On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators

A one-parameter family of time-reversible systems on three-dimensional torus is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the so-called mixed dynamics phenomenon which corresponds to a persistent intersection of the closure of the stable periodic orbits and the closure of the completely unstable periodic orbits. We search for the stable and unstable periodic orbits indirectly, by finding non-conservative saddle periodic orbits and heteroclinic connections between them. In this way, we are able to claim the existence of mixed dynamics for a large range of parameter values. We investigate local and global bifurcations that can be used for the detection of mixed dynamics

On form factors in N=4 sym

In this paper we study the form factors for the half-BPS operators $\mathcal{O}^{(n)}_I$ and the $\mathcal{N}=4$ stress tensor supermultiplet current $W^{AB}$ up to the second order of perturbation theory and for the Konishi operator $\mathcal{K}$ at first order of perturbation theory in $\mathcal{N}=4$ SYM theory at weak coupling. For all the objects we observe the exponentiation of the IR divergences with two anomalous dimensions: the cusp anomalous dimension and the collinear anomalous dimension. For the IR finite parts we obtain a similar situation as for the gluon scattering amplitudes, namely, apart from the case of $W^{AB}$ and $\mathcal{K}$ the finite part has some remainder function which we calculate up to the second order. It involves the generalized Goncharov polylogarithms of several variables. All the answers are expressed through the integrals related to the dual conformal invariant ones which might be a signal of integrable structure standing behind the form factors.Comment: 35 pages, 7 figures, LATEX2

Genetic Basis of Virulence Attenuation Revealed by Comparative Genomic Analysis of Mycobacterium tuberculosis Strain H37Ra versus H37Rv

Tuberculosis, caused by Mycobacterium tuberculosis, remains a leading infectious disease despite the availability of chemotherapy and BCG vaccine. The commonly used avirulent M. tuberculosis strain H37Ra was derived from virulent strain H37 in 1935 but the basis of virulence attenuation has remained obscure despite numerous studies. We determined the complete genomic sequence of H37Ra ATCC25177 and compared that with its virulent counterpart H37Rv and a clinical isolate CDC1551. The H37Ra genome is highly similar to that of H37Rv with respect to gene content and order but is 8,445 bp larger as a result of 53 insertions and 21 deletions in H37Ra relative to H37Rv. Variations in repetitive sequences such as IS6110 and PE/PPE/PE-PGRS family genes are responsible for most of the gross genetic changes. A total of 198 single nucleotide variations (SNVs) that are different between H37Ra and H37Rv were identified, yet 119 of them are identical between H37Ra and CDC1551 and 3 are due to H37Rv strain variation, leaving only 76 H37Ra-specific SNVs that affect only 32 genes. The biological impact of missense mutations in protein coding sequences was analyzed in silico while nucleotide variations in potential promoter regions of several important genes were verified by quantitative RT-PCR. Mutations affecting transcription factors and/or global metabolic regulations related to in vitro survival under aging stress, and mutations affecting cell envelope, primary metabolism, in vivo growth as well as variations in the PE/PPE/PE-PGRS family genes, may underlie the basis of virulence attenuation. These findings have implications not only for improved understanding of pathogenesis of M. tuberculosis but also for development of new vaccines and new therapeutic agents