We present a new approach to Davie's theorem on the uniqueness of solutions to the equation dX t = b(t, X t ) dt + dW t for almost all Brownian paths. A generalization of this result and a discussion of some close problems are given.

We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we present a negative solution of the long-standing problem of existence of Sobolev extensions of functions in Gaussian Sobolev spaces from a convex domain to the whole space.

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JAK/STAT is one of the conservative signaling pathways in higher eukaryotes which plays a critical role in different ontogenesis processes. This article gives a review of the pathway structure at the molecular level, mainly in a model organism Drosophila. There are data about relationship of the signaling pathway and transcription machinery of higher eukaryotes.