Stabilization of heterodimensional cycles

We consider diffeomorphisms $f$ with heteroclinic cycles associated to saddles $P$ and $Q$ of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to $f$ with a robust cycle associated to hyperbolic sets containing the continuations of $P$ and $Q$. We focus on the case where the indices of these two saddles differ by one. We prove that, excluding one particular case (so-called twisted cycles that additionally satisfy some geometrical restrictions), all such cycles can be stabilized.Comment: 31 pages, 9 figure

Singularities of the susceptibility of an SRB measure in the presence of stable-unstable tangencies

Let $\rho$ be an SRB (or "physical"), measure for the discrete time evolution given by a map $f$, and let $\rho(A)$ denote the expectation value of a smooth function $A$. If $f$ depends on a parameter, the derivative $\delta\rho(A)$ of $\rho(A)$ with respect to the parameter is formally given by the value of the so-called susceptibility function $\Psi(z)$ at $z=1$. When $f$ is a uniformly hyperbolic diffeomorphism, it has been proved that the power series $\Psi(z)$ has a radius of convergence $r(\Psi)>1$, and that $\delta\rho(A)=\Psi(1)$, but it is known that $r(\Psi)<1$ in some other cases. One reason why $f$ may fail to be uniformly hyperbolic is if there are tangencies between the stable and unstable manifolds for $(f,\rho)$. The present paper gives a crude, nonrigorous, analysis of this situation in terms of the Hausdorff dimension $d$ of $\rho$ in the stable direction. We find that the tangencies produce singularities of $\Psi(z)$ for $|z|1$ if $d>1/2$. In particular, if $d>1/2$ we may hope that $\Psi(1)$ makes sense, and the derivative $\delta\rho(A)=\Psi(1)$ has thus a chance to be definedComment: 12 page

A Note on Commuting Diffeomorphisms on Surfaces

Let S be a closed surface with nonzero Euler characteristic. We prove the existence of an open neighborhood V of the identity map of S in the C^1-topology with the following property: if G is an abelian subgroup of Diff^1(S) generated by any family of elements in V then the elements of G have common fixed points. This result generalizes a similar result due to Bonatti and announced in his paper "Diffeomorphismes commutants des surfaces et stabilite des fibrations en tores".Comment: 16 page

Infinitely Many Stochastically Stable Attractors

Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the basins of attraction of each attractor covers Lebesgue almost all points of M. We prove that the time averages of almost all orbits under random perturbations are given by a finite number of probability measures. Moreover these probability measures are close to the probability measures supported by the attractors when the perturbations are close to the original map f.Comment: 14 pages, 2 figure

Left atrial size after cardioversion for atrial fibrillation: effect of external DC shock

OBJECTIVE: The aim of this study was to evaluate the effect of external direct current (DC) shock on left atrial (LA) dimension and volumes after cardioversion for atrial fibrillation, and the relation between LA size and atrial function. METHODS: We evaluated 180 patients who were randomly cardioverted with DC shock (90 patients) or drugs (90 patients). Echocardiographic evaluations included LA size and volumes. LA passive and active emptying volumes were calculated, and LA function was measured as atrial ejection force. Changes in LA diameters and volumes were correlate with atrial systolic function. RESULTS: The LA was dilated in all patients during arrhythmia and decreased after the restoration of sinus rhythm. The entity of reduction was different in the 2 groups of patients. LA maximal and minimal volumes were increased after DC shock as compared with patients treated with drugs (LA maximal volume 34 +/- 4 vs 31 +/- 5; P <.01; LA minimal volume 18 +/- 2.6 vs 15 +/- 3.6; P <.01). The atrial function was also depressed after DC shock and the delay in the recovery of atrial contractility was related to LA dilation. Patients treated with drugs had a higher atrial ejection force that was associated with a more marked reduction in LA maximal volume after the restoration of in sinus rhythm. A relationship between LA volumes and atrial ejection force was observed in the group of patients with depressed atrial mechanic function (r = -0.78; P <.001). The active emptying fraction was lower, although not significantly, in this group, whereas the conduit volume was increased. CONCLUSION: External DC shock induced a depressed atrial mechanic function in many patients and this was associated with a persistence of LA dilation

The Structure on Invariant Measures of C1C^1 generic diffeomorphisms

Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism f\in\Diff(M). We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in $\Lambda$ (which implies the set of irregular$^+$ points is also residual in $\Lambda$). As an application, we show that the non-uniform hyperbolicity of irregular$^+$ points in $\Lambda$ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in $\Lambda$) determines the uniform hyperbolicity of $\Lambda$

Left atrial size and function after spontaneous cardioversion of atrial fibrillation and their relation to N-terminal atrial natriuretic peptide

In conclusion, higher levels of N-ANP during AF were independently associated with spontaneous conversion, as well as with smaller LA volume.An inverse correlation existed between LA volume and N-AN

Computing Compliant Anonymisations of Quantified ABoxes w.r.t. EL Policies

We adapt existing approaches for privacy-preserving publishing of linked data to a setting where the data are given as Description Logic (DL) ABoxes with possibly anonymised (formally: existentially quantified) individuals and the privacy policies are expressed using sets of concepts of the DL EL. We provide a chacterization of compliance of such ABoxes w.r.t. EL policies, and show how optimal compliant anonymisations of ABoxes that are non-compliant can be computed. This work extends previous work on privacy-preserving ontology publishing, in which a very restricted form of ABoxes, called instance stores, had been considered, but restricts the attention to compliance. The approach developed here can easily be adapted to the problem of computing optimal repairs of quantified ABoxes

Unconventional secretion of α-Crystallin B requires the Autophagic pathway and is controlled by phosphorylation of its serine 59 residue

α-Crystallin B (CRYAB or HspB5) is a chaperone member of the small heat-shock protein family that prevents aggregation of many cytosolic client proteins by means of its ATP-independent holdase activity. Surprisingly, several reports show that CRYAB exerts a protective role also extracellularly, and it has been recently demonstrated that CRYAB is secreted from human retinal pigment epithelial cells by an unconventional secretion pathway that involves multi-vesicular bodies. Here we show that autophagy is crucial for this unconventional secretion pathway and that phosphorylation at serine 59 residue regulates CRYAB secretion by inhibiting its recruitment to the autophagosomes. In addition, we found that autophagosomes containing CRYAB are not able to fuse with lysosomes. Therefore, CRYAB is capable to highjack and divert autophagosomes toward the exocytic pathway, inhibiting their canonical route leading to the lysosomal compartment. Potential implications of these findings in the context of disease-associated mutant proteins turn-over are discussed