The aim of this course is to address the complexity of counting and sampling problems from an algorithmic perspective. Typically we will be interested in counting the size of a collection of combinatorial structures of a graph, e.g., the number of spanning trees of a graph. We will soon see that this style of counting problem is intimately related to the sampling problem which asks for a random...

Shot hole disease of stone fruit trees, caused by Wilsonomyces carpophilus (Lév.) Adaskaveg, Ogawa & Butler(= Stigmina carpophila (Lév.) M.B. Ellis and Coryneum beijerinckii Oud.) is a serious disease of Prunus species in West Azerbaijan province. The pathogen was obtained from infected leaves, fruits and twigs of Prunus orchards during spring and summer of 2007. Samples were cultured on PDA, M...

This research has an aim to assess agricultural students' satisfaction from their field of study. The statistical population consisted of 1040 students from the University of Bu Ali Sina (800 bachelor and 240 master students) during the years of 2011 to 2013. Through stratified random sampling method 240 bachelor and 80 master students were selected. Data was collected by means of a researcher ...

spatio-temporal variability of throughfall (tf) has an important role on the biogeochemical processes,soil, watershed hydrology as well as the nutrient cycle in forests. spatial distribution and temporalstability of tf patterns by five individual persian oak trees (quercus brantii var. persica) in thezagros forests of western iran, ilam, was quantified. sixteen tf manual gauges were placed bene...

A wide range of evolutionary models for species-level (and higher) diversification have been developed. These models can be used to test evolutionary hypotheses and provide comparisons with phylogenetic trees constructed from real data. To carry out these tests and comparisons, it is often necessary to sample, or simulate, trees from the evolutionary models. Sampling trees from these models is ...