Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Tesis Doctorals - Departament - Matemàtiques i Informàtica

Permanent URI for this collectionhttps://hdl.handle.net/2445/99760

 Statistics

Browse

Recent Submissions

Now showing 1 - 20 of 77
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Topology-Enhanced Deep Learning
    (Universitat de Barcelona, 2026-04-07) Ballester Bautista, Rubén; Escalera Guerrero, Sergio; Casacuberta, Carles; Grossenbacher Rieck, Bastian; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] This thesis presents a comprehensive examination of topological deep learning through two complementary approaches: utilizing topological tools to analyze and improve traditional neural networks, and testing and developing novel architectures for learning on high-order topological domains such as simplicial or cellular complexes. The thesis is organized into three thematic blocks. First, we establish the theoretical foundations of TDA and TDL, providing a comprehensive literature review of existing methodologies. Second, we exploit persistent homology —a fundamental TDA tool that quantifies multi-scale topological features— to analyze neural network activations and their relationship to neural network performance and generalization. We use the differentiability theory of persistent homology to develop topological regularization methods that demonstrably improve neural network performance on selected problems. In the third block, we address the challenges of learning on high-order domains such as simplicial and cellular complexes. We introduce MANTRA, a novel topological dataset specifically designed to evaluate the capacity of TDL methods to leverage high-order structural information. Furthermore, we develop the Cellular Transformer, an adaptation of the transformer architecture to cellular complexes that addresses some of the limitations of message passing neural networks, such as their general inability to capture long-range interactions. This thesis advances both the theoretical understanding of neural networks through a topological lens and the practical capabilities of learning algorithms on topological structures. The empirical results obtained in this thesis demonstrate that topology provides valuable insights into the geometric processes underlying deep learning while enabling more effective feature extraction from complex data representations. Thus, the research presented here expands the state-of-the-art in topological deep learning, establishing a foundation for more interpretable, topologically-aware neural architectures while opening promising avenues for future research at the intersection of algebraic topology and deep learning.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Moduli spaces of stable bundles, prioritary bundles and Brill–Noether Theory
    (Universitat de Barcelona, 2026-03-20) Macías Tarrío, Irene; Costa Farràs, Laura; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] In this thesis, we primarily consider moduli spaces of slope-stable vector bundles with fixed rank and Chern classes, with a particular focus on Brill-Noether theory, and wall-and-chamber structures. As well, we will focus on the closely related class of prioritary vector bundles, which are characterized by specific cohomological properties. The first main part of the thesis addresses Brill-Noether theory of stable vector bundles on ruled surfaces over a smooth irreducible curve. In this context, Brill-Noether loci are defined as subvarieties of the moduli space that parametrize stable bundles with a prescribed number of global sections. General results on the existence of these loci are known, but their geometry remains largely unexplored beyond the curve case. We obtain new results on the non-emptiness of Brill-Noether loci of stable rank two vector bundles on ruled surfaces. A second line of investigation focuses on the construction of higher-rank prioritary vector bundles on ruled surfaces, which is the subject of Chapter 3. Using extension techniques, generalized Cayley-Bacharach properties and inductive constructions, we construct simple prioritary bundles of arbitrary rank with many global sections. These constructions provide explicit families of vector bundles that play an important role in the study of moduli spaces. The third main theme of the thesis is the study of moduli spaces of stable bundles on varieties of dimension greater than or equal to three. In Chapter 4, we introduce a modified wall-and-chamber theory that overcomes the limitations that other theories have in higher dimension. This new framework allows us to compare moduli spaces associated with different polarizations and to study their decomposition across walls. Applying this theory in Chapter 5, we investigate moduli spaces of stable rank two vector bundles on ruled threefolds over IP'2. We describe the wall-and-chamber structure explicitly, analyze the decomposition of moduli spaces, and identify rational components in certain cases. Finally, we apply these results to prove the non-emptiness of several Brill-Noether loci.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Theory and applications of rough volatility models
    (Universitat de Barcelona, 2026-03-19) García Lorite, David; Alòs, Elisa; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] This doctoral dissertation investigates some classical problems in modern quantitative finance. Due to the increasing complexity of markets, some non-classical models, as those based on the fractional Brownian motion (rough volatilities) have been introduced in recent times. These models require, because of the lack of properties as Markovianity, a new set of methodologies, as those presented in this dissertation, based on Malliavin calculus. The study focuses on two primary areas: the asymptotic behavior of implied volatility surfaces — in both the Markovian and non-Markovian frameworks — and convexity adjustments in interest rate derivatives. The analysis is grounded in advanced probabilistic techniques, notably Malliavin calculus and Watanabe expansions, which facilitate tractable representations and analytical approximations of key financial quantities. The first part of the dissertation examines the short-term dynamics of the at-the-money implied volatility level, skew, and curvature under both Markovian and non-Markovian settings. Particular attention is given to the role of the Hurst parameter in rough volatility models and its influence on the implied volatility smile associated with variance derivatives and VIX options. The second part addresses convexity corrections in the pricing of interest rate instruments, including forward rate agreements (FRAs), swaps, and constant maturity swap (CMS) derivatives. A novel methodology based on Malliavin calculus is introduced to derive closed-form expressions for convexity adjustments, capturing the effects of local volatility skew and curvature. Furthermore, a new pricing approach for CMS caps and floors is proposed, leveraging Malliavin calculus and Watanabe expansions to evaluate the quadratic payoffs that arise from convexity effects. This approach is broadly applicable and can be extended to other payoffs, such as cash-settled swaptions. Moreover, the methodology presented allows for the study of rough-type models in the interest rate framework. The theoretical developments are supported by numerical experiments, which confirm the accuracy and robustness of the proposed methodologies.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Recommender Systems: from Click-Through Rate Prediction to True Personalization
