A comparison of techniques for the reconstruction of leaf surfaces from scanned data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

Brain network efficiency and topology depend on the fiber tracking method: 11 tractography algorithms compared in 536 subjects

As connectivity analyses become more popular, claims are often made about how the brain's anatomical networks depend on age, sex, or disease. It is unclear how results depend on tractography methods used to compute fiber networks. We applied 11 tractography methods to high angular resolution diffusion images of the brain (4-Tesla 105-gradient HARDI) from 536 healthy young adults. We parcellated 70 cortical regions, yielding 70×70 connectivity matrices, encoding fiber density. We computed popular graph theory metrics, including network efficiency, and characteristic path lengths. Both metrics were robust to the number of spherical harmonics used to model diffusion (4th-8th order). Age effects were detected only for networks computed with the probabilistic Hough transform method, which excludes smaller fibers. Sex and total brain volume affected networks measured with deterministic, tensor-based fiber tracking but not with the Hough method. Each tractography method includes different fibers, which affects inferences made about the reconstructed networks.

Investigation and application of methods for enumerating heterotrophs and Escherichia coli in the air within piggery sheds

Aims: To investigate methods for the recovery of airborne bacteria within pig sheds and to then use the appropriate methods to determine the levels of heterotrophs and Escherichia coli in the air within sheds. Methods and Results: AGI-30 impingers and a six-stage Andersen multi-stage sampler (AMS) were used for the collection of aerosols. Betaine and catalase were added to impinger collection fluid and the agar plates used in the AMS. Suitable media for enumerating E. coli with the Andersen sampler were also evaluated. The addition of betaine and catalase gave no marked increase in the recovery of heterotrophs or E. coli. No marked differences were found in the media used for enumeration of E. coli. The levels of heterotrophs and E. coli in three piggeries, during normal pig activities, were 2Æ2 · 105 and 21 CFU m)3 respectively. Conclusions: The failure of the additives to improve the recovery of either heterotrophs or E. coli suggests that these organisms are not stressed in the piggery environment. The levels of heterotrophs in the air inside the three Queensland piggeries investigated are consistent with those previously reported in other studies. Flushing with ponded effluent had no marked or consistent effect on the heterotroph or E. coli levels. Significance and Impact of the Study: Our work suggests that levels of airborne heterotrophs and E. coli inside pig sheds have no strong link with effluent flushing. It would seem unlikely that any single management activity within a pig shed has a dominant influence on levels of airborne heterotrophs and E. coli

Natural enemies of Paropsis atomaria Olivier (Coleoptera: Chrysomelidae) in south-eastern Queensland eucalypt plantations

A field survey for natural enemies of Paropsis atomaria was conducted at two south-eastern Queensland Eucalyptus cloeziana plantation sites during 2004-2005. Primary egg and larval parasitoids and associated hyperparasitoids were identified to genus or species, and parasitism rates were determined throughout the season. Predators were identified to family level but their impact was not quantified. P. atomaria adults were also examined as potential hosts for parasitic mites and nematodes. An undescribed species of Neopolycystus (Pteromalidae) was the major primary egg parasitoid species reared from egg batches, parasitising half of all egg batches collected. Three hyperparasitoid species (Baeoanusia albifunicle (Encyrtidae), Neblatticida sp. (Encyrtidae) and Aphaneromella sp. (Platygasteridae) were present, representing around one-quarter to one-third of all emergent wasps; this is the first host association record for Neopolycystus-B. albifunicle. In contrast to populations of P. atomaria from the Australian Capital Territory, primary larval parasitism was very low, around 1%, and attributable only to the tachinid flies Anagonia sp. and Paropsivora sp. However, the presence of the sit-and-wait larval hyperparasitoid, Perilampus sp. (Perilampidae) was high, emerging from around 17% of tachinid pupae, with planidia infesting a further 40% of unparasitised hosts. Three species of podapolipid mites parasitised sexually mature P. atomaria adults, while no nematodes were found in this study. Spiders were the most common predators and their abundance was positively correlated with P. atomaria adult and egg numbers. Although natural enemy species composition was identical between our two study sites, significant differences in abundance and frequency were found between sites.

