Liviu I. Ignat, Alejandro Pozo
In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of first order. We also analyze the large-time behavior of the approximated solution by obtaining the first term in the asymptotic expansion. We prove that, when time increases, these solutions behave as the self-similar solutions of the viscous Burgers equation
Carlos Arriaga, Alejandro Pozo, Javier Conde et al.
Automatic speech recognition (ASR) systems generate real-time transcriptions but often miss nuances that human interpreters capture. While ASR is useful in many contexts, interpreters-who already use ASR tools such as Dragon-add critical value, especially in sensitive settings such as diplomatic meetings where subtle language is key. Human interpreters not only perceive these nuances but can adjust in real time, improving accuracy, while ASR handles basic transcription tasks. However, ASR systems introduce a delay that does not align with real-time interpretation needs. The user-perceived latency of ASR systems differs from that of interpretation because it measures the time between speech and transcription delivery. To address this, we propose a new approach to measuring delay in ASR systems and validate if they are usable in live interpretation scenarios.
Liviu I. Ignat, Alejandro Pozo
In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain $L^1$-$L^p$ decay rates. The asymptotic behavior of the solution is obtained by showing that the influence of the convolution term $K*u_{xx}$ is the same as $u_{xx}$ for large times. Then, we propose a semi-discrete numerical scheme that preserves this asymptotic behavior, by introducing two correcting factors in the discretization of the non-local term. Numerical experiments illustrating the accuracy of the results of the paper are also presented.