixed models. Finally, the models were fitted using the mortality data from Galicia from the ten years preceding the year to be predicted, thus obtaining the expected deaths for each of the years in the period 2019-2022.
This work has been developed under modality B of the final projects for the Master's in Statistical Techniques, through an internship carried out at the Epidemiology Service of the Dirección Xeral de Saúde Pública (DXSP) of the Consellería de Sanidade. The main objective of this report is to identify the excess or deficit of deaths in a specific year, based on deaths that occurred in previous years. The secondary objective is to identify the causes that contribute to the observed variations. This analysis was justified by a notable increase in excess deaths in Galicia for the year 2022, detected by the MoMo system (daily mortality monitoring for all causes), which prompted a more in-depth study by the DXSP. First, a bibliographic review was conducted on the existing analysis methods for predicting expected deaths, to determine the difference between observed and expected deaths. Second, the most appropriate techniques for achieving the best possible prediction were identified, including generalized linear models and mixed models. Finally, the models were fitted using the mortality data from Galicia from the ten years preceding the year to be predicted, thus obtaining the expected deaths for each of the years in the period 2019-2022.
Direction
CRUJEIRAS CASAIS, ROSA MARÍA (Tutorships)
CRUJEIRAS CASAIS, ROSA MARÍA (Tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Lombardía Cortiña, María José (Chairman)
GONZALEZ RUEDA, ANGEL MANUEL (Secretary)
Gómez Rúa, María (Member)
Cost allocation for transport problems: revision and comparative study.
Authorship
P.S.R.
Master in Statistical Techniques
P.S.R.
Master in Statistical Techniques
Defense date
06.25.2024 09:00
06.25.2024 09:00
Summary
An interesting question that arises in the field of transportation is how to allocate the toll collected by the users of a highway to each of the transportation companies in charge of its management and maintenance, and which are located along the road. In this work we solve this problem from a game theoretic perspective. To this end, the most representative solutions of classical game theory are studied, as well as other more recent ones in the literature. Finally, the results offered by different methods on two real cases are compared.
An interesting question that arises in the field of transportation is how to allocate the toll collected by the users of a highway to each of the transportation companies in charge of its management and maintenance, and which are located along the road. In this work we solve this problem from a game theoretic perspective. To this end, the most representative solutions of classical game theory are studied, as well as other more recent ones in the literature. Finally, the results offered by different methods on two real cases are compared.
Direction
CASAS MENDEZ, BALBINA VIRGINIA (Tutorships)
CASAS MENDEZ, BALBINA VIRGINIA (Tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
State of the Art of ML Technologies in Time Series and Value Proposition to Improve Them
Authorship
C.P.A.M.
Master in Statistical Techniques
C.P.A.M.
Master in Statistical Techniques
Defense date
06.25.2024 10:00
06.25.2024 10:00
Summary
This work develops the use of two libraries for time series analysis in Python: Sktime and Skforecast, rescuing their most important characteristics. In the first chapter, the justification for the review of both libraries is presented. The second and third chapters, mathematically describes the prediction methods to be used, followed by a variety of metrics for evaluation. Chapter 4 examines the distinctive characteristics of both libraries. Finally, in Chapter 5 a practical application is carried out using data provided by the company SDGroup.
This work develops the use of two libraries for time series analysis in Python: Sktime and Skforecast, rescuing their most important characteristics. In the first chapter, the justification for the review of both libraries is presented. The second and third chapters, mathematically describes the prediction methods to be used, followed by a variety of metrics for evaluation. Chapter 4 examines the distinctive characteristics of both libraries. Finally, in Chapter 5 a practical application is carried out using data provided by the company SDGroup.
Direction
AMEIJEIRAS ALONSO, JOSE (Tutorships)
AMEIJEIRAS ALONSO, JOSE (Tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
Multilevel functional regression for modelling postprandial glucose as a function of glycemic load
Authorship
A.C.R.
Master in Statistical Techniques
A.C.R.