    (Universitat de Barcelona, 2026-02-06) Duran, Paula G.; Vitrià i Marca, Jordi; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] Recommender Systems (RS) have revolutionized the way we navigate the over-whelming amount of digital content available on the internet. Originating in the 1990s, these systems were developed to address the challenge of information over-load and help users find relevant content based on their preferences. Since then, RS have become integral to various domains, serving billions of users with personalized recommendations. Advancements in RS can be categorized into three key areas. Firstly, researchers have focused on refining models through deep learning algorithms, enabling more ac-curate predictions by identifying patterns within large datasets. Secondly, evaluation metrics have evolved beyond accuracy, considering factors like fairness and diversity to provide recommendations aligned with users’ preferences. Ethical considerations have also emerged, leading to frameworks ensuring responsible deployment of RS, addressing biases and protecting user privacy. In this work, we explore the progress made in RS research. We discuss novel approaches leveraging deep learning and uncertainty, innovative evaluation metrics, and ethical considerations. The aim is to develop more accurate, diverse, and ethically sound RS that empower users to embark on personalized content discovery journeys.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Advances in Fairness Analysis in Artificial Intelligence for Healthcare
    (Universitat de Barcelona, 2026-01-30) Dang, Ngoc Vien; Lekadir, Karim, 1977-; Hernández-González, Jerónimo; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] The expanding role of artificial intelligence (AI) in healthcare promises earlier diagnosis, more personalized treatment, and consistent decision-making. Yet, models developed from observational data may inadvertently embed and amplify long-standing inequities in healthcare delivery. This dissertation investigates fairness challenges in AI for both tabular clinical data and medical imaging, proposing new diagnostic frameworks and methods to mitigate bias and advance equitable and trustworthy healthcare AI. The dissertation begins by establishing a theoretical foundation, outlining supervised classification, formal definitions of fairness notions, and trade-offs between fairness and predictive performance. Building on this foundation, six core studies address fairness from complementary perspectives. The first three studies, focusing on tabular clinical data, show that algorithmic bias in healthcare seems to be systematic. The first study, on depression risk prediction, observed disparities by sex, ethnicity, socioeconomic status, and comorbidity. To address these inequities, the Population Sensitivity-Guided Threshold Adjustment (PSTA) method was introduced, a post-hoc approach that adapts decision thresholds to improve early risk detection in underserved groups while maintaining reliable overall performance. The second study conducted a systematic evaluation of seven post-processing methods, spanning calibration-based, threshold-adjustment, and decision-boundary techniques. The evaluation showed that their effectiveness strongly depends on dataset characteristics and fairness criteria, with no single technique performing best across all settings. Beyond algorithmic adjust-ments, the third study highlighted the value of richer data: incorporating early-life factors significantly improved multimorbidity risk prediction, especially for comorbid patients, thereby narrowing subgroup disparities without sacrificing accuracy. Together, these findings emphasize that fairness requires a careful alignment of debiasing strategies, data representativeness, and clinical objectives. Shifting focus to medical imaging, the next set of studies addresses fair-ness challenges in Alzheimer’s disease diagnosis with T1-weighted MRI. Audits of convolutional neural networks (CNNs) revealed pronounced disparities, including higher underdiagnosis rates for women, ethnic minorities, and APOE4 carriers, as well as overdiagnosis in elderly populations. These age-related biases motivated the development of the Calibration and Group Threshold Optimization (C-GTOP) method, which combines probability calibration with group-specific thresholds to reduce overdiagnosis among older adults while preserving overall diagnostic accuracy. Beyond group-level corrections, a layer-wise diagnostic evaluation framework was introduced to analyze how sensitive attributes such as age and scanner type are encoded across two different architectures like CNNs and Vision Transformers (ViTs), and how this encoding influences fairness. This framework showed that CNNs tend to entangle bias-inducing signals with disease features, while ViTs preserve sensitive in-formation in a more disentangled form, leading to fairer subgroup predictions and reducing shortcut learning. Together, these studies show that achieving fairness in clinical neuroimaging depends not only on correcting subgroup disparities but also on understanding how bias is represented within model architectures. In conclusion, this dissertation demonstrates that fairness in healthcare AI requires not only algorithmic adjustments but also principled choices of fairness criteria, representative data collection, and architecture-aware model auditing that examines how different neural network designs encode and prop-agate bias. By proposing new debiasing methods as well as diagnostic evaluation frameworks, this work advances strategies to reduce subgroup disparities and offers tools for systematic fairness auditing. These advances pave the way for fairer clinical AI applications that better serve diverse patient populations and enhance trust in healthcare innovation.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    On the Move: Towards Realistic and Controllable Human Motion Generation
    (Universitat de Barcelona, 2026-01-30) Barquero Garcia, German; Escalera Guerrero, Sergio; Palmero Cantariño, Cristina; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] In recent years, we have witnessed the arrival of algorithms capable of understanding human behavior and generating the motion that drives virtual human-like avatars or robots. This ability, known as human motion generation, has emerged thanks to major advances in deep learning, parameterized human body models, and large-scale motion capture datasets. Together, these developments have enabled the synthesis of lifelike movement from minimal or abstract input such as natural language descriptions, or short clips of prior motion. These generative capabilities are unlocking new applications in animation, extended reality, robotics, and behavior-aware autonomous systems, helping to design digital humans or humanoids that both look and behave in a human-like way. Such advances represent an essential step towards developing fully immersive, human-centric experiences. This thesis focuses on enhancing human motion generation along two key axes: realism and control. Specifically, I make progress in three important topics. First, in human motion prediction, I show that the prevailing focus of maximizing coordinate-level diversity encourages unrealistic predictions. I overturn this status quo by proposing a model that delivers behavioral diversity and state-of-the-art realism. Second, I improve the controllability of motion generation models by enabling users to specify both the description and duration of consecutive actions within arbitrarily long motion sequences. For this, I propose a new technique that eliminates the need for post-processing, and promotes smooth and realistic transitions between actions. Finally, I address the challenge of real-time full-body motion synthesis from head-mounted sensors and vision-based hand-tracking inputs, which are often noisy and unreliable. In particular, I present the first method able to preserve motion continuity and realism through signal losses. I complement it with the release of the first dataset with paired headset-captured tracking and ground-truth motion capture during real virtual-reality interactions. I use it to reveal the performance gap when deploying existing methods trained on synthetic data in real-life conditions. In addition to these three core contributions, this thesis also introduces novel evaluation metrics that improve the way motion quality is assessed. I propose two smoothness metrics that correlate with perceptual quality in motion prediction, and jerk-based transition metrics that quantify motion discontinuities during action transitions. Collectively, these contributions push the boundaries of human motion generation in realism and controllability and provide a toolkit for next-generation systems that must generate lifelike human movement on demand.
