The Length of Shortest Vertex Paths in Binary Occupancy Grids Compared to Shortest r-Constrained Ones

We study the problem of finding a short path from a start to a goal within a two-dimensional continuous and isotropic terrain that has been discretized into an array of accessible and blocked cells. A classic approach obtains a grid path where each step is along the edge of an accessible cell or diagonally across one. Grid paths suffer from `digitization bias' -- even if two locations have line-of-sight, the minimum travelling cost between them can be greater than the distance along the line-of-sight. In a vertex path, steps are allowed from a cell corner to any other cell corner if they have line-of-sight. While the `digitization bias' is smaller, shortest vertex paths are impractical to find by brute force. Recent research has thus turned to methods for finding short (but not necessarily shortest) vertex paths. To establish the methods' potential utility, we calculate upper bounds on the difference in length between the shortest vertex paths versus the shortest r-constrained ones where an r-constrained path consists of line segments that each traverse at most r rows and at most r columns of cells. The difference in length reduces as r increases -- indeed the shortest vertex paths are at most 1 percent shorter than the shortest 4-constrained ones. This article will be useful to developers and users of short(est) vertex paths algorithms who want to trade path length for improved runtimes in a predictable manner.

Lignin masks the presence of fibrillar network structure in the cell corner middle lamella (CCML)

The presence of fibrillar structures (FS) in the cell corner middle lamella (CCML) regions was demonstrated in several species of plants. The FS in the CCML of bass wood, oak wood, and bamboo became clearly visible after removal of lignin by wood decay fungi. The occurrence of FS in the CCML was also confirmed by examining early stages of cell wall formation in silver poplar, Japanese red pine, Arabidopsis and alfalfa. The fibrillar texture became increasingly less defined with the onset of lignification as the interfibrillar spaces were masked by lignin polymers and the fibrillar network became embedded within the lignin matrix. The FS stained positively with PATAg and ruthenium red, which is interpreted to be an indicator of the presence of structural polysaccharides (non-cellulosics and pectins). Our work demonstrated that fibrillar network is a characteristic feature of CCML of plant cell walls that is clearly visible prior to lignification of this cell wall region, but becomes invisible after the deposition of lignin.

The Massaria disease of plane trees:its wood decay mechanism

Branches of Platanus × hispanica with distinct symptoms of the Massaria disease were investigated by light and transmission electron microscopy and cellular UVmicrospectrophotometry. The samples collected in the city of Mannheim, Germany, were infected in vivo with the fungus Splanchnonema platani and showed various degrees of wood decay. The investigations were focused on the decay pattern of cell walls in the different cells, i.e., fibres, vessels as well as ray and axial parenchyma cells. The following results were obtained. Hyphae of the ascomycete fungus Splanchnonema platani penetrated from cell to cell through the pits and not through the cell wall middle lamella, by the formation of thin perforation hyphae. During this process, the 1–5 μm thick hyphae became narrower without attacking the wall around the pit canal. After penetration through a pit, the hyphae again enlarged to their original diameter. This is true for all pit pairs connecting the various cell types. Late decay stages did not show a decay of cell corner regions and middle lamellae of fibres as well as vessel and parenchyma cell walls. Phenolic deposits in parenchyma cells were still present in severely attacked xylem tissue. These features point to a low lignolytic capacity of the fungus. The frequently found microscopic decay pattern with the formation of oval or spherical cavities in the S2 layer of the secondary wall with an often structurally intact S3 layer is a characteristic of softrot decay. This classification is also supported by the remaining cell corner and middle lamella regions in advanced decay stages. As a consequence of this decay type, branches fracture in a brittle mode.

