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Boolean Matrices and their Applications to Covering Reductions

Zhu K., Liu G., Feng Y.

Fundamenta Informaticae

2015

Vol. 139, nr 4

421--433

This paper proposes two different covering reduction algorithms by means of Boolean matrices. We define a dual notion of product on Boolean matrices and establish the relationship between characteristic matrix of a covering and relational matrices of two covering-induced relations, i.e. the minimum and the maximum relations in a covering. This paper shows that relational matrices of minimum and maximum relations in a covering can be written as intersection and union of many “elementary” matrices and each “elementary” matrix is corresponding to one element in the covering, respectively. Finally, as an application of this result, we propose two types of covering reduction algorithms.

Species abundance-distribution relationship : the differences among oak (Quercus liaotungensis Koidz) forest layers

Feng Y., Ma K., Zhang Y., Anand M., He K.

Polish Journal of Ecology

2011

Vol. 59, nr 1

55-62

Species abundance-distribution relationship is currently a hot topic in community ecology. Previous studies have suggested that a positive abundance-distribution relationship is a widespread feature of ecological assemblage across a wide variety of organisms, but how this relationship varies among different functional groups remains unclear. In this study, the species abundance-distribution relationship in the tree layer, shrub layer, and herb layer were analyzed respectively in an oak forest (Quercus liaotungensis Koidz.), Beijing region, China. Ten transects were set up from the foot to the top of every west slope to create a continuous altitude gradient (1020-1770 m). The width of each transect was 10 m and the length of each transect ranged from 80.200 m, depending on the altitude range and slope degree. This study area consisted of 119 quadrats, each 10 x 10 m2. Within each quadrat, three sub-quadrats (1m x 1m) were randomly selected for the inventory of herb layer. Our results showed that the relationship between local species abundance and the regional distribution was significantly positive while the frequency distribution was unimodal in the three layers, indicating that locally abundant species were widely spread whereas locally rare species had restricted regional distributions. Variance partitioning of species abundance showed that the contribution of environmental variation and spatial variation to regulating the species abundance-distribution relationship of different layers are different: the pure geographical variation decreased and the pure soil variation increased in the order of tree layer, shrub layer, to herb layer, while the response due to total soil variation was similar in all three layer communities. The distribution of tree layer and shrub layer are mainly influenced by large-scale factors while herb layer distribution is more likely determined by local-scale factors.