Yehia Badr

Medieval Arabic algebra books intended for practical training generally have in common a first “book” which is divided into two sections: one on the methods of solving simplified equations and manipulating expressions, followed by one consisting of worked-out problems. By paying close attention to the wording of the problems in the books of al-Khwārizmī, Abū Kāmil, and Ibn Badr, we reveal the different ways the word māl was used. In the enunciation of a problem it is a common noun meaning “quantity,” while in the solution it is the proper noun naming the square of “thing” (shay '). We then look into the differences between the wording of enunciations and equations, which clarify certain problems solved without “thing,” and help explain the development of algebra before the time of al-Khwārizmī.

In this paper, we describe research to extend the capability of an existing talking head, Baldi, to be multilingual. We use parsimonious client/server architecture to impose autonomy in the functioning of an auditory speech module and a visual speech synthesis module. This scheme enables the implementation and the joint application of text-to-speech synthesis and facial animation in many languages simultaneously. Additional languages can be added to the system by defining a unique phoneme set and unique phoneme definitions for the visible speech for each language. The accuracy of these definitions is tested in perceptual experiments in which human observers identify auditory speech in noise presented alone or paired with the synthetic versus a comparable natural face. We illustrate the development of an Arabic talking head, Badr, and demonstrate how the empirical evaluation enabled the improvement of the visible speech synthesis from one version to another.