Author profile: González Díaz, Rocío
Institutional data
Name | González Díaz, Rocío |
Department | Matemática Aplicada I |
Knowledge area | Matemática Aplicada |
Professional category | Catedrática de Universidad |
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Statistics
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No. publications
110
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No. visits
11422
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No. downloads
18410
Publications |
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Article
![]() 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 ... |
Final Degree Project
![]() 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 ... |
Final Degree Project
![]() 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 ... |
Master's Final Project
![]() 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 ... |
Master's Final Project
![]() 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 ... |
Article
![]() 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 ... |
Article
![]() 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 ... |
Final Degree Project
![]() 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 ... |
Article
![]() 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 ... |
Master's Final Project
![]() 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 ... |
Article
![]() 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 ... |
PhD Thesis
![]() 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 ... |
Master's Final Project
![]() 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 ... |
Presentation
![]() Image = Structure + Few Colors
(Springer, 2021)
Topology plays an important role in computer vision by capturing the structure of the objects. Nevertheless, its potential ... |
Article
![]() 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, ... |
Article
![]() 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 ... |
Final Degree Project
![]() 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 ... |
Article
![]() 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 ... |
Article
![]() 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 ... |
Article
![]() Characterizing slope regions
(Springer, 2021)
This paper provides a theoretical characterization of monotonically connected image surface regions, called slope regions. ... |
Article
![]() 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 ... |
Article
![]() 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, ... |
Master's Final Project
![]() 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 ... |
Presentation
![]() 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 ... |
Presentation
![]() 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), ... |
Article
![]() 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 ... |
Article
![]() Digitization
(Springer, 2020)
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Article
![]() 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 ... |
Article
![]() 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 ... |
Presentation
![]() 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 ... |
Presentation
![]() 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 ... |
Article
![]() 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 ... |
Article
![]() 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 ... |
Presentation
![]() 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 ... |
Presentation
![]() 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 ... |
Article
![]() 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 ... |
Presentation
![]() 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 ... |
Article
![]() 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 ... |
Presentation
![]() 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 ... |
Presentation
![]() 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 ... |
Article
![]() 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 ... |
Article
![]() 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 ... |
Presentation
![]() 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 ... |
Article
![]() 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, ... |
Article
![]() 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 ... |
Article
![]() 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 ... |
Article
![]() 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. ... |
Article
![]() 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 ... |
Article
![]() 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 ... |
Article
![]() 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 ... |
Presentation
![]() 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 ... |
Presentation
![]() 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 ... |
Article
![]() 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 ... |
Presentation
![]() 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) ... |
Presentation
![]() 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 ... |
Article
![]() An entropy-based persistence barcode
(2015)
In persistent homology, the persistence barcode encodes pairs of simplices meaning birth and death of homology classes. ... |
Chapter of Book
![]() 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 ... |
Presentation
![]() 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 ... |
Article
![]() 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. ... |
Article
![]() 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) ... |
Article
![]() 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, ... |
Chapter of Book
![]() 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 ... |
Chapter of Book
![]() 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 ... |
Article
![]() 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. ... |
Chapter of Book
![]() 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, ... |
Chapter of Book
![]() Towards Minimal Barcodes
(2013)
In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs ... |
Article
![]() 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, ... |
Article |
Article
![]() 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 ... |
Article
![]() 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 ... |
Chapter of Book
![]() 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 ... |
Chapter of Book
![]() Human gait identification using persistent homology
(2012)
This paper shows an image/video application using topological invariants for human gait recognition. Using a background ... |
Article
![]() Computational Topology in Image Context
(Elsevier, 2012)
|
Article
![]() 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 ... |
Chapter of Book
![]() 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 ... |
Article
![]() 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 ... |
Chapter of Book
![]() 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, ... |
Article
![]() 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 ... |
Chapter of Book
![]() 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 ... |
Article
![]() Cubical cohomology ring of 3D photographs
(2011)
Cohomology groups and the cohomology ring of three-dimensional (3D) objects are topological invariants that characterize ... |
Article
![]() 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, ... |
Article
![]() 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 ... |
Article
![]() 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. ... |
Article
![]() 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 ... |
Presentation
![]() 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 ... |
Chapter of Book
![]() 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 ... |
Chapter of Book
![]() 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 ... |
Chapter of Book
![]() 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 ... |
Presentation
![]() Imágenes digitales y complejos simploidales
(Universidad de Cádiz, Servicio de Publicaciones, 2007)
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PhD Thesis
![]() 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 ... |
Article
![]() 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 ... |
Chapter of Book
![]() 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 ... |
Chapter of Book
![]() 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 ... |
Article
![]() 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 ... |
Chapter of Book
![]() 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, ... |
Article
![]() 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 ... |
Article
![]() HPT and cocyclic operations
(International Press, 2005)
We reinterpret the classical theory of cocyclic operations in terms of permutations and homotopy equivalences of ... |
Article
![]() Cohomología 3D y visualización
(Real Sociedad Matemática Española, 2004)
Proponemos un método para visualizar conceptos altamente abstractos en objetos tridimensionales, representados éstos como ... |
Presentation
![]() Computing the cohomology ring on simplicial complexes
(Universidad de Sevilla, Departamento de Matemática Aplicada I, 2003)
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Article
![]() 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 ... |
Chapter of Book
![]() 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 ... |
Article
![]() 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 ... |
Presentation
![]() 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, ... |
Presentation
![]() 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 ... |
PhD Thesis
![]() 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 ... |
Presentation
![]() 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 ... |
Presentation
![]() Steenrod reduced powers and computability
(International Association for Mathematics and Computers in Simulation, 1999)
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Presentation
![]() 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 ... |
Article
![]() 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 ... |
Article
![]() Una curiosa combinación de Topología, Álgebra y Combinatoria: los cuadrados de Steenrod
(Real Sociedad Matemática Española, 1998)
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