Mixed Linear Layouts of Planar Graphs

A $k$-stack (respectively, $k$-queue) layout of a graph consists of a total order of the vertices, and a partition of the edges into $k$ sets of non-crossing (non-nested) edges with respect to the vertex ordering. In 1992, Heath and Rosenberg conjectured that every planar graph admits a mixed $1$-stack $1$-queue layout in which every edge is assigned to a stack or to a queue that use a common vertex ordering. We disprove this conjecture by providing a planar graph that does not have such a mixed layout. In addition, we study mixed layouts of graph subdivisions, and show that every planar graph has a mixed subdivision with one division vertex per edge.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

The Vienna RNA Websuite

The Vienna RNA Websuite is a comprehensive collection of tools for folding, design and analysis of RNA sequences. It provides a web interface to the most commonly used programs of the Vienna RNA package. Among them, we find folding of single and aligned sequences, prediction of RNA–RNA interactions, and design of sequences with a given structure. Additionally, we provide analysis of folding landscapes using the barriers program and structural RNA alignments using LocARNA. The web server together with software packages for download is freely accessible at http://rna.tbi.univie.ac.at/

Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth $k$, the maximum thickness and the maximum geometric thickness both equal $\lceil{k/2}\rceil$. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth $k$, the maximum book thickness equals $k$ if $k \leq 2$ and equals $k+1$ if $k \geq 3$. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.Comment: A preliminary version of this paper appeared in the "Proceedings of the 13th International Symposium on Graph Drawing" (GD '05), Lecture Notes in Computer Science 3843:129-140, Springer, 2006. The full version was published in Discrete & Computational Geometry 37(4):641-670, 2007. That version contained a false conjecture, which is corrected on page 26 of this versio

How to compare arc-annotated sequences: The alignment hierarchy

International audienceWe describe a new unifying framework to express comparison of arc-annotated sequences, which we call alignment of arc-annotated sequences. We first prove that this framework encompasses main existing models, which allows us to deduce complexity results for several cases from the literature. We also show that this framework gives rise to new relevant problems that have not been studied yet. We provide a thorough analysis of these novel cases by proposing two polynomial time algorithms and an NP-completeness proof. This leads to an almost exhaustive study of alignment of arc-annotated sequences

Freiburg RNA Tools: a web server integrating IntaRNA, ExpaRNA and LocARNA

The Freiburg RNA tools web server integrates three tools for the advanced analysis of RNA in a common web-based user interface. The tools IntaRNA, ExpaRNA and LocARNA support the prediction of RNA–RNA interaction, exact RNA matching and alignment of RNA, respectively. The Freiburg RNA tools web server and the software packages of the stand-alone tools are freely accessible at http://rna.informatik.uni-freiburg.de

Using and Joining a Franchised Private Sector Provider Network in Myanmar

BACKGROUND: Quality is central to understanding provider motivations to join and remain within a social franchising network. Quality also appears as a key issue from the client's perspective, and may influence why a client chooses to use a franchised provider over another type of provider. The dynamic relationships between providers of social franchising clinics and clients who use these services have not been thoroughly investigated in the context of Myanmar, which has an established social franchising network. This study examines client motivations to use a Sun Quality Health network provider and provider motivations to join and remain in the Sun Quality Health network. Taken together, these two aims provide an opportunity to explore the symbiotic relationship between client satisfaction and provider incentives to increase the utilization of reproductive health care services. METHODS AND FINDINGS: Results from a series of focus group discussions with clients of reproductive health services and franchised providers shows that women chose health services provided by franchised private sector general practitioners because of its perceived higher quality, associated with the availability of effective, affordable, drugs. A key finding of the study is associated with providers. Provider focus group discussions indicate that a principle determinate for joining and remaining in the Sun Quality Health Network was serving the poor

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

Physicochemical analysis of rotavirus segment 11 supports a 'modified panhandle' structure and not the predicted alternative tRNA-like structure (TRLS)

.Rotaviruses are a major cause of acute gastroenteritis, which is often fatal in infants. The viral genome consists of 11 double-stranded RNA segments, but little is known about their cis-acting sequences and structural elements. Covariation studies and phylogenetic analysis exploring the potential structure of RNA11 of rotaviruses suggested that, besides the previously predicted "modified panhandle" structure, the 5' and 3' termini of one of the isoforms of the bovine rotavirus UKtc strain may interact to form a tRNA-like structure (TRLS). Such TRLSs have been identified in RNAs of plant viruses, where they are important for enhancing replication and packaging. However, using tRNA mimicry assays (in vitro aminoacylation and 3'- adenylation), we found no biochemical evidence for tRNA-like functions of RNA11. Capping, synthetic 3' adenylation and manipulation of divalent cation concentrations did not change this finding. NMR studies on a 5'- and 3'-deletion construct of RNA11 containing the putative intra-strand complementary sequences supported a predominant panhandle structure and did not conform to a cloverleaf fold despite the strong evidence for a predicted structure in this conserved region of the viral RNA. Additional viral or cellular factors may be needed to stabilise it into a form with tRNA-like properties