Por motivos de mantenimiento se ha deshabilitado el inicio de sesión temporalmente. Rogamos disculpen las molestias.
NameGonzález Díaz, Rocío
DepartmentMatemática Aplicada I
Knowledge areaMatemática Aplicada
Professional categoryCatedrática de Universidad
E-mailRequest
           
  • No. publications

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Final Degree Project
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Detección Visual de Anomalías para Robots Móviles

Candil Salas, Adrián; González Díaz, Rocío; Perera Lago, Javier (2024)
En este trabajo se realiza un estudio sobre una arquitectura diseñada para el reconocimiento de anomalías mediante ...
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Trainable and explainable simplicial map neural networks

Paluzo Hidalgo, Eduardo; González Díaz, Rocío; Gutiérrez Naranjo, Miguel Ángel (ELSEVIER SCIENCE INC, 2024)
Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal ...
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An in-depth analysis of data reduction methods for sustainable deep learning

Perera Lago, Javier; Toscano Durán, Víctor; Paluzo Hidalgo, Eduardo; González Díaz, Rocío; Gutiérrez Naranjo, Miguel Ángel (F1000 Research / European Commission, 2024)
In recent years, Deep Learning has gained popularity for its ability to solve complex classification tasks, increasingly ...
PhD Thesis
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Barcodes of Persistence Modules: from Summaries to Matchings

Soriano Trigueros, Manuel; González Díaz, Rocío; Jiménez Rodríguez, María José (2023)
During recent decades, the application of topology to data analysis has experienced a revolution due to persistent homology. ...
Final Degree Project
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Análisis topológico de las matrices de ocurrencias en la red de Bitcoin

Villalonga Álvaro, Joan; González Díaz, Rocío; Atienza Martínez, María Nieves (2023)
Tras el nacimiento de Bitcoin, se ha producido una profunda transformación en los mercados digitales y la bolsa, dando ...
Final Degree Project
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Estudio del conocimiento actual en la compresión de datos para el aprendizaje automático

Peralta Egea, Ricardo; González Díaz, Rocío; Paluzo Hidalgo, Eduardo (2023)
En este trabajo fin de grado se estudian tantos los métodos actuales como el contexto en el ámbito de empresas, investigaciones ...
Master's Final Project
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Análisis Topológico de Datos y Aprendizaje Automático en la Detección De Ríos Atmosféricos

Vázquez Fernández, David; González Díaz, Rocío (2022)
Un río atmosférico (RA) es una banda alargada y estrecha de humedad muy concentrada en la parte inferior de la troposfera ...
Master's Final Project
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Predicción de Aristas para Data Augmentation en Problemas de Clasificación de Nodos con Graph Neural Networks

Carmona López, Gonzalo; González Díaz, Rocío; Paluzo Hidalgo, Eduardo (2022)
En este trabajo, repasamos detalladamente el planteamiento de un problema de aprendizaje supervisado en general, sobre ...
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Topology-based representative datasets to reduce neural network training resources

González Díaz, Rocío; Gutiérrez Naranjo, Miguel Ángel; Paluzo Hidalgo, Eduardo (Springer, 2022)
One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such ...
Article
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Continuous Well-Composedness Implies Digital Well-Composedness in n-D

Boutry, Nicolas; González Díaz, Rocío; Najman, Laurent; Géraud, Thierry (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 ...
Final Degree Project
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Análisis y estudio del grafo de transacciones de Bitcoin

Claros Barrero, Fernando; González Díaz, Rocío; Atienza Martínez, María Nieves (2022)
Durante los últimos años, el mundo del Bitcoin y las criptomonedas ha revolucionado por completo el concepto de pago y ...
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Emotion recognition in talking-face videos using persistent entropy and neural networks

Paluzo Hidalgo, Eduardo; González Díaz, Rocío; Aguirre Carrazana, Guilermo (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 ...
Master's Final Project
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On the Categorical Theory of Persistence Modules

Rodríguez Sakamoto, Riu; González Díaz, Rocío (2021)
¿Cómo se infieren formas a partir de datos? Se pueden emplear técnicas del álgebra y la topología computacional para ...
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Simplicial-Map Neural Networks Robust to Adversarial Examples

