Perfil del autor: González Díaz, Rocío
Datos institucionales
Nombre | González Díaz, Rocío |
Departamento | Matemática Aplicada I |
Área de conocimiento | Matemática Aplicada |
Categoría profesional | Catedrática de Universidad |
Correo electrónico | Solicitar |
Estadísticas
-
Nº publicaciones
111
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Nº visitas
12859
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Nº descargas
19746
Publicaciones |
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Artículo
Trainable and explainable simplicial map neural networks
(ELSEVIER SCIENCE INC, 2024)
Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal ... |
Artículo
An in-depth analysis of data reduction methods for sustainable deep learning
(F1000 Research / European Commission, 2024)
In recent years, Deep Learning has gained popularity for its ability to solve complex classification tasks, increasingly ... |
Trabajo Fin de Grado
Análisis topológico de las matrices de ocurrencias en la red de Bitcoin
(2023)
Tras el nacimiento de Bitcoin, se ha producido una profunda transformación en los mercados digitales y la bolsa, dando ... |
Trabajo Fin de Grado
Estudio del conocimiento actual en la compresión de datos para el aprendizaje automático
(2023)
En este trabajo fin de grado se estudian tantos los métodos actuales como el contexto en el ámbito de empresas, investigaciones ... |
Trabajo Fin de Máster
Análisis Topológico de Datos y Aprendizaje Automático en la Detección De Ríos Atmosféricos
(2022)
Un río atmosférico (RA) es una banda alargada y estrecha de humedad muy concentrada en la parte inferior de la troposfera ... |
Trabajo Fin de Máster
Predicción de Aristas para Data Augmentation en Problemas de Clasificación de Nodos con Graph Neural Networks
(2022)
En este trabajo, repasamos detalladamente el planteamiento de un problema de aprendizaje supervisado en general, sobre ... |
Artículo
Topology-based representative datasets to reduce neural network training resources
(Springer, 2022)
One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such ... |
Artículo
Continuous Well-Composedness Implies Digital Well-Composedness in n-D
(Springer, 2022)
In this paper, we prove that when a n-D cubical set is continuously well-composed (CWC), that is, when the boundary of its ... |
Trabajo Fin de Grado
Análisis y estudio del grafo de transacciones de Bitcoin
(2022)
Durante los últimos años, el mundo del Bitcoin y las criptomonedas ha revolucionado por completo el concepto de pago y ... |
Artículo
Emotion recognition in talking-face videos using persistent entropy and neural networks
(American Institute of Mathematical Sciences (AIMS), 2022)
The automatic recognition of a person’s emotional state has become a very active research field that involves scientists ... |
Trabajo Fin de Máster
On the Categorical Theory of Persistence Modules
(2021)
¿Cómo se infieren formas a partir de datos? Se pueden emplear técnicas del álgebra y la topología computacional para ... |
Artículo
Simplicial-Map Neural Networks Robust to Adversarial Examples
(MDPI [Commercial Publisher], 2021)
Broadly speaking, an adversarial example against a classification model occurs when a small perturbation on an input data ... |
Tesis Doctoral
Computational topology on neural networks: from the data to the model
(2021)
Machine learning is drawn from a dataset that needs to be explained. Following this aim, a model is described to make ... |
Trabajo Fin de Máster
Un estudio sobre la homología persistente con coeficientes enteros
(2021)
La homología persistente es una técnica que se usa para analizar la evolución de una cierta propiedad algebraica, la ... |
Ponencia
Image = Structure + Few Colors
(Springer, 2021)
Topology plays an important role in computer vision by capturing the structure of the objects. Nevertheless, its potential ... |
Artículo
Making Sullivan Algebras Minimal Through Chain Contractions
(Springer, 2021)
