45 research outputs found
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