NameReal Jurado, Pedro
DepartmentMatemática Aplicada I
Knowledge areaMatemática Aplicada
Professional categoryCatedrático de Universidad
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Article
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Parallel homological calculus for 3D binary digital images

Díaz del Río, Fernando; Molina Abril, Helena; Real Jurado, Pedro; Onchis, Darian M.; Blanco Trejo, Sergio (Springer, 2024)
Topological representations of binary digital images usually take into consideration different adjacency types between ...
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Analysis of Connectome Graphs Based on Boundary Scale

Morón Fernández, María José; Amedeo, Ludovica Maria; Monterroso Muñoz, Alberto; Molina Abril, Helena; Díaz del Río, Fernando; Bini, Fabiano; Marinozzi, Franco; Real Jurado, Pedro (MDPI, 2023)
The purpose of this work is to advance in the computational study of connectome graphs from a topological point of view. ...
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Autonomous Underwater Vehicles: Identifying Critical Issues and Future Perspectives in Image Acquisition

Monterroso Muñoz, Alberto; Morón Fernández, María José; Cascado Caballero, Daniel; Díaz del Río, Fernando; Real Jurado, Pedro (MDPI, 2023)
Underwater imaging has been present for many decades due to its relevance in vision and navigation systems. In recent ...
Chapter of Book
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Versatilidad y eficiencia de los autómatas celulares para la simulación y análisis de sistemas complejos en Ingeniería

Sánchez Cuevas, Pablo; Díaz del Río, Fernando; Cagigas Muñiz, Daniel; Guisado Lízar, José Luís; Morón Fernández, María José; Real Jurado, Pedro (3ciencias, 2022)
Los autómatas celulares se componen de un conjunto de celdas (generalmente simples) interactuantes que evolucionan en pasos ...
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On the Topological Disparity Characterization of Square-Pixel Binary Image Data by a Labeled Bipartite Graph

Sánchez Cuevas, Pablo; Real Jurado, Pedro; Díaz del Río, Fernando; Molina Abril, Helena; Morón Fernández, María José (Springer, 2022)
Given an nD digital image I based on cubical n-xel, to fully characterize the degree of internal topological dissimilarity ...
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A Topologically Consistent Color Digital Image Representation by a Single Tree

Sánchez Cuevas, Pablo; Díaz del Río, Fernando; Molina Abril, Helena; Real Jurado, Pedro (Springer, 2021)
A novel, flexible (non-unique) and topologically consistent representation called CRIT (Contour-Region incidence Tree) for ...
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Building Hierarchical Tree Representations Using Homological-Based Tools

Díaz del Río, Fernando; Sánchez Cuevas, Pablo; Molina Abril, Helena; Real Jurado, Pedro; Morón Fernández, María José (Springer, 2021)
A new algorithm for computing the α-tree hierarchical repre sentation of a grey-scale digital image is presented here. The ...
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Timely-automatic procedure for estimating the endocardial limits of the left ventricle assessed echocardiographically in clinical practice

Onchis, Darian M.; Istin, Codruta; Tudoran, Cristina; Tudoran, Mariana; Real Jurado, Pedro (MDPI, 2020)
In this paper, we propose an analytical rapid method to estimate the endocardial borders of the left ventricular walls on ...
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Parallel connected-Component-Labeling based on homotopy trees

Díaz del Río, Fernando; Sánchez Cuevas, Pablo; Molina Abril, Helena; Real Jurado, Pedro (Elsevier, 2020)
Taking advantage of the topological and isotopic properties of binary digital images, we present here anew algorithm for ...
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CDrift: An Algorithm to Correct Linear Drift From A Single High-Resolution STEM Image

Bárcena González, Guillermo; Guerrero Lebrero, María de la Paz; Guerrero Vázquez, Elisa; Yañez, Andres; Nuñez Moraleda, Bernardo Miguel; Fernández Reyes, Daniel; Real Jurado, Pedro; González, David; Galindo Riañ, Pedro Luis (Cambridge University Press, 2020)
In this work, a new method to determine and correct the linear drift for any crystalline orientation in a single-column-resolved ...
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Generating (co)homological information using boundary scale

