Abstract: A forward pass through a sequence of strokes representing a handwritten equation is performed from the first stroke to the last stroke in the sequence. At each stroke, a path score is determined for a plurality of symbol-relation pairs that each represents a symbol and its spatial relation to a predecessor symbol. A symbol graph having nodes and links is constructed by backtracking through the strokes from the last stroke to the first stroke and assigning scores to the links based on the path scores for the symbol-relation pairs. The symbol graph is used to recognize a mathematical expression based in part on the scores for the links and the mathematical expression is stored.

Abstract: An opinion system infers the opinion of a sentence of a product review based on a probability that the sentence contains certain sequences of parts of speech that are commonly used to express an opinion as indicated by the training data and the probabilities of the training data. When provided with the sentence, the opinion system identifies possible sequences of parts of speech of the sentence that are commonly used to express an opinion and the probability that the sequence is the correct sequence for the sentence. For each sequence, the opinion system then retrieves a probability derived from the training data that the sequence contains an opinion word that expresses an opinion. The opinion system then retrieves a probability from the training data that the opinion words of the sentence are used to express an opinion. The opinion system then combines the probabilities to generate an overall probability that the sentence with that sequence expresses an opinion.