Efficient Truss Maintenance in Evolving Networks

Truss was proposed to study social network data represented by graphs. A k-truss of a graph is a cohesive subgraph, in which each edge is contained in at least k-2 triangles within the subgraph. While truss has been demonstrated as superior to model the close relationship in social networks and efficient algorithms for finding trusses have been extensively studied, very little attention has been paid to truss maintenance. However, most social networks are evolving networks. It may be infeasible to recompute trusses from scratch from time to time in order to find the up-to-date $k$-trusses in the evolving networks. In this paper, we discuss how to maintain trusses in a graph with dynamic updates. We first discuss a set of properties on maintaining trusses, then propose algorithms on maintaining trusses on edge deletions and insertions, finally, we discuss truss index maintenance. We test the proposed techniques on real datasets. The experiment results show the promise of our work

Cycle and flow trusses in directed networks

When we represent real-world systems as networks, the directions of links often convey valuable information. Finding module structures that respect link directions is one of the most important tasks for analyzing directed networks. Although many notions of a directed module have been proposed, no consensus has been reached. This lack of consensus results partly because there might exist distinct types of modules in a single directed network, whereas most previous studies focused on an independent criterion for modules. To address this issue, we propose a generic notion of the so-called truss structures in directed networks. Our definition of truss is able to extract two distinct types of trusses, named the cycle truss and the flow truss, from a unified framework. By applying the method for finding trusses to empirical networks obtained from a wide range of research fields, we find that most real networks contain both cycle and flow trusses. In addition, the abundance of (and the overlap between) the two types of trusses may be useful to characterize module structures in a wide variety of empirical networks. Our findings shed light on the importance of simultaneously considering different types of modules in directed networks.Comment: 26 pages, 7 figures. Supplementary Materials can be found in the journal referenc

Proportions - disposition relationship analysis of a historical truss in a rural house in Vápenná Village, Czech Republic

We have analysed historical trusses based on previous building-historical researches, particularly focusing on sacral buildings, in chosen regions of Slovakia, with one of the primary goals to examine geometric concepts and proportional relationships used for their construction. The knowledge of proportional principles and relationships used in various historical sacral trusses, additionally supported by contemporary literature, was applied to a village house truss from 1774 in Vapenna, Jeseniky district of the Czech Republic.Web of Science12211511

Behaviour of traditional Portuguese timber roof structures

The aim of this paper is to present the results of a structural analysis of common trusses traditionally used in roof construction in Portugal. The study includes the results of a preliminary survey intending to assess the geometry, materials and on site pathologies, as well as a twodimensional linear elastic static and dynamic analysis. The trusses behaviour under symmetric and non-symmetric loads, the king post/tie-beam connection, the stiffness of the joints and the incorrect positioning of the purlins, were some of the structural aspects that have been investigated

Flower and fruit development in processing tomatoes : a thesis presented in partial fulfilment of the requirements for the degree of Master of Horticultural Science in Vegetable Production at Massey University

