This final degree project consists in the implementation of First Order Logic theory and algorithms in Haskell, a functional programming language. Furthermore, a relation between maths and programming based on Curry-Howard correspondence is established, giving an intuitive sort of examples. Moreover, it aims to give an introduction to Haskell...
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July 26, 2017 (v1)PublicationUploaded on: March 27, 2023
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August 6, 2021 (v1)Publication
En aprendizaje automático partimos de un conjunto de datos que queremos explicar. Con ese objetivo, se diseña un modelo que permite hacer predicciones. Estos conjuntos de datos pueden ser de muy distinta naturaleza, así como los problemas que plantean: clasificación supervisada o no supervisada, regresión... En este trabajo, hemos estudiado,...
Uploaded on: December 4, 2022 -
June 30, 2022 (v1)Publication
The automatic recognition of a person's emotional state has become a very active research field that involves scientists specialized in different areas such as artificial intelligence, computer vi sion, or psychology, among others. Our main objective in this work is to develop a novel approach, using persistent entropy and neural networks as...
Uploaded on: December 4, 2022 -
June 22, 2020 (v1)Publication
The canon of the baroque Spanish literature has been thoroughly studied with philological techniques. The major representatives of the poetry of this epoch are Francisco de Quevedo and Luis de Góngora y Argote. They are commonly classified by the literary experts in two different streams: Quevedo belongs to the Conceptismo and Góngora to the...
Uploaded on: March 27, 2023 -
July 1, 2022 (v1)Publication
One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such a training process consists of an iterative change of parameters trying to minimize a loss function. These changes are driven by a dataset, which can be seen as a set of labeled points in an n-dimensional space. In this...
Uploaded on: December 4, 2022 -
June 17, 2020 (v1)Publication
It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the existence, but it does not provide a method for...
Uploaded on: March 27, 2023 -
June 22, 2020 (v1)Publication
Filtration simplification consists of simplifying a given filtration while simultaneously controlling the perturbation in the associated persistence diagrams. In this paper, we propose a filtration simplification algorithm for orientable 2-dimensional (2D) manifolds with or without boundary ( meshes ) represented by2D combinatorial maps. Given...
Uploaded on: December 4, 2022 -
June 17, 2020 (v1)Publication
One of the main drawbacks of the practical use of neural networks is the long time needed in the training process. Such training process consists in an iterative change of parameters trying to minimize a loss function. These changes are driven by a dataset, which can be seen as a set of labeled points in an n-dimensional space. In this paper,...
Uploaded on: December 2, 2022 -
June 17, 2020 (v1)Publication
Neural networks present big popularity and success in many fields. The large training time process problem is a very important task nowadays. In this paper, a new approach to get over this issue based on reducing dataset size is proposed. Two algorithms covering two different shape notions are shown and experimental results are given.
Uploaded on: March 27, 2023 -
April 3, 2023 (v1)Publication
It is well-known that artificial neural networks are universal approximators. The classical existence result proves that, given a continuous function on a compact set embedded in an n-dimensional space, there exists a one-hidden-layer feed-forward network that approximates the function. In this paper, a constructive approach to this problem is...
Uploaded on: April 14, 2023 -
June 11, 2019 (v1)Publication
Emotion recognition and classification is a very active area of research. In this paper, we present a first approach to emotion classification using persistent entropy and support vector machines. A topology-based model is applied to obtain a single real number from each raw signal. These data are used as input of a support vector machine to...
Uploaded on: March 27, 2023 -
February 3, 2021 (v1)Publication
This paper proposes a method for learning the process of curve fitting through a general class of totally positive rational bases. The approximation is achieved by finding suitable weights and control points to fit the given set of data points using a neural network and a training algorithm, called AdaMax algorithm, which is a first-order...
Uploaded on: March 26, 2023 -
October 6, 2021 (v1)Publication
In this paper, we de ne a new avour of well-composedness, called Euler well-composedness, in the general setting of regular cell complexes: A regular cell complex is Euler well-composed if the Euler characteristic of the link of each boundary vertex is 1. A cell decomposi- tion of a picture I is a pair of regular cell complexes ����� K(I);K(...
Uploaded on: March 25, 2023 -
September 23, 2016 (v1)Publication
En este artículo se resuelven una serie de problemas extraídos de diferentes situaciones de la vida real con ayuda de técnicas propias de la Teoría de Grafos. Se pretende con ello dar a conocer al profesorado de Matemáticas de Secundaria y Bachillerato una nueva forma de abordar con éxito problemas de esas características, consiguiendo con...
Uploaded on: December 4, 2022 -
February 3, 2021 (v1)Publication
Broadly speaking, an adversarial example against a classification model occurs when a small perturbation on an input data point produces a change on the output label assigned by the model. Such adversarial examples represent a weakness for the safety of neural network applications, and many different solutions have been proposed for minimizing...
Uploaded on: March 25, 2023 -
October 20, 2021 (v1)Publication
Simplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial complexes. It has been proved that simplicial-map neural networks are universal approximators and that they can be refined to be robust to adversarial attacks. In this paper, the refinement toward robustness is optimized...
Uploaded on: December 4, 2022 -
March 21, 2022 (v1)Publication
In this paper, we define a new flavour of well-composedness, called strong Euler well composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an (n−1)-dimensional...
Uploaded on: March 25, 2023 -
July 12, 2024 (v1)Publication
Machine learning algorithms are fundamental components of novel data-informed Artificial Intelligence architecture. In this domain, the imperative role of representative datasets is a cornerstone in shaping the trajectory of artificial intelligence (AI) development. Representative datasets are needed to train machine learning components...
Uploaded on: July 13, 2024 -
February 8, 2024 (v1)Publication
Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known...
Uploaded on: February 11, 2024 -
July 17, 2024 (v1)Publication
In recent years, Deep Learning has gained popularity for its ability to solve complex classification tasks, increasingly delivering better results thanks to the development of more accurate models, the availability of huge volumes of data and the improved computational capabilities of modern computers. However, these improvements in performance...
Uploaded on: July 18, 2024