Paluzo Hidalgo, Eduardo; González Díaz, Rocío; Gutiérrez Naranjo, Miguel Ángel; Heras, Jónathan (MDPI [Commercial Publisher], 2021)
Broadly speaking, an adversarial example against a classification model occurs when a small perturbation on an input data ...
PhD Thesis
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Computational topology on neural networks: from the data to the model

Paluzo Hidalgo, Eduardo; González Díaz, Rocío; Gutiérrez Naranjo, Miguel Ángel (2021)
Machine learning is drawn from a dataset that needs to be explained. Following this aim, a model is described to make ...
Master's Final Project
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Un estudio sobre la homología persistente con coeficientes enteros

Perera Lago, Javier; González Díaz, Rocío (2021)
La homología persistente es una técnica que se usa para analizar la evolución de una cierta propiedad algebraica, la ...
Presentation
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Image = Structure + Few Colors

Batavia, Darshan; González Díaz, Rocío; Kropatsch, Walter G. (Springer, 2021)
Topology plays an important role in computer vision by capturing the structure of the objects. Nevertheless, its potential ...
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Making Sullivan Algebras Minimal Through Chain Contractions

Garvin, Antonio; González Díaz, Rocío; Marco, Miguel Ángel; Medrano Garfia, Belén (Springer, 2021)
In this note, we provide an algorithm that, starting with a Sullivan algebra gives us its minimal model. More concretely, ...
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Optimizing the Simplicial-Map Neural Network Architecture

Paluzo Hidalgo, Eduardo; González Díaz, Rocío; Gutiérrez Naranjo, Miguel Ángel; Heras, Jónathan (MDPI, 2021)
Simplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial ...
Final Degree Project
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Visualizando la evolución de los casos de COVID-19 con TDA

Casasola Calzadilla, María; González Díaz, Rocío; Paluzo Hidalgo, Eduardo (2021)
A continuación, se expone en este documento la memoria del trabajo de fin de grado basado en el análisis de datos de ...
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Strong Euler well-composedness

Boutry, Nicolas; González Díaz, Rocío; Jiménez Rodríguez, María José; Paluzo Hidalgo, Eduardo (Springer, 2021)
In this paper, we define a new flavour of well-composedness, called strong Euler well composedness. In the general setting ...
Article
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Persistence Partial Matchings Induced by Morphisms between Persistence Modules

González Díaz, Rocío; Soriano Trigueros, Manuel (Cornell University, 2021)
The notion of persistence partial matching, as a generalization of partial matchings between persistence modules, is ...
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Characterizing slope regions

González Díaz, Rocío; Batavia, Darshan; Moreno Casablanca, Rocío; Kropatsch, Walter G. (Springer, 2021)
This paper provides a theoretical characterization of monotonically connected image surface regions, called slope regions. ...
Article
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Neural-Network-Based Curve Fitting Using Totally Positive Rational Bases

González Díaz, Rocío; Mainardes, Emerson; Paluzo Hidalgo, Eduardo; Rubio Serrano, Beatriz (MDPI, 2020)
This paper proposes a method for learning the process of curve fitting through a general class of totally positive rational ...
Article
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Two-hidden-layer feed-forward networks are universal approximators: A constructive approach

Paluzo Hidalgo, Eduardo; González Díaz, Rocío; Gutiérrez Naranjo, Miguel Ángel (ScienceDirect, 2020)
It is well-known that artificial neural networks are universal approximators. The classical existence result proves that, ...
Master's Final Project
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Análisis topológico de datos: aplicación al reconocimiento de emociones

Aguirre Carrazana, Guilermo; González Díaz, Rocío; Paluzo Hidalgo, Eduardo (2020)
Emotion recognition consists of a series of processes to detect human emotions from facial human expressions. Humans ...
Presentation
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A 4D counter-example showing that DWCness does not imply CWCness in n-D

Boutry, Nicolas; González Díaz, Rocío; Najman, Laurent; Géraud, Thierry (Springer, 2020)
In this paper, we prove that the two avours of well-compo- sedness called Continuous Well-Composedness (shortly CWCness), ...
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Approximating lower-star persistence via 2D combinatorial map simplification

