The selective regularization of a linear regression model

This paper discusses constructing a linear regression model with regularization of the system matrix of normal equations. In contrast to the conventional ridge regression, where positive parameters are added to all diagonal terms of a matrix, in the method proposed only those matrix diagonal entries that correspond to the data with a high correlation are increased. This leads to a decrease in the matrix conditioning and, therefore, to a decrease in the corresponding coefficients of the regression equation. The selection of the entries to be increased is based on the triangular decomposition of the correlation matrix of the original dataset. The effectiveness of the method is tested on a known dataset, and it is performed not only with a ridge regression, but also with the results of applying the widespread algorithms LARS and Lasso.

Task-Space Admittance Controller with Adaptive Inertia Matrix Conditioning

Whenrobots physically interact with the environment, compliant behaviors should be imposed to prevent damages to all entities involved in the interaction. Moreover, during physical interactions, appropriate pose controllers are usually based on the robot dynamics, in which the ill-conditioning of the joint-space inertia matrix may lead to poor performance or even instability. When the control is not precise, large interaction forces may appear due to disturbed end-effector poses, resulting in unsafe interactions. To overcome these problems, we propose a task-space admittance controller in which the inertia matrix conditioning is adapted online. To this end, the control architecture consists of an admittance controller in the outer loop, which changes the reference trajectory to the robot end-effector to achieve a desired compliant behavior; and an adaptive inertia matrix conditioning controller in the inner loop to track this trajectory and improve the closed-loop performance. We evaluated the proposed architecture on a KUKA LWR4+ robot and compared it, via rigorous statistical analyses, to an architecture in which the proposed inner motion controller was replaced by two widely used ones. The admittance controller with adaptive inertia conditioning presents better performance than with a controller based on the inverse dynamics with feedback linearization, and similar results when compared to the PID controller with gravity compensation in the inner loop.

Dynamics of Confined Short-Chain alkanol in MCM-41 by Dielectric Spectroscopy: Effects of matrix and system Treatments and Filling Factor

The dynamics of n-propanol confined in regular MCM-41 matrix with the pore size Dpore = 40 Å, under various matrix conditioning and sample confining conditions, using broadband dielectric spectroscopy (BDS), is reported. First, various drying procedures with the capacitor filling under air or N2 influence the BDS spectra of the empty MCM-41 and the confined n-PrOH/MCM-41 systems, but have a little effect on the maximum relaxation time of the main process. Finally, various filling factors of n-PrOH medium in the optimally treated MCM-41 system lead to unimodal or bimodal spectra interpreted in terms of the two distinct dynamic phases in the confined states.

Correlation Between Mesh Geometry and Stiffness Matrix Conditioning for Nonlocal Diffusion Models

Nonlocal diffusion models involve integral equations that account for nonlocal interactions and do not explicitly employ differential operators in the space variables. Due to the nonlocality they might look different from classical partial differential equation (PDE) models, but their local limit reduces to partial differential equations. The effect of mesh element anisotropy mesh refinement and kernel functions on the conditioning of the stiffness matrix for a nonlocal diffusion model on 2D geometric domains is considered, and the results compared with those obtained from typical local PDE models. Numerical experiments show that the condition number is bounded by (where c is a constant) for an integrable kernel function, and is not affected by the choice of the basis function. In contrast to local PDE models, mesh anisotropy and refinement affect the condition number very little.

TLOCI: A Fully Loaded Speckle Killing Machine

A new high-contrast imaging subtraction algorithm (TLOCI) is presented to maximize a planet signal-to-noise ratio. The technique uses an input spectrum and template PSFs to optimize the reference image coefficient determination to minimize the flux contamination via self-subtraction (thus maximizing its throughput wavelength per wavelength) of any planet that have a similar spectrum to the template spectrum in the image, while trying, at the same time, to maximize the speckle noise subtraction. The optimization is performed by a correlation matrix conditioning. Using laboratory Gemini Planet Imager data, the new algorithm is shown to be superior to the simple/double difference, polynomial fit and original LOCI algorithm.

A Direct Eigenanalysis of Multibody System in Equilibrium

This paper presents a direct eigenanalysis procedure for multibody system in equilibrium. The first kind Lagrange’s equation of the dynamics of multibody system is a set of differential algebraic equations, and the equations can be used to solve the equilibrium of the system. The vibration of the system about the equilibrium can be described by the linearization of the governing equation with the generalized coordinates and the multipliers as the perturbed variables. But the multiplier variables and the generalize coordinates are not in the same dimension. As a result, the system matrices in the perturbed vibration equations are badly conditioned, and a direct application of the mature eigensolvers does not guarantee a correct solution to the corresponding eigenvalue problem. This paper discusses the condition number of the problem and proposes a method for preconditioning the system matrices, then the corresponding eigenvalue problem of the multibody system about equilibrium can be smoothly solved with standard eigensolver such as ARPACK. In addition, a necessary frequency shift technology is also presented in the paper. The importance of matrix conditioning and the effectiveness of the presented method for preconditioning are demonstrated with numerical examples.