A Branch and Bound Algorithm for a Transportation Type Problem with Piecewise Linear Convex Objective Function

A branch and bound type algorithm is presented in this paper to the problem of finding a transportation schedule which minimises the total transportation cost, where the transportation cost over each route is assumed to be a piecewice linear continuous convex function with increasing slopes. The algorithm is an extension of the work done by Balachandran and Perry, in which the transportation cost over each route is assumed to beapiecewise linear discontinuous function with decreasing slopes. A numerical example is solved illustrating the algorithm.

What was behind the bark? : An assessment of decay among urban Tilia, Betula and Acer trees felled as hazardous in the Helsinki City area

Old trees growing in urban environments are often felled due to symptoms of mechanical defects that could be hazardous to people and property. The decisions concerning these removals are justified by risk assessments carried out by tree care professionals. The major motivation for this study was to determine the most common profiles of potential hazard characteristics for the three most common urban tree genera in Helsinki City: Tilia, Betula and Acer, and in this way improve management practices and protection of old amenity trees. For this research, material from approximately 250 urban trees was collected in cooperation with the City of Helsinki Public Works Department during 2001 - 2004. From the total number of trees sampled, approximately 70% were defined as hazardous. The tree species had characteristic features as potential hazard profiles. For Tilia trees, hollowed heartwood with low fungal activity and advanced decay caused by Ganoderma lipsiense were the two most common profiles. In Betula spp., the primary reason for tree removal was usually lowered amenity value in terms of decline of the crown. Internal cracks, most often due to weak fork formation, were common causes of potential failure in Acer spp. Decay caused by Rigidoporus populinus often increased the risk of stem breakage in these Acer trees. Of the decay fungi observed, G. lipsiense was most often the reason for the increased risk of stem collapse. Other fungi that also caused extensive decay were R. populinus, Inonotus obliquus, Kretzschmaria deusta and Phellinus igniarius. The most common decay fungi in terms of incidence were Pholiota spp., but decay caused by these species did not have a high potential for causing stem breakage, because it rarely extended to the cambium. The various evaluations used in the study suggested contradictions in felling decisions based on trees displaying different stages of decay. For protection of old urban trees, it is crucial to develop monitoring methods so that tree care professionals could better analyse the rate of decay progression towards the sapwood and separate those trees with decreasing amounts of sound wood from those with decay that is restricted to the heartwood area.

Interactions between transgenic trees and mycorrhizal and pathogenic fungi

The development of biotechnology techniques in plant breeding and the new commercial applications have raised public and scientific concerns about the safety of genetically modified (GM) crops and trees. To find out the feasibility of these new technologies in the breeding of commercially important Finnish hardwood species and to estimate the ecological risks of the produced transgenic plants, the experiments of this study have been conducted as a part of a larger project focusing on the risk assessment of GM-trees. Transgenic Betula pendula and Populus trees were produced via Agrobacterium mediated transformation. Stilbene synthase (STS) gene from pine (Pinus sylvestris) and chitinase gene from sugar beet (Beta vulgaris) were transferred to (hybrid) aspen and birch, respectively, to improve disease resistance against fungal pathogens. To modify lignin biosynthesis, a 4-coumarate:coenzyme A ligase (4CL) gene fragment in antisense orientation was introduced into two birch clones. In in vitro test, one transgenic aspen line expressing pine STS gene showed increased resistance to decay fungus Phellinus tremulae. In the field, chitinase transgenic birch lines were more susceptible to leaf spot (Pyrenopeziza betulicola) than the non-transgenic control clone while the resistance against birch rust (Melampsoridium betulinum) was improved. No changes in the content or composition of lignin were detected in the 4CL antisense birch lines. In order to evaluate the ecological effects of the produced GM trees on non-target organisms, an in vitro mycorrhiza experiment with Paxillus involutus and a decomposition experiment in the field were performed. The expression of a transgenic chitinase did not disturb the establishment of mycorrhizal symbiosis between birch and P. involutus in vitro. 4CL antisense transformed birch lines showed retarded root growth but were able to form normal ectomycorrhizal associations with the mycorrhizal fungus in vitro. 4CL lines also showed normal litter decomposition. Unexpected growth reductions resulting from the gene transformation were observed in chitinase transgenic and 4CL antisense birch lines. These results indicate that genetic engineering can provide a tool in increasing disease resistance in Finnish tree species. More extensive data with several ectomycorrhizal species is needed to evaluate the consequences of transgene expression on beneficial plant-fungus symbioses. The potential pleiotropic effects of the transgene should also be taken into account when considering the safety of transgenic trees.

