Nonlinear transformation is one of the major obstacles to analyzing the properties of multilayer perceptrons. In this letter, we prove that the correlation coefficient between two jointly Gaussian random variables decreases when each of them is transformed under continuous nonlinear transformations, which can be approximated by piecewise linear functions. When the inputs or the weights of a mul...

Exponential Linear Units (ELUs) are a useful rectifier for constructing deep learning architectures, as they may speed up and otherwise improve learning by virtue of not have vanishing gradients and by having mean activations near zero [1]. However, the ELU activation as parametrized in [1] is not continuously differentiable with respect to its input when the shape parameter α is not equal to 1...

Determination of the state space equations for a given transfer matrix is a classical problem, called the realization problem, which has been addressed in many papers and books (Farina and Rinaldi, 2000; Benvenuti and Farina, 2004; Kaczorek, 1992; 2009b; 2011d; 2012; Shaker and Dixon, 1977). An overview on the positive realization problem is given by Farina and Rinaldi (2000), Kaczorek (2002), ...

Direct volume-rendering has proven to be an effective and flexible visualization method for 3D scalar fields. Transfer functions are fundamental to direct volume-rendering because their role is essentially to make the data visible: by assigning optical properties like color and opacity to the voxel data, the volume can be rendered with traditional computer graphics methods. Good transfer functi...

One of the most important prediction problems in finite population is the prediction of a linear function of characteristic values of a finite population. In this paper the admissibility of linear predictors of an arbitrary linear function of characteristic values in a finite population under reflected normal loss function is considered. Under the super-population model, we obtain the condition...

Transfer functions have been shown to provide monotonic approximations to the resolvent 2-norm of A, R(z) = (A − zI), when associated with a sequence of nested spaces. This paper addresses the open question of the effectiveness of the transfer function scheme for the computation of the pseudospectrum of large matrices. It is shown that the scheme can be combined with certain Krylov type linear ...

For many years, various methods for the identification and estimation of parameters in linear, discrete-time transfer functions have been available and implemented in widely available Toolboxes for Matlab. This paper considers a unified Refined Instrumental Variable (RIV) approach to the estimation of discrete and continuous-time transfer functions characterized by a unified operator that can b...

An algorithm to compute a reduced-order model of a linear dynamic system is described. It is based on the rational Krylov method, which is an extension of the shift-and-invert Arnoldi method where several shifts (interpolation points) are used to compute an orthonormal basis for a sub-space. It is discussed how to generate a reduced-order model of a linear dynamic system, in such a way that the...

Many methods have been proposed for modeling head-related transfer functions (HRTFs) and yield a good performance level in terms of log-spectral distortion (LSD). However, most of them utilize linear weighting to reconstruct or interpolate HRTFs, but not consider the inherent nonlinearity relationship between the basis function and HRTFs. Motivated by this, a domain knowledge-assisted nonlinear...