Molina Abril, Helena; Real Jurado, Pedro; Díaz del Río, Fernando (Elsevier, 2020)
In this paper we develop a new computational technique called boundary scale-space theory. This tech- nique is based on ...
Presentation
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Enhanced Parallel Generation of Tree Structures for the Recognition of 3D Images

Real Jurado, Pedro; Molina Abril, Helena; Díaz del Río, Fernando; Blanco Trejo, Sergio; Onchis, Darian M. (Springer, 2019)
Segmentations of a digital object based on a connectivity criterion at n-xel or sub-n-xel level are useful tools in image ...
Presentation
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Generating Second Order (Co)homological Information within AT-Model Context

Real Jurado, Pedro; Molina Abril, Helena; Díaz del Río, Fernando; Onchis, Darian M. (Springer, 2019)
In this paper we design a new family of relations between (co)homology classes, working with coefficients in a field and ...
Presentation
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Topological Homogeneity for Electron Microscopy Images

Molina Abril, Helena; Díaz del Río, Fernando; Guerrero Lebrero, María P.; Real Jurado, Pedro; Barcena, Guillermo; Braza, Verónica; Guerrero Vázquez, Elisa; González, David; Galindo Riaño, Pedro Luis (Springer, 2019)
In this paper, the concept of homogeneity is defined, from a topological perspective, in order to analyze how uniform is ...
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Homological Region Adjacency Tree for a 3D Binary Digital Image via HSF Model

Real Jurado, Pedro; Molina Abril, Helena; Díaz del Río, Fernando; Blanco Trejo, Sergio (Springer, 2019)
Given a 3D binary digital image I, we define and compute an edge-weighted tree, called Homological Region Tree (or ...
Presentation
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Computing the Component-Labeling and the Adjacency Tree of a Binary Digital Image in Near Logarithmic-Time

Díaz del Río, Fernando; Molina Abril, Helena; Real Jurado, Pedro (Springer, 2019)
Connected component labeling (CCL) of binary images is one of the fundamental operations in real time applications. The ...
Presentation
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Refined Deep Learning for Digital Objects Recognition via Betti Invariants

Onchis, Darian M.; Istin, Codruta; Real Jurado, Pedro (Springer, 2019)
In this paper, we make use of the topological invariants of 2D images for an accelerated training and an improved recognition ...
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Fractal Topological Analysis for 2D Binary Digital Images

Blanco Trejo, Sergio; Alemán Morillo, C.; Díaz del Río, Fernando; Real Jurado, Pedro (Springer, 2019)
Fractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we propose a method of ...
PhD Thesis
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Parallelization strategies for extraction of (co)homological information of digital objects.

Reina Molina, Raúl; Díaz Pernil, Daniel; Real Jurado, Pedro (2018)
Un objeto digital es un conjunto de n-xels en de una imagen digital n-dimensional. El estudio de la conectividad de estos ...
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Numerical stability of spline-based Gabor-like systems

Onchis, Darian M.; Zappalá, Simone; Real Jurado, Pedro; Istin, Codruta (IEEE Computer Society, 2018)
The paper provides a theorem for the characteriza- tion of numerical stability of spline-type systems. These systems are ...
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Space-Variant Gabor Decomposition for Filtering 3D Medical Images

Onchis, Darian M.; Istin, Codruta; Real Jurado, Pedro (Springer, 2017)
This is an experimental paper in which we introduce the possibility to analyze and to synthesize 3D medical images by using ...
Presentation
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Toward Parallel Computation of Dense Homotopy Skeletons for nD Digital Objects

Real Jurado, Pedro; Díaz del Río, Fernando; Onchis, Darian M. (Springer, 2017)
An appropriate generalization of the classical notion of abstract cell complex, called primal-dual abstract cell complex ...
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Allowing cycles in discrete Morse theory

González Lorenzo, Aldo; Bac, Alexandra; Mari, Jean-Luc; Real Jurado, Pedro (Elsevier, 2017)
Discrete gradient vector fields are combinatorial structures that can be used for accelerating the homology computation ...
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Labeling Color 2D Digital Images in Theoretical Near Logarithmic Time