  • Thumbnail Image
    Doctoral thesis
    Two-frequency dynamical phenomena in three-dimensional volume-preserving maps
    (Universitat de Barcelona, 2026-01-23) Murillo López, Ainoa; Vieiro Yanes, Arturo; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] The dynamics of three-dimensional real-analytic volume-preserving maps (VPMs) have recently attracted much attention due to their rich dynamical behaviour and relevance in various physical contexts. Although structurally simpler, volume-preserving maps share many properties with higher-dimensional symplectic maps. However, their lack of a full Hamiltonian structure allows for a broader range of bifurcation phenomena, such as the creation of bubbles of stability. This intermediate position makes volume-preserving maps a natural setting to explore complex dynamical phenomena within a manageable framework, while also motivating the use of general analytical and numerical tools beyond the symplectic setting. The phase space skeleton of a VPM involves fixed and periodic points, invariant curves, and invariant two-dimensional tori, together with their stable and unstable invariant manifolds when these objects are hyperbolic. On the other hand, the description of the phase space evolution involves global bifurcations such as the breakdown of invariant tori and the splitting of separatrices. Previous studies have addressed several aspects of the dynamics of VPMs, including the existence of KAM tori [CS90, Xia92] and the breakdown of two-dimensional invariant tori [FM13, Mei12]. Also, the geometric mechanisms leading to transport in phase space were studied in [LM00, LM03, MM12] and the stickiness properties near stability regions were analyzed in [MMSV18, DB20]. Beyond their mathematical interest, volume-preserving maps also arise in various physical applications. They appear, for instance, when modelling the motion of passive tracers in incompressible fluids [FKP88, CFP96] and in the study of magnetic field line configurations in plasma physics [LF92]. Moreover, near-identity volume-preserving maps are related to three-dimensional divergence-free vector fields, and we refer to [Bro81, BH19] for an overview of bifurcations in that context. This connection has further motivated the study of three-dimensional volume-preserving flows (VPFs), which are particularly relevant in fluid dynamics. In the absence of additional symmetries that allow for dimensional reduction, the velocity field of an incompressible fluid naturally defines a three-dimensional flow [FKP88, Hol84, Mez94]. Unsteady fluid flows, in which the conditions (the velocity, the pressure, and the cross-section) change over time, lead to time-dependent perturbations of divergence-free vector fields. In particular, volume-preserving flows with broken rotational symmetry and periodic forcing have been proposed to model such periodically time-dependent velocity fields in incompressible fluid flows, and have been studied both theoretically and experimentally [MNZ95, SCVH04, SMOW08]. A central object of study in these systems is the separatrix surface, whose structure plays a role in determining the transport and mixing properties of the flow. This has been explored in different related settings and applications, see, for example, [MM12, NV99, NSV03, VWG07]. This work investigates the evolution of the phase space of VPMs under conservative perturbations, with special attention to genuinely three-dimensional structures and mechanisms that distinguish them from planar area-preserving maps. In particular, we focus on phase space regions where the dynamics can be described as a two-angle one-action map and the interaction of two frequencies becomes crucial. As will be detailed later in this introduction, we consider direct perturbations of discrete 3D VPMs as well as periodic forcings of divergence-free 3D flows. These systems are related to a conservative unfolding of the Hopf-zero singularity, and they have a bubble of stability delimited by the two-dimensional invariant manifolds of a pair of saddle-focus fixed points. Inside this bubble, there is a foliation by two-dimensional tori organized around a normally elliptic invariant curve.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Efficient Deep Learning for Medical Imaging: Precision Segmentation and Beyond
    (Universitat de Barcelona, 2026-01-22) Gago, Lucas Martín ; Igual Muñoz, Laura; Remeseiro López, Beatriz; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] This thesis advances automated medical image analysis by introducing four deep learning frameworks that systematically address core technical barriers to clinical deployment, including computational efficiency, variability in image quality, and the robust integration of imaging with clinical data. Through a compendium of research articles, we develop state-of-the-art solutions spanning ultrasound and MRI. First, we present an end-to-end framework for carotid intima-media thickness (CIMT) measurement in ultrasound images, achieving state-of-the-art atherosclerotic plaque characterization while delivering a 20x speed improvement (0.79 to 0.04 seconds per image). The system provides comprehensive outputs, including segmentation masks, automated measurements, and binary plaque detection, eliminating domain-specific post-processing requirements. Secondly, leveraging the features extracted by our end-to-end model, we pioneer their integration into clinical survival models, demonstrating that learned imaging biomarkers significantly enhance cardiovascular risk stratification with a 20% improvement in patient risk reclassification beyond traditional clinical variables. Third, we develop a multilevel EfficientNet-UNet++ architecture for 3D carotid vessel wall segmentation in black-blood MRI that achieves state-of-the-art performance through contextual slice concatenation and resolution optimization. The framework demonstrates optimal performance at 256 x 256 input resolution (6x original size) while maintaining computational efficiency through targeted multilevel processing. Finally, we introduce a quality-aware segmentation framework with custom loss functions for explicit quality modeling during training. When applied to ultrasound colon wall segmentation, this approach achieves a 20% improvement on medium-quality images and a 31% improvement on low-quality images, directly addressing ultrasound's fundamental challenge of variable image quality. Collectively, these contributions establish the technical foundations for robust clinical imaging through efficient segmentation architectures, the integration of imaging with clinical data, explicit quality modeling, and comprehensive clinical validation across two medical imaging modalities.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Generative Deep Learning for Cancer Image analysis
