Jorge Elorza

Genomic regulation of CTLA4 and Multiple Sclerosis

The cytotoxic T lymphocyte antigen 4 gene (CTLA4) is a critical regulator of T-cell activation and it is an important therapeutic target for cancer and autoimmune diseases. Here, we analyzed the genomic regulation of CTLA4 gene expression in order to identify single nucleotide polymorphisms (SNPs) that affect its expression and splicing, and to assess their association with Multiple Sclerosis (MS). We analyzed 152 healthy subjects and 146 patients with MS, of which 52 controls and 51 patients were used for gene expression analysis. We genotyped 17 SNPs in the CTLA4 gene using the SNaPshot Multiplex Kit, and in addition gene expression of the soluble (sCTLA4) and full length (flCTLA4) isoforms was quantified by real-time PCR, while protein levels of sCTLA4 were measured by ELISA. We found that the SNPs at -1577, +6230, +10242, +10717 and +12310 influence CTLA4 expression and the combination of the -1577 GG and +6230 GG genotypes provokes the strongest decrease in CTLA4 gene expression. We found that the SNP at -658 only acted as a regulatory SNP in patients with MS, suggesting the existence of epigenetic changes due to this disease. We also identified a decrease in CTLA4 gene expression levels in patients receiving chemotherapy, although no association was observed between MS and any of the polymorphisms studied. In conclusion, we have identified several SNPs in the CTLA4 gene and studied their influence on its genetic regulation. The involvement of CTLA4 in the pathogenesis of MS may be subtle and related to the functional changes in its pathway rather than predisposing genetic polymorphisms.

On the relation between fuzzy preorders and fuzzy consequence operators

The purpose of this paper is to analyze the operators induced by relations and conversely the relations induced by operators in fuzzy logic. Given a t-norm * and given a non-empty universal set X, it is well known that if R is a fuzzy *-preorder on X then the operator induced by R, , is a fuzzy consequence operator (FCO). In fact, is a *-coherent FCO. It is also known that if C is a *-coherent FCO then the relation induced by C, RC, is a fuzzy *-preorder. We explore the *-coherence axiom because we do not know in the literature any example of non-coherent operator. Then, several families of these operators will be shown. Moreover we prove that the equivalence between fuzzy preorders and fuzzy consequence operators is held in only one way. As a result, a characterization of the *-preorder concept using the induced operator is given. Also some characterizations which show when an operator induces a *-preorder are proved. Finally, we will show that the characterization of the operators induced by relations given for finite universes cannot be generalized for infinite universes.

On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems

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.

Shock-induced termination of reentrant cardiac arrhythmias: comparing monophasic and biphasic shock protocols.

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 × 10(6) 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.

Permutable fuzzy consequence and interior operators and their connection with fuzzy relations

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 Zadehs 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.

Permutability of Fuzzy Consequence Operators and Fuzzy Interior Operators

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.

On the Preservation of an Equivalence Relation Between Fuzzy Subgroups

Two fuzzy subgroups \(\mu ,\eta \) of a group G are said to be equivalent if they have the same family of level set subgroups. Although it is well known that given two fuzzy subgroups \(\mu ,\eta \) of a group G their maximum is not always a fuzzy subgroup, it is clear that the maximum of two equivalent fuzzy subgroups is a fuzzy subgroup. We prove that the composition of two equivalent fuzzy subgroups by means of an aggregation function is again a fuzzy subgroup. Moreover, we prove that if two equivalent subgroups have the sup property their corresponding compositions by any aggregation function also have the sup property. Finally, we characterize the aggregation functions such that when applied to two equivalent fuzzy subgroups, the obtained fuzzy subgroup is equivalent to both of them. These results extend the particular results given by Jain for the maximum and the minimum of two fuzzy subgroups.

Influence of gap junction dynamics on the stability of reentrant waves in cardiac tissue

Constant conductances are often assumed when modeling 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 tissue 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 formulation in inducing intra-cellular conductance variations. We have found that the monodomain formulation gives conductance variations a factor four to five larger with respect to the bidomain formulation.

Permutability of Fuzzy Consequence Operators Induced by Fuzzy Relations

In this paper we study the permutability of the composition of fuzzy consequence operators when they are induced by fuzzy relations using the usual Zadehs 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.

On the Induction of New Fuzzy Relations, New Fuzzy Operators and Their Aggregation

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.