Díaz del Río, Fernando; Real Jurado, Pedro; Onchis, Darian M. (Springer, 2017)
A design of a parallel algorithm for labeling color flat zones (precisely, 4-connected components) of a gray-level or color ...
PhD Thesis
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Computational Homology Applied to Discrete Objects

González Lorenzo, Aldo; Mari, Jean-Luc; Bac, Alexandra; Real Jurado, Pedro (2016)
Homology theory formalizes the concept of hole in a space. For a given subset of the Euclidean space, we define a sequence ...
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On Homotopy Continuation for Speech Restoration

Onchis, Darian M.; Real Jurado, Pedro (Springer, 2016)
In this paper, a homotopy-based method is employed for the recovery of speech recordings from missing or corrupted samples ...
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Detection of the mandibular canal in orthopantomography using a Gabor-filtered anisotropic generalized Hough transform

Onchis Moaca, Darian; Zappalá, Simone; Gotia, Smaranda Laura; Real Jurado, Pedro; Pricop, Marius (Elsevier, 2016)
In this paper, we explore the possibility of applying the anisotropic generalized Hough transform (AGHT) enhanced with a ...
Presentation
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Parallel Image Processing Using a Pure Topological Framework

Díaz del Río, Fernando; Molina Abril, Helena; Real Jurado, Pedro; Sánchez-Cuevas, Pablo; Ríos Navarro, José Antonio (Universidad de Extremadura, 2016)
Image processing is a fundamental operation in many real time applications, where lots of parallelism can be extracted. ...
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Topological Comparisons of Fluvial Reservoir Rock Volumes Using Betti Numbers: Application to CO2 Storage Uncertainty Analysis

Dahrabou, Asmae; Viseur, Sophie; González Lorenzo, Aldo; Rohmer, Jérémy; Bac, Alexandra; Real Jurado, Pedro; Mari, Jean-Luc; Audigane, Pascal (Springer, 2016)
To prevent the release of large quantities of CO2 into the atmosphere, carbon capture and storage (CCS) represents a ...
Presentation
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Two Measures for the Homology Groups of Binary Volumes

González Lorenzo, Aldo; Bac, Alexandra; Mari, Jean-Luc; Real Jurado, Pedro (Springer, 2016)
Given a binary object (2D or 3D), its Betti numbers characterize the number of holes in each dimension. They are obtained ...
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A parallel Homological Spanning Forest framework for 2D topological image analysis

Díaz del Río, Fernando; Real Jurado, Pedro; Onchis, Darian M. (Elsevier, 2016)
In [14], a topologically consistent framework to support parallel topological analysis and recognition for2 D digital ...
Presentation
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Fast, Simple and Separable Computation of Betti Numbers on Three-dimensional Cubical Complexes

González Lorenzo, Aldo; Juda, Mateusz; Bac, Alexandra; Mari, Jean-Luc; Real Jurado, Pedro (Springer, 2016)
Betti numbers are topological invariants that count the number of holes of each dimension in a space. Cubical complexes ...
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Effective homology of k-D digital objects (partially) calculated in parallel

Reina Molina, Raúl; Díaz Pernil, Daniel; Real Jurado, Pedro; Berciano, Ainhoa (Elsevier, 2016)
In [18], a membrane parallel theoretical framework for computing (co)homology information of fore- ground or background ...
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Computation of cubical homology, cohomology, and (co)homological operations via chain contraction

Pilarczyk, Pawel; Real Jurado, Pedro (2015)
We introduce algorithms for the computation of homology, cohomology, and related operations on cubical cell complexes, ...
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Membrane parallelism for discrete Morse theory applied to digital images

Reina Molina, Raúl; Díaz Pernil, Daniel; Real Jurado, Pedro; Berciano Alcaraz, Ainhoa (2015)
In this paper, we propose a bio-inspired membrane computational framework for constructing discrete Morse complexes for ...
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On higher dimensional cocyclic Hadamard matrices

