Nuestros investigadores

Jorge Elorza Barbajero

Física y Matemática Aplicada
Facultad de Ciencias. Universidad de Navarra
Líneas de investigación
Soft Computing, Fuzzy Logic, Approximate Reasoning, Biophysics
Índice H
4, (WoS, 30/08/2017)

Publicaciones científicas más recientes (desde 2010)

Autores: Chasco, María Jesús; Elorza, Jorge; et al.
ISSN 0165-0114  Vol. 373  2019  págs. 164 - 179
In this paper we study the class of all fuzzy subgroups defined with respect to a given t-norm on a fixed group. We find necessary and sufficient conditions over two t-norms to guarantee that the class of all fuzzy subgroups induced by the first t-norm is contained in the class of all fuzzy subgroups with respect to by the second one. We characterize the functions that transform fuzzy subgroups into fuzzy subgroups. The close relationship between indistinguishability operators and fuzzy subgroups allows us to obtain similar results for some classes of indistinguishability operators.
Autores: Elorza, Jorge; Wittt, A.; et al.
ISSN 0218-1274  Vol. 29  Nº 8  2019  págs. 1930021
Connexins are specialized ionic channels that control the action potential propagation between cardiac myocytes. In this paper, we study the connexin dynamics in a one-dimensional model of cardiac tissue. We show that the connexin dynamics may lead to a spatial organization of the gap junction conductance. In the numerical simulations presented in this paper we have found two different regimes for the spatial organization of the conductances: (a) a spatially uniform conductance; (b) a spatially complex pattern of local values of high and low conductances. in addition, we have observed that, locally, the two final states are limit cycles with a period equal to the period associated with the external excitation of the tissue strand. The conductance dispersion usually takes place on a very large time scale, i.e. thousands of heart beats, and on a very short spatial scale. Due to its simplicity, the one-dimensional setting allows a detailed study of the emerging structure and in particular very long simulations. We have studied the transition between the two aforementioned states as a function of the gap junction conductance characteristics. Furthermore, we have studied the effect of initially added noises on the outcome of the system. Finally, using spatial autocorrelation functions we have characterized the spatial dispersion in conductance values.
Autores: Ardanza-Trevijano, Sergio; Chasco, María Jesús; Elorza, Jorge, (Autor de correspondencia)
ISSN 0165-0114  Vol. 369  2018  págs. 122 - 131
We implement the notion of annihilator into fuzzy subgroups of an abelian group. There are different uses for the term annihilator in algebraic contexts that have been used fuzzy systems. In this paper we refer to another type of annihilator which is essential in classical duality theory and extends the widely applied notion of orthogonal complement in Euclidean spaces. We find that in the natural algebraic duality of a group, a fuzzy subgroup can be recovered after taking the inverse annihilator of its annihilator. We also study the behavior of annihilators with respect to unions and intersections. Some illustrative examples of annihilators of fuzzy subgroups are shown, both with finite and infinite rank.
Autores: Bragard, Jean René Alfred; Laroze, D.; et al.
ISSN 2470-0045  Vol. 92  Nº 6  2015  págs. 2919
Defibrillation is the standard clinical treatment used to stop ventricular fibrillation. An electrical device delivers a controlled amount of electrical energy via a pair of electrodes in order to reestablish a normal heart rate. We propose a technique that is a combination of biphasic shocks applied with a four-electrode system rather than the standard two-electrode system. We use a numerical model of a one-dimensional ring of cardiac tissue in order to test and evaluate the benefit of this technique. We compare three different shock protocols, namely a monophasic and two types of biphasic shocks. The results obtained by using a four-electrode system are compared quantitatively with those obtained with the standard two-electrode system. We find that a huge reduction in defibrillation threshold is achieved with the four-electrode system. For the most efficient protocol (asymmetric biphasic), we obtain a reduction in excess of 80% in the energy required for a defibrillation success rate of 90%. The mechanisms of successful defibrillation are also analyzed. This reveals that the advantage of asymmetric biphasic shocks with four electrodes lies in the duration of the cathodal and anodal phase of the shock.
Autores: Carmona, N. ; Elorza, Jorge; Recasens, J. ; et al.
ISSN 0020-0255  Vol. 310  2015  págs. 36 - 51
Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the outcome. We characterize permutability in the case of the composition of fuzzy consequence operators and the dual case of fuzzy interior operators. We prove that for these cases, permutability is completely connected to the preservation of the operator type. We also study the particular case of fuzzy operators induced by fuzzy relations through Zadeh¿s compositional rule and the inf-¿¿ composition. For this cases, we connect permutability of the fuzzy relations (using the sup-¿ composition) with permutability of the induced operators. Special attention is paid to the cases of operators induced by fuzzy preorders and similarities. Finally, we use these results to relate the operator induced by the transitive closure of the composition of two reflexive fuzzy relations with the closure of the operator this composition induces.