In this note, we provide an algorithm that, starting with a Sullivan algebra gives us its minimal model. More concretely, ... |
Artículo
Optimizing the Simplicial-Map Neural Network Architecture
(MDPI, 2021)
Simplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial ... |
Trabajo Fin de Grado
Visualizando la evolución de los casos de COVID-19 con TDA
(2021)
A continuación, se expone en este documento la memoria del trabajo de fin de grado basado en el análisis de datos de ... |
Artículo
Strong Euler well-composedness
(Springer, 2021)
In this paper, we define a new flavour of well-composedness, called strong Euler well composedness. In the general setting ... |
Artículo
Persistence Partial Matchings Induced by Morphisms between Persistence Modules
(Cornell University, 2021)
The notion of persistence partial matching, as a generalization of partial matchings between persistence modules, is ... |
Artículo
Characterizing slope regions
(Springer, 2021)
This paper provides a theoretical characterization of monotonically connected image surface regions, called slope regions. ... |
Artículo
Neural-Network-Based Curve Fitting Using Totally Positive Rational Bases
(MDPI, 2020)
This paper proposes a method for learning the process of curve fitting through a general class of totally positive rational ... |
Artículo
Two-hidden-layer feed-forward networks are universal approximators: A constructive approach
(ScienceDirect, 2020)
It is well-known that artificial neural networks are universal approximators. The classical existence result proves that, ... |
Trabajo Fin de Máster
Análisis topológico de datos: aplicación al reconocimiento de emociones
(2020)
Emotion recognition consists of a series of processes to detect human emotions from facial human expressions. Humans ... |
Ponencia
A 4D counter-example showing that DWCness does not imply CWCness in n-D
(Springer, 2020)
In this paper, we prove that the two avours of well-compo- sedness called Continuous Well-Composedness (shortly CWCness), ... |
Artículo
Approximating lower-star persistence via 2D combinatorial map simplification
(Elsevier, 2020)
Filtration simplification consists of simplifying a given filtration while simultaneously controlling the perturbation in ... |
Artículo
Digitization
(Springer, 2020)
|
Artículo
Basis-independent partial matchings induced by morphisms between persistence modules
(Cornell University, 2020)
In this paper, we study how basis-independent partial matchings induced by morphisms between persistence modules (also ... |
Ponencia
Euler Well-Composedness
(Springer, 2020)
In this paper, we de ne a new avour of well-composedness, called Euler well-composedness, in the general setting of regular ... |
Artículo
Representative Datasets: The Perceptron Case
(Cornell University, 2019)
One of the main drawbacks of the practical use of neural networks is the long time needed in the training process. Such ... |
Ponencia
One More Step Towards Well-Composedness of Cell Complexes over nD Pictures
(Springer, 2019)
An nD pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K, the set of n-cells incident ... |
Ponencia
A topological entropy‐based approach for damage detection of civil engineering structures
(Editorial Club Universitario, 2019)
In this study, a new method based on topological entropy, the so‐called persistent entropy, is presented for addressing ... |
Artículo
Topological signature for periodic motion recognition
(Cornell University, 2019)
In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such ... |
Artículo
Weakly well-composed cell complexes over nD pictures
(Elsevier, 2019)
In previous work we proposed a combinatorial algorithm to \locally repair" the cubical complex Q(I) that is canonically ... |
Ponencia
Towards Emotion Recognition: A Persistent Entropy Application
(Springer, 2019)
Emotion recognition and classification is a very active area of research. In this paper, we present a first approach to ... |
Ponencia
Congratulations! Dual Graphs are Now Orientated!