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (2015)
Provided that a cohomological model for G is known, we describe a method for constructing a basis for n-cocycles over G, ...
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Cellular Skeletons: A New Approach to Topological Skeletons with Geometric Features

González Lorenzo, Aldo; Bac, Alexandra; Mari, Jean-Luc; Real Jurado, Pedro (2015)
This paper introduces a new kind of skeleton for binary volumes called the cellular skeleton. This skeleton is not a subset ...
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Connectivity calculus of fractal polyhedrons

Molina Abril, Helena; Real Jurado, Pedro; Nakamura, Akira; Klette, Reinhard (2015)
The paper analyzes the connectivity information (more precisely, numbers of tunnels and their homological (co)cycle ...
Presentation
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A Parallel Implementation for Computing the Region-Adjacency-Tree of a Segmentation of a 2D Digital Image

Díaz del Río, Fernando; Real Jurado, Pedro; Onchis, Darian M. (Springer, 2015)
A design and implementation of a parallel algorithm for computing the Region-Adjacency Tree of a given segmentation of a ...
Presentation
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Double Hough Transform for Estimating the Position of the Mandibular Canal in Dental Radiographs

Onchis Moaca, Darian; Zappalá, Simone; Gotia, Smaranda Laura; Real Jurado, Pedro (Springer, 2015)
In this work, a multiple generalised anisotropic Hough transform (AGHT) is used to detect the mandibular canal in dental ...
Article
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Searching combinatorial optimality using graph-based homology information

Real Jurado, Pedro; Molina Abril, Helena; González Lorenzo, Aldo; Bac, Alexandra; Mari, Jean-Luc (2015)
This paper analyses the topological information of a digital object O under a combined combinatorial-algebraic point of ...
Presentation
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Computing Homological Information Based on Directed Graphs within Discrete Objects

González Lorenzo, Aldo; Bac, Alexandra; Mari, Jean-Luc; Real Jurado, Pedro (IEEE Computer Society, 2014)
n-dimensional discrete objects can be interpreted as cubical complexes which are suitable for the study of their homology ...
Presentation
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Extraction d’information homologique des objets discrets s’appuyant sur des graphes orientés

González Lorenzo, Aldo; Bac, Alexandra; Mari, Jean-Luc; Real Jurado, Pedro (CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication, 2014)
Tout objet discret n-dimensionnel peut être transformé en complexe cubique, dont on peut étudier les groupes d’homologie ...
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Computer Analysis of Images and Patterns

Real Jurado, Pedro (Springer, 2013)
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A continuous analog for 4-dimensional objects

Pacheco Martínez, Ana María; Mari, Jean-Luc; Real Jurado, Pedro (2013)
In this paper, we follow up on the studies developed by Kovalevsky (Comput Vis Graph Image Process 46:141–161, 1989) and ...
PhD Thesis
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Homological Spanning Forests for Discrete Objects

Molina Abril, Helena; Real Jurado, Pedro (2012)
Computing and representing topological information form an important part in many applications such as image representation ...
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Homological spanning forest framework for 2D image analysis

Molina Abril, Helena; Real Jurado, Pedro (2012)
A 2D topology-based digital image processing framework is presented here. This framework consists of the computation of a ...
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Homological optimality in Discrete Morse Theory through chain homotopies

Molina Abril, Helena; Real Jurado, Pedro (2012)
Morse theory is a fundamental tool for analyzing the geometry and topology of smooth manifolds. This tool was translated ...
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Searching high order invariants in computer imagery

Berciano Alcaraz, Ainhoa; Molina Abril, Helena; Real Jurado, Pedro (2012)
In this paper, we present a direct computational application of Homological Perturbation Theory (HPT, for short) to computer ...
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Designing a new software tool for digital imagery based on P systems

Díaz Pernil, Daniel; Gutiérrez Naranjo, Miguel Ángel; Molina Abril, Helena; Real Jurado, Pedro (2012)
In this paper we present a new software tool for dealing with the problem of segmentation in Digital Imagery. The ...
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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 ...
PhD Thesis
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Extracting cell complexes from 4-dimensional digital images