    (Universitat de Barcelona, 2025-10-22) Osuala, Richard; Lekadir, Karim, 1977-; Díaz, Oliver; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] Accurate and timely detection of cancerous lesions in medical imaging is essential for effective treatment. However, the diagnosis remains challenging due to, among others, tumor heterogeneity, imaging constraints, and observer variability. Deep learning architectures, such as convolutional and transformer-based networks, have been showing promise in improving cancer image analysis by learning complex patterns within features from raw imaging data, allowing for earlier, more precise detection and consistent, data-driven decision-making. Despite its potential, clinical adoption of deep learning is restricted by the need for large, annotated training datasets, which are scarce due to privacy and labeling cost constraints, as well as due to its variability in performance when applied in settings of domain shift, imaging artifacts, variation in imaging protocols, and patient populations. This thesis identifies and addresses the challenges in deep learning for cancer imaging through five core publications that propose novel frameworks, methods, and solutions. First, a large-scale survey of generative models in cancer imaging is conducted leading to the identification of key challenges and problems in the field alongside ideation of potential solutions. Based on these findings, the SynTRUST meta-analysis framework is derived to assess the trustworthiness and maturity level of cancer image synthesis studies and solutions. Second, conditional generative adversarial networks (GANs) are applied to the challenges of scarcity of cancer images and tumor annotations, by simulating dynamic contrast-enhanced breast magnetic resonance imaging (DCEMRI) sequences. Without relying on physical contrast agents or DCE-MRI data from real patients, this approach enables unsupervised tumor detection, localization, and characterization, along with providing synthetic training data for increasing the robustness of downstream task models such as tumor segmentation models. Third, a multi-conditional latent diffusion models is developed to translate non-contrast enhanced MRI images into variable time-dependent synthetic DCE-MRI images localizing tumors and predicting their contrast enhancement kinetic patterns. Addressing the need for respective quantitative evaluation metrics, the Fréchet Radiomics Distance (FRD) is proposed to measure (synthetic) image quality based on biomarker variability. Fourth, a mass malignancy-conditioned generative adversarial network (MCGAN) is proposed to generated synthetic data as privacy-preservation mechanism for training deep learning models without individual patient data. Via comparison and combination with differential privacy, the synthetic mammography data is shown to improve the performance in multiple privacy-preserving cancer classification scenarios. Fifth, the medigan library is introduced as sharing platform for pretrained generative models that enable researchers to generate high-quality synthetic data across diverse imaging modalities without requiring direct access to sensitive patient data. Additionally, medigan’s generative models are comprehensive analyzed based on the Fréchet Inception Distance (FID) using both radiology domain-specific and standard domain-invariant feature extractors. In conclusion, this thesis highlights the potential of generative deep learning to address the key challenges in cancer imaging, presenting novel methods in contrast enhancement simulation, tumor localization, privacy-preserving cancer classification, and tools for sharing and assessing generative models, paving the way for these models towards integration into clinical practice to the end of advancing healthcare for both individual patients and society at large.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Constructive Methods in KAM Theory for Quasi-Periodic Time-Dependent Hamiltonian Systems and Applications
    (Universitat de Barcelona, 2025-11-04) Porras Flores, Pedro; Calleja Castillo, Renato Carlos; Haro, Àlex; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] In this work, we prove a KAM theorem and present an algorithm formulated in an a-posteriori format, using the parameterization method to look invariant tori in non-autonomous Hamiltonian systems with n degrees of freedom that depend periodically or quasi-periodically (QP) on time, with f external frequencies. Such a system is described by a Hamiltonian function in the 2n-dimensional phase space, M, that depends also on f angles, ϕ ∈ TR. We take advantage of the fibbered structure of the extended phase space M × TR. As a result of our approach, the parameterization of tori requires the last f variables, to be precise ϕ, while the first 2n components are determined by an invariance equation. This reduction decreases the dimension of the problem where the unknown is a parameterization from 2(n + f) to 2n. We employ a quasi-Newton method, in order to prove the KAM theorem. This iterative method begins with an initial parameterization of an approximately invariant torus, meaning it approximately satisfies the invariance equation. The approximation is refined by applying corrections that reduce quadratically the invariance equation error. This process converges to a torus in a complex strip of size ρ∞, provided suitable Diophantine (γ, τ ) conditions and a non-degeneracy condition on the torsion are met. Given the nature of the proof, this provides a numerical method that can be effectively implemented on a computer, We exhibit the algorithm with two models. The first is a Tokamak model [CVC+05, VL21], which proposes a control method to create barriers to the diffusion of magnetic field lines through a small modification in the magnetic perturbation. The second model [dCN00], known as the vorticity defect model, describes the nonlinear evolution of localized vorticity perturbations in a constant vorticity flow. This model was originally derived in the context of plasma physics and fluid dynamics.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Astronomical observation Scheduling Problem: a comprehensive study and novel metaheuristic solutions