Processing tomato crops are mechanically harvested from a single destructive harvest. The timing of this harvest to coincide with the maximum yield of factory grade fruit is of considerable importance to the efficiency of the field operation. There is a lack of information regarding where the factory grade fruit is produced on the plant and for how long the yield of factory grade fruit is maintained at its maximum level in the field. Two experiments were carried out in the Manawatu using the processing cultivars Castlehye 1204 Improved and UC 82B. The first experiment determined the time of flowering of all the flowers on the plant, the trusses in which these flowers were to be found and the position of these trusses on the plant. 132 days after planting all the plants were harvested and the number and position on the plant of the flowers which set fruit was determined. A normal distribution was found to satisfactorily describe the relationship between the number of flowers reaching anthesis and time. Plants on average carried up to 37 trusses. 65% of the yield was carried on the first 10 trusses to flower with 95% of the yield carried on the first 20 trusses to flower. The efficiency of trusses in producing fruit varied from 66% with the earlier flowering trusses down to negligible levels. Plants had up to 8 main order laterals and together with their attached sub laterals each carried from 4-5 trusses. The efficiency of flowering decreased with the position of the truss up the lateral. It was suggested that the competition between trusses for assimilates is far more important within laterals than between laterals. These results have implications for both crop management and plant breeding programmes. In the second experiment 9 successional destructive harvests were carried out commencing at the first sign of coloured fruit. Ethryl was not applied to the crop. The yield of red and factory grade fruit was found to peak sharply over time. The normal distribution curve was found to satisfactorily describe the relationship between time and the yield of both red and factory grade fruit and fruit numbers of these grades of fruit. Harvesting one week earlier or one week later than the optimum harvest date resulted in a loss of factory grade fruit of from 10-15 tonnes per hectare. The major cause for this rapid fall in yield from the optimum was due to an increase in the yield of red rotten fruit. In fact over half of the total number of fruit had rotted by 136 days after planting. This included a significant number of green fruit. The magnitude of this loss was only apparent because successional harvests were carried out. The total yield of fruit (all grades) was maintained over a considerable period as the loss in fruit numbers was balanced by the increase in mean fruit weight of the crop. The mean fruit weight of fruit did not increase once they had coloured. The percent soluble solids of red fruit decreased the week following any significant amount of rainfall. In the light of this research the effect of ethryl on the maturity characteristics of processing tomato crops needs to be re-examined by the use of successional harvests. Reliable techniques also need to be developed to predict the time of optimum harvest as these results suggest that it is much shorter than is commonly thought. The importance of fruit rots in reducing yields and thus effecting the length of the optimum harvest period is also apparent and is another area of research which requires further study. In the first experiment, the Normal Distribution Curve was found to describe the frequency of flower anthesis versus time relationship in two processing tomato cultivars; Castlehye 1204 Improved and UC 82B. Early fruit setting flowers acted as a strong sink as 90% of the final yield was carried on the first 18 trusses. Yield contributing trusses followed a pattern of increasing distance from the root system the later they flowered. Competition for photosynthate was mainly within laterals but also there was some between lateral competition. Flower trusses exhibited decreasing efficiencies in producing red fruit the later first flower anthesis occurred on the flower truss. In the second experiment, the yield of Factory Grade tomato fruit from the same two processing tomato cultivars peaked sharply over time. Harvesting one week earlier or later than the optimum harvest date resulted in a Factory Grade yield loss of up to 10-15 t ha-1for both cultivars. The Normal Distribution Curve was found to describe the relationship between Factory Grade fruit weight and number over time for both cultivars. Both red and coloured fruit weight were also found to follow the Normal Distribution. Over half of the total number of fruit rotted by 136 days after planting. Percentage Soluble Solids of red fruit decreased as rainfall increased in the week preceding harvest, with the converse also shown to apply

Designing Volumetric Truss Structures

We present the first algorithm for designing volumetric Michell Trusses. Our method uses a parametrization approach to generate trusses made of structural elements aligned with the primary direction of an object's stress field. Such trusses exhibit high strength-to-weight ratios. We demonstrate the structural robustness of our designs via a posteriori physical simulation. We believe our algorithm serves as an important complement to existing structural optimization tools and as a novel standalone design tool itself

Probabilistic structural analysis of adaptive/smart/intelligent space structures

A three-bay, space, cantilever truss is probabilistically evaluated for adaptive/smart/intelligent behavior. For each behavior, the scatter (ranges) in buckling loads, vibration frequencies, and member axial forces are probabilistically determined. Sensitivities associated with uncertainties in the structure, material and load variables that describe the truss are determined for different probabilities. The relative magnitude for these sensitivities are used to identify significant truss variables that control/classify its behavior to respond as an adaptive/smart/intelligent structure. Results show that the probabilistic buckling loads and vibration frequencies increase for each truss classification, with a substantial increase for intelligent trusses. Similarly, the probabilistic member axial forces reduce for adaptive and intelligent trusses and increase for smart trusses

Measuring Strain in Trusses

Strain is an important quantity in engineering and materials science that relates the deformation of a material to its original length as a percent. Different materials exhibit particular qualities under loading, for example the amount of strain due to a certain magnitude of force, or the amount of strain that can be borne before failure. This experiment aims to compare the relative strengths of three common truss configurations by measuring the strain in their members under loading