Pacheco Martínez, Ana María; Real Jurado, Pedro (2012)
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Using membrane computing for effective homology

Díaz Pernil, Daniel; Christinal, Hepzibah A.; Gutiérrez Naranjo, Miguel Ángel; Real Jurado, Pedro (2012)
Effective Homology is an algebraic-topological method based on the computational concept of chain homotopy equivalence on ...
Article
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Homological models for semidirect products of finitely generated Abelian groups

Álvarez Solano, Víctor; Frau García, María Dolores; Real Jurado, Pedro; Armario Sampalo, José Andrés (2012)
Let G be a semidirect product of finitely generated Abelian groups. We provide a method for constructing an explicit ...
Presentation
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Color Segmentation Of 2D Images With Thresholding

Christinal, Hepzibah A.; Díaz Pernil, Daniel; Real Jurado, Pedro; Easter Selvan, S. (Springer, 2012)
Membrane Computing is a biologically inspired computational model. Its devices are called P systems and they perform ...
Chapter of Book
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An efficient algorithm to compute subsets of points in ℤ n

Pacheco Martínez, Ana María; Real Jurado, Pedro (2012)
In this paper we show a more efficient algorithm than that in [8] to compute subsets of points non-congruent by isometries. ...
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Computational Topology in Image Context

González Díaz, Rocío; Real Jurado, Pedro (Elsevier, 2012)
Chapter of Book
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Triangle mesh compression and homological spanning forests

Carnero Iglesias, Javier; Molina Abril, Helena; Real Jurado, Pedro (2012)
Triangle three-dimensional meshes have been widely used to represent 3D objects in several applications. These meshes are ...
Chapter of Book
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A homological–based description of subdivided nD objects

Molina Abril, Helena; Real Jurado, Pedro (2011)
We present here a topo–geometrical description of a subdivided nD object called homological spanning forest representation. ...
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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 ...
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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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Associating cell complexes to four dimensional digital objects

Pacheco Martínez, Ana María; Real Jurado, Pedro (2011)
The goal of this paper is to construct an algebraic-topological representation of a 80–adjacent doxel-based 4–dimensional ...
Article
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Region-based segmentation of 2D and 3D images with tissue-like P systems

Christinal, Hepzibah A.; Díaz Pernil, Daniel; Real Jurado, Pedro (2011)
Membrane Computing is a biologically inspired computational model. Its devices are called P systems and they perform ...
Article
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Algebraic tools in geometrical modeling with topological control

Pacheco Martínez, Ana María; Real Jurado, Pedro (Universidad de Sevilla, 2011)
In this paper we show a method to create a look-up table with all the possible bricks which can made up an object. Moreover, ...
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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, ...
Chapter of Book
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A bio-inspired software for segmenting digital images.

Díaz Pernil, Daniel; Molina Abril, Helena; Real Jurado, Pedro; Gutiérrez Naranjo, Miguel Ángel (2010)
Segmentation in computer vision refers to the process of partitioning a digital image into multiple segments (sets of ...
Presentation
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A Cellular Way to Obtain Homology Groups in Binary 2D Images

Díaz Pernil, Daniel; Gutiérrez Naranjo, Miguel Ángel; Real Jurado, Pedro; Sánchez Canales, Vanesa (Fénix Editora, 2010)
In this paper we present a P systems-based solution for the Homology Groups of Binary 2D Image (HGB2I) Problem, a classical ...
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Computing Homology Groups in Binary 2D Imagery by Tissue-like P Systems

Díaz Pernil, Daniel; Gutiérrez Naranjo, Miguel Ángel; Real Jurado, Pedro; Sánchez Canales, Vanesa (Romanian Academy, Section for Information Science and Technology, 2010)
We present a new solution for the Homology Groups of Binary 2D Image (HGB2I) Problem by using Membrane Computing techniques. ...
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Image Segmentation Inspired by Cellular Models using hardware programming

