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This paper describes mathematical models widely used in speech recognition systems, including linear predictive analysis, cepstral analysis, dynamic time warping (DTW), the stochastic models of sentence speech recognition systems, hidden Markov models (HMMs), and stochastic language models. Stochastic models such as HMMs and stochastic language models are now used in most advanced speech recognition systems, because they are powerful and useful if large speech and language databases are available for training and if the characteristics of those databases are maintained in the utterances to be recognized. However, in many cases, speakers, microphones, transmission systems, and additive noise usually differ between the training samples and the utterances to be recognized. Even if they are the same, manner of speaking changes with the speaker. Language characteristics are also variable. For example, words and their sequences that were not included in the language database often appear in the utterances to be recognized. Therefore, robustness and adaptability are very important characteristics for these stochastic models.

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Technology Computer-Aided Design (TCAD) is described both in terms of its function in Integrated Circuit (IC) design and in terms of the underlying physics and numerical modeling. TCAD provides IC designers with the ability to look inside chip technology and understand complex interdependence of parameters that affect performance and manufacturability. The simulation tools that are used for TCAD involve a close coupling of physical models and advanced numerical algorithms. An example of the interplay of electrical effects at the device level and underlying fabrication process steps is given for the latchup problem. Several examples of process modeling are used to illustrate the intimate connection of physical effects such as oxidation, impurity diffusion and plasma etching with the numerical models. Finally, some of the software engineering and computational issues are outlined. Very exciting challenges in parallel computing and advanced visualization techniques are suggested.

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This paper contains some criticism against the prevailing model of parallel computation, to be called PB (Parallel over Blocks) model. It spreads mainly due to its easy construction of hardware based upon that model, while it often fails to achieve totally efficient parallel computation. It also produces the tendency to accept HPF (High Performance Fortran) widely as its parallel programming language. This paper asserts that such movement may raise an unhappy situation for both users and system sides, by showing sample programs addressed for those machines based upon the PB model. On the other hand, the paper proposes the author's own model, say, ADEPS (Alternating Direction Execution of 'Parallel over Segments') and it shows that ADEPS allows directly to express many standard parallel schemes for many kinds of problems by using new parallel language ADETRAN4, which is also based upon ADEPS and is designed by the author.

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