Damiand, Guillaume; Paluzo Hidalgo, Eduardo; Slechta, Ryan; González Díaz, Rocío (Elsevier, 2020)
Filtration simplification consists of simplifying a given filtration while simultaneously controlling the perturbation in ...
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Digitization

González Díaz, Rocío; Stelldinger, Peer; Latecki, Longin Jan (Springer, 2020)
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Basis-independent partial matchings induced by morphisms between persistence modules

González Díaz, Rocío; Soriano Trigueros, Manuel (Cornell University, 2020)
In this paper, we study how basis-independent partial matchings induced by morphisms between persistence modules (also ...
Presentation
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Euler Well-Composedness

Boutry, Nicolas; González Díaz, Rocío; Jiménez Rodríguez, María José; Paluzo Hidalgo, Eduardo (Springer, 2020)
In this paper, we de ne a new avour of well-composedness, called Euler well-composedness, in the general setting of regular ...
Article
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Representative Datasets: The Perceptron Case

González Díaz, Rocío; Gutiérrez Naranjo, Miguel Ángel; Paluzo Hidalgo, Eduardo (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 ...
Presentation
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One More Step Towards Well-Composedness of Cell Complexes over nD Pictures

Boutry, Nicolas; González Díaz, Rocío; Jiménez Rodríguez, María José (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 ...
Presentation
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A topological entropy‐based approach for damage detection of civil engineering structures

Jiménez Alonso, Javier Fernando; López Martínez, Javier; Blanco Claraco, José Luis; González Díaz, Rocío; Sáez Pérez, Andrés (Editorial Club Universitario, 2019)
In this study, a new method based on topological entropy, the so‐called persistent entropy, is presented for addressing ...
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Topological signature for periodic motion recognition

Lamar León, Javier; García Reyes, Edel; González Díaz, Rocío (Cornell University, 2019)
In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such ...
Article
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Weakly well-composed cell complexes over nD pictures

Boutry, Nicolas; González Díaz, Rocío; Jiménez Rodríguez, María José (Elsevier, 2019)
In previous work we proposed a combinatorial algorithm to \locally repair" the cubical complex Q(I) that is canonically ...
Presentation
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Towards Emotion Recognition: A Persistent Entropy Application

González Díaz, Rocío; Paluzo Hidalgo, Eduardo; Quesada Moreno, José Francisco (Springer, 2019)
Emotion recognition and classification is a very active area of research. In this paper, we present a first approach to ...
Presentation
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Congratulations! Dual Graphs are Now Orientated!

Batavia, Darshan; Kropatsch, Walter G.; Moreno Casablanca, Rocío; González Díaz, Rocío (Springer, 2019)
A digital image can be perceived as a 2.5D surface consisting of pixel coordinates and the intensity of pixel as height ...
Article
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Towards a Philological Metric through a Topological Data Analysis Approach

Paluzo Hidalgo, Eduardo; González Díaz, Rocío; Gutiérrez Naranjo, Miguel Ángel (Cornell University, 2019)
The canon of the baroque Spanish literature has been thoroughly studied with philological techniques. The major representatives ...
Presentation
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On the Space Between Critical Points

Kropatsch, Walter G.; Moreno Casablanca, Rocío; Batavia, Darshan; González Díaz, Rocío (Springer, 2019)
The vertices of the neighborhood graph of a digital picture P can be interpolated to form a 2-manifold M with critical ...
Article
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Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach

González Díaz, Rocío; Gutiérrez Naranjo, Miguel Ángel; Paluzo Hidalgo, Eduardo (Cornell University, 2019)
It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a ...
Presentation
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Persistent Homology Computation Using Combinatorial Map Simplification

Damiand, Guillaume; González Díaz, Rocío (Springer, 2019)
We propose an algorithm for persistence homology computation of orientable 2-dimensional (2D) manifolds with or without ...
Presentation
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Computing and reducing slope complexes

Kropatsch, Walter G.; Moreno Casablanca, Rocío; Batavia, Darshan; González Díaz, Rocío (Springer, 2019)
In this paper we provide a new characterization of cell de- composition (called slope complex) of a given 2-dimensional ...
Article
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An algorithm to compute minimal Sullivan algebras

