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Smaug is an RNA-binding protein that induces the degradation and represses the translation of mRNAs in the early Drosophila embryo. Smaug has two identified direct target mRNAs that it differentially regulates: nanos and Hsp83. Smaug represses the translation of nanos mRNA but has only a modest effect on its stability, whereas it destabilizes Hsp83 mRNA but(More)
The Wright–Fisher equation, which was introduced as a model to study demography in the presence of diffusion, has had a renaissance as a model for the migration of alleles in the genome. Our goal in this paper is to give a careful analysis of the fundamental solution to the Wright–Fisher equation, with particular emphasis on its behavior for a short time(More)
This work aims to extend part of the two dimensional results of Duplantier and Sheffield on Liouville quantum gravity [DS11] to four dimensions, and indicate possible extensions to other even-dimensional spaces R2n as well as Riemannian manifolds. Let Θ be the Gaussian free field on R4 with the underlying Hilbert space H2 ( R4 ) and the inner product ( (I(More)
We are interested in two kinds of GFF. The rst one, mainly referred as GFF in the forth comings, is indexed by H(D), where D ⊆ R is some bounded domain, and H (D) is the closure of C∞ c (D) under the Dirichlet inner product (·, ·)∇ on D. The other one is the massive GFF. which is indexed by the standard Sobolev space H (R). As we can see from [3] and [4],(More)
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