    (Universitat de Barcelona, 2025-11-12) Nakhjiri, Nariman; Salamó Llorente, Maria; Sànchez i Marrè, Miquel, 1964-; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] As the complexity of large-scale astronomical surveys increases, the need for intelligent and adaptive scheduling systems has become critical to maximizing scientific return. The Astronomical Observation Scheduling (AOS) problem represents a complex and highly constrained case of combinatorial optimization, characterized by strict computational time limits and frequent changes. Its unique structure and challenges motivate focused research to develop flexible and scalable scheduling solutions. This research is organized into two main phases, which together comprise its four core contributions. The first phase focuses on heuristic research with the aim of developing efficient heuristic strategies that effectively address the specific constraints and structure of the AOS problem. The first core contribution is the introduction of the Conflict Resolution Unit (CRU) heuristic algorithm and its variants, designed to fulfill the objectives of this phase. The second and principal phase focuses on metaheuristic research, aiming to design algorithms that are both flexible and scalable, and capable of addressing the diverse level of complexities and changes in AOS. To ensure that these metaheuristics are well-adapted to the problem, they incorporate the heuristics developed in the first phase as core components. The second contribution is the Accumulative Planner (AP) algorithm, which integrates the CRU heuristic with a greedy strategy to form a fast, primarily local optimization algorithm for AOS, with competent results. These results were used as a baseline for further improvements. The third core contribution is the Hybrid Accumulative Planner (HAP) algorithm, developed to overcome the limitations of AP. HAP uses a modified version of CRU and a multi-start strategy to enable a broader and more robust search process. The fourth and final core contribution is the Forgetful Swarm Optimization (FSO) algorithm. It combines another CRU variant with a Destroy-and-Repair strategy and a Swarm Intelligence framework to deliver a capable global optimization method. FSO is designed to balance the search in exploration and exploitation, achieving high-quality results within a reasonable computational time, while preserving the precision of domain-specific heuristics. The core contributions are adapted to a real-world example of AOS problems and evaluated using its available datasets. These datasets present a variety of test scenarios with diverse characteristics, highlighting the challenges that the algorithms must address. Besides the core contributions, the evaluation includes other adapted algorithms for this real-world problem to provide a better perspective on relative performance. These include an Evolutionary Algorithm, an Iterated Local Search, and a Hill-Climbing Greedy. The results show the effectiveness of the proposed heuristic, CRU, and its variants in handling different tasks and constraints of AOS. Furthermore, all metaheuristics that leverage CRU as a core component produce high-quality solutions. The mostly local optimization algorithm of AP competes with global approaches in terms of solution quality, even surpassing them in some cases, while operating at a fraction of their computational cost. On the other hand, FSO consistently outperforms all other algorithms across the evaluated datasets, with a significantly lower computational cost than other global optimization algorithms, such as the evaluated Evolutionary Algorithm. The HAP algorithm performs between the two other proposed metaheuristics in terms of both solution quality and computational cost. Additionally, this thesis presents an algorithm design framework that formalizes the development process leading to these solutions. This work advances the state of the art in AOS research. The novel proposals, in particular the FSO algorithm, aim to set a benchmark for future studies.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Contributions to the Theory of Large Cardinals Beyond Choice
    (Universitat de Barcelona, 2025-10-30) Mohammd, Marwan Salam; Bagaria, Joan; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] This thesis investigates large cardinals that are inconsistent with the Axiom of Choice. First, we characterize Berkeley cardinals in terms of a restricted form of Vopěnka’s Principle, and determine the consistency strength of several related theories. Next, we present a method for producing elementary embeddings from homomorphisms, which is then used to show that the Strongly Rigid Relation Principle is a weak Choice principle. We also provide a characterization of rank-Berkeley cardinals in terms of a strong failure of this principle. We then explore the connection between elementary embeddings from the universe into itself and eventually dominating functions, culminating in an alternative proof of Kunen’s Inconsistency Theorem. Finally, using the method of forcing, we establish the consistency (relative to large cardinals) of the successor of the first singular cardinal being supercompact in the transitive model of Hereditarily Ordinal Definable sets.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Methods and Benchmarks for Trustworthy AI in Breast Imaging
    (Universitat de Barcelona, 2025-12-17) Garrucho Moras, Lidia; Lekadir, Karim, 1977-; Igual Muñoz, Laura; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] Breast cancer remains one of the most pressing global health challenges, with early detection and effective treatment planning relying heavily on advanced imaging and accurate interpretation. This PhD thesis addresses critical limitations in artificial intelligence (AI) applications for breast cancer imaging, specifically the lack of generalisability across clinical centres and the need for improved fairness across patient subgroups. The work focuses on two key modalities: digital mammography for early lesion detection, and dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) for tumor segmentation and treatment response prediction. Four core contributions are presented: (1) a deep learning-based domain generalization framework for robust mass detection across unseen mammography domains; (2) a GAN-based augmentation method to improve detection in women with dense breast tissue, addressing a known fairness gap; (3) an image synthesis and domain adaptation strategy to harmonize MRI protocol variability and improve tumor segmentation; and (4) the development of a large-scale, multi-centre breast DCEMRI dataset with expert annotations and clinical outcome labels. These efforts culminated in the organization of the international MAMA-MIA Challenge (MICCAI 2025)—the first benchmark to evaluate breast MRI segmentation and treatment response prediction with integrated subgroup-aware fairness metrics. Together, these contributions demonstrate that targeted algorithmic innovation, inclusive data design, and open benchmarking can substantially enhance the robustness, equity, and translational potential of AI in breast cancer imaging. This thesis lays the foundation for next-generation decision support systems that are not only technically reliable, but also ethically aligned with the goals of personalized and equitable cancer care.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Abelian Varieties of GLn-type and Galois Representations
