Existence of a Reversible T-Point Heteroclinic Cycle in a Piecewise Linear Version of the Michelson System

The proof of the existence of a global connection in differential systems is generally a difficult task. Some authors use numerical techniques to show this existence, even in the case of continuous piecewise linear systems. In this paper we give an analytical proof of the existence of a reversible T-point heteroclinic cycle in a continuous piecewise linear version of the widely studied Michelson system. The principal ideas of this proof can be extended to other piecewise linear systems

Conexiones globales en sistemas tridimensionales lineales a trozos

Presentamos en esta comunicación una técnica para probar de forma analítica la existencia de conexiones globales en sistemas dinámicos continuos lineales a trozos. Más concretamente, utilizamos esta técnica para demostrar la existencia de dos conexiones homoclinas directas (aquellas que cortan al plano de separación exactamente dos veces) y un ciclo heteroclino directo tipo punto-T (cuya conexión por las variedades unidimensionales corta exactamente tres veces al plano de separación mientras que su conexión por las variedades bidimensionales sólo lo hará en un punto) en una familia uniparamétrica de sistemas tridimensionales continuos lineales a trozos con dos zonas, reversibles y con trazas nulas

Integrative epigenomics in Sjögren´s syndrome reveals novel pathways and a strong interaction between the HLA, autoantibodies and the interferon signature

Primary Sjögren's syndrome (SS) is a systemic autoimmune disease characterized by lymphocytic infiltration and damage of exocrine salivary and lacrimal glands. The etiology of SS is complex with environmental triggers and genetic factors involved. By conducting an integrated multi-omics study, we confirmed a vast coordinated hypomethylation and overexpression effects in IFN-related genes, what is known as the IFN signature. Stratified and conditional analyses suggest a strong interaction between SS-associated HLA genetic variation and the presence of Anti-Ro/SSA autoantibodies in driving the IFN epigenetic signature and determining SS. We report a novel epigenetic signature characterized by increased DNA methylation levels in a large number of genes enriched in pathways such as collagen metabolism and extracellular matrix organization. We identified potential new genetic variants associated with SS that might mediate their risk by altering DNA methylation or gene expression patterns, as well as disease-interacting genetic variants that exhibit regulatory function only in the SS population. Our study sheds new light on the interaction between genetics, autoantibody profiles, DNA methylation and gene expression in SS, and contributes to elucidate the genetic architecture of gene regulation in an autoimmune population

O31 Integrative analysis reveals a molecular stratification of systemic autoimmune diseases

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Saddle-node canard cycles in slow-fast planar piecewise linear differential systems

By applying a singular perturbation approach, canard explosions exhibited by a general family of singularly perturbed planar Piecewise Linear (PWL) differential systems are analyzed. The performed study involves both hyperbolic and non-hyperbolic canard limit cycles appearing after both, a supercritical and a subcritical Hopf bifurcation. The obtained results are comparable with those obtained for smooth vector fields. In some sense, the manuscript can be understood as an extension towards the PWL framework of the results obtained for smooth systems by Dumortier and Roussarie in Mem. Am. Math. Soc. 1996, and Krupa and Szmolyan in J. Differ. Equ. 2001. In addition, some novel slow–fast behaviors are obtained. In particular, in the supercritical case, and under suitable conditions, it is proved that the limit cycles are organized along a curve exhibiting two folds. Each of these folds corresponds to a saddle–node bifurcation of canard limit cycles, one involving headless canard cycles, and the other involving canard cycles with head. This configuration also occurs in smooth systems with N-shaped fast nullcline. However, it has not been previously reported in the Van der Pol system. Our results provide justification for this observation

Saddle-node bifurcation of canard limit cycles in piecewise linear systems

We study saddle-node bifurcations of canard limit cycles in PWL systems by using singular perturbation theory tools. We distinguish two cases: the subcritical and the supercritical. In the subcritical case, we find saddle-node bifurcations of canard cycles both with head and without head. Moreover, we detect a transition between them. In the supercritical case, we find situations with two saddle-node bifurcations, which take place exponentially close in the parameter space; one of headless canards and another of canards with head. There, three canard cycles can coexist.Ministerio de Ciencia, Innovación y Universidades (Spain) PGC2018- 096265-B-I00Ministerio de Ciencia, Innovación y Universidades (Spain) RTI2018-093521-B-C31Ministerio de Economía y Competitividad (Spain) / AEI/ERDF (EU) MTM2017-83568-

Integrative epigenomics in Sjögren´s syndrome reveals novel pathways and a strong interaction between the HLA, autoantibodies and the interferon signature

International audienceAbstract Primary Sjögren’s syndrome (SS) is a systemic autoimmune disease characterized by lymphocytic infiltration and damage of exocrine salivary and lacrimal glands. The etiology of SS is complex with environmental triggers and genetic factors involved. By conducting an integrated multi-omics study, we confirmed a vast coordinated hypomethylation and overexpression effects in IFN-related genes, what is known as the IFN signature. Stratified and conditional analyses suggest a strong interaction between SS-associated HLA genetic variation and the presence of Anti-Ro/SSA autoantibodies in driving the IFN epigenetic signature and determining SS. We report a novel epigenetic signature characterized by increased DNA methylation levels in a large number of genes enriched in pathways such as collagen metabolism and extracellular matrix organization. We identified potential new genetic variants associated with SS that might mediate their risk by altering DNA methylation or gene expression patterns, as well as disease-interacting genetic variants that exhibit regulatory function only in the SS population. Our study sheds new light on the interaction between genetics, autoantibody profiles, DNA methylation and gene expression in SS, and contributes to elucidate the genetic architecture of gene regulation in an autoimmune population