Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere

We consider the multi-dimensional generalisation of the problem of a sphere, with axi-symmetric mass distribution, that rolls without slipping or spinning over a plane. Using recent results from Garc\'ia-Naranjo (arXiv: 1805:06393) and Garc\'ia-Naranjo and Marrero (arXiv: 1812.01422), we show that the reduced equations of motion possess an invariant measure and may be represented in Hamiltonian form by Chaplygin's reducing multiplier method. We also prove a general result on the existence of first integrals for certain Hamiltonisable Chaplygin systems with internal symmetries that is used to determine conserved quantities of the problem.Comment: 23 pages, 1 figure. Submitted to the special issue of Theor. Appl. Mech. in honour of Chaplygin's 150th anniversar

Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane

It is known that the reduced equations for an axially symmetric homogeneous ellipsoid that rolls without slipping on the plane possess a smooth invariant measure. We show that such an invariant measure does not exist in the case when all of the semi-axes of the ellipsoid have different length.Comment: v2: Minor changes after journal review. This text uses the theory developed in arXiv:1304.1788 for the specific example of a homogeneous ellipsoid rolling on the plan

Histone Mutants Separate R Loop Formation from Genome Instability Induction

R loops have positive physiological roles, but they can also be deleterious by causing genome instability, and the mechanisms for this are unknown. Here we identified yeast histone H3 and H4 mutations that facilitate R loops but do not cause instability. R loops containing single-stranded DNA (ssDNA), versus RNA-DNA hybrids alone, were demonstrated using ssDNA-specific human AID and bisulfite. Notably, they are similar size regardless of whether or not they induce genome instability. Contrary to mutants causing R loop-mediated instability, these histone mutants do not accumulate H3 serine-10 phosphate (H3S10-P). We propose a two-step mechanism in which, first, an altered chromatin facilitates R loops, and second, chromatin is modified, including H3S10-P, as a requisite for compromising genome integrity. Consistently, these histone mutations suppress the high H3S10 phosphorylation and genomic instability of hpr1 and sen1 mutants. Therefore, contrary to what was previously believed, R loops do not cause genome instability by themselves.European Research Council ERC2014 AdG669898Ministerio de Economía y Competitividad BFU2013-42918-P, BFU2016-75058-