Master in Statistical Techniques
Defense date
06.25.2024 11:00
06.25.2024 11:00
Summary
Glycaemic load of a food is a value used to assess the impact of that food on postprandial glucose levels (glucose level recorded after food intake). The effect of this value is uncertain in real life conditions, so throughout this paper we will see the effect on non-diabetic participants of Glycation project, who have not changed their diet or habits. Glycaemic load will be calculated with a program based on the intakes that participants wrote down in a notebook. The main objective of this work is to study how glycemic load of meals affects postprandial glucose taking into account age, body mass index and sex. To investigate this, a functional multilevel regression model with mixed effects will be applied to data and we will see if this model is better than the one already implemented in the refund package available on R. Functional regression will be used since we will work on glucose curves of the study participants, which are constructed with measurements taken by continuous glucose monitoring devices every five minutes.
Glycaemic load of a food is a value used to assess the impact of that food on postprandial glucose levels (glucose level recorded after food intake). The effect of this value is uncertain in real life conditions, so throughout this paper we will see the effect on non-diabetic participants of Glycation project, who have not changed their diet or habits. Glycaemic load will be calculated with a program based on the intakes that participants wrote down in a notebook. The main objective of this work is to study how glycemic load of meals affects postprandial glucose taking into account age, body mass index and sex. To investigate this, a functional multilevel regression model with mixed effects will be applied to data and we will see if this model is better than the one already implemented in the refund package available on R. Functional regression will be used since we will work on glucose curves of the study participants, which are constructed with measurements taken by continuous glucose monitoring devices every five minutes.
Direction
CONDE AMBOAGE, MERCEDES (Tutorships)
CONDE AMBOAGE, MERCEDES (Tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
Clinical-epidemiological study of breast cancer
Authorship
N.Q.A.
Master in Statistical Techniques
N.Q.A.
Master in Statistical Techniques
Defense date
06.25.2024 12:00
06.25.2024 12:00
Summary
Epidemiology studies the distribution and phenomena or determinants related to health, with the aim of understanding the causes of a diseases and improving their diagnosis and treatment. In this work we carried out a statistical study on breast cancer, first reviewing previous studies on this disease, which has been widely studied. Subsequently, using a breast cancer database provided by the Galician Breast Cancer Consortium, BREOGAN, we performed an exploratory analysis and fitted different logistic regression models to identify which variables are risk or protective factors for breast cancer. The database is composed of 672 observations of cases (300) and controls (372), which has a total of 36 variables related to age, menarche, menopause, genetic factors, lifestyle habits, anthropometric characteristics and the concentration of some cell types of blood. Finally, we have studied the diagnostic capacity of logistic regression models using ROC curves. RStudio software was used for this purpose.
Epidemiology studies the distribution and phenomena or determinants related to health, with the aim of understanding the causes of a diseases and improving their diagnosis and treatment. In this work we carried out a statistical study on breast cancer, first reviewing previous studies on this disease, which has been widely studied. Subsequently, using a breast cancer database provided by the Galician Breast Cancer Consortium, BREOGAN, we performed an exploratory analysis and fitted different logistic regression models to identify which variables are risk or protective factors for breast cancer. The database is composed of 672 observations of cases (300) and controls (372), which has a total of 36 variables related to age, menarche, menopause, genetic factors, lifestyle habits, anthropometric characteristics and the concentration of some cell types of blood. Finally, we have studied the diagnostic capacity of logistic regression models using ROC curves. RStudio software was used for this purpose.
Direction
SAAVEDRA NIEVES, PAULA (Tutorships)
SAAVEDRA NIEVES, PAULA (Tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
Application of statistical techniques in the existing relationship between video game addiction and gaming hours.
Authorship
A.F.T.
Master in Statistical Techniques
A.F.T.