Development of a Rapid Multiplex PCR Assay To Genotype Pasteurella multocida Strains by Use of the Lipopolysaccharide Outer Core Biosynthesis Locus

Pasteurella multocida is a Gram-negative bacterial pathogen that is the causative agent of a wide range of diseases in many animal species, including humans. A widely used method for differentiation of P. multocida strains involves the Heddleston serotyping scheme. This scheme was developed in the early 1970s and classifies P. multocida strains into 16 somatic or lipopolysaccharide (LPS) serovars using an agar gel diffusion precipitin test. However, this gel diffusion assay is problematic, with difficulties reported in accuracy, reproducibility, and the sourcing of quality serovar-specific antisera. Using our knowledge of the genetics of LPS biosynthesis in P. multocida, we have developed a multiplex PCR (mPCR) that is able to differentiate strains based on the genetic organization of the LPS outer core biosynthesis loci. The accuracy of the LPS-mPCR was compared with classical Heddleston serotyping using LPS compositional data as the "gold standard." The LPS-mPCR correctly typed 57 of 58 isolates; Heddleston serotyping was able to correctly and unambiguously type only 20 of the 58 isolates. We conclude that our LPS-mPCR is a highly accurate LPS genotyping method that should replace the Heddleston serotyping scheme for the classification of P. multocida strains.

X-Pro peptides: Synthesis and solution conformation of benzyloxycarbonyl-(Aib-Pro)4methyl ester. Evidence for a novel helical structure

The synthesis of the octapeptide, benzyloxycarbonyl-(-aminoisobutyryl-L-prolyl)4-methyl ester [Z-(Aib-Pro)4-OMe] and an analysis of its solution conformation is reported. The octapeptide is shown to possess three strong intramolecular hydrogen bonds on the basis of studies of the solvent and temperature dependence of NH chemical shifts and rates of hydrogen-deuterium exchange. 13C studies are consistent with a structure involving only trans Aib-Pro bonds, while ir experiments support a hydrogen-bonded conformation. The Aib 3, 5, and 7 NH groups are shown to participate in hydrogen bonding. A 310 helical conformation compatible with the spectroscopic data is suggested. The proposed conformation consists of three type III -turns with Aib and Pro at the corners and stabilized by 4 1 intramolecular hydrogen bonds.

A geometric approach to stationary defect solutions in one space dimension

In this manuscript, we consider the impact of a small jump-type spatial heterogeneity on the existence of stationary localized patterns in a system of partial dierential equations in one spatial dimension...

Immobilization of Aspergillus oryzae alpha-galactosidase in gelatin and its application in removal of flatulence-inducing sugars in soymilk

Raffinose oligosaccharides (RO) are the major factors responsible for flatulence following ingestion of soybean-derived products. Removal of RO from seeds or soymilk would then have a positive impact on the acceptance of soy-based foods. In this study, alpha-galactosidase from Aspergillus oryzae was entrapped in gelatin using formaldehyde as the hardener. The immobilization yield was 64.3% under the optimum conditions of immobilization. The immobilized alpha-galactosidase showed a shift in optimum pH from 4.8 to 5.4 in acetate buffer. The optimum temperature also shifted from 50 degrees C to 57 degrees C compared with soluble enzyme. Immobilized alpha-galactosidase was used in batch, repeated batch and continuous mode to degrade RO present in soymilk. In the repeated batch, 45% reduction of RO was obtained in the fourth cycle. The performance of immobilized alpha-galactosidase was tested in a fluidized bed reactor at different flow rates and 86% reduction of RO in soymilk was obtained at 25 ml h(-1) flow rate. The study revealed that immobilized alpha-galactosidase in continuous mode is efficient in reduction of RO present in soymilk.