Species-site matching in mixed species plantations of native trees in tropical Australia

Mixed species plantations using native trees are increasingly being considered for sustainable timber production. Successful application of mixed species forestry systems requires knowledge of the potential spatial interaction between species in order to minimise the chance of dominance and suppression and to maximise wood production. Here, we examined species performances across 52 experimental plots of tree mixtures established on cleared rainforest land to analyse relationships between the growth of component species and climate and soil conditions. We derived site index (SI) equations for ten priority species to evaluate performance and site preferences. Variation in SI of focus species demonstrated that there are strong species-specific responses to climate and soil variables. The best predictor of tree growth for rainforest species Elaeocarpus grandis and Flindersia brayleyana was soil type, as trees grew significantly better on well-draining than on poorly drained soil profiles. Both E. grandis and Eucalyptus pellita showed strong growth response to variation in mean rain days per month. Our study generates understanding of the relative performance of species in mixed species plantations in the Wet Tropics of Australia and improves our ability to predict species growth compatibilities at potential planting sites within the region. Given appropriate species selections and plantation design, mixed plantations of high-value native timber species are capable of sustaining relatively high productivity at a range of sites up to age 10 years, and may offer a feasible approach for large-scale reforestation.

Herbert Strauss seated under trees in a park reading the newspaper; Potsdam.

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Decision trees for detection of activity intensity in youth with cerebral palsy

PURPOSE To develop and test decision tree (DT) models to classify physical activity (PA) intensity from accelerometer output and Gross Motor Function Classification System (GMFCS) classification level in ambulatory youth with cerebral palsy (CP); and 2) compare the classification accuracy of the new DT models to that achieved by previously published cut-points for youth with CP. METHODS Youth with CP (GMFCS Levels I - III) (N=51) completed seven activity trials with increasing PA intensity while wearing a portable metabolic system and ActiGraph GT3X accelerometers. DT models were used to identify vertical axis (VA) and vector magnitude (VM) count thresholds corresponding to sedentary (SED) (<1.5 METs), light PA (LPA) (>/=1.5 and <3 METs) and moderate-to-vigorous PA (MVPA) (>/=3 METs). Models were trained and cross-validated using the 'rpart' and 'caret' packages within R. RESULTS For the VA (VA_DT) and VM decision trees (VM_DT), a single threshold differentiated LPA from SED, while the threshold for differentiating MVPA from LPA decreased as the level of impairment increased. The average cross-validation accuracy for the VC_DT was 81.1%, 76.7%, and 82.9% for GMFCS levels I, II, and III, respectively. The corresponding cross-validation accuracy for the VM_DT was 80.5%, 75.6%, and 84.2%, respectively. Within each GMFCS level, the decision tree models achieved better PA intensity recognition than previously published cut-points. The accuracy differential was greatest among GMFCS level III participants, in whom the previously published cut-points misclassified 40% of the MVPA activity trials. CONCLUSION GMFCS-specific cut-points provide more accurate assessments of MVPA levels in youth with CP across the full spectrum of ambulatory ability.

