Universitat de Barcelona
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[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 ...
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 ...
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 ...
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 ...
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 ...
The aim of this dissertation is to present some new results on stochastic analysis. It consists on three works that deal with two Gaussian processes: the Brownian motion and the fractional Brownian motion with Hurst parameter ...
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 ...
Several computer vision approaches have been proposed for tackling food analysis problems, due to the challenging problem it poses, the ease collection of food images, and its numerous applications to health and leisure. ...
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 ...
This thesis deals with the jet transport for numerical integrators and the effective invariant object computation of delay differential equations. Firstly we study how automatic differentiation (AD) affects when ...
[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 ...
The representation (or feature) learning has been an emerging concept in the last years, since it collects a set of techniques that are present in any theoretical or practical methodology referring to artificial intelligence. ...
En esta tesis se estudian problemas relacionados con acciones de grupos finitos en 4-variedades diferenciables y simplécticas. Se prueba que toda 4-variedad diferenciable cerrada X admite una constante C>0 tal que cualquier ...
The theory of Bergman spaces has been a central subject of study in complex analysis during the past decades. The book [7] by S. Bergman contains the first systematic treat-ment of the Hilbert space of square integrable ...
En esta tesis abordamos el problema de la aproximación de anillos locales por anillos de Gorenstein en el caso cero-dimensional. Nos centramos en el estudio y el cálculo efectivo de la colongitud de Gorenstein, una noción ...
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 ...
The main goal of this work is to study vector-valued Bergman spaces and to obtain the weak factorization of these spaces. In order to do that we need to study small Hankel operators with operator-valued holomorphic symbols. ...
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 ...
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 ...
Facial expressions are vital ways of communication between humans in social contexts. They are used as conversational markers and they convey information about affective and cognitive state. Many applications would benefit ...