Carnero Iglesias, Javier; Díaz Pernil, Daniel; Molina Abril, Helena; Real Jurado, Pedro (Universidad de Sevilla, 2010)
Several features of image segmentation make it suitable for bio–inspired techniques. It can be parallelized, locally solved ...
Article
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Cartan's contructions and the twisted Eilenberg-Zilber theorem

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (De Gruyter, 2010)
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P systems and computational algebraic topology

Christinal, Hepzibah A.; Díaz Pernil, Daniel; Real Jurado, Pedro (2010)
Membrane Computing is a paradigm inspired from biological cellular communication. Membrane computing devices are called P ...
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Towards optimality in discrete Morse Theory through chain homotopies

Real Jurado, Pedro; Molina Abril, Helena (Universidad de Sevilla, 2010)
Once a discrete Morse function has been defined on a finite cell complex, information about its homology can be deduced ...
Article
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Obtaining cell complexes associated to four dimensional digital objects

Pacheco Martínez, Ana María; Mari, Jean-Luc; Real Jurado, Pedro (Universidad de Sevilla, 2010)
In this paper, we determine a cell complex representation of a 80–adjacent doxelbased 4-dimensional object. The homological ...
Article
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Gabor frames and topology-based strategies for astronomical images

Onchis, Darian M.; Real Jurado, Pedro; Gillich, Gilbert-Rainer (Universidad de Sevilla, 2010)
The topic of this paper is the description of procedures to remove the fringes from complicated astronomical data sets, ...
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Estudio de una ecuación del calor semilineal en dominios no-cilíndricos

Marín Rubio, Pedro; Kloeden, Peter E.; Real Jurado, Pedro (2009)
En esta comunicación presentaremos resultados de existencia y unicidad de soluciones que verifican una igualdad de energía ...
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Obtaining Homology Groups in Binary 2D Images Using P Systems

Christinal, Hepzibah A.; Díaz Pernil, Daniel; Real Jurado, Pedro (IEEE Computer Society, 2009)
Membrane Computing is a new paradigms inspired from cellular communication. We use in this paper the computational devices ...
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Algebra Structures on the Comparison of the Reduced Bar Construction and the Reduced W-Construction

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (Taylor and Francis, 2009)
For a simplicial augmented algebra K, Eilenberg–Mac Lane constructed a chain map . They proved that g is a reduction ...
Chapter of Book
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Homological computation using spanning trees

Molina Abril, Helena; Real Jurado, Pedro (2009)
We introduce here a new F2 homology computation algorithm based on a generalization of the spanning tree technique on a ...
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The homological reduction method for computing cocyclic Hadamard matrices

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (2009)
An alternate method for constructing (Hadamard) cocyclic matrices over a finite group GG is described. Provided that a ...
Chapter of Book
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Getting topological information for a 80-adjacency doxel-based 4D volume through a polytopal cell complex

Pacheco Martínez, Ana María; Real Jurado, Pedro (2009)
Given an 80-adjacency doxel-based digital four-dimensional hypervolume V, we construct here an associated oriented ...
Chapter of Book
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Segmentation in 2D and 3D image using Tissue-Like P System

Christinal, Hepzibah A.; Díaz Pernil, Daniel; Real Jurado, Pedro (2009)
Membrane Computing is a biologically inspired computational model. Its devices are called P systems and they perform ...
Chapter of Book
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Cell AT-models for digital volumes

Real Jurado, Pedro; Molina Abril, Helena (2009)
In [4], given a binary 26-adjacency voxel-based digital volume V, the homological information (that related to n-dimensional ...
Chapter of Book
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Decomposing cavities in digital volumes into products of cycles

Berciano Alcaraz, Ainhoa; Molina Abril, Helena; Pacheco Martínez, Ana María; Pilarczyk, Pawel; Real Jurado, Pedro (2009)
The homology of binary 3–dimensional digital images (digital volumes) provides concise algebraic description of their ...
Chapter of Book
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Homological tree-based strategies for image analysis

Real Jurado, Pedro; Molina Abril, Helena; Kropatsch, Walter G. (2009)
Homological characteristics of digital objects can be obtained in a straightforward manner computing an algebraic map φ ...
Chapter of Book
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Using membrane computing for obtaining homology groups of binary 2D digital images

