The convergence properties of the gradient descent algorithm in the case of the linear perceptron may be obtained from the response function. We derive a general expression for the response function and apply it to the case of data with simple input correlations. It is found that correlations severely may slow down learning. This explains the success of PCA as a method for reducing training tim...

[1] Similarity analysis offers the ability to model hydrological response using quantifiable landscape descriptors. It is possible to develop similarity indices based on analytical solutions to the governing dynamic equations (Brutsaert, 2005). Berne et al. (2005) provide derivation of such a similarity index (the hillslope Péclet number) of subsurface flow and saturation for hillslopes with ex...

It has been reported that independent component analysis (ICA) of natural image sequences yields spatio-temporal "lters of non-separable spatio-temporal properties. On the contrary, sign changing "lters with separable spatio-temporal properties have not been found via ICA. We show that extending the ICA to temporally convolved inputs develops such receptive "elds (RFs). We argue that temporal c...

A simple model of adaptive control of promotional spending is analyzed. In the model, company sales (and therefore profits) are functions of promotional spending rate. Sales response to the promotion changes with time as a result of changes in a parameter of the sales response function. Information about sales response is collected in each time period by performing an experiment. On the basis o...

Several methods have been proposed in the literature to find a state-space model for the wave-radiation forces. In this paper, we compared four methods, two in the frequency domain and two in the time domain. The frequency-response function and the impulse response of the resulting state-space models were compared against those derived from the numerical code WAMIT. A new state-space module was...

This paper is the second part of a two-part paper devoted to the study of the spectral correlation of CPM modulations. The first part gave the exact analytical expression of the theoretical spectral correlation for the special case of the CPKSF modulations (CPM 1-REC). A generalisation to all CPM modulations (full response CPMs other than 1-REC, and partial response CPMs) seems to be unrealisab...

Azimuthal angles and Doppler frequencies of radar targets usually suffer from estimation uncertainty in practice, which poses a big challenge in target detection. In this work, we consider the problem of target detection in the presence of uncertainty in the azimuthal angle and Doppler frequency. This uncertainty is characterized by a subspace model. Precisely, the spatial and temporal steering...

In this document, we present several methods for approximating the indices σj and ηj associated with the second-order variance-based sensitivity analysis technique discussed in the Main text. We first review a number of multivariate representation schemes for the response function of a biochemical reaction system that can be used to analytically map the complex relationship between the biochemi...

In general, microrheology is carried out using active or passive particle-tracking techniques. In the present paper, a novel technique based on the out-of-plane bending vibrations of a microcantilever beam immersed into a liquid is proposed for microrheological property measurement. We propose to analytically link the damped beam motion with the rheological properties of the fluid in order to e...

Blocking and starving of a buffered production line is investigated from the viewpoint of nonlinear dynamics. A strategy to avoid blocking and starving, which utilizes frequency response and H∞-norm, is proposed. The proposed strategy does not need to tune all the work cells. Furthermore, we provide a systematic procedure for selecting and tuning the work cells. The numerical simulations are sh...