Weak quasi-randomness for uniform hypergraphs

We study quasi-random properties of k-uniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known Chung-Graham-Wilson theorem for quasi-random graphs. Moreover, let K(k) be the complete graph on k vertices and M(k) the line graph of the graph of the k-dimensional hypercube. We will show that the pair of graphs (K(k),M(k)) has the property that if the number of copies of both K(k) and M(k) in another graph G are as expected in the random graph of density d, then G is quasi-random (in the sense of the Chung-Graham-Wilson theorem) with density close to d. (C) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 1-38, 2012

Yield mapping, soil fertility and tree gaps in an orange orchard

The current high competition on Citrus industry demands from growers new management technologies for superior efficiency and sustainability. In this context, precision agriculture (PA) has developed techniques based on yield mapping and management systems that recognize field spatial variability, which contribute to increase profitability of commercial crops. Because spatial variability is often not perceived the orange orchards are still managed as uniform and adoption of PA technology on citrus farms is low. Thus, the objective of the present study was to characterize the spatial variability of three factors: fruit yield, soil fertility and occurrence of plant gaps caused by either citrus blight or huanglongbing (HLB) in a commercial Valencia orchard in Brotas, São Paulo State, Brazil. Data from volume, geographic coordinates and representative area of the bags used on harvest were recorded to generate yield points that were then interpolated to produce the yield map. Soil chemical characteristics were studied by analyzing samples collected along planting rows and inter-rows in 24 points distributed in the field. A map of density of tree gaps was produced by georeferencing individual gaps and later by counting the number of gaps within 500 m² cells. Data were submitted to statistical and geostatistical analyses. A t test was used to compare means of soil chemical characteristics between sampling regions. High variation on yield and density of tree gaps was observed from the maps. It was also demonstrated overlapping regions of high density of plant absence and low fruit yield. Soil fertility varied depending on the sampling region in the orchard. The spatial variability found on yield, soil fertility and on disease occurrence demonstrated the importance to adopt site specific nutrient management and disease control as tools to guarantee efficiency of fruit production.