Christinal, Hepzibah A.; Díaz Pernil, Daniel; Real Jurado, Pedro (2009)
Membrane Computing is a new paradigm inspired from cellular communication. Until now, P systems have been used in research ...
Chapter of Book
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Connectivity forests for homological analysis of digital volumes

Real Jurado, Pedro (2009)
In this paper, we provide a graph-based representation of the homology (information related to the different “holes” the ...
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A System of Equations for Describing Cocyclic Hadamard Matrices

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (Wiley, 2008)
Given a basis equation image for 2-cocycles equation image over a group G of order equation image, we describe a nonlinear ...
Chapter of Book
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Advanced homology computation of digital volumes via cell complexes

Molina Abril, Helena; Real Jurado, Pedro (2008)
Given a 3D binary voxel-based digital object V, an algorithm for computing homological information for V via a polyhedral ...
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; Real Jurado, Pedro; Molina Abril, Helena (2008)
Starting from an nD geometrical object, a cellular subdivision of such an object provides an algebraic counterpart from ...
Chapter of Book
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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 ...
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Rectifications of A-Algebras

Real Jurado, Pedro; Jiménez Rodríguez, María José (2007)
In this article, in the setting of connected DG-modules, we prove that, for any A -algebra M mi i≥1 , there is a chain ...
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 ...
Presentation
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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)
Chapter of Book
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On the Computation of Ainfinity-Maps

Berciano Alcaraz, Ainhoa; Jiménez Rodríguez, María José; Real Jurado, Pedro (2007)
Starting from a chain contraction (a special chain homotopy equivalence) connecting a differential graded algebra A with ...
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 ...
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Algebra Structures on the Twisted Eilenberg–Zilber Theorem

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (Taylor and Francis, 2007)
Let G, G′, and G ×τ G′ be three simplicial groups (not necessarily abelian) and C N (G) ⊗ t C N (G′) be the “twisted” ...
PhD Thesis
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Cálculo simbólico y técnicas de control de A∞-estructuras

Berciano Alcaraz, Ainhoa; Real Jurado, Pedro; Sergeraert, Francis (2006)
Mostramos aquí diversos aspectos importantes relacionados con el estudio de las A∞-estructuras, las cuales juegan un papel ...
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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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Reducing Computational Costs in the Basic Perturbation Lemma

Real Jurado, Pedro; Berciano Alcaraz, Ainhoa; Jiménez Rodríguez, María José (2006)
Homological Perturbation Theory [11, 13] is a well-known general method for computing homology, but its main algorithm, ...
Chapter of Book
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A Mathematica Notebook for Computing the Homology of Iterated Products of Groups

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (2006)
Let G be a group which admits the structure of an iterated product of central extensions and semidirect products of abelian ...
Chapter of Book
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A genetic algorithm for cocyclic hadamard matrices

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (2006)
A genetic algorithm for finding cocyclic Hadamard matrices is described. Though we focus on the case of dihedral groups, ...
Chapter of Book
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Calculating cocyclic hadamard matrices in Mathematica: exhaustive and heuristic searches

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (2006)
We describe a notebook in Mathematica which, taking as input data a homological model for a finite group G of order |G| = ...
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 ...
Chapter of Book
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Comparison maps for relatively free resolutions

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (2006)
Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGA-algebra) and X be a relatively ...
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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 ...
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; Sáchez 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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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 ...
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Transferring TTP-structures via contraction

Frau García, María Dolores; Real Jurado, Pedro; Armario Sampalo, José Andrés; Álvarez Solano, Víctor (2005)
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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 ...
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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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A[símbolo de infinito]–coalgebra structures on the Zp-homology of Eilenberg-Mac Lane spaces

Berciano Alcaraz, Ainhoa; Real Jurado, Pedro (Universidad de Cantabria, 2004)
We study here the A(1)-coalgebra structure of the homology H (K( , n);Zp) of an Eilenberg-Mac Lane space K( , n), where ...
PhD Thesis
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A[símbolo de infinito]-estructuras y perturbación homológica

