Beyond Outerplanarity

We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., convex drawings. We consider two families of graph classes with nice convex drawings: outer $k$-planar graphs, where each edge is crossed by at most $k$ other edges; and, outer $k$-quasi-planar graphs where no $k$ edges can mutually cross. We show that the outer $k$-planar graphs are $(\lfloor\sqrt{4k+1}\rfloor+1)$-degenerate, and consequently that every outer $k$-planar graph can be $(\lfloor\sqrt{4k+1}\rfloor+2)$-colored, and this bound is tight. We further show that every outer $k$-planar graph has a balanced separator of size $O(k)$. This implies that every outer $k$-planar graph has treewidth $O(k)$. For fixed $k$, these small balanced separators allow us to obtain a simple quasi-polynomial time algorithm to test whether a given graph is outer $k$-planar, i.e., none of these recognition problems are NP-complete unless ETH fails. For the outer $k$-quasi-planar graphs we prove that, unlike other beyond-planar graph classes, every edge-maximal $n$-vertex outer $k$-quasi planar graph has the same number of edges, namely $2(k-1)n - \binom{2k-1}{2}$. We also construct planar 3-trees that are not outer $3$-quasi-planar. Finally, we restrict outer $k$-planar and outer $k$-quasi-planar drawings to \emph{closed} drawings, where the vertex sequence on the boundary is a cycle in the graph. For each $k$, we express closed outer $k$-planarity and \emph{closed outer $k$-quasi-planarity} in extended monadic second-order logic. Thus, closed outer $k$-planarity is linear-time testable by Courcelle's Theorem.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Molecular developmental evidence for a subcoxal origin of pleurites in insects and identity of the subcoxa in the gnathal appendages

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ The attached file is the published version of the article

Expression of Distal-less, dachshund, and optomotor blind in Neanthes arenaceodentata (Annelida, Nereididae) does not support homology of appendage-forming mechanisms across the Bilateria

The similarity in the genetic regulation of arthropod and vertebrate appendage formation has been interpreted as the product of a plesiomorphic gene network that was primitively involved in bilaterian appendage development and co-opted to build appendages (in modern phyla) that are not historically related as structures. Data from lophotrochozoans are needed to clarify the pervasiveness of plesiomorphic appendage forming mechanisms. We assayed the expression of three arthropod and vertebrate limb gene orthologs, Distal-less (Dll), dachshund (dac), and optomotor blind (omb), in direct-developing juveniles of the polychaete Neanthes arenaceodentata. Parapodial Dll expression marks premorphogenetic notopodia and neuropodia, becoming restricted to the bases of notopodial cirri and to ventral portions of neuropodia. In outgrowing cephalic appendages, Dll activity is primarily restricted to proximal domains. Dll expression is also prominent in the brain. dac expression occurs in the brain, nerve cord ganglia, a pair of pharyngeal ganglia, presumed interneurons linking a pair of segmental nerves, and in newly differentiating mesoderm. Domains of omb expression include the brain, nerve cord ganglia, one pair of anterior cirri, presumed precursors of dorsal musculature, and the same pharyngeal ganglia and presumed interneurons that express dac. Contrary to their roles in outgrowing arthropod and vertebrate appendages, Dll, dac, and omb lack comparable expression in Neanthes appendages, implying independent evolution of annelid appendage development. We infer that parapodia and arthropodia are not structurally or mechanistically homologous (but their primordia might be), that Dll’s ancestral bilaterian function was in sensory and central nervous system differentiation, and that locomotory appendages possibly evolved from sensory outgrowths

Evolution of a Novel Appendage Ground Plan in Water Striders Is Driven by Changes in the Hox Gene Ultrabithorax

Water striders, a group of semi-aquatic bugs adapted to life on the water surface, have evolved mid-legs (L2) that are long relative to their hind-legs (L3). This novel appendage ground plan is a derived feature among insects, where L2 function as oars and L3 as rudders. The Hox gene Ultrabithorax (Ubx) is known to increase appendage size in a variety of insects. Using gene expression and RNAi analysis, we discovered that Ubx is expressed in both L2 and L3, but Ubx functions to elongate L2 and to shorten L3 in the water strider Gerris buenoi. Therefore, within hemimetabolous insects, Ubx has evolved a new expression domain but maintained its ancestral elongating function in L2, whereas Ubx has maintained its ancestral expression domain but evolved a new shortening function in L3. These changes in Ubx expression and function may have been a key event in the evolution of the distinct appendage ground plan in water striders

Separable functions of wingless in distal and ventral patterning of the Tribolium leg