Garvín, Antonio; González Díaz, Rocío; Medrano Garfia, Belén (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 ...
Article
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Persistent entropy for separating topological features from noise in vietoris-rips complexes

Atienza Martínez, María Nieves; González Díaz, Rocío; Rucco, Matteo (Springer, 2019)
Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called ...
Presentation
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Counting slope regions in the surface graphs

Batavia, Darshan; Kropatsch, Walter G.; González Díaz, Rocío; Moreno Casablanca, Rocío (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 ...
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A new entropy based summary function for topological data analysis

Atienza Martínez, María Nieves; González Díaz, Rocío; Soriano Trigueros, Manuel (Elsevier, 2018)
Topological data analysis (TDA) aims to obtain useful information from data sets using topological concepts. In particular, ...
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On the stability of persistent entropy and new summary functions for Topological Data Analysis

Atienza Martínez, María Nieves; González Díaz, Rocío; Soriano Trigueros, Manuel (Cornell University, 2018)
Persistent entropy of persistence barcodes, which is based on the Shannon entropy, has been recently defined and successfully ...
Article
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Representative datasets for neural networks

González Díaz, Rocío; Paluzo Hidalgo, Eduardo; Gutiérrez Naranjo, Miguel Ángel (Elsevier, 2018)
Neural networks present big popularity and success in many fields. The large training time process problem is a very ...
Article
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Topological tracking of connected components in image sequences

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (Elsevier, 2018)
Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. ...
Article
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Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (Springer, 2017)
A 3D binary image I can be naturally represented by a combinatorial-algebraic structure called cubical complex and denoted ...
Article
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Persistent-homology-based gait recognition

Lamar León, Javier; Alonso Baryolo, Raúl; García Reyes, Edel; González Díaz, Rocío (Cornell University, 2017)
Gait recognition is an important biometric technique for video surveillance tasks, due to the advantage of using it at ...
Article
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A new topological entropy-based approach for measuring similarities among piecewise linear functions

Rucco, Matteo; González Díaz, Rocío; Jiménez Rodríguez, María José; Atienza Martínez, María Nieves; Cristalli, Cristina; Concettoni, Enrico; Ferrante, Andrea; Merelli, Emanuela (Elsevier, 2017)
In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing ...
Presentation
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Separating Topological Noise from Features Using Persistent Entropy

Atienza Martínez, María Nieves; González Díaz, Rocío; Rucco, Matteo (Springer, 2016)
Topology is the branch of mathematics that studies shapes and maps among them. From the algebraic definition of topology ...
Presentation
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Parallel Homology Computation of Meshes

Damiand, Guillaume; González Díaz, Rocío (Springer, 2016)
In this paper, we propose a method to compute, in parallel, the homology groups of closed meshes (i.e., orientable 2D ...
Article
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Topology-based image segmentation using LBP pyramids

Cerman, Martin; Janusch, Ines; González Díaz, Rocío; Kropatsch, Walter G. (Springer, 2016)
In this paper, we present a new image segmentation algorithmwhich is based on local binary patterns (LBPs) and the ...
Presentation
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Encoding Specific 3D Polyhedral Complexes Using 3D Binary Images

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (Springer, 2016)
We build upon the work developed in [4] in which we presented a method to “locally repair” the cubical complex Q(I) ...
Presentation
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Persistent homology-based gait recognition robust to upper body variations

Lamar León, Javier; Alonso Baryolo, Raúl; García Reyes, Edel; González Díaz, Rocío (IEEE Computer Society, 2016)
Gait recognition is nowadays an important biometric technique for video surveillance tasks, due to the advantage of using ...
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An entropy-based persistence barcode

Chintakunta, Harish; Gentimis, Thanos; González Díaz, Rocío; Jiménez Rodríguez, María José; Krim, Hamid (2015)
In persistent homology, the persistence barcode encodes pairs of simplices meaning birth and death of homology classes. ...
Chapter of Book
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LBP and irregular graph pyramids

Cerman, Martin; González Díaz, Rocío; Kropatsch, Walter G. (2015)
In this paper, a new codification of Local Binary Patterns (LBP) is given using graph pyramids. The LBP code characterizes ...
Presentation
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Spatiotemporal Barcodes for Image Sequence Analysis