(Springer, 2019)
A digital image can be perceived as a 2.5D surface consisting of pixel coordinates and the intensity of pixel as height ... |
Artículo
Towards a Philological Metric through a Topological Data Analysis Approach
(Cornell University, 2019)
The canon of the baroque Spanish literature has been thoroughly studied with philological techniques. The major representatives ... |
Ponencia
On the Space Between Critical Points
(Springer, 2019)
The vertices of the neighborhood graph of a digital picture P can be interpolated to form a 2-manifold M with critical ... |
Artículo
Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
(Cornell University, 2019)
It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a ... |
Ponencia
Persistent Homology Computation Using Combinatorial Map Simplification
(Springer, 2019)
We propose an algorithm for persistence homology computation of orientable 2-dimensional (2D) manifolds with or without ... |
Ponencia
Computing and reducing slope complexes
(Springer, 2019)
In this paper we provide a new characterization of cell de- composition (called slope complex) of a given 2-dimensional ... |
Artículo
An algorithm to compute minimal Sullivan algebras
(Cornell University, 2019)
In this note, we give an algorithm that starting with a Sullivan algebra gives us its minimal model. This algorithm is a ... |
Artículo
Persistent entropy for separating topological features from noise in vietoris-rips complexes
(Springer, 2019)
Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called ... |
Ponencia
Counting slope regions in the surface graphs
(TUGraz OPEN Library, 2019)
The discrete version of a continuous surface sampled at optimum sampling rate can be well expressed in form of a neighborhood ... |
Artículo
A new entropy based summary function for topological data analysis
(Elsevier, 2018)
Topological data analysis (TDA) aims to obtain useful information from data sets using topological concepts. In particular, ... |
Artículo
On the stability of persistent entropy and new summary functions for Topological Data Analysis
(Cornell University, 2018)
Persistent entropy of persistence barcodes, which is based on the Shannon entropy, has been recently defined and successfully ... |
Artículo
Representative datasets for neural networks
(Elsevier, 2018)
Neural networks present big popularity and success in many fields. The large training time process problem is a very ... |
Artículo
Topological tracking of connected components in image sequences
(Elsevier, 2018)
Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. ... |
Artículo
Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images
(Springer, 2017)
A 3D binary image I can be naturally represented by a combinatorial-algebraic structure called cubical complex and denoted ... |
Artículo
Persistent-homology-based gait recognition
(Cornell University, 2017)
Gait recognition is an important biometric technique for video surveillance tasks, due to the advantage of using it at ... |
Artículo
A new topological entropy-based approach for measuring similarities among piecewise linear functions
(Elsevier, 2017)
In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing ... |
Ponencia
Separating Topological Noise from Features Using Persistent Entropy
(Springer, 2016)
Topology is the branch of mathematics that studies shapes and maps among them. From the algebraic definition of topology ... |
Ponencia
Parallel Homology Computation of Meshes
(Springer, 2016)
In this paper, we propose a method to compute, in parallel, the homology groups of closed meshes (i.e., orientable 2D ... |
Artículo
Topology-based image segmentation using LBP pyramids
(Springer, 2016)
In this paper, we present a new image segmentation algorithmwhich is based on local binary patterns (LBPs) and the ... |
Ponencia
Encoding Specific 3D Polyhedral Complexes Using 3D Binary Images
(Springer, 2016)
We build upon the work developed in [4] in which we presented a method to “locally repair” the cubical complex Q(I) ... |
Ponencia
Persistent homology-based gait recognition robust to upper body variations
(IEEE Computer Society, 2016)
Gait recognition is nowadays an important biometric technique for video surveillance tasks, due to the advantage of using ... |
Artículo
An entropy-based persistence barcode
(2015)
In persistent homology, the persistence barcode encodes pairs of simplices meaning birth and death of homology classes. ... |
Capítulo de Libro
LBP and irregular graph pyramids
(2015)
In this paper, a new codification of Local Binary Patterns (LBP) is given using graph pyramids. The LBP code characterizes ... |
Ponencia
Spatiotemporal Barcodes for Image Sequence Analysis
(Springer, 2015)
Taking as input a time-varying sequence of two-dimensional (2D) binary images, we develop an algorithm for computing a ... |
Artículo
3D well-composed polyhedral complexes
(2015)
A binary three-dimensional (3D) image II is well-composed if the boundary surface of its continuous analog is a 2D manifold. ... |