Lignin chemistry and topochemistry during kraft delignification of Eucalyptus globulus genotypes with contrasting pulpwood characteristics

Eucalyptus globulus Labill. is a short-fibre resource for pulp and paper production. Ten different E. globulus genotypes with varied pulpwood quality and chemical composition were evaluated under kraft pulping conditions. Characterisation of the wood and pulp samples by thioacidolysis indicated that the content of syringyl units in β-O-4 linkages (S-β-O-4) was distinct for the studied genotypes. The highest S-β-O-4 levels were detected in the samples with the lowest original lignin and highest glucan levels. This group of samples provided the pulps with the lowest final lignin content at higher yields. UV microspectrophotometric (UMSP) evaluation of the wood chips revealed that the samples with the lowest lignin levels have the lowest UV absorbances at 278 nm (A278 nm) in the secondary walls (S2). During kraft pulping, lignin from the S2 was dissolved, whereas lignins from the middle lamella and cell corner lignin was not removed not even for prolonged reaction periods, independently of the evaluated genotype. The A278 nm values of the S2 were significantly lower in the pulps from the genotypes with less original lignin content.

Cellular distribution of coniferin in differentiating xylem of Chamaecyparis obtusa as revealed by Raman microscopy

Cellular distribution of coniferin in differentiating xylem of Japanese cypress (Chamaecyparis obtusa) was analyzed by Raman microscopy. Small blocks were collected from differentiating xylem, frozen, cut on their surface with a sliding microtome, and then freeze-dried. Scanning electron microscopy showed numerous needle-like deposits in the tracheid lumina from the beginning of the S1 layer formation to the S2 layer-forming stage. The Raman spectrum of the deposits in the tracheid lumen was similar to that of coniferin. The presence of coniferin in a water extract from differentiating xylem was confirmed by matrix-assisted laser desorption/ionization time-of-flight mass spectroscopy and 1H- and 13C-nuclear magnetic resonance spectra. Differential Raman spectra taken from samples before and after washing with water and dehydration in an ethanol showed that developing secondary walls contained coniferin during the S2 layer-forming stage and also after S3 layer formation. In contrast, coniferin was detected in the cell corner middle lamella during the S2 layer-forming stage, and the differential spectra were different from that of coniferin after S3 layer formation. The differential spectrum in this stage was similar to that of a dehydrogenation polymer of coniferyl alcohol prepared by the “zulauf” method (bulk polymerization). These results suggest that free lignin oligomers of the type bulk polymerizate might exist in the cell corner middle lamella during the S3 layer-forming stage and can be removed from specimens during washing and dehydration. The results can be interpreted in a way that no such oligomer exists in the secondary wall during the same stage owing to endwise addition of monolignols (in analogy to a “zutropf” polymerization).

A Fourth-Order-Centered Finite-Volume Scheme for Regular Hexagonal Grids

Fourth-order-centered operators on regular hexagonal grids with the ZM-grid arrangement are described. The finite-volume method is used and operators are defined at hexagonal cell centers. The gradient operator is calculated from 12 surrounding cell center scalars. The divergence operator is defined from 12 surrounding cell corner vectors. A linear combination of local or interpolated values generates cell corner values used to calculate the operators. The flux-divergence operator applies the same cell corner values as those used in the gradient and divergence operators. The fourth-order convergence of the gradient and divergence operators is obtained in numerical tests using sufficiently smooth and differentiable test functions. The flux-divergence operator is formally second-order accurate. However, the results from a cone advection test show that the flux-divergence operator performs better than a commonly used second-order flux-divergence operator. Numerical dispersion and phase error are small because mean wind advection is computed with fourth-order accuracy.

Comparing Mechanical Properties of Secondary Wall and Cell Corner Middle Lamella in Spruce Wood

Mechanical characterizations of the S2 layers and the cell corner middle lamella in the axial direction were investigated in spruce wood, A mechanical properties microprobe capable of measuring hardness and Young's modulus on a spatially resolved basis similar to that of an electron beam microprobe was used. Hardness of the cell comer middle lamella was found to be almost as high as that of the secondary wall, but the Young's modulus of the cell corner middle lamella was 50% less than that of the S2' The S2 showed constant hardness over its range of Young's modulus, but the cell corner middle lamella exhibited a strong correlation (R2 = 0.55) between hardness and the Young's modulus. Further investigations are needed to directly combine chemical and micromechanical properties and also to investigate the mechanical effects of the high variability of cell corner middle lamella chemistry.