Bucolic Complexes

We introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. They are defined as simply connected prism complexes satisfying some local combinatorial conditions. We study various approaches to bucolic complexes: from graph-theoretic and topological perspective, as well as from the point of view of geometric group theory. In particular, we characterize bucolic complexes by some properties of their 2-skeleta and 1-skeleta (that we call bucolic graphs), by which several known results are generalized. We also show that locally-finite bucolic complexes are contractible, and satisfy some nonpositive-curvature-like properties.Comment: 45 pages, 4 figure

Hypercellular graphs: partial cubes without Q3−Q_3^- as partial cube minor

We investigate the structure of isometric subgraphs of hypercubes (i.e., partial cubes) which do not contain finite convex subgraphs contractible to the 3-cube minus one vertex $Q^-_3$ (here contraction means contracting the edges corresponding to the same coordinate of the hypercube). Extending similar results for median and cellular graphs, we show that the convex hull of an isometric cycle of such a graph is gated and isomorphic to the Cartesian product of edges and even cycles. Furthermore, we show that our graphs are exactly the class of partial cubes in which any finite convex subgraph can be obtained from the Cartesian products of edges and even cycles via successive gated amalgams. This decomposition result enables us to establish a variety of results. In particular, it yields that our class of graphs generalizes median and cellular graphs, which motivates naming our graphs hypercellular. Furthermore, we show that hypercellular graphs are tope graphs of zonotopal complexes of oriented matroids. Finally, we characterize hypercellular graphs as being median-cell -- a property naturally generalizing the notion of median graphs.Comment: 35 pages, 6 figures, added example answering Question 1 from earlier draft (Figure 6.

Ramified rectilinear polygons: coordinatization by dendrons

Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure

A new real-time high speed ultrasonic imaging system

An ultrasonic imaging technique was to be developed for sizing and characterization of defects in thick sections of steel. The problems generally found with the existing techniques in such applications are low speed, inadequate image quality, large size and high cost. [Continues.

Helly groups

Helly graphs are graphs in which every family of pairwise intersecting balls has a non-empty intersection. This is a classical and widely studied class of graphs. In this article we focus on groups acting geometrically on Helly graphs -- Helly groups. We provide numerous examples of such groups: all (Gromov) hyperbolic, CAT(0) cubical, finitely presented graphical C(4)$-$T(4) small cancellation groups, and type-preserving uniform lattices in Euclidean buildings of type $C_n$ are Helly; free products of Helly groups with amalgamation over finite subgroups, graph products of Helly groups, some diagram products of Helly groups, some right-angled graphs of Helly groups, and quotients of Helly groups by finite normal subgroups are Helly. We show many properties of Helly groups: biautomaticity, existence of finite dimensional models for classifying spaces for proper actions, contractibility of asymptotic cones, existence of EZ-boundaries, satisfiability of the Farrell-Jones conjecture and of the coarse Baum-Connes conjecture. This leads to new results for some classical families of groups (e.g. for FC-type Artin groups) and to a unified approach to results obtained earlier

Over-expression of UDP-glucose pyrophosphorylase in hybrid poplar affects carbon allocation

The effects of the over-expression of the Acetobacter xylinum UDP-glucose pyrophosphorylase (UGPase) under the control of the tandem repeat Cauliflower Mosaic Virus promoter (2335S) on plant metabolism and growth were investigated in hybrid poplar (Populus alba3grandidentata). Transcript levels, enzyme activity, growth parameters, leaf morphology, structural and soluble carbohydrates, and soluble metabolite levels were quantified in both transgenic and wild-type trees. Transgenic 2335S::UGPase poplar showed impaired growth rates, displaying reduced height growth and stem diameter. Morphologically, 2335S::UGPase trees had elongated axial shoots, and leaves that were substantially smaller in size when compared with wild-type trees at equivalent developmental stages. Biochemical analysis revealed significant increases in soluble sugar, starch, and cellulose contents, and concurrent decreases in lignin content. Lignin monomer composition was altered in favour of syringyl moieties. Detailed soluble metabolite analysis revealed that 2335S::UGPase trees had as much as a 270-fold increase in the salicylic acid 2-O-b-Dglucoside (SAG), a compound typically associated with the stress response. These data suggest that while it is possible to alter the allocation of carbon in favour of cellulose biosynthesis, whole plant changes result in unexpected decreases in growth and an increase in defence metabolites

Over-expression of UDP-glucose pyrophosphorylase in hybrid poplar affects carbon allocation

The effects of the over-expression of the Acetobacter xylinum UDP-glucose pyrophosphorylase (UGPase) under the control of the tandem repeat Cauliflower Mosaic Virus promoter (2335S) on plant metabolism and growth were investigated in hybrid poplar (Populus alba3grandidentata). Transcript levels, enzyme activity, growth parameters, leaf morphology, structural and soluble carbohydrates, and soluble metabolite levels were quantified in both transgenic and wild-type trees. Transgenic 2335S::UGPase poplar showed impaired growth rates, displaying reduced height growth and stem diameter. Morphologically, 2335S::UGPase trees had elongated axial shoots, and leaves that were substantially smaller in size when compared with wild-type trees at equivalent developmental stages. Biochemical analysis revealed significant increases in soluble sugar, starch, and cellulose contents, and concurrent decreases in lignin content. Lignin monomer composition was altered in favour of syringyl moieties. Detailed soluble metabolite analysis revealed that 2335S::UGPase trees had as much as a 270-fold increase in the salicylic acid 2-O-b-Dglucoside (SAG), a compound typically associated with the stress response. These data suggest that while it is possible to alter the allocation of carbon in favour of cellulose biosynthesis, whole plant changes result in unexpected decreases in growth and an increase in defence metabolites