Artículo
Characterizing Configurations of critical points through LBP Extended Abstract
(Universidad de Sevilla, 2015)
In this abstract we extend ideas and results submitted to [3] in which a new codification of Local Binary Patterns (LBP) ... |
Artículo
Computing cup products in \(\mathbb {Z}_2\)-cohomology of 3D polyhedral complexes
(2014)
Let \(I=(\mathbb {Z}^3,26,6,B)\) be a three-dimensional (3D) digital image, let \(Q(I)\) be an associated cubical complex, ... |
Capítulo de Libro
Topological features for monitoring human activities at distance
(2014)
In this paper, a topological approach for monitoring human activities is presented. This approach makes possible to protect ... |
Capítulo de Libro
Gait-based carried object detection using persistent homology
(2014)
There are surveillance scenarios where it is important to emit an alarm when a person carrying an object is detected. In ... |
Artículo
Removal and contraction operations in nD generalized maps for efficient homology computation
(2014)
In this paper, we show that contraction operations preserve the homology of nD generalized maps, under some conditions. ... |
Capítulo de Libro
Gait-based gender classification using persistent homology
(2013)
In this paper, a topological approach for gait-based gender recognition is presented. First, a stack of human silhouettes, ... |
Capítulo de Libro
Towards Minimal Barcodes
(2013)
In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs ... |
Artículo
An application for gait recognition using persistent homology
(Universidad de Sevilla, 2013)
This Demo presents an application for gait recognition using persistent homology. Using a background subtraction approach, ... |
Artículo |
Artículo
Cups products in Z2-cohomology of 3D polyhedral complexes
(2012)
Let I=(Z3,26,6,B) be a 3D digital image, let Q(I) be the associated cubical complex and let ∂Q(I) be the subcomplex of ... |
Artículo
Geometric Objects and Cohomology Operations
(Cornell University, 2012)
Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology ... |
Capítulo de Libro
Removal operations in nD generalized maps for efficient homology computation
(2012)
In this paper, we present an efficient way for computing homology generators of nD generalized maps. The algorithm proceeds ... |
Capítulo de Libro
Human gait identification using persistent homology
(2012)
This paper shows an image/video application using topological invariants for human gait recognition. Using a background ... |
Artículo
Computational Topology in Image Context
(Elsevier, 2012)
|
Artículo
A tool for integer homology computation: lambda-AT- model
(2011)
In this paper, we formalize the notion of lambda-AT-model (where λ is a non-null integer) for a given chain complex, which ... |
Capítulo de Libro
Incremental-Decremental Algorithm for Computing AT-Models and Persistent Homology
(2011)
In this paper, we establish a correspondence between the incremental algorithm for computing AT-models [8,9] and the one ... |
Artículo
Chain Homotopies for Object Topological Representations
(2011)
This paper presents a set of tools to compute topological information of simplicial complexes, tools that are applicable ... |
Capítulo de Libro
Well-Composed Cell Complexes
(2011)
Well-composed 3D digital images, which are 3D binary digital images whose boundary surface is made up by 2D manifolds, ... |
Artículo
Invariant representative cocycles of cohomology generators using irregular graph pyramids
(2011)
Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological ... |
Capítulo de Libro
Cup products on polyhedral approximations of 3D digital images
(2011)
Let I be a 3D digital image, and let Q(I) be the associated cubical complex. In this paper we show how to simplify the ... |
Artículo
Cubical cohomology ring of 3D photographs
(2011)
Cohomology groups and the cohomology ring of three-dimensional (3D) objects are topological invariants that characterize ... |
Artículo
Proceedings of the Workshop on Computational Topology in Image Context 2010
(2010)
It has been an honor and a pleasure to organize the 3rd International Workshop on Computational Topology in Image Context, ... |
Artículo
Algorithm to Compute a Minimal Length Basis of Representative Cocycles of Cohomology Generators
(Universidad de Sevilla, 2010)
An algorithm to compute a minimal length basis of representative cocycles of cohomology generators for 2D images is proposed. ... |
Artículo
Human gait recognition using topological information
(Universidad de Sevilla, 2010)
This paper shows an image/video application using topological invariants in human gait recognition. The 3D volume of a ... |
Artículo
Irregular graph pyramids and representative cocycles of cohomology generators
(2009)
Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological ... |
Ponencia
Incremental-Decremental Technique for Delineating Tunnels and Pockets in 3D Digital Images
