4-Manifolds With Inequivalent Symplectic Forms and 3-Manifolds With Inequivalent Fibrations

We exhibit a closed, simply connected 4-manifold $X$ carrying two symplectic structures whose first Chern classes in $H^2 (X, \mathbb{Z})$ lie in disjoint orbits of the diffeomorphism group of $X$. Consequently, the moduli space of symplectic forms on $X$ is disconnected. The example $X$ is in turn based on a 3-manifold $M$. The symplectic structures on $X$ come from a pair of fibrations $\pi_0, \pi_1 : M \rightarrow S^1$ whose Euler classes lie in disjoint orbits for the action of $\mathrm{Diff}(M)$ on $H_1(M, \mathbb{R})$.Mathematic

Model transcriptional networks with continuously varying expression levels

<p>Abstract</p> <p>Background</p> <p>At a time when genomes are being sequenced by the hundreds, much attention has shifted from identifying genes and phenotypes to understanding the networks of interactions among genes. We developed a gene network developmental model expanding on previous models of transcription regulatory networks. In our model, each network is described by a matrix representing the interactions between transcription factors, and a vector of continuous values representing the transcription factor expression in an individual.</p> <p>Results</p> <p>In this work we used the gene network model to look at the impact of mating as well as insertions and deletions of genes in the evolution of complexity of these networks. We found that the natural process of diploid mating increases the likelihood of maintaining complexity, especially in higher order networks (more than 10 genes). We also show that gene insertion is a very efficient way to add more genes to a network as it provides a much higher chance of developmental stability.</p> <p>Conclusions</p> <p>The continuous model affords a more complete view of the evolution of interacting genes. The notion of a continuous output vector also incorporates the reality of gene networks and graded concentrations of gene products.</p

Vortices and monopoles: structure of static gauge theories

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