Timing of Infection and Development of Alternaria Diseases in the Canopy of Apple Trees

Alternaria leaf blotch and fruit spot of apple caused by Alternaria spp. cause annual losses to the Australian apple industry. Erratic control using protectant fungicides is often experienced and may be due to the lack of understanding of the timing of infection and epidemiology of the diseases. We found that Alternaria leaf blotch infection began about 20 days after bloom (DAB) and the highest disease incidence occurred from 70 to 110 DAB. Alternaria fruit spot infection occurred about 100 DAB in the orchard. Fruit inoculations in planta showed that there was no specific susceptible stage of fruit. Leaves and fruit in the lower canopy of trees showed higher levels of leaf blotch and fruit spot incidence than those in the upper canopy and the incidence of leaf blotch in shoot leaves was higher than in spur leaves. Temperature, relative humidity, and rainfall affected leaf blotch and fruit spot incidence. The gained knowledge on the timing of infection and development of disease may aid in the development of more effective disease management strategies.

Veneer based composite hollow utility poles manufactured from hardwood plantation thinned trees

Australia’s utility pole network is aging and approaching its end of life. It is estimated that 70% of the 5 million poles currently in-service nationally were installed within the 20 years following the end of World War II and require replacement or remedial maintenance. Additionally, an estimated 21,700 high-durability new poles are required each year to support the expansion of the energy network. Utility poles were traditionally cut from native forest hardwood species. However, due to agreements which progressively phase out logging of native forests around Australia, finding new sources for utility poles presents a challenge. This paper presents the development of veneer based composite hardwood hollow utility poles manufactured from mid-rotation Gympie messmate (Eucalyptus cloeziana) plantation thinned trees (also referred to as “thinning”), as an alternative to solid hardwood poles. The incentives behind the project and benefits of the proposed products are introduced in the paper. Small diameter poles, of nominal 115 mm internal diameter and 15 mm wall-thickness, were manufactured in two half-poles butt jointed together, using 9 hardwood veneers per half-pole. The poles were tested in bending and shear, and experimental test results are presented. The mechanical performance of the hollow poles is discussed and compared to hardwood poles sourced from mature trees and of similar size. Additionally, the required dimensions of the proposed hollow pole to replace actual solid poles are estimated. Results show that the proposed product represents a viable technical solution to the current shortage of utility poles. Future research and different options for improving the current concept are proposed in order to provide a more reliable and cost effective product for structural and architectural applications in general.

Rapid monitoring of nitrogen in mango trees

Nitrogen (N) is an essential nutrient in mango, influencing both productivity and fruit quality. In Australian mango orchards, tree N is traditionally assessed once a year at the dormant pre-flowering stage using laboratory analysis of leaf N. This single assessment is insufficient to determine tree N status at all stages of the annual phenological cycle. Development of a field-based rapid N test would allow more frequent monitoring of tree N status and improved fertiliser management. These experiments examined the accuracy and useability of several devices used in other horticultural crops to rapidly assess mango leaf N in the field; the Konica Minolta 'SPAD-502 chlorophyll meter', Horiba 'Cardy Meter' and the Merck 'RQflex 10.' Regression and correlation analyses were used to determine the relationship between total leaf N and the measurements from the rapid test devices. The relationship between the chlorophyll index measured by the SPAD-502 meter and leaf N was highly significant at late fruit set (R 2=0.72, n=40) and post-harvest (R 2=0.81, n=40) stages and significant at the flowering stage (R 2=0.51, n=40) in the cultivar 'Kensington Pride', indicating the device can be used to rapidly assess mango leaf N in the field. Correlation analysis indicated the relationship between petiole sap measured with the Cardy or Merck devices and leaf N was non-significant.

Convex-transitive Banach spaces and their hyperplanes

The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.

Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

Weinstein-Levin family trees 1862-1987

2 volumes each containing the geneaelogy of the family of Jack Weinstein: the Weinstein and the Levin families. Volumes contain photographs, newspaper clippings and other materials relevant to history of the two families.