Jiménez Rodríguez, María José; Real Jurado, Pedro (2003)
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)
PhD Thesis
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Desarrollo cocíclico de diseños y aplicaciones

Frau García, María Dolores; Real Jurado, Pedro; Álvarez Solano, Víctor (2003)
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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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Matrices cocíclicas de Hadamard sobre productos semidirectos

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro (Alberto Márquez, 2002)
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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, ...
PhD Thesis
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Complejos reducidos de resoluciones y perturbación homológica

Álvarez Solano, Víctor; Real Jurado, Pedro (2001)
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 ...
Presentation
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“Coalgebra” Structures on 1-Homological Models for Commutative Differential Graded Algebras

Jiménez Rodríguez, María José; Real Jurado, Pedro (Springer, 2001)
In [3] “small” 1-homological model H of a commutative differential graded algebra is described. Homological Perturbation ...
Chapter of Book
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An algorithm for computing cocyclic matrices developed over some semidirect products

Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro; Álvarez Solano, Víctor (2001)
An algorithm for calculating a set ofgenerators ofrepresentative 2-cocycles on semidirect product offinite abelian groups ...
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 ...
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On p-minimal homological models of twisted tensor products of elementary complexes localised over a prime

Armario Sampalo, José Andrés; Real Jurado, Pedro; Silva Gallardo, Beatriz (American Mathematical Society, 1999)
In this paper, working over Z(p) and using algebra perturbation results from [18], p-minimal homological models of twisted ...
Presentation
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An algorithm for computing the first homology groups of CDGAs with linear differential

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Frau García, María Dolores; Real Jurado, Pedro; Silva Gallardo, Beatriz (Research Institute for Symbolic Computation, 1999)
We design here a primary platform for computing the basic homological information of Commutative Differential Graded ...
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Steenrod reduced powers and computability

González Díaz, Rocío; Real Jurado, Pedro (International Association for Mathematics and Computers in Simulation, 1999)
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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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analyzing the transference of the coalgebra structure on the homology CDGAs

Jiménez Rodríguez, María José; Real Jurado, Pedro; Silva Gallardo, Beatriz (International Association for Mathematics and Computers in Simulation, 1999)
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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 ...
PhD Thesis
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Estructuras multiplicativas y homología de fibrados

Armario Sampalo, José Andrés; Real Jurado, Pedro (1999)
Como es bien conocido, los principales mecanismos algebraicos para obtener información homológica de los espacios fibrados ...
PhD Thesis
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Modelos homológicos pequeños de DGA-Álgebras conmutativas

Silva Gallardo, Beatriz; Real Jurado, Pedro (1998)
En esta memoria proponemos un método para calcular la n -homología de una DGA-álgebra conmutativa, basado esencialmente ...
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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)
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On the computability of the p-local homology of twisted cartesian products of Eilenberg-Mac Lane spaces

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Real Jurado, Pedro (Universidade do Minho, 1997)
Working in the framework of the Simplicial Topology, a method for calculating the p-local homology of a twisted cartesian ...
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Homological perturbation theory and computability of Hochschild and cyclic homologies of CDGAs

Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Real Jurado, Pedro; Silva Gallardo, Beatriz (Diffiety Institute of the Russian Academy of Natural Sciences, 1997)
We establish an algorithm computing the homology of commutative differential graded algebras (briefly, CDGAs). The main ...
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An algorithm computing homotopy groups

Real Jurado, Pedro (Elsevier, 1996)
An algorithm computing homotopy groups of a reduced simplicial set with effective homology is described, using the Whitehead tower method.
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On the computability of the Steenrod squares

Real Jurado, Pedro (Springer, 1996)
In questo lavoro offriamo in modo esplicito le formule di una serie de morfismi che controUano la mancanza di commutativit~ ...
PhD Thesis
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Algoritmos de cálculo de homología efectiva de los espacios clasificantes

Real Jurado, Pedro; Quintero Toscano, Antonio Rafael; Sergeraert, Francis (1993)
El propósito esencial de esta memoria es el de describir varios algoritmos de cálculo de homología efectiva de los espacios ...