    (Universitat de Barcelona, 2025-11-28) Florit Zacarías, Enric; Dieulefait, L. V. (Luis Victor); Fité Naya, Francesc; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] In this thesis, the artimetic properties of abelian manifolds are considered in relation to their algebras of endomorphisms. More precisely, we study the good reductions of an abelian manifold defined over a field of numbers, as well as those of associated Galois representations. We also give some results of modularity of abelian manifolds with respect to modular Siegel forms. Chapter 1 gives some definitions and preliminary results on simple algebras and abelian manifolds. The work itself begins with Chapter 2, where we study the immersions of simple algebras. We have placed special emphasis on characterizing the existence of an immersion between two simple algebras. We give a specialization of a Chia-Fu Yu criterion for algebras on global and local bodies, which plays an important role in Chapters 3, 5 and 7. Chapter 3 studies the properties of abelian manifolds defined on finite fields under the hypothesis that the algebra of endomorphisms is noncommutative. We focus on classifying the 4-abelian manifolds with quaternionic multiplication. We prove the following result: an abelian manifold over a field of numbers with noncommutative endomorphisms is a non-simple modulus all first out of a finite set. This statement generalizes the analogous result for the so-called "false elliptical curves", and makes one of the directions of the Murty and Patankar Conjecture more precise. On the other hand, we also give an example of a 4-abelian manifold with exactly two geometrically simple reductions. In Chapter 4, we begin the description of Galois representations associated with abelian manifolds with some non-integer endomorphism. We describe the irreducible components of the Tate modulus in terms of the algebra of endomorphisms, and prove that Galois representations take values in a form of the algebraic group GLn. We also explain the nature of Weil's pairing in these irreducible components, which depends on the Albert type of the algebra of endomorphisms. Chapter 5 is based on a joint work with F. Fité and X. Guitart. We define the notion of genuinely GLn-type abelian manifold, generalizing the GL2-type abelian manifolds without potential complex multiplication considered by Ribet. The system of representations associated with these manifolds has the property of being absolutely irreducible when making a change of basis to a finite extension. We give a theory of building blocks for these varieties. Under a certain technical hypothesis, we also define the inner twists and the character of an abelian variety, called Nebentipus. We characterize the manifolds with symplectic or orthogonal Galois representation, which we genuinely call GSpn or GOn type, respectively. In this way, we extend the class of abelian varieties with such representations given earlier by Banaszak, Gajda and Krasoń. Finally, we show that a genuinely GL4 type abelian manifold is Siegel's modular if and only if it is genuinely GSp4 type. In Chapter 6 we construct a GL4 family of building blocks. These are given by the Jacobian women of certain curves of genus 2 with a Richelot isogeny in their Galois conjugates. Under certain conditions, Weil's constraint gives us examples of 4-abelian manifolds genuinely of type GSp4. The family includes examples of images of Galois representations in GSp4 and non-trivial Nebentype. Chapter 7 is based on a joint work with A. Pacetti. It deals with Galois representations associated with abelian k-manifolds. One of the main points is that we do not assume that all endomorphisms of the manifold are defined on the base field. We give a procedure to construct a representation of the absolute Galois group of k associated with a k-abelian manifold. In addition, we give some results on the induced Weil pairing to these representations. As an application, we demonstrate that abelian surfaces over Q with potential quaternionic multiplication are Siegel modulars.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Deep Learning Solutions for Semantic Segmentation of Topographic Airborne LiDAR Point Clouds
    (Universitat de Barcelona, 2026-02-13) Carós, Mariona; Vitrià i Marca, Jordi; Seguí Mesquida, Santi; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] Airbome LiDAR has become a key technology for large-scale mapping, providing dense three-dimensional point clouds that capture both natural landscapes and human-made infrastructure. Transforming these raw data into semantic information, however, remains a challenge due to irregular sampling patterns, strong class imbalance, and distribution shifts across regions and acquisition conditions. This thesis addresses these challenges by developing deep learning solutions tailored to the semantic segmentation of topographic airborne LiDAR point clouds, with an emphasis on operational applicability in national mapping workflows. We first introduce object-centric methods for detecting and segmenting vertical objects in cluttered scenes, proposing a constrained sampling that enhances the characterization of vertical structures embedded in vegetation. We then investigate training and inference procedures to handle variability in density and scale, demonstrating how inductive biases and uncertainty-based inference substantially improve robustness without requiring architectural modifications. To reduce reliance on costly manual annotation, we adapt self-supervised learning to airborne LiDAR data, showing that Barlow Twins pre-training improves downstream segmentation, particularly for underrepresented classes. Finally, we explore domain adaptation and incremental learning, integrating LoRA into PointNet++ to achieve parameter-efficient fine-tuning. We show how LoRA facilitates the addition of new semantic categories with minimal overhead. Beyond methodological advances, this research contributes new resources to the community, including the release of the TerLiDAR dataset. In addition, several of the proposed methods have also been transferred to productive workflows at the Institut Cartografíe i Geologic de Catalunya, where they support tasks such as refining digital surface models, detecting missing transmission towers, recovering filtered power lines, and classifying wind turbines. Together, these contributions demonstrate how deep learning can be scaled and adapted for reliable, real-world airborne LiDAR semantic segmentation, bridging the gap between research innovation and productive workflows.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Training More Efficient Neural Networks
    (2025-12-04) Riera Molina, Carles Roger; Puertas i Prats, Eloi
