Thomas Decomposition and Nonlinear Control Systems

This paper applies the Thomas decomposition technique to nonlinear control systems, in particular to the study of the dependence of the system behavior on parameters. Thomas' algorithm is a symbolic method which splits a given system of nonlinear partial differential equations into a finite family of so-called simple systems which are formally integrable and define a partition of the solution set of the original differential system. Different simple systems of a Thomas decomposition describe different structural behavior of the control system in general. The paper gives an introduction to the Thomas decomposition method and shows how notions such as invertibility, observability and flat outputs can be studied. A Maple implementation of Thomas' algorithm is used to illustrate the techniques on explicit examples

Topological structures of adiabatic phase for multi-level quantum systems

The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) have a monopole structure, the curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures.Comment: 15 pages, no figures. Accepted by J.Phys.

Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I

We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of 2nd order systems with a 3rd order or a 4th order symmetry and 3rd order systems with a 5th order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made.Comment: 60 pages, 6 tables; added one remark in section 4.2.17 (p.33) plus several minor changes, to appear in J.Phys.

On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation

The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead of one and the use of the residue theorem. The application of our approach to the quintic complex one-dimensional Ginzburg-Landau equation (CGLE5) allows to find elliptic solutions in the wave form. We also find restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5. Using the investigation of the CGLE5 as an example, we demonstrate that to find elliptic solutions the analysis of a system of differential equations is more preferable than the analysis of the equivalent single differential equation.Comment: LaTeX, 21 page

Genetic mapping of microbial and host traits reveals production of immunomodulatory lipids by Akkermansia muciniphila in the murine gut.

The molecular bases of how host genetic variation impacts the gut microbiome remain largely unknown. Here we used a genetically diverse mouse population and applied systems genetics strategies to identify interactions between host and microbe phenotypes including microbial functions, using faecal metagenomics, small intestinal transcripts and caecal lipids that influence microbe-host dynamics. Quantitative trait locus (QTL) mapping identified murine genomic regions associated with variations in bacterial taxa; bacterial functions including motility, sporulation and lipopolysaccharide production and levels of bacterial- and host-derived lipids. We found overlapping QTL for the abundance of Akkermansia muciniphila and caecal levels of ornithine lipids. Follow-up in vitro and in vivo studies revealed that A. muciniphila is a major source of these lipids in the gut, provided evidence that ornithine lipids have immunomodulatory effects and identified intestinal transcripts co-regulated with these traits including Atf3, which encodes for a transcription factor that plays vital roles in modulating metabolism and immunity. Collectively, these results suggest that ornithine lipids are potentially important for A. muciniphila-host interactions and support the role of host genetics as a determinant of responses to gut microbes

StoryML: An XML Extension for Woven Stories

StoryML is an XML-based representation of metadata elements connected to collaboratively written stories. The StoryML specification gives means to interpret and specify the core characteristics of stories. Hence, StoryML supports the functionality of information retrieval, filtering and adaptive representation of stories. These intelligence properties make collaboratively written stories a significant platform for truly activating, open learning environments