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In previous work, we introduced a simple algorithm for producing motion by mean curvature of a surface, in which the motion is generated by alternately diiusing and renormalizing a characteristic function. This procedure is interesting due to its extreme simplicity, and because it isolates the connection between diiusion and curvature motion. However, it(More)
A collaborative convex framework for factoring a data matrix <i>X</i> into a nonnegative product <i>AS</i> , with a sparse coefficient matrix <i>S</i>, is proposed. We restrict the columns of the dictionary matrix <i>A</i> to coincide with certain columns of the data matrix <i>X</i>, thereby guaranteeing a physically meaningful dictionary and dimensionality(More)
We study minimization of the difference of l1 and l2 norms as a non-convex and Lipschitz continuous metric for solving constrained and unconstrained compressed sensing problems. We establish exact (stable) sparse recovery results under a restricted isometry property (RIP) condition for the constrained problem, and a full-rank theorem of the sensing matrix(More)
A two-dimensional cochlear model is presented, which couples the classical second order partial differential equations of the basilar membrane (BM) with a discrete feed-forward (FF) outer hair cell (OHC) model for enhanced sensitivity. The enhancement (gain) factor in the model depends on BM displacement in a nonlinear nonlocal manner in order to capture(More)
Vocal fold (VF) motion is a fundamental process in voice production, and is also a challenging problem for 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. The traditional modeling approach makes use of(More)
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, and is a one-dimensional (in space) damped dispersive nonlinear PDE based on the mechanics and phenomenology of hearing. It(More)
We establish the variational principle of Kolmogorov-PetrovskyPiskunov (KPP) front speeds in a one dimensional random drift which is a mean zero stationary ergodic process with mixing property and local Lipschitz continuity. To prove the variational principle, we use the path integral representation of solutions, hitting time and large deviation estimates(More)
We consider a one-dimensional model biodegradation system consisting of two reaction–advection equations for nutrient and pollutant concentrations and a rate equation for biomass. The hydrodynamic dispersion is ignored. Under an explicit condition on the decay and growth rates of biomass, the system can be approximated by two component models by setting(More)
Unmixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require finding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how aspects of these problems, such as misalignment of DOAS references and uncertainty in hyperspectral endmembers, can be(More)