Abstract: Let {Xi}i≥1 be a martingale difference sequence with
Xi = Si - Si-1. Under some regularity conditions, we show that
(X2
1+· · ·+X2N
n)-1/2SNn is asymptotically normal, where {Ni}i≥1
is a sequence of positive integer-valued random variables tending
to infinity. In a similar manner, a backward (or reverse) martingale
central limit theorem with random indices is provided.
Abstract: A New features are extracted and compared to
improve the prediction of protein-protein interactions. The basic idea
is to select and use the best set of features from the Tensor matrices
that are produced by the frequency vectors of the protein sequences.
Three set of features are compared, the first set is based on the
indices that are the most common in the interacting proteins, the
second set is based on the indices that tend to be common in the
interacting and non-interacting proteins, and the third set is
constructed by using random indices. Moreover, three encoding
strategies are compared; that are based on the amino asides polarity,
structure, and chemical properties. The experimental results indicate
that the highest accuracy can be obtained by using random indices
with chemical properties encoding strategy and support vector
machine.