On the Approximation of Toeplitz Operators for Nonparametric H∞\mathcal{H}_\infty-norm Estimation

Given a stable SISO LTI system $G$, we investigate the problem of estimating the $\mathcal{H}_\infty$-norm of $G$, denoted $||G||_\infty$, when $G$ is only accessible via noisy observations. Wahlberg et al. recently proposed a nonparametric algorithm based on the power method for estimating the top eigenvalue of a matrix. In particular, by applying a clever time-reversal trick, Wahlberg et al. implement the power method on the top left $n \times n$ corner $T_n$ of the Toeplitz (convolution) operator associated with $G$. In this paper, we prove sharp non-asymptotic bounds on the necessary length $n$ needed so that $||T_n||$ is an $\varepsilon$-additive approximation of $||G||_\infty$. Furthermore, in the process of demonstrating the sharpness of our bounds, we construct a simple family of finite impulse response (FIR) filters where the number of timesteps needed for the power method is arbitrarily worse than the number of timesteps needed for parametric FIR identification via least-squares to achieve the same $\varepsilon$-additive approximation

Conceptualizing interdependences between regulatory and monetary policies. Some preliminary considerations

In this paper we investigate the interplay between regulatory and monetary policies. We analyze how changes in institutional settings modify the functioning of various channels of monetary transmission. The paper begins with a brief presentation of the main channels of monetary transmission, including credit channel, exchange rate channel, Tobin q theory, and the credit channel. After that we define a positive institutional change and we check how such adjustments can be put into the logic of monetary transmission. We show that the most profound way institutions impact the monetary transmission is via its effect on the elasticity of investments to changes in interest rates.monetary transmission channels, monetary policy, regulatory policy, institutional change, financial globalization

The Noisy Power Method: A Meta Algorithm with Applications

We provide a new robust convergence analysis of the well-known power method for computing the dominant singular vectors of a matrix that we call the noisy power method. Our result characterizes the convergence behavior of the algorithm when a significant amount noise is introduced after each matrix-vector multiplication. The noisy power method can be seen as a meta-algorithm that has recently found a number of important applications in a broad range of machine learning problems including alternating minimization for matrix completion, streaming principal component analysis (PCA), and privacy-preserving spectral analysis. Our general analysis subsumes several existing ad-hoc convergence bounds and resolves a number of open problems in multiple applications including streaming PCA and privacy-preserving singular vector computation.Comment: NIPS 201

Electric double layer structure close to the three-phase contact line in an electrolyte wetting a solid substrate

The electric double layer structure in an electrolyte close to a solid substrate near the three-phase contact line is approximated by considering the linearized Poisson-Boltzmann equation in a wedge geometry. The mathematical approach complements the semi-analytical solutions reported in the literature by providing easily available characteristic information on the double layer structure. In particular, the model contains a length scale that quantifies the distance from the fluid-fluid interface over which this boundary influences the electric double layer. The analysis is based on an approximation for the equipotential lines. Excellent agreement between the model predictions and numerical results is achieved for a significant range of contact angles. The length scale quantifying the influence of the fluid-fluid interface is proportional to the Debye length and depends on the wall contact angle. It is shown that for contact angles approaching 90{\deg} there is a finite range of boundary influence.Comment: 6 pages, 9 figures; http://link.aps.org/doi/10.1103/PhysRevE.86.02260

Five Deaths a Day: Workplace Fatalities in Canada, 1993-2005

According to data collected by the Association of Workers’ Compensation Boards of Canada, 1,097 workplace fatalities were recorded in Canada in 2005, up from 758 in 1993. As Canadians work on average 230 days per year, this means that there were nearly five work-related deaths per work day in this country. The objective of this study is to provide a detailed analysis of the characteristics of persons who die on the job and the reasons they die, and to gain a better understanding of developments over time in this key indicator of job quality and labour market well-being.Workplace fatalities, Worker's compensation, Dangerous industries, Occupational diseases, International comparisions.