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

Optimizing the computation of overriding

We introduce optimization techniques for reasoning in DLN---a recently introduced family of nonmonotonic description logics whose characterizing features appear well-suited to model the applicative examples naturally arising in biomedical domains and semantic web access control policies. Such optimizations are validated experimentally on large KBs with more than 30K axioms. Speedups exceed 1 order of magnitude. For the first time, response times compatible with real-time reasoning are obtained with nonmonotonic KBs of this size

Category-based grouping in working memory and multiple object tracking

Two prominent cognitive capacity limitations are the maximal number of objects we can place in working memory (WM) and the maximal number of objects we can track in a display. Both are believed to have a numeric value of 3 or 4, which has led to the proposal that we have a general cognitive capacity, and that this capacity is most likely linked to limitations of how many objects we can attend simultaneously. Based on previous results showing that we can memorize more objects if they come from different categories than if they come from the same category (e.g., Feigenson & Halberda, 2008; Wood, 2008; Wong, Peterson, & Thompson, 2008), we compare how category-based grouping affects performance for WM and multiple object tracking (MOT). We present participants with either “pure” displays of either cars or faces, or with “mixed” displays of cars and faces. Overall, the effects of category are weak. In some analyses but not others, we replicate the mixed advantage for WM, albeit with a small effect size. In contrast, we observe a weak pure advantage for MOT tasks, at least in a meta-analysis of five experiments, but not in all experiments. Accordingly, WM and MOT tasks differed significantly in their sensitivity to category membership. We also find that WM is slightly better for faces than for cars, but that no such difference exists for MOT. We tentatively suggest that cognitive capacity limitations in different domains are at least partially due to limitations of distinct mechanisms

Cantor Spectrum for Schr\"odinger Operators with Potentials arising from Generalized Skew-shifts

We consider continuous $SL(2,\mathbb{R})$-cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove that any cocycle which is not uniformly hyperbolic can be approximated by one which is conjugate to an $SO(2,\mathbb{R})$-cocycle. Using this, we show that if a cocycle's homotopy class does not display a certain obstruction to uniform hyperbolicity, then it can be $C^0$-perturbed to become uniformly hyperbolic. For cocycles arising from Schr\"odinger operators, the obstruction vanishes and we conclude that uniform hyperbolicity is dense, which implies that for a generic continuous potential, the spectrum of the corresponding Schr\"odinger operator is a Cantor set.Comment: Final version. To appear in Duke Mathematical Journa

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

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

Collision, explosion and collapse of homoclinic classes

Homoclinic classes of generic $C^1$-diffeomorphisms are maximal transitive sets and pairwise disjoint. We here present a model explaining how two different homoclinic classes may intersect, failing to be disjoint. For that we construct a one-parameter family of diffeomorphisms $(g_s)_{s\in [-1,1]}$ with hyperbolic points $P$ and $Q$ having nontrivial homoclinic classes, such that, for $s>0$, the classes of $P$ and $Q$ are disjoint, for $s<0$, they are equal, and, for $s=0$, their intersection is a saddle-node.Comment: This is the final version, accepted in 200

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