    [eng] This thesis centers on a critical reassessment of standard practices in the training and pruning of deep neural networks, with the ultimate goal of exploring more efficient, interpretable, and theoretically grounded alternatives. Traditionally, deep learning models rely on a range of architectural and optimization techniques-such as residual connections (ResNet) or batch normalization-that, while effective in facilitating training and improving convergence, can introduce significant limitations. These methods often promote the use of overparameterized networks, where many parameters are underused or entirely inactive, and where certain training data points are effectively ignored, producing zero outputs or gradients. In this context, the first objective of the thesis is to show that it is possible to train neural networks effectively and robustly without relying on these conventional strategies, as long as both parameters and data are more fully utilized. This goal is realized through the introduction of two contributions: Linked Neurons and Jumpstart. Linked Neurons represent a family of activation functions that combine various nonlinear behaviors while sharing parameters, ensuring that every weight receives meaningful gradients and avoiding the problem of dead units. This enables improved model performance without increasing network size. In parallel, Jumpstart is a regularization technique designed to penalize both dead and purely linear units, thereby promoting effective nonlinear activation across all neurons. This regularization ensures that every unit contributes actively to the learning process, improving gradient flow and enabling more efficient use of training data. This mechanism not only enhances the capacity utilization of the model but also allows for the training of deeper networks without the need for traditional architectural crutches such as ResNet or BatchNorm-fulfilling one of the thesis's core objectives. The second objective is to revisit the Lottery Ticket Hypothesis (LTH), which posits that within a randomly initialized neural network, there exist subnetworks-or "winning tickets"-that can be trained in isolation to achieve performance comparable to the full model. However, this hypothesis currently depends on iterative pruning and the rewinding of selected weights to their original initialization, introducing a strong dependency on initialization and a significant computational overhead. With the integration of Jumpstart, the thesis demonstrates that both rewinding and iterative pruning can be eliminated, as enhanced gradient flow reduces sensitivity to initialization and allows sparse networks to be trained directly. Finally, the third objective of the thesis is to replace heuristic pruning strategies-such as magnitude-based pruning-that lack theoretical justification and may harm model performance. In response, the thesis propases a novel pruning algorithm based on the analysis of how each unit permutes the dataset samples. This method identifies and removes redundant units while preserving the original decision function of the model, yielding a sparse yet functional representation of the network. Taken together, this thesis offers an alternative and complementary vision to current deep learning practice, addressing efficiency, robustness, and theoretical grounding in the training and compression of deep neural networks.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Topological Data Analysis Across Domains: From Point Clouds to Graphs
    (Universitat de Barcelona, 2025-12-18) Ferrà Marcús, Aina; Casacuberta, Carles; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] This thesis builds on the foundational principle of topological data analysis (TDA), i.e., tracking the evolution of homological features in filtered spaces, and demonstrates the broad applicability of TDA through five studies conducted in distinct scientific contexts. In each study, the practical part was carried out in collaboration with experts from the cor-responding fields: neuroscience, artificial intelligence, complex systems, and cardiovascular medicine. Across these studies, TDA techniques are integrated with machine learning mod-els, yielding improvements in classification accuracy and interpretability of the resulting pipelines. Besides the experimental analyses, our work contributes novel methodologies and theo-retical insights. Specifically: (1) We develop a TDA-based classifier based on the variation of persistence descriptors when new points are added to a point cloud, and show that the classifier's accuracy can be used to estímate an inherent dimension of a data set, which, in our case, carne from a behavioral neuroscience study. (2) We design a method of importance attribution by selecting the most informative landscape levels for a neural network classifier of time series. (3) We prove that topological radiomics extracted from cardiovascular magnetic resonance images serve as a complement to standard collections of radiomic variables, achieving comparable accuracies with shorter feature vectors and less training time. (4) We implement extended persistence of cycles in graphs and introduce a new algorithm to replace an edge-weigthed graph with a vertex-weigthed one with the same persistence diagram, and we built a database of almost 800 000 graphs on which a neural network model was trained for latent dimensionality estimation of real-world net-works. (5) We enhance Mapper graphs with quantitave indices, which are used to achieve statistical significance using a dataset from a study of hemodynamic response to cardiac resynchronization therapy.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Deep Learning Approaches for Human Activity Understanding
    (Universitat de Barcelona, 2025-06-12) Zhang, Zejian; Escalera Guerrero, Sergio; Palmero Cantariño, Cristina; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] Understanding human activities is crucial for developing practical applications that benefit society. Temporal action localization (TAL) in untrimmed videos is one of the most challenging tasks in this field. While significant progress has been made over the years, the methods developed are still far from being suitable for real-world use, and TAL remains an ongoing challenge. This thesis aims to address this challenge task through three contributions. First, we propose a dual hierarchical model capable of extracting and fusing both local, fine-grained boundary details and broader, high-level semantic contexts for TAL. In this method, the second hierarchical design enables the model to uncover actions of varying durations, leveraging the features learned from the first hierarchy. Our findings show that fusing temporal contexts at different scales is essential for precise TAL. In this approach, the model utilizes the self-attention mechanism in Transformer encoders. However, due to the quadratic complexity of self-attention, methods relying on it may struggle to handle real-world-length videos. Next, we present a comprehensive experimental comparison to determine which temporal feature encoder should be selected under different conditions. We analyzed 12 models, equipped with pure Transformer encoders, pure Mamba Blocks, and combinations of both into a unified encoder for TAL. The experimental results suggest that the choice of encoder depends heavily on the specific dataset. Nevertheless, the pure Mamba Block emerges as the preferred option for unknown datasets due to its performance and lower complexity. Finally, we introduce UDIVA-HHOI, a novel large-scale audio-visual dyadic human-human-object interaction dataset. This dataset provides rich, extremely short-duration and concurrent actions, featuring both low-level physical actions and high-level goal-oriented actions and the objects involved in these actions—elements not typically represented in commonly used TAL benchmarks. UDIVA-HHOI opens up new possibilities for addressing the detection of complex interactive actions in real-world scenarios. Our preliminary study confirms its potential, and our analysis also offers recommendations for selecting an appropriate feature encoder for future research on this new benchmark, with the Mamba Block being the preferred choice.