Autores: Elorza, Jorge; Fuentes-González, R.; Bragard, Jean René Alfred; et al.
ISSN 0165-0114  Vol. 218  2013  págs. 73 - 89
In a previous paper, Elorza and Burillo explored the coherence property in fuzzy consequence operators. In this paper we show that fuzzy closing operators of mathematical morphology are always coherent operators. We also show that the coherence property is the key to link the four following families: fuzzy closing morphological operators, fuzzy consequence operators, fuzzy preorders and fuzzy closure and co-closure systems. This will allow to translate important well-known properties from the field of approximate reasoning to the field of image processing.
Autores: Bragard, Jean René Alfred; Elorza, Jorge; et al.
Revista: CHAOS (EEUU)
ISSN 1054-1500  Vol. 23  2013  págs. 043119
In this article, we compare quantitatively the efficiency of three different protocols commonly used in commercial defibrillators. These are based on monophasic and both symmetric and asymmetric biphasic shocks. A numerical one¿dimensional model of cardiac tissue using the bidomain formulation is used in order to test the different protocols. In particular, we performed a total of 4.8 × 106 simulations by varying shock waveform, shock energy, initial conditions, and heterogeneity in internal electrical conductivity. Whenever the shock successfully removed the reentrant dynamics in the tissue, we classified the mechanism. The analysis of the numerical data shows that biphasic shocks are significantly more efficient (by about 25%) than the corresponding monophasic ones. We determine that the increase in efficiency of the biphasic shocks can be explained by the higher proportion of newly excited tissue through the mechanism of direct activation.
Autores: Elorza, Jorge; Recasens, J. ;
Libro:  Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
2015  págs. 59 - 65
Three ways to find lower approximations of a given fuzzy operator are given. A Representation Theorem for fuzzy consequence operators is obtained.
Autores: Hawks, C. ; Elorza, Jorge; Echebarria, B. ; et al.
Libro:  Computing in Cardiology 2015
Vol. 42  2015  págs. 437 - 440
Constant conductances are often assumed when model- ing cardiac tissue. However experimental evidences have shown that gap junctions (GJ) actually connect adjacent cardiac myocytes. These GJ are complex proteins of the connexin family (Cx40; Cx43; Cx45 are the most common in human). These GJ modify the conductances between cardiac cell through a dynamical process. The aim of this study is to develop a bidomain model of the cardiac tis- sue where the dynamics of the connexins is also included. In particular we will compare the differences associated with the use of a monodomain versus bidomain formula- tion in inducing intra-cellular conductance variations. We have found that the monodomain formulation gives con- ductance variations a factor four to five larger with respect to the bidomain formulation.
Autores: Carmona, N.; Elorza, Jorge; Recasens, J.; et al.
2014  págs. 45 - 49
Composition of fuzzy operators often appears and it is natural to ask when the order of compo- sition does not change the result. In previous pa- pers, we characterized permutability in the case of fuzzy consequence operators and fuzzy inte- rior operators. We also showed the connection between the permutability of the fuzzy relations and the permutability of their induced fuzzy op- erators. In this work we present some examples of permutability and non permutability of fuzzy operators and fuzzy relations in order to illustrate these results.
Autores: Cantalapiedra, I. R.; Elorza, Jorge; et al.
Libro:  Computing in Cardiology 2014
Vol. 41  2014  págs. 505 - 508
In the absence of a better solution, ventricular fibrillation is treated by applying one or several large electrical shocks to the patient. The question of how to lower the energy required for a successful shock is still a current issue in both fundamental research and clinical practice. In the study presented here we will compare defibrillation applied through a four electrode device with the standard procedure using two electrodes. The method is tested through intensive numerical simulations. Here we have used a one dimensional geometry. At the level of the cardiac tissue, the bidomain and the modified Beeler-Reuter models were used. Three different shock waveforms are tested: monophasic and two types of biphasic shocks. The results are compared with those obtained with standard two electrode device. A significant reduction in defibrillation thresholds is achieved for all the three tested waveforms when we use a four electrode device.
Autores: Carmona, N.; Elorza, Jorge; Recasens, J.; et al.
