Gaussian target function

Figure 8.3 (a) One-dimensional example of a plane wave basis set for a unit cell of length 2 consisting of 3 functions, (b) Application of the basis to generate a target function which is a periodic set of Gaussians. 

In this section, the kernel-based matched signal detectors, such as the kernel MSD (KMSD), kernel ASD (KASD), kernel OSP (KOSP) and kernel SMF (KSMF) as well as the corresponding conventional detectors are implemented based on two different types of data sets - illustrative toy data sets and a real hyperspectral image that contains militaiy targets. The Gaussian RBF kernel, k(x,y) = exp-, was used to implement the kernel-based detectors, c represents the width of the Gaussian distribution and the value of c was chosen such that the overall data variations can be fully exploited by the Gaussian RBF function. In this paper, the values of c were determined experimentally. 

In the optimization process, the target function is the average Kullack-Leibler (KL) distance for all heavy atoms, which characterizes the difference between two Gaussian probability distributions defined by the theoretical and experimental ADPs [30,42,46], Given the eigenvalues (ofT, p e 1,2,3) and eigenvectors... 

Feature selection techniques are used for finding the chief factors influencing the target. Preliminary statistical analysis indicates that the data set has inclusive structure, so we can use two methods for this feature selection work one is based on KNN method, and the other is based on SVR using Gaussian kernel function. Fortunately both methods... 

In the context of our discussion in this chapter, we represent the measurement obtained using the waveform 4> as a Gaussian measurement with covariance Rfy The current state of the system is represented by the state covariance matrix P. Of course, the estimated position and velocity of the target is also important for the tracking function of the radar, but in this context they play no role in the choice of waveforms. In a clutter rich (and varying) scenario, the estimate of the target parameters will clearly play a more important role. The expected information obtained from a measurement with such a waveform, given the current state of... 

This model suggests at once the type of distribution of energy that will result. It must involve the law governing chance events, the Gaussian distribution law. Thus, if one repeatedly shoots abullet at a target, and the causes giving rise to the near-misses of the bullseye are all due to chance (e.g., ticks in the nervous system of the aimer), the number of near-misses is related to distance from the target (x) by a so-called error function ... 

Figure 1. Optimal control between Gaussian random vectors in a 64 x 64 random matrix system by the Zhu-Botina-Rabitz scheme with T — 20 and a = 1. a) The optimal field after 100 iterations b) its power spectrum (c) the optimal evolution of the squared overlap with the target (([)(r) (py) as well as its magnified values near the target time in the inset (d) the convergence behavior of the overlap Jq (solid curve) and the functional J (dashed curve) versus the number of iteration steps.

As an initial wavefunction we employ a Gaussian that is located in the potential well at negative distances, as indicated in Fig. 43. The interaction of the LCT field induces an average motion over the reaction barrier where afterwards a cooling takes place. This is demonstrated in Fig. 44 which contains the coordinate expectation value as a function of time (upper panel). Also shown is the target-state population, which we define as... 

An optimisation procedure was used to split the complex function into Gaussian functional elements. The task can be reduced to the search of the target (z) function minimum in the space of 2n variables ... 

A further class of ligand-based 3D-methods focuses on the comparison of the shape of molecules. This is done either on the basis of a solvent accessible surface or the shape is approximated by atom-centered soft Gaussian functions. Maximizing the overlay of these Gaussian functions maximizes the overlap between a query molecule and a single conformation of the target molecule. This is used in the Rapid... 

Laser-Etching Process. In certain photo-etching processes, a laser pointed at a target area rg causes an emission of surface atoms with a gaussian distribution in velocities, i.e., we have the initial state for the single atom distribution function as (see Fig. 2.4)... 

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