Departament de Matemàtiques i Informàtica: Recent submissions
Now showing items 1-20 of 40
Efficient and convergent natural gradient based optimization algorithms for machine learning
[eng] Many times machine learning is casted as an optimization problem. This is the case when an objective function assesses the success of an agent in a certain task and hence, learning is accomplished by optimizing that ...
About the connectivity of Fatou components for some families of rational maps
[eng] Rational iteration is the study of the asymptotic behaviour of the sequences given by the iterates of a rational map on the Riemann sphere. According to Montel's theory on normal families, the phase space (also called ...
Higher regularity of free boundaries in obstacle problems
In the thesis we consider higher regularity of the free boundaries in different variations of the obstacle problem, that is, when the Laplace operator b. is replaced with another elliptic or parabolic operator. In the ...
Aleatoric Uncertainty Modelling in Regression Problems using Deep Learning
Nowadays, we live in an intrinsically uncertain world from our perspective. We do not know what will happen in the future but, to infer it, we build the so-called models. These models are abstractions of the world we live ...
Chern degree functions and Prym semicanonical pencils
Abelian varieties are projective algebraic varieties endowed with a group structure. They constitute one of the most explored objects in Algebraic Geometry throughout the last decades. On the one hand, abelian varieties ...
Invariant manifolds and transport in a Sun-perturbed Earth-Moon system
This dissertation is devoted to the analysis of the motion of small bodies, like asteroids, in the neighbourhood of the Earth-Moon system from a celestial mechanics approach. This is an extensive area of research where ...
Hitting probabilities for g-Gaussian processes
We develop criteria for hitting probabilities of Gaussian random fields with associated canonical metric given by a class of gauge functions. This yields upper and lower bounds in terms of general notions of Hausdorff ...
Weighted restricted weak-type extrapolation on classical Lorentz spaces
An important result in Harmonic Analysis is the extrapolation theorem of Rubio de Francia. In its original version says that if T is a sublinear operator that is bounded in Lp0 pvq, for some p0 ě 1 and every v P Ap , then ...
Lifestyle Understanding through the Analysis of Egocentric Photo-streams
Describing people’s lives has become a hot topic in several disciplines. Lifelogging appeared in the 1960s as the process of recording and tracking personal activity data generated by the daily behaviour of a person. The ...
Value-aligned norm selection
Norms have been widely enacted in both human and agent societies to regulate the actions that individuals can perform. However, although legislators may have ethics in mind when establishing norms, moral values are seldom ...
Gröbner's problem and the geometry of GT-varieties
Within the framework of algebraic geometry and commutative algebra, this thesis makes advances in (1) the Gröbner's longstanding problem of determining whether a monomial projection of the Veronese variety Vn,d is an aCM ...
Adapting by copying. Towards a sustainable machine learning
Despite the rapid growth of machine learning in the past decades, deploying automated decision making systems in practice remains a challenge for most companies. On an average day, data scientists face substantial barriers ...
Option Price Decomposition for Local and Stochastic Volatility Jump Diffusion Models
In this thesis, an option price decomposition for local and stochastic volatility jump diffusion models is studied. On the one hand, we generalise and extend the Alòs decomposition to be used in a wide variety of models ...
On Logics and Semantics for Interpretability
In the central part of this thesis we study for different interpretability logics the following aspects: completeness for modal semantics, decidability and algorithmic complexity. In particular, we will study two basic ...
Deep Multimodal Learning for Egocentric Storytelling and Food Analysis
The world of Machine Learning and Computer Vision has experienced a revolution since the last years. The appearance of Deep Learning algorithms and Convolutional Neural Networks, altogether with the increased processing ...
On the effect of the Sun's gravity around the Earth-Moon L1 and L2 libration points
In this thesis we explored some aspects of the dynamics around the Earth-Moon L1 and L2 points in the context of two Restricted Four Body Problems: the Bicircular Problem (BCP) and the Quasi-bicircular Problem (QBCP). Both ...
Modelling Uncertainty in Black-box Classification Systems
Currently, thanks to the Big Data boom, the excellent results obtained by deep learning models and the strong digital transformation experienced over the last years, many companies have decided to incorporate machine ...
Contributions to the theory of Large Cardinals through the method of Forcing
The present dissertation is a contribution to the field of Mathematical Logic and, more particularly, to the subfield of Set Theory. Within Set theory, we are mainly concerned with the interactions between the largecardinal ...
Statistical modelling of avalanche observables: criticality and universality
Complex systems can be understood as an entity composed by a large number of interactive elements whose emergent global behaviour cannot be derived from the local laws characterizing their constituents. The observables ...
Blow-up algebras in Algebra, Geometry and Combinatorics
The primary topic of this thesis lies at the crossroads of Commutative Algebra and its interactions with Algebraic Geometry and Combinatorics. It is mainly focused around the following themes: I Defining equations ...
