Our visual system faces the challenging task to construct integrated visual representations from the visual input projected on our retinae. Previous research has provided mixed evidence as to whether visual awareness of the stimulus parts is required for such integration to occur. Here, we address this issue by taking a novel approach in which we combine a monocular rivalry stimulus (i.e., a bi...

In this paper we extend complex uniform convexity estimates for $\mathbb{C}$ to $\mathbb{R}^n$ and determine best constants. Furthermore, provide the link log-Sobolev inequalities hypercontractivity ultraspherical measures.

We prove that if a non-singular planar map $\Lambda \in C^2(\mathbb R^2,\mathbb R^2)$ has convex component, then it is injective. do not assume strict convexity.

[1] The channel network (S) is a nonconvex set, while its basin [C(S)] is convex. We remove open-end points of the channel connectivity network iteratively to generate a traveltime sequence of networks (Sn). The convex hulls of these traveltime networks provide an interesting topological quantity, which has not been noted thus far. We compute lengths of shrinking traveltime networks L(Sn) and a...

We consider two different notions of convexity of metric spaces, namely (strict/uniform) ball convexity and (strict/uniform) distance convexity. Our main theorem states that (strict/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict/uniform) ball convexity, not even when consider...