From 2D conformal to 4D self-dual theories: quaternionic analyticity

It is shown that self-dual theories generalize to four dimensions both the conformal and analytic aspects of two-dimensional conformal field theories. In the harmonic space language there appear several ways to extend complex analyticity (natural in two dimensions) to quaternionic analyticity (natural in four dimensions). To be analytic, conformal transformations should be realized on $CP^3$, which appears as the coset of the complexified conformal group modulo its maximal parabolic subgroup. In this language one visualizes the twistor correspondence of Penrose and Ward and consistently formulates the analyticity of Fueter.Comment: 24 pages, LaTe

Neurodevelopment Genes in Lampreys Reveal Trends for Forebrain Evolution in Craniates

The forebrain is the brain region which has undergone the most dramatic changes through vertebrate evolution. Analyses conducted in lampreys are essential to gain insight into the broad ancestral characteristics of the forebrain at the dawn of vertebrates, and to understand the molecular basis for the diversifications that have taken place in cyclostomes and gnathostomes following their splitting. Here, we report the embryonic expression patterns of 43 lamprey genes, coding for transcription factors or signaling molecules known to be involved in cell proliferation, stemcellness, neurogenesis, patterning and regionalization in the developing forebrain. Systematic expression patterns comparisons with model organisms highlight conservations likely to reflect shared features present in the vertebrate ancestors. They also point to changes in signaling systems –pathways which control the growth and patterning of the neuroepithelium-, which may have been crucial in the evolution of forebrain anatomy at the origin of vertebrates