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The X-ray emission spectra have been analyzed by the genetic algorithm. The X-ray peaks are represented by Gaussians or Lorentzians and the best estimates of their parameters are determined with the optimization strategy based on the mechanism of natural selection and natural genetics. The calculated results for artificial, pseudo-experimental, and experimental spectra are compared with those obtained by other methods and the validity of the present method is demonstrated.

Analytic second derivative of molecular energy with respect to all parameters for floating Gaussian type orbitals were proposed for the first time in our group.¹ In the present study, further simplification and application has been made and the viability of the method was demonstrated by writing a program and computing the analytic force constant of H₂, LiH and BH molecules. It is shown that this method is efficient both in accuracy and saving in computational time.

Transverse momentum $(p_T)$ spectra of ${\pi }^{-}$ mesons calculated using ultra-relativistic quantum molecular dynamic (UrQMD) model (Latest version 3.3-p2) simulations have been compared with $p_T$ spectra of ${\pi }^{-}$ mesons, obtained experimentally in interactions of protons beam with carbon nuclei (propane as target) at momentum of 4.2 GeV/c. Spectral temperatures of negative pions obtained in experimental and UrQMD model simulated interactions of protons beam with carbon nuclei have been calculated by fitting both spectra with four different fitting functions, i.e. Hagedorn thermodynamic, Boltzmann distribution, Gaussian and exponential functions. These functions are used commonly for describing hadron spectra and their spectral temperatures. Hagedorn thermodynamic function has been recommended as the most suitable function to extract the temperature of negative pions at above momentum among these four functions.

Noise reduction in images, also known as image smoothing, is an essential and first step before further processings of the image. The key to image smoothing is to preserve important features while removing noise from the image. Gaussian function is widely used in image smoothing. Recently it has been reported that exponential functions (value of the exponent is not equal to 2) perform substantially better than Gaussian functions in modeling and preserving image features. In this paper we propose a family of exponential functions, that include Gaussian when the value of the exponent is 2, for image smoothing. We experiment with a variety of images, artificial and real, and demonstrate that optimal results are obtained when the value of the exponent is within a certain range.

Many machine learning applications rely on learning distance functions with side information. Most of these distance metric learning approaches learns a Mahalanobis distance. While these approaches may work well when data is in low dimensionality, they become computationally expensive or even infeasible for high dimensional data. In this paper, we propose a novel method of learning nonlinear distance functions with side information while clustering the data. The new semi-supervised clustering approach is called Semi-Supervised Fuzzy clustering with Learnable Cluster dependent Kernels (SS-FLeCK). The proposed algorithm learns the underlying cluster-dependent dissimilarity measure while finding compact clusters in the given data set. The learned dissimilarity is based on a Gaussian kernel function with cluster dependent parameters. This objective function integrates penalty and reward cost functions. These cost functions are weighted by fuzzy membership degrees. Moreover, they use side-information in the form of a small set of constraints on which instances should or should not reside in the same cluster. The proposed algorithm uses only the pairwise relation between the feature vectors. This makes it applicable when similar objects cannot be represented by a single prototype. Using synthetic and real data sets, we show that SS-FLeCK outperforms several other algorithms.