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The sample matrix inversion (SMI) beamformer implements Capon's minimum variance distortionless (MVDR) beamforming using the sample covariance matrix (SCM). In a snapshot limited environment, the SCM is poorly conditioned resulting in a…
A stress equilibration procedure for linear elasticity is proposed and analyzed in this paper with emphasis on the behavior for (nearly) incompressible materials. Based on the displacement-pressure approximation computed with a stable…
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…
In some parameter and solution regimes, a minimally coupled nonrelativistic quantum particle in 1d is isomorphic to a much heavier, vibrating, very thin Euler-Bernoulli rod in 3d, with ratio of bending modulus to linear density…
This paper is concerned with the stability analysis of a lossless Euler-Bernoulli beam that carries a tip payload which is coupled to a nonlinear dynamic feedback system. This setup comprises nonlinear dynamic boundary controllers…
In this letter, we propose a robust beamforming design for non-orthogonal multiple access (NOMA) based multiple-input single-output (MISO) downlink systems. In particular, the robust power minimization problem is studied with imperfect…
Designing high-performance electric machines that maintain their efficiency and reliability under uncertain material and operating conditions is crucial for industrial applications. In this paper, we present a novel framework for robust…
Many geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given noisy measurements of a subset of their pairwise relative transforms. This problem is…
We consider the problem of recovering fusion frame sparse signals from incomplete measurements. These signals are composed of a small number of nonzero blocks taken from a family of subspaces. First, we show that, by using a-priori…
In the dynamics of linear structures, the impulse response function is of fundamental interest. In some cases one examines the short term response wherein the disturbance is still local and the boundaries have not yet come into play, and…
Maximizing submodular objectives under constraints is a fundamental problem in machine learning and optimization. We study the maximization of a nonnegative, non-monotone $\gamma$-weakly DR-submodular function over a down-closed convex…
We investigate an alternative solution method to the joint signal-beamformer optimization problem considered by Setlur and Rangaswamy[1]. First, we directly demonstrate that the problem, which minimizes the received noise, interference, and…
We will give general sufficient conditions under which a controller achieves robust regulation for a boundary control and observation system. Utilizing these conditions we construct a minimal order robust controller for an arbitrary order…
Precision motion stages are playing a prominent role in various manufacturing equipment. The drastically increasing demand for higher throughput in integrated circuit (IC) manufacturing and inspection calls for the next-generation precision…
We consider three-dimensional elastic frames constructed out of Euler-Bernoulli beams and describe extension of matching conditions by relaxing the vertex-rigidity assumption and the case in which concentrated mass may exists. This…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
This work presents an optimization framework for tailoring the nonlinear dynamic response of lightly damped mechanical systems using Spectral Submanifold (SSM) reduction. We derive the SSM-based backbone curve and its sensitivity with…
Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…
We develop a unified framework that reconciles a barrier based geometric model of periodic sphere packings with a provably convergent discrete time dynamics. First, we introduce a C2 interior barrier U_nu that is compatible with a strict…
This paper examines the performance of ridge regression in reproducing kernel Hilbert spaces in the presence of noise that exhibits a finite number of higher moments. We establish excess risk bounds consisting of subgaussian and polynomial…