In C-tests the hypothesis of items local independence is violated, which doesn't permit to consider them as real tests. It is suggested to determine the distances between separate C-test items (blanks) and to combine items into clusters. Weights, inversely proportional to the number of items in corresponding clusters, are assigned to items. As a result, the C-test structure becomes similar to t...

For integers n ≥ 1, k ≥ 0, the stable Kneser graph SGn,k (also called the Schrijver graph) has as vertex set the stable n-subsets of [2n + k] and as edges disjoint pairs of n-subsets, where a stable n-subset is one that does not contain any 2-subset of the form {i, i + 1} or {1, 2n + k}. The stable Kneser graphs have been an interesting object of study since the late 1970’s when A. Schrijver de...

Bayesian networks (BNs) are used for inference and sampling by exploiting conditional independence among random variables. Context specific independence (CSI) is a property of graphical models where additional independence relations arise in the context of particular values of random variables (RVs). Identifying and exploiting CSI properties can simplify inference. Some generative network model...