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Bridging Natural Language and Hierarchical Multivariate Data Visualisation to Support Data Analysis
    (Universitat de Barcelona, 2025-04-23) Kavaz, Ecem; Rodríguez Santiago, Inmaculada; Puig Puig, Anna; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] Tracking and analysing the vast amounts of data generated from social networks and digital platforms presents important challenges, not only due to the overwhelming volume but also the complex relationships embedded within the data. This thesis addresses these challenges through data visualisation techniques, focusing on hierarchical and multivariate data, where visual clutter and effective use of space are key concerns. Furthermore, the rise of Visual Natural Language Interfaces (V-NLIs), also referred to in this thesis as VisChatbots, offers new opportunities to facilitate the interaction with data visualisations via natural language. This thesis contributes to the fields of Hierarchical Multivariate Data Visualisation and Visualisation-oriented Natural Language Interfaces. Specifically, we introduce a novel categorization algorithm to classify hierarchical data, from which we propose the most suitable visual designs for their visualisation. Additionally, we propose a new incremental design methodology for Vis-Chatbots, called VisChat. This structured approach guides the development of chatbots integrated into visualisation platforms, establishing smooth communication among stakeholders—end users, designers, and developers—and introducing new design artefacts, such as the VisAgent persona, visualisation conversation patterns, and conversational transcripts that help guide and validate the design of the VisChatbot. Following the VisChat methodology, we have integrated a VisChatbot into a platform for visualising hierarchical and multivariate data. To validate our proposal, we present a case study on the analysis of hate speech in online news articles, where the suitability of the proposed visualisations was evaluated, as well as the capability of the visualisation chatbot to enable users to easily explore and understand, through Natural Language interactions, both the structural relationships and the feature-based relationships within the data. In conclusion, this thesis not only advances data visualisation techniques for multivariate hierarchical data but also establishes a framework for integrating natural language interfaces intov isual analysis platforms, thereby promoting a more efficient and effective analysis of data.
  • Thumbnail Image
    logoOpenAccessDoctoral thesis
    Large and iterated finite group actions on aspherical manifolds
    (Universitat de Barcelona, 2025-07-11) Daura Serrano, Jordi; Mundet i Riera, Ignasi; Universitat de Barcelona. Departament de Matemàtiques i Informàtica
    [eng] Finite transformation group theory investigates the finite symmetries of topological objects, such as manifolds or CW-complexes. In this thesis, we focus on actions on closed topological manifolds and adopt the following approach: instead of directly studying the action properties of a finite group G to a manifold M, we focus on the properties of action restricted to certain subgroups H of bounded index. Several problems align with this philosophy, such as determining whether the group of homeomorphisms of a manifold is Jordan, calculating the discrete degree of symmetry of a manifold, determining whether a manifold is quasi-asymmetric, and studying the number and size of isotropy subgroups for finite group actions on manifolds. In the first part of the thesis, we provide solutions to these problems for two general classes of manifolds, namely: (1) Closed, connected and aspherical manifolds, whose fundamental group has a group of external Minkowski automorphisms (a group G is Minkowski if there exists a constant C such that every finite subgroup H of G has order at most C). (2) Closed, connected and orientable manifolds that admit a non-zero degree application to a nilmanifold. We show that the group of external automorphisms of a lattice of a connected Lie group is Minkowski, which allows us to apply our results to locally homogeneous aspherical closed manifolds. In addition, we provide the earliest known examples of manifolds M and M' with isomorphic cohomology rings such that Homeo(M) is Jordan but Homeo(M') is not. We establish two stiffness results for the discrete degree of symmetry: if M is a closed, connected, aspherical manifold and the external automorphism group of the fundamental group of M is Minkowski, or if M admits a non-zero degree application to a nilmanifold and its fundamental group is virtually solvable, then M is homeomorphic to a torus if its discrete degree of symmetry is equal to the dimension of M. In the second part, we refine the concept of group actions to explore in greater depth the topological and cohomology rigidity of closed and connected manifolds. This framework allows us to analyze in more detail the structure of closed aspherical manifolds and those that admit a non-zero degree application to a nilmanifold. We define new invariants, such as the iterated length of a manifold, which is closely related to its self-coatings, and introduce a refined version of the discrete degree of symmetry, called the discrete degree of iterate symmetry. We show that if M is a closed, oriented manifold that admits a non-zero degree application to a nilmanifold of nilpotency class 2, and both manifolds have the same discrete degree of iterated symmetry, then the rational cohomology of M is isomorphic to that of the nilmanifold. Furthermore, if the fundamental group of M is virtually solvable, then M is homeomorphic to the nilmanifold. We also prove that if M is a locally homogeneous closed aspherical manifold with a discrete degree of iterated symmetry equal to its dimension, then M is homeomorphic to a nilmanifold of nilpotency class 2.