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (Springer, 2015)
Taking as input a time-varying sequence of two-dimensional (2D) binary images, we develop an algorithm for computing a ...
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3D well-composed polyhedral complexes

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (2015)
A binary three-dimensional (3D) image II is well-composed if the boundary surface of its continuous analog is a 2D manifold. ...
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Characterizing Configurations of critical points through LBP Extended Abstract

González Díaz, Rocío; Kropatsch, Walter G.; Cerman, Martin; Lamar León, Javier (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) ...
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Computing cup products in \(\mathbb {Z}_2\)-cohomology of 3D polyhedral complexes

González Díaz, Rocío; Lamar León, Javier; Umble, Ronald (2014)
Let \(I=(\mathbb {Z}^3,26,6,B)\) be a three-dimensional (3D) digital image, let \(Q(I)\) be an associated cubical complex, ...
Chapter of Book
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Topological features for monitoring human activities at distance

Lamar León, Javier; Alonso Baryolo, Raúl; García Reyes, Edel; González Díaz, Rocío (2014)
In this paper, a topological approach for monitoring human activities is presented. This approach makes possible to protect ...
Chapter of Book
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Gait-based carried object detection using persistent homology

Lamar León, Javier; Alonso Baryolo, Raúl; García Reyes, Edel; González Díaz, Rocío (2014)
There are surveillance scenarios where it is important to emit an alarm when a person carrying an object is detected. In ...
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Removal and contraction operations in nD generalized maps for efficient homology computation

Damiand, Guillaume; González Díaz, Rocío; Peltier, Samuel (2014)
In this paper, we show that contraction operations preserve the homology of nD generalized maps, under some conditions. ...
Chapter of Book
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Gait-based gender classification using persistent homology

Lamar León, Javier; Cerri, Andrea; García Reyes, Edel; González Díaz, Rocío (2013)
In this paper, a topological approach for gait-based gender recognition is presented. First, a stack of human silhouettes, ...
Chapter of Book
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Towards Minimal Barcodes

González Díaz, Rocío; Jiménez Rodríguez, María José; Krim, Hamid (2013)
In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs ...
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An application for gait recognition using persistent homology

Lamar León, Javier; García Reyes, Edel; González Díaz, Rocío; Alonso Baryolo, Raúl (Universidad de Sevilla, 2013)
This Demo presents an application for gait recognition using persistent homology. Using a background subtraction approach, ...
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DGCI 2013 Demo Session 7th IAPR International Conference on Discrete Geometry for Computer Imagery. Foreword

Díaz Pernil, Daniel; Fondón García, Irene; González Díaz, Rocío; Jiménez Rodríguez, María José (2013)
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Cups products in Z2-cohomology of 3D polyhedral complexes

González Díaz, Rocío; Lamar León, Javier; Umble, Ronald (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 ...
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Geometric Objects and Cohomology Operations

González Díaz, Rocío; Real Jurado, Pedro (Cornell University, 2012)
Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology ...
Chapter of Book
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Removal operations in nD generalized maps for efficient homology computation

Damiand, Guillaume; González Díaz, Rocío; Peltier, Samuel (2012)
In this paper, we present an efficient way for computing homology generators of nD generalized maps. The algorithm proceeds ...
Chapter of Book
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Human gait identification using persistent homology

Lamar León, Javier; García Reyes, Edel; González Díaz, Rocío (2012)
This paper shows an image/video application using topological invariants for human gait recognition. Using a background ...
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Computational Topology in Image Context

González Díaz, Rocío; Real Jurado, Pedro (Elsevier, 2012)
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A tool for integer homology computation: lambda-AT- model

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén; Real Jurado, Pedro (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 ...
Chapter of Book
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Incremental-Decremental Algorithm for Computing AT-Models and Persistent Homology

González Díaz, Rocío; Adrian, Ion; Jiménez Rodríguez, María José; Poyatos, Regina (2011)
In this paper, we establish a correspondence between the incremental algorithm for computing AT-models [8,9] and the one ...
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Chain Homotopies for Object Topological Representations