Master in Statistical Techniques
Defense date
02.01.2024 16:00
02.01.2024 16:00
Summary
Video games are currently one of the main sources of leisure in society, especially in childhood and adolescence. However, despite the many positive aspects related to video games, concerns persist about the possible addictive component associated with them. Given the significant difficulties in understanding the development of problematic use patterns and the ongoing debate in their conceptualization, it is crucial to differentiate between central and peripheral symptoms, especially when considering the role of play time. This study aims to comprehensively study the relationship between hours of play and problem gambling and to analyze the possible moderating role of gender in this relationship. Cluster sampling was used, gathering a final sample of 6,278 students of Compulsory Secondary Education, aged 12 to 16 years. Data were collected through an online survey in which sociodemographic variables (age and gender), gaming habits and problematic video game use were incorporated through the application of the Gaming Addiction Scale for Adolescents, a screening tool. Data analysis included both parametric procedures through logistic regression and non-parametric procedures through the use of generalized additive models. The findings revealed on the one hand the existence of a significant non-linear relationship between hours of gaming and hours of play, and on the other hand, the importance of gender variable on this relationship, finding significatively higher rates of problematic gaming on male gender.
Video games are currently one of the main sources of leisure in society, especially in childhood and adolescence. However, despite the many positive aspects related to video games, concerns persist about the possible addictive component associated with them. Given the significant difficulties in understanding the development of problematic use patterns and the ongoing debate in their conceptualization, it is crucial to differentiate between central and peripheral symptoms, especially when considering the role of play time. This study aims to comprehensively study the relationship between hours of play and problem gambling and to analyze the possible moderating role of gender in this relationship. Cluster sampling was used, gathering a final sample of 6,278 students of Compulsory Secondary Education, aged 12 to 16 years. Data were collected through an online survey in which sociodemographic variables (age and gender), gaming habits and problematic video game use were incorporated through the application of the Gaming Addiction Scale for Adolescents, a screening tool. Data analysis included both parametric procedures through logistic regression and non-parametric procedures through the use of generalized additive models. The findings revealed on the one hand the existence of a significant non-linear relationship between hours of gaming and hours of play, and on the other hand, the importance of gender variable on this relationship, finding significatively higher rates of problematic gaming on male gender.
Direction
AMEIJEIRAS ALONSO, JOSE (Tutorships)
AMEIJEIRAS ALONSO, JOSE (Tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
Characterization of different heart failure phenotypes
Authorship
A.V.G.
Master in Statistical Techniques
A.V.G.
Master in Statistical Techniques
Defense date
02.01.2024 17:00
02.01.2024 17:00
Summary
Given a database comprising patients from the Hospital Clínico Universitario de Santiago (CHUS), who have undergone an atrial fibrillation procedure, first of all, these patients will be classified into three groups: patients without heart failure, patients with heart failure and preserved LVEF (Left Ventricular Ejection Fraction) and patients with heart failure and reduced LVEF. This classification is based on scores used in biomedical literature. The aim of this work is to obtain a model able to classify new patients in one of these three groups, according to atrial fibrosis of the patinet and different biomarkers. For this purpose, we start by examining how the distribution of these variables varies within each group. Later, regression models with categorical response variables are proposed to investigate the influence of the considered variables on the probability of belonging to each group. Finall, ROC curves are introduced to assess the predictive capability of the selected logistic model
Given a database comprising patients from the Hospital Clínico Universitario de Santiago (CHUS), who have undergone an atrial fibrillation procedure, first of all, these patients will be classified into three groups: patients without heart failure, patients with heart failure and preserved LVEF (Left Ventricular Ejection Fraction) and patients with heart failure and reduced LVEF. This classification is based on scores used in biomedical literature. The aim of this work is to obtain a model able to classify new patients in one of these three groups, according to atrial fibrosis of the patinet and different biomarkers. For this purpose, we start by examining how the distribution of these variables varies within each group. Later, regression models with categorical response variables are proposed to investigate the influence of the considered variables on the probability of belonging to each group. Finall, ROC curves are introduced to assess the predictive capability of the selected logistic model
Direction
CONDE AMBOAGE, MERCEDES (Tutorships)
Reyes Santías, Francisco (Co-tutorships)
CONDE AMBOAGE, MERCEDES (Tutorships)
Reyes Santías, Francisco (Co-tutorships)
Court
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)
AMEIJEIRAS ALONSO, JOSE (Coordinator)
Aneiros Perez, Germán (Chairman)
SAAVEDRA NIEVES, ALEJANDRO (Secretary)
SESTELO PEREZ, MARTA (Member)