Wnt-Ryk signalling mediates medial-lateral retinotectal topographic mapping

Computational modelling has suggested that at least two counteracting forces are required for establishing topographic maps. Ephrin-family proteins are required for both anterior-posterior and medial-lateral topographic mapping, but the opposing forces have not been well characterized. Wnt-family proteins are recently discovered axon guidance cues. We find that Wnt3 is expressed in a medial-lateral decreasing gradient in chick optic tectum and mouse superior colliculus. Retinal ganglion cell (RGC) axons from different dorsal-ventral positions showed graded and biphasic response to Wnt3 in a concentration-dependent manner. Wnt3 repulsion is mediated by Ryk, expressed in a ventral-to-dorsal decreasing gradient, whereas attraction of dorsal axons at lower Wnt3 concentrations is mediated by Frizzled(s). Overexpression of Wnt3 in the lateral tectum repelled the termination zones of dorsal RGC axons in vivo. Expression of a dominant-negative Ryk in dorsal RGC axons caused a medial shift of the termination zones, promoting medially directed interstitial branches and eliminating laterally directed branches. Therefore, a classical morphogen, Wnt3, acting as an axon guidance molecule, plays a role in retinotectal mapping along the medial-lateral axis, counterbalancing the medial-directed EphrinB1-EphB activity.     

含临界指数的双调和问题非平凡解的存在性

讨论如下含临界指数的双调和方程非平凡解的存在性{Δ2u=μ(u)/(|x|s) |u|2*-2u λu f(x), x∈Ω,u=((e)u)/((e)v)=0, x∈(e)Ω .其中Ω(∪)RN是有界光滑区域,0∈Ω, N≥5, 0≤s≤4,0≤μ＜(-μ)=(N(N-4)/4)2,2*=(2N)/(N-4)为W2,2(Ω)中Sobolev嵌入的临界指数,u, v表示(e)Ω的外法线方向,f(x)为给定函数.通过变分方法,我们证明了含临界指数的双调和方程非平凡解的存在性.     

Potential impacts of a warming climate on water availability in snow-dominated regions

All currently available climate models predict a near-surface warming trend under the influence of rising levels of greenhouse gases in the atmosphere. In addition to the direct effects on climate--for example, on the frequency of heatwaves--this increase in surface temperatures has important consequences for the hydrological cycle, particularly in regions where water supply is currently dominated by melting snow or ice. In a warmer world, less winter precipitation falls as snow and the melting of winter snow occurs earlier in spring. Even without any changes in precipitation intensity, both of these effects lead to a shift in peak river runoff to winter and early spring, away from summer and autumn when demand is highest. Where storage capacities are not sufficient, much of the winter runoff will immediately be lost to the oceans. With more than one-sixth of the Earth's population relying on glaciers and seasonal snow packs for their water supply, the consequences of these hydrological changes for future water availability--predicted with high confidence and already diagnosed in some regions--are likely to be severe.