Libro:  Advances in artificial intelligence
Vol. 8109  2013  págs. 62 - 69
In this paper we study the permutability of the composition of fuzzy consequence operators (fuzzy closings) and fuzzy interior operators (fuzzy openings). We establish several characterizations and we show the relation of permutability with the fuzzy closure and fuzzy interior of a fuzzy operator. We also study the connection between permutability and the preservation of the operator type through the composition. More precisely, when the composition of two openings is an opening and the composition of two closings is a closing.
Autores: Carmona, N.; Rua-Seoane, J. C.; Elorza, Jorge; et al.
Libro:  Computing in Cardiology Conference 2013
Vol. 40  2013  págs. 1031 - 1034
The aim of this work was to find evidence of aging of ECG indicators in a population of young adults (52 subjects of age 19 ± 0.6 in 2002). For this purpose, an application which analyzes ECG signals was designed and implemented. The data consist in four different series for each subject of the studied population. Two ECG signals of 5 minute duration (one at rest and one after a mild effort) were taken in 2002 and the exact same procedure was repeated for each subject five years later in 2007. All these electrocardiographic signals were examined by computational techniques in order to extract the RR and QT intervals and the energy content of the T-wave. Next, we have compared all the data using first return maps and measured the data dispersion by evaluating the covariance ellipses. Relations between each of the four data series were studied. The analysis also included the gender and the categorical aspect ¿practicing sport¿.
Autores: Carmona, N.; Elorza, Jorge; Recasens, J.; et al.
Libro:  Modeling decisions for artificial intelligence
Vol. 8234  2013  págs. 237 - 247
In this paper we study the permutability of the composition of fuzzy consequence operators when they are induced by fuzzy relations using the usual Zadeh's compositional rule. In particular, we study the case of fuzzy indistinguishability operators and fuzzy preorders. We study the connection between the permutability of the fuzzy relations and the permutability of their induced fuzzy operators.
Autores: Carmona, N.; Elorza, Jorge; Recasens, J.; et al.
Libro:  Aggregation functions in theory and in practise
Vol. 228  2013  págs. 295 - 306
In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator, one from a fuzzy operator and a fuzzy relation and the other one from two fuzzy operators. The first one is an extension of the well-known fuzzy operator induced by a fuzzy relation through Zadeh¿s compositional rule. Finally, we aggregate these operators using the quasi-arithmetic mean associated to a continuous Archimedean t-norm. The aim is to compare the operator induced by the quasi-arithmetic mean of the generators with the quasi-arithmetic mean of the generated operators.
Autores: Bragard, Jean René Alfred; Elorza, Jorge; Cherry, E. M.; et al.
Libro:  Computing in Cardiology Conference 2013
Vol. 40  2013  págs. 851 - 854
We develop and validate a three-dimensional model of ventricular fibrillation for use in studying defibrillation. Specifically, we use a rabbit ventricular geometry as a realistic model system for evaluating the efficacy of defibrillatory shocks. Data obtained from the simulations are analyzed in terms of a dose-response curve. In agreement with clinically relevant values, we find that an electric field strength of about 6.6 V/cm indicates a 50% probability of successful defibrillation for a 12-ms monophasic shock in our model. Our validated model will be useful for optimizing defibrillation protocols and for performing detailed studies of defibrillation mechanisms.
Autores: Elorza, Jorge; Fuentes-González, R.; Bragard, Jean René Alfred; et al.
Libro:  Actas del XVI Congreso Español sobre Tecnologías y Lógica Fuzzy
2012  págs. 54-59
Paer we show a comprehensive summary on the relationship between fuzzy morphological operators, fuzzy consequence operators and fuzzy preorders and we motivate the study of morphological operators by using binary relations as structuring elements in a more general context, i.e., the context of fuzzy re- lational systems for obtaining relevant infor- mation.
Autores: Elorza, Jorge; Fuentes-González, R.; Bragard, Jean René Alfred; et al.
Libro:  Actas del XV Congreso Español sobre Tecnologías y Lógica Fuzzy
2010  págs. 133 - 138
In a previous paper [10] we explored the no- tion of coherent fuzzy consequence operator. It is well-known that the operator induced by a fuzzy preorder through Zadeh's compo- sitional rule is always a coherent fuzzy con- sequence operator. It is also known that the relation induced by a fuzzy consequence operator is a fuzzy preorder if such opera- tor is coherent [7]. Fuzzy closing operators of mathematical morphology can be consid- ered as fuzzy consequence operators. In [12] we showed that they are coherent operators. The aim of this paper is to analyze the rela- tions between both classes of operators and the class of all fuzzy preorders in order to translate well know properties from Approxi- mate Reasoning to the one of Image Process- ing.