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Browsing by Author "Pacheco Martínez, Ana María"
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A continuous analog for 4dimensional objects [Article]
Pacheco Martínez, Ana María; Mari, JeanLuc; 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 Kenmochi et al. (Comput Vis Image Underst 71:281–293, 1998), which defined a continuous analog for a ...

A faithful functor among algebras and graphs [Presentation]
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad (Computational and Mathematical Methods in Science and Engineering, 2016)The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertexcolored graphs, we ...

Algebraic tools in geometrical modeling with topological control [Article]
Pacheco Martínez, Ana María; Real Jurado, Pedro (Universidad de Sevilla, 2011)In this paper we show a method to create a lookup table with all the possible bricks which can made up an object. Moreover, we generate a procedure to recreate any object starting from this table. More concretely, the ...

An efficient algorithm to compute subsets of points in ℤ n [Chapter of Book]
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 noncongruent by isometries. This algorithm can be used to reconstruct the object from the digital image. Both algorithms are ...

Associating cell complexes to four dimensional digital objects [Chapter of Book]
Pacheco Martínez, Ana María; Real Jurado, Pedro (2011)The goal of this paper is to construct an algebraictopological representation of a 80–adjacent doxelbased 4–dimensional digital object. Such that representation consists on associating a cell complex homologically ...

Classification of filiform Lie algebras up to dimension 7 over finite fields [Article]
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad (Ovidius University, 2016)This paper tries to develop a recent research which consists in using Discrete Mathematics as a tool in the study of the problem of the classification of Lie algebras in general, dealing in this case with filiform Lie ...

Computation of isotopisms of algebras over finite fields by means of graph invariants [Article]
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad (Elsevier, 201707)In this paper we define a pair of faithful functors that map isomorphic and isotopic finitedimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually ...

Decomposing cavities in digital volumes into products of cycles [Chapter of Book]
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 topology in terms of connected components, tunnels and cavities. Homology generators corresponding to ...

Directed pseudographs and Lie algebras over finite fields [Article]
Boza Prieto, Luis; Fedriani Martel, Eugenio Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad (Institute of Mathematics, Czech Academy of Sciences, 201403)The main goal of this paper is to show an application of Graph Theory to classifying Lie algebras over finite fields. It is rooted in the representation of each Lie algebra by a certain pseudograph. As partial results, ...

Extracting cell complexes from 4dimensional digital images [PhD Thesis]
Pacheco Martínez, Ana María (2012) 
Getting topological information for a 80adjacency doxelbased 4D volume through a polytopal cell complex [Chapter of Book]
Pacheco Martínez, Ana María; Real Jurado, Pedro (2009)Given an 80adjacency doxelbased digital fourdimensional hypervolume V, we construct here an associated oriented 4–dimensional polytopal cell complex K(V), having the same integer homological information (that related ...

Lowdimensional filiform Lie algebras over finite fields [Presentation]
Falcón Ganfornina, Óscar Jesús; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad (World Scientific and Engineering Academy and Society Press, 2011)In this paper we use some objects of Graph Theory to classify lowdimensional filiform Lie algebras over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some ...

Obtaining cell complexes associated to four dimensional digital objects [Article]
Pacheco Martínez, Ana María; Mari, JeanLuc; Real Jurado, Pedro (Universidad de Sevilla, 2010)In this paper, we determine a cell complex representation of a 80–adjacent doxelbased 4dimensional object. The homological information of this polyhedral cell complex can be employed to specify topological features and ...