This paper describes a unique method for mapping natural language texts to canonical terms that identify the contents of the texts. This method learns empirical associations between free-form texts and canonical terms from human-assigned matches and determines a Linear Least Squares Fit (LLSF) mapping function which represents weighted connections between words in the texts and the canonical te...

We present and analyse two new Volume-of-Fluid (VOF) reconstruction algorithms that approximate the interface separating two immiscible fluids as a linear function in each grid cell (PLIC Piecewise Linear Interface Calculation). The first one is based on two simple geometrical criteria for the reconstruction of a linear interface, the second one minimizes a distance functional to find the plane...

We discuss the general characteristics of the orbits of the Martian satellites, Phobos and Deimos. We provide a concise review of the various descriptions of the orbits by both analytical theories and direct numerical integrations of their equations of motion. After summarizing the observational data used to determine the orbits, we discuss the results of our latest orbits obtained from a least...

Segmentation of time-varying systems and signals into models whose parameters are piecewise constant in time is an important and well studied problem. It is here formulated as a least-squares problem with sumof-norms regularization over the state parameter jumps, a generalization of `1-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the reg...

This paper proposes a general convex framework for the identification of switched linear systems. The proposed framework uses over-parameterization to avoid solving the otherwise combinatorially forbidding identification problem and takes the form of a least-squares problem with a sum-of-norms regularization, a generalization of the `1-regularization. The regularization constant regulates compl...

Let data of a univariate process be given. If the data are related by a sigmoid curve, but the sigmoid property has been lost due to the errors of the measuring process, then the least sum of squares change to the data that provides nonnegative third divided differences may be required. It is a structured quadratic programming calculation, which is solved very efficiently by a special least squ...

Introduction: Quantifying magnetic susceptibility of biological tissue using MRI has important clinical implications such as quantifying iron deposition in liver and sub-cortical structures, measuring oxygen saturation in blood, differentiating a hemorrhagic lesion as acute or chronic and identifying calcifications etc.. MR susceptometry of substances taken in standard sphere or cylinder geomet...

This paper focuses on the development of parameter estimation techniques for models quantifying hysteresis and constitutive nonlinearities in ferroelectric materials. These models are formulated as integral equations with known kernels and unknown densities to be identified through least squares fit to data. Due to the compactness of the integral operators, the resulting discretized models inhe...

Interpreting entropy as a prior probability suggests a universal but “purely empirical” measure of “goodness of fit”. This allows statistical techniques to be used in situations where the correct theory — and not just its parameters — is still unknown. As developed illustratively for least-squares nonlinear regression, the measure proves to be a transformation of the R statistic. Unlike the lat...