We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an expansive quotient of the dynamics and study some dynamical consequences related to this quotient.

This article presents an emotion-regularized conditional variational autoencoder (Emo-CVAE) model for generating emotional conversation responses. In conventional CVAE-based response generation, emotion labels are simply used as additional conditions in prior, posterior and decoder networks. Considering that styles naturally entangled with semantic contents the language space, Emo-CVAE utilizes...

Most of the practical applications that require optimization often involve multiple objectives. These objectives, when conflicting in nature, pose both as well decision-making challenges. An procedure for such a multi-objective problem requires computing (computer-based search) and decision making to identify most preferred solution. Researchers practitioners working various domains have integr...

1 13 4. Free rational curves 14 5. Uniruledness 16 5.1. Definitions equivalent to uniruledness 16 5.2. Examples and consequences of uniruledness 18 6. Rational connectivity 20 6.1. Definitions equivalent to rational connectivity 21 6.2. Rational chain-connectivity implies rational connectivity 22 6.3. Examples and consequences of rational connectivity 26 7. The MRC quotient 27 7.1. Quotients by...

We use circular sequences to give an improved lower bound on the minimum number of (≤ k)– sets in a set of points in general position. We then use this to show that if S is a set of n points in general position, then the number (S) of convex quadrilaterals determined by the points in S is at least 0.37533 ` n 4 ́ + O(n). This in turn implies that the rectilinear crossing number cr(Kn) of the com...

The main contribution of this paper is a new approach for enumerating Hamilton cycles in bounded degree graphs – deriving thereby extremal bounds. We describe an algorithm which enumerates all Hamilton cycles of a given 3-regular n-vertex graph in time O(1.276), improving on Eppstein’s previous bound. The resulting new upper bound of O(1.276) for the maximum number of Hamilton cycles in 3-regul...