Jiménez Rodríguez, María José; Medrano Garfia, Belén; Real Jurado, Pedro; González Díaz, Rocío (2011)
This paper presents a set of tools to compute topological information of simplicial complexes, tools that are applicable ...
Chapter of Book
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Well-Composed Cell Complexes

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (2011)
Well-composed 3D digital images, which are 3D binary digital images whose boundary surface is made up by 2D manifolds, ...
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Invariant representative cocycles of cohomology generators using irregular graph pyramids

González Díaz, Rocío; Ion, Adrián; Iglesias Ham, Mabel; Kropatsch, Walter G. (2011)
Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological ...
Chapter of Book
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Cup products on polyhedral approximations of 3D digital images

González Díaz, Rocío; Lamar León, Javier; Umble, Ronald (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 ...
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Cubical cohomology ring of 3D photographs

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (2011)
Cohomology groups and the cohomology ring of three-dimensional (3D) objects are topological invariants that characterize ...
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Proceedings of the Workshop on Computational Topology in Image Context 2010

González Díaz, Rocío; Real Jurado, Pedro (2010)
It has been an honor and a pleasure to organize the 3rd International Workshop on Computational Topology in Image Context, ...
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Algorithm to Compute a Minimal Length Basis of Representative Cocycles of Cohomology Generators

Iglesias Ham, Mabel; García Reyes, Edel; Kropatsch, Walter G.; González Díaz, Rocío (Universidad de Sevilla, 2010)
An algorithm to compute a minimal length basis of representative cocycles of cohomology generators for 2D images is proposed. ...
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Human gait recognition using topological information

Lamar León, Javier; García Reyes, Edel; González Díaz, Rocío;  (Universidad de Sevilla, 2010)
This paper shows an image/video application using topological invariants in human gait recognition. The 3D volume of a ...
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Irregular graph pyramids and representative cocycles of cohomology generators

González Díaz, Rocío; Ion, Adrián; Iglesias Ham, Mabel; Kropatsch, Walter G. (2009)
Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological ...
Presentation
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Incremental-Decremental Technique for Delineating Tunnels and Pockets in 3D Digital Images

González Díaz, Rocío; González Molinillo, A.; Jiménez Rodríguez, María José; Postigo Gutiérrez, J.A. (WikiCFP, 2009)
In this paper, we combine two complementary techniques for computing homol- ogy: Incremental Algorithm for computing ...
Chapter of Book
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Integral operators for computing homology generators at any dimension

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén; Molina Abril, Helena; Real Jurado, Pedro (2008)
Starting from an nD geometrical object, a cellular subdivision of such an object provides an algebraic counterpart from ...
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Extending the notion of AT-Model for integer homology computation

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén; Real Jurado, Pedro (2007)
When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing ...
Chapter of Book
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A Graph-with-Loop Structure for a Topological Representation of 3D Objects

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén; Real Jurado, Pedro (2007)
Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the ...
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Imágenes digitales y complejos simploidales

González Díaz, Rocío; Jiménez Rodríguez, María José; Real Jurado, Pedro; Ruiz Cárdenas, Yolanda (Universidad de Cádiz, Servicio de Publicaciones, 2007)
PhD Thesis
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Modelo álgebro-topológico de representación de imágenes digitales en nD

Medrano Garfia, Belén; González Díaz, Rocío; Real Jurado, Pedro (2007)
Para introducir este trabajo es necesario hablar de TOPOLOG´IA. La topología es la rama de las matemáticas que estudia las ...
Article
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Computing Adem Cohomology Operations

González Díaz, Rocío; Real Jurado, Pedro (Cornell University, 2006)
We deal with the problem of obtaining explicit simplicial formu- lae defining the classical Adem cohomology operations at ...
Chapter of Book
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Reusing integer homology information of binary digital images

González Díaz, Rocío; Medrano Garfia, Belén; Sánchez Peláez, Javier; Real Jurado, Pedro (2006)
In this paper, algorithms for computing integer (co)homology of a simplicial complex of any dimension are designed, extending ...
Chapter of Book
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Simplicial perturbation techniques and effective homology

