Time Domain Computation of a Nonlinear Nonlocal Cochlear Model with Applications to Multitone Interaction in Hearing

A nonlinear nonlocal cochlear model of the transmission line type is studied in order to capture the multitone interactions and resulting tonal suppression effects. The model can serve as a module for voice signal processing, it is a one dimensional (in space) damped dispersive nonlinear PDE based on mechanics and phenomenology of hearing. It describes the motion of basilar membrane (BM) in the cochlea driven by input pressure waves. Both elastic damping and selective longitudinal fluid damping are present. The former is nonlinear and nonlocal in BM displacement, and plays a key role in capturing tonal interactions. The latter is active only near the exit boundary (helicotrema), and is built in to damp out the remaining long waves. The initial boundary value problem is numerically solved with a semi-implicit second order finite difference method. Solutions reach a multi-frequency quasi-steady state. Numerical results are shown on two tone suppression from both high-frequency and low-frequency sides, consistent with known behavior of two tone suppression. Suppression effects among three tones are demonstrated by showing how the response magnitudes of the fixed two tones are reduced as we vary the third tone in frequency and amplitude. We observe qualitative agreement of our model solutions with existing cat auditory neural data. The model is thus simple and efficient as a processing tool for voice signals.Comment: 23 pages,7 figures; added reference

RARTS: a Relaxed Architecture Search Method

Differentiable architecture search (DARTS) is an effective method for data-driven neural network design based on solving a bilevel optimization problem. In this paper, we formulate a single level alternative and a relaxed architecture search (RARTS) method that utilizes training and validation datasets in architecture learning without involving mixed second derivatives of the corresponding loss functions. Through weight/architecture variable splitting and Gauss-Seidel iterations, the core algorithm outperforms DARTS significantly in accuracy and search efficiency, as shown in both a solvable model and CIFAR-10 based architecture search. Our model continues to out-perform DARTS upon transfer to ImageNet and is on par with recent variants of DARTS even though our innovation is purely on the training algorithm

Modeling Vocal Fold Motion with a New Hydrodynamic Semi-Continuum Model

Vocal fold (VF) motion is a fundamental process in voice production, and is also a challenging problem for direct numerical computation because the VF dynamics depend on nonlinear coupling of air flow with the response of elastic channels (VF), which undergo opening and closing, and induce internal flow separation. A traditional modeling approach makes use of steady flow approximation or Bernoulli's law which is known to be invalid during VF opening. We present a new hydrodynamic semi-continuum system for VF motion. The airflow is modeled by a quasi-one dimensional continuum aerodynamic system, and the VF by a classical lumped two mass system. The reduced flow system contains the Bernoulli's law as a special case, and is derivable from the two dimensional compressible Navier-Stokes equations. Since we do not make steady flow approximation, we are able to capture transients and rapid changes of solutions, e.g. the double pressure peaks at opening and closing stages of VF motion consistent with experimental data. We demonstrate numerically that our system is robust, and models in-vivo VF oscillation more physically. It is also much simpler than a full two-dimensional Navier-Stokes system.Comment: 27 pages,6 figure