Energy scattering in weakly non-linear systems.

The Chinese Tam-Tam exhibits non-linear behavior in its vibro-acoustic response. The frequency content of the response during free, unforced vibration smoothly changes, with energy being progressively smeared out over a greater bandwidth with time. This is used as a motivating case for the general study of the phenomenon of energy cascading through weak nonlinearity. Numerical models based upon the Fermi-Pasta-Ulam system of non-linearly coupled oscillators, modified with the addition of damping, have been developed. These were used to study the response of ensembles of systems with randomized natural frequencies. Results from simulations will be presented here. For un-damped systems, individual ensemble members exhibit cyclical energy exchange between linear modes, but the ensemble average displays a steady state. For the ensemble response of damped systems, lightly damped modes can exhibit an effective damping which is higher than predicated by linear theory. The presence of a non-linearity provides a path for energy flow to other modes, increasing the apparent damping spectrum at some frequencies and reducing it at others. The target of this work is a model revealing the governing parameters of a generic system of this type and leading to predictions of the ensemble response.

RNAi, DRD1, and histone methylation actively target developmentally important Non-CG DNA methylation in Arabidopsis

Cytosine DNA methylation protects eukaryotic genomes by silencing transposons and harmful DNAs, but also regulates gene expression during normal development. Loss of CG methylation in the Arabidopsis thaliana met1 and ddm1 mutants causes varied and stochastic developmental defects that are often inherited independently of the original met1 or ddm1 mutation. Loss of non-CG methylation in plants with combined mutations in the DRM and CMT3 genes also causes a suite of developmental defects. We show here that the pleiotropic developmental defects of drm1 drm2 cmt3 triple mutant plants are fully recessive, and unlike phenotypes caused by met1 and ddm1, are not inherited independently of the drm and cmt3 mutations. Developmental phenotypes are also reversed when drm1 drm2 cmt3 plants are transformed with DRM2 or CMT3, implying that non-CG DNA methylation is efficiently re-established by sequence-specific signals. We provide evidence that these signals include RNA silencing though the 24-nucleotide short interfering RNA (siRNA) pathway as well as histone H3K9 methylation, both of which converge on the putative chromatin-remodeling protein DRD1. These signals act in at least three partially intersecting pathways that control the locus-specific patterning of non-CG methylation by the DRM2 and CMT3 methyltransferases. Our results suggest that non-CG DNA methylation that is inherited via a network of persistent targeting signals has been co-opted to regulate developmentally important genes. © 2006 Chan et al.

Consensus in non-commutative spaces

Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. The Lyapunov function used in the early analysis by Tsitsiklis is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of the Hilbert metric for any positive homogeneous monotone map, provides an early yet general convergence result for consensus algorithms. Because Birkhoff theorem holds in arbitrary cones, we extend consensus algorithms to the cone of positive definite matrices. The proposed generalization finds applications in the convergence analysis of quantum stochastic maps, which are a generalization of stochastic maps to non-commutative probability spaces. ©2010 IEEE.

Capacity approaching codes for non-coherent orthogonal modulation

This paper describes a curve-fitting approach for the design of capacity approaching coded modulation for orthogonal signal sets with non-coherent detection. In particular, bit-interleaved coded modulation with iterative decoding is considered. Decoder metrics are developed that do not require knowledge of the signal-to-noise ratio, yet still offer very good performance. © 2007 IEEE.