(t) and c (t) are the input gate, forget gate, output gate, and memory cell activation vector at time-step t respectively, all of which have the same size as the hidden vector  LSTM is supposed to capture the long-term and short-term dependencies simultaneously, but when dealing with considerably long texts, LSTM also fails on capturing and understanding significant sentiment message (Le et al., 2015).
the error signal would nevertheless suffer from gradient vanishing in modeling long texts with hundreds of words and thus the network is difficult to train.