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This paper develops a new method for identifying econometric models with partially latent covariates. Such data structures arise in industrial organization and labor economics settings where data are collected using an input-based sampling…
In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…
The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…
Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
In the recent years we have witnessed a rapid development of new algorithmic techniques for parameterized algorithms for graph separation problems. We present experimental evaluation of two cornerstone theoretical results in this area:…
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are…
A computational method is introduced for choosing the regularization parameter for total variation (TV) regularization. The approach is based on computing reconstructions at a few different resolutions and various values of regularization…
The parameter selection is crucial to regularization based image restoration methods. Generally speaking, a spatially fixed parameter for regularization item in the whole image does not perform well for both edge and smooth areas. A larger…
This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…
We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged…
The goal of quantitative elastography is to identify biomechanical parameters from interior displacement data, which are provided by other modalities, such as ultrasound or magnetic resonance imaging. In this paper, we analyze the stability…
In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three…
We assume a second-order source separation model where the observed multivariate time series is a linear mixture of latent, temporally uncorrelated time series with some components pure white noise. To avoid the modelling of noise, we…
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…
In this contribution, we address the estimation of the frequency-dependent elastic parameters of polymers in the ultrasound range, which is formulated as an inverse problem. This inverse problem is implemented as a nonlinear regression-type…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge Laplace problem on a differential complex. On the other hand, we…
In this paper, we consider time-harmonic elastic wave scattering governed by the Lam\'e system. It is known that the elastic wave field can be decomposed into the shear and compressional parts, namely, the pressure and shear waves that are…