The robustness of a biometric identity verification (IV) system is best evaluated by monitoring its behavior under impostor attacks. Such attacks may include the transformation of one, many, or all of the biometric modalities. In this paper, we present the transformation of both speech and visual appearance of a speaker and evaluate its effects on the IV system. We propose MixTrans, a novel method for voice transformation. MixTrans is a mixture-structured bias voice transformation technique in the cepstral domain, which allows a transformed audio signal to be estimated and reconstructed in the temporal domain. We also propose a face transformation technique that allows a frontal face image of a client speaker to be animated. This technique employs principal warps to deform defined MPEG-4 facial feature points based on determined facial animation parameters (FAPs). The robustness of the IV system is evaluated under these attacks.

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In this paper, we study the optimal level of cash for the firm to hold. We model the cash level with inflows and outflows due to deposits and withdrawals; in between, the cash level is a stochastic process where it signals a time to sell. After modeling the continuous jump, we implemented first step analysis method to find the probability of the event with initial cash and we were able to calculate data driven by set of difference equations. These data are used to determine the length of the period of the investment. Then, we adopt the probabilistic decision model where it goes under mathematical optimization. This model let the investor to maximize the probability of success or to stop on one of the largest fortunes using the equation of the principle of optimality. Finally, to solve these optimal equations, we used the result of positive dynamic programming and we elaborated them by proves.

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