The gene wingless (wg) in Drosophila is an important factor in leg development. During embryonic development wg is involved in the allocation of the limb primordia. During imaginal disk development wg is involved in distal development and it has a separate role in ventral development. The expression pattern of wg is highly conserved in all arthropods (comprising data from insects, myriapods, crustaceans, and chelicerates), suggesting that its function in leg development is also conserved. However, recent work in other insects (e.g. the milkweed bug Oncopeltus fasciatus) argued against a role of wg in leg development. We have studied the role of wg in leg development of the flour beetle Tribolium castaneum. Using stage-specific staggered embryonic RNAi in wild-type and transgenic EGFP expressing enhancer trap lines we are able to demonstrate separable functions of Tribolium wg in distal and in ventral leg development. The distal role affects all podomeres distal to the coxa, whereas the ventral role is restricted to cells along the ventral midline of the legs. In addition, severe leg defects after injection into early embryonic stages are evidence that wg is also involved in proximal development and limb allocation in Tribolium. Our data suggest that the roles of wg in leg development are highly conserved in the holometabolous insects. Further studies will reveal the degree of conservation in other arthropod groups

A conserved function of the zinc finger transcription factor Sp8/9 in allometric appendage growth in the milkweed bug Oncopeltus fasciatus

The genes encoding the closely related zinc finger transcription factors Buttonhead (Btd) and D-Sp1 are expressed in the developing limb primordia of Drosophila melanogaster and are required for normal growth of the legs. The D-Sp1 homolog of the red flour beetle Tribolium castaneum, Sp8 (appropriately termed Sp8/9), is also required for the proper growth of the leg segments. Here we report on the isolation and functional study of the Sp8/9 gene from the milkweed bug Oncopeltus fasciatus. We show that Sp8/9 is expressed in the developing appendages throughout development and that the downregulation of Sp8/9 via RNAi leads to antennae, rostrum, and legs with shortened and fused segments. This supports a conserved role of Sp8/9 in allometric leg segment growth. However, all leg segments including the claws are present and the expression of the leg genes Distal-less, dachshund, and homothorax are proportionally normal, thus providing no evidence for a role of Sp8/9 in appendage specification

Calpain 3 is important for muscle regeneration: Evidence from patients with limb girdle muscular dystrophies

<p>Abstract</p> <p>Background</p> <p>Limb girdle muscular dystrophy (LGMD) type 2A is caused by mutations in the CAPN3 gene and complete lack of functional calpain 3 leads to the most severe muscle wasting. Calpain 3 is suggested to be involved in maturation of contractile elements after muscle degeneration. The aim of this study was to investigate how mutations in the four functional domains of calpain 3 affect muscle regeneration.</p> <p>Methods</p> <p>We studied muscle regeneration in 22 patients with LGMD2A with calpain 3 deficiency, in five patients with LGMD2I, with a secondary reduction in calpain 3, and in five patients with Becker muscular dystrophy (BMD) with normal calpain 3 levels. Regeneration was assessed by using the developmental markers neonatal myosin heavy chain (nMHC), vimentin, MyoD and myogenin and counting internally nucleated fibers.</p> <p>Results</p> <p>We found that the recent regeneration as determined by the number of nMHC/vimentin-positive fibers was greatly diminished in severely affected LGMD2A patients compared to similarly affected patients with LGMD2I and BMD. Whorled fibers, a sign of aberrant regeneration, was highly elevated in patients with a complete lack of calpain 3 compared to patients with residual calpain 3. Regeneration is not affected by location of the mutation in the <it>CAPN3 </it>gene.</p> <p>Conclusions</p> <p>Our findings suggest that calpain 3 is needed for the regenerative process probably during sarcomere remodeling as the complete lack of functional calpain 3 leads to the most severe phenotypes.</p

Isolation of Hox Cluster Genes from Insects Reveals an Accelerated Sequence Evolution Rate

Among gene families it is the Hox genes and among metazoan animals it is the insects (Hexapoda) that have attracted particular attention for studying the evolution of development. Surprisingly though, no Hox genes have been isolated from 26 out of 35 insect orders yet, and the existing sequences derive mainly from only two orders (61% from Hymenoptera and 22% from Diptera). We have designed insect specific primers and isolated 37 new partial homeobox sequences of Hox cluster genes (lab, pb, Hox3, ftz, Antp, Scr, abd-a, Abd-B, Dfd, and Ubx) from six insect orders, which are crucial to insect phylogenetics. These new gene sequences provide a first step towards comparative Hox gene studies in insects. Furthermore, comparative distance analyses of homeobox sequences reveal a correlation between gene divergence rate and species radiation success with insects showing the highest rate of homeobox sequence evolution

Homeosis in a scorpion supports a telopodal origin of pectines and components of the book lungs

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A search for the decay modes B+/- to h+/- tau l

We present a search for the lepton flavor violating decay modes B+/- to h+/- tau l (h= K,pi; l= e,mu) using the BaBar data sample, which corresponds to 472 million BBbar pairs. The search uses events where one B meson is fully reconstructed in one of several hadronic final states. Using the momenta of the reconstructed B, h, and l candidates, we are able to fully determine the tau four-momentum. The resulting tau candidate mass is our main discriminant against combinatorial background. We see no evidence for B+/- to h+/- tau l decays and set a 90% confidence level upper limit on each branching fraction at the level of a few times 10^-5.Comment: 15 pages, 7 figures, submitted to Phys. Rev.