(WikiCFP, 2009)
In this paper, we combine two complementary techniques for computing homol- ogy: Incremental Algorithm for computing ... |
Capítulo de Libro
Integral operators for computing homology generators at any dimension
(2008)
Starting from an nD geometrical object, a cellular subdivision of such an object provides an algebraic counterpart from ... |
Capítulo de Libro
Extending the notion of AT-Model for integer homology computation
(2007)
When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing ... |
Capítulo de Libro
A Graph-with-Loop Structure for a Topological Representation of 3D Objects
(2007)
Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the ... |
Ponencia
Imágenes digitales y complejos simploidales
(Universidad de Cádiz, Servicio de Publicaciones, 2007)
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Tesis Doctoral
Modelo álgebro-topológico de representación de imágenes digitales en nD
(2007)
Para introducir este trabajo es necesario hablar de TOPOLOG´IA. La topología es la rama de las matemáticas que estudia las ... |
Artículo
Computing Adem Cohomology Operations
(Cornell University, 2006)
We deal with the problem of obtaining explicit simplicial formu- lae defining the classical Adem cohomology operations at ... |
Capítulo de Libro
Reusing integer homology information of binary digital images
(2006)
In this paper, algorithms for computing integer (co)homology of a simplicial complex of any dimension are designed, extending ... |
Capítulo de Libro
Simplicial perturbation techniques and effective homology
(2006)
In this paper, we deal with the problem of the computation of the homology of a finite simplicial complex after an “elementary ... |
Artículo
Simplification techniques for maps in simplicial topology
(2005)
This paper offers an algorithmic solution to the problem of obtaining “economical” formulae for some maps in Simplicial ... |
Capítulo de Libro
Algebraic topological analysis of time-sequence of digital images
(2005)
This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary–valued images, ... |
Artículo
On the cohomology of 3D digital images
(2005)
We propose a method for computing the cohomology ring of three-dimensional (3D) digital binary-valued pictures. We obtain ... |
Artículo
HPT and cocyclic operations
(International Press, 2005)
We reinterpret the classical theory of cocyclic operations in terms of permutations and homotopy equivalences of ... |
Artículo
Cohomología 3D y visualización
(Real Sociedad Matemática Española, 2004)
Proponemos un método para visualizar conceptos altamente abstractos en objetos tridimensionales, representados éstos como ... |
Ponencia
Computing the cohomology ring on simplicial complexes
(Universidad de Sevilla, Departamento de Matemática Aplicada I, 2003)
|
Artículo
Computation of cohomology operations of finite simplicial complexes
(2003)
We propose a method for calculating cohomology operations on finite simplicial complexes. Of course, there exist well–known ... |
Capítulo de Libro
Towards digital cohomology
(2003)
We propose a method for computing the Z 2–cohomology ring of a simplicial complex uniquely associated with a three–dimensional ... |
Artículo
Algorithms in Algebraic Topology and Homological Algebra: Problem of Complexity
(Springer, 2002)
This review tackles the problem of the high computational complexity lying in most algorithms in algebraic topology and ... |
Ponencia
An example in combinatorial cohomology
(Universidad de La Rioja, 2001)
Steenrod cohomology operations are algebraic tools for distinguishing non–homeomorphic topological spaces. In this paper, ... |
Ponencia
El Proyecto CHATA
(Universidad de Sevilla, 2001)
En este art´ıculo, se pretende dar una visi´on general y lo m´as divulgativa posible sobre los prop´ositos y objetivos del ... |
Tesis Doctoral
Operaciones cohomológicas: un enfoque combinatorial
(2000)
En esta memoria se establece un enfoque puramente combinatorio de las operaciones cohomológicas de Steenrod y Adem a nivel ... |
Ponencia
Computing “Small” 1–Homological Models for Commutative Differential Graded Algebras
(Springer, 2000)
We use homological perturbation machinery specific for the algebra category [13] to give an algorithm for computing the ... |
Ponencia
Steenrod reduced powers and computability
(International Association for Mathematics and Computers in Simulation, 1999)
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Ponencia
Computing Cocycles on Simplicial Complexes
(Springer, 1999)
In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing ... |
Artículo
A combinatorial method for computing Steenrod squares
(Elsevier, 1999)
We present here a combinatorial method for computing Steenrod squares of a simplicial set X. This method is essentially ... |
Artículo
Una curiosa combinación de Topología, Álgebra y Combinatoria: los cuadrados de Steenrod
(Real Sociedad Matemática Española, 1998)
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