A note on the 1-prevalence of continuous images with full Hausdorff dimension

We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image is as large as possible, namely 1. We extend this result by showing that `prevalent' can be replaced by `1-prevalent', i.e. it is possible to \emph{witness} this prevalence using a measure supported on a one dimensional subspace. Such one dimensional measures are called \emph{probes} and their existence indicates that the structure and nature of the prevalence is simpler than if a more complicated `infinite dimensional' witnessing measure has to be used.Comment: 8 page

The Hausdorff dimension of graphs of prevalent continuous functions

We prove that the Hausdorff dimension of the graph of a prevalent continuous function is 2. We also indicate how our results can be extended to the space of continuous functions on $[0,1]^d$ for $d \in \mathbb{N}$ and use this to obtain results on the `horizon problem' for fractal surfaces. We begin with a survey of previous results on the dimension of a generic continuous function

The effects of confinement as a factor in manned space flight

Psychophysiological effects of confinement on man, especially isolation and sensory deprivation, as factor in manned space fligh

Xwnt-5A: a maternal Wnt that affects morphogenetic movements after overexpression in embryos of Xenopus laevis

To contribute to an understanding of the roles and mechanisms of action of Wnts in early vertebrate development, we have characterized the normal expression of Xenopus laevis Wnt-5A, and investigated the consequences of misexpression of this putative signalling factor. Xwnt-5A transcripts are expressed throughout development, and are enriched in both the anterior and posterior regions of embryos at late stages of development, where they are found primarily in ectoderm, with lower levels of expression in mesoderm. Overexpression of Xwnt-5A in Xenopus embryos leads to complex malformations distinct from those achieved by ectopic expression of Xwnts −1, −3A, or −8. This phenotype is unlikely to result from Xwnt-5A acting as an inducing agent, as overexpression of Xwnt-5A does not rescue dorsal structures in UV-irradiated embryos, does not induce mesoderm in blastula caps, and Xwnt-5A does not alter the endogenous patterns of expression of goosecoid, Xbra, or Xwnt-8. To pursue whether Xwnt-5A has the capacity to affect morphogenetic movements, we investigated whether overexpression of Xwnt-5A alters the normal elongation of blastula cap explants induced by activin. Intriguingly, Xwnt-5A blocks the elongation of blastula caps in response to activin, without blocking the differentiation of either dorsal or ventral mesoderm within these explants. The data are consistent with Xwnt-5A having the potential activity of modifying the morphogenetic movements of tissues