González Díaz, Rocío; Medrano Garfia, Belén; Sánchez Peláez, Javier; Real Jurado, Pedro (2006)
In this paper, we deal with the problem of the computation of the homology of a finite simplicial complex after an “elementary ...
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Simplification techniques for maps in simplicial topology

González Díaz, Rocío; Real Jurado, Pedro (2005)
This paper offers an algorithmic solution to the problem of obtaining “economical” formulae for some maps in Simplicial ...
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On the cohomology of 3D digital images

González Díaz, Rocío; Real Jurado, Pedro (2005)
We propose a method for computing the cohomology ring of three-dimensional (3D) digital binary-valued pictures. We obtain ...
Article
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HPT and cocyclic operations

González Díaz, Rocío; Real Jurado, Pedro (International Press, 2005)
We reinterpret the classical theory of cocyclic operations in terms of permutations and homotopy equivalences of ...
Chapter of Book
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Algebraic topological analysis of time-sequence of digital images

González Díaz, Rocío; Medrano Garfia, Belén; Real Jurado, Pedro; Sánchez Peláez, Javier (2005)
This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary–valued images, ...
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Cohomología 3D y visualización

González Díaz, Rocío; Real Jurado, Pedro (Real Sociedad Matemática Española, 2004)
Proponemos un método para visualizar conceptos altamente abstractos en objetos tridimensionales, representados éstos como ...
Presentation
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Computing the cohomology ring on simplicial complexes

González Díaz, Rocío; Real Jurado, Pedro (Universidad de Sevilla, Departamento de Matemática Aplicada I, 2003)
Article
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Computation of cohomology operations of finite simplicial complexes

González Díaz, Rocío; Real Jurado, Pedro (2003)
We propose a method for calculating cohomology operations on finite simplicial complexes. Of course, there exist well–known ...
Chapter of Book
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Towards digital cohomology

González Díaz, Rocío; Real Jurado, Pedro (2003)
We propose a method for computing the Z 2–cohomology ring of a simplicial complex uniquely associated with a three–dimensional ...
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Algorithms in Algebraic Topology and Homological Algebra: Problem of Complexity

Real Jurado, Pedro; Álvarez Solano, Víctor; Armario Sampalo, José Andrés; González Díaz, Rocío (Springer, 2002)
This review tackles the problem of the high computational complexity lying in most algorithms in algebraic topology and ...
Presentation
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An example in combinatorial cohomology

González Díaz, Rocío; Real Jurado, Pedro (Universidad de La Rioja, 2001)
Steenrod cohomology operations are algebraic tools for distinguishing non–homeomorphic topological spaces. In this paper, ...
Presentation
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El Proyecto CHATA

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; González Díaz, Rocío; Jiménez Rodríguez, María José; Real Jurado, Pedro; Silva Gallardo, Beatriz (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 ...
PhD Thesis
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Operaciones cohomológicas: un enfoque combinatorial

González Díaz, Rocío; Real Jurado, Pedro (2000)
En esta memoria se establece un enfoque puramente combinatorio de las operaciones cohomológicas de Steenrod y Adem a nivel ...
Presentation
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Computing “Small” 1–Homological Models for Commutative Differential Graded Algebras

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; González Díaz, Rocío; Jiménez Rodríguez, María José; Real Jurado, Pedro; Silva Gallardo, Beatriz (Springer, 2000)
We use homological perturbation machinery specific for the algebra category [13] to give an algorithm for computing the ...
Presentation
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Steenrod reduced powers and computability

González Díaz, Rocío; Real Jurado, Pedro (International Association for Mathematics and Computers in Simulation, 1999)
Presentation
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Computing Cocycles on Simplicial Complexes

González Díaz, Rocío; Real Jurado, Pedro (Springer, 1999)
In this note, working in the context of simplicial sets [17], we give a detailed study of the complexity for computing ...
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A combinatorial method for computing Steenrod squares

González Díaz, Rocío; Real Jurado, Pedro (Elsevier, 1999)
We present here a combinatorial method for computing Steenrod squares of a simplicial set X. This method is essentially ...
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Una curiosa combinación de Topología, Álgebra y Combinatoria: los cuadrados de Steenrod

González Díaz, Rocío; Real Jurado, Pedro (Real Sociedad Matemática Española, 1998)