J.P. Braga

SVM-KM: speeding SVMs learning with a priori cluster selection and k-means

A procedure called SVM-KM, based on clustering by k-means and to accelerate the training of support vector machines, is the main objective of the work. During the support vector machines (SVMs) optimization phase, training vectors near the separation margins, are likely to become support vector and must be preserved. Conversely, training vectors far from the margins are not in general taken into account for the SVMs design process. SVM-KM groups the training vectors in many clusters. Clusters formed only by a vector that belongs to the same class label can be disregard and only cluster centers are used. On the other hand, clusters with more than one class label are unchanged and all training vectors belonging to them are considered. Clusters with mixed composition are likely to happen near the separation margins and they may hold some support vectors. Consequently, the number of vectors in a SVM training is smaller and the training time can be decreased without compromising the generalization capability of the SVM.

Unified description of chemical bonding in H2 isotopomers, including Ps2, μ2 and bi-excitons

Abstract We developed an unified treatment of the low-lying states of the general A + A + e − e − systems based on the concepts of chemical bonding, using an intuitive valence bond electronic wavefunction. A reduced mass correction accounts for the effects of the finite masses of nuclei A. The potential energy curves, the electronic densities and the ionic contribution show similar behaviour for all systems. The number of vibrational states versus the mass relation λ is obtained and compared to theoretical predictions. We verified that the use of atomic masses instead of nuclear masses is fundamental in order to obtain the only bound state in the cases λ ≃1.

Spherical potential energy function from second virial coefficient using Tikhonov regularization and truncated singular value decomposition

Abstract The inverse problem to determine the potential energy surface from the second virial coefficient data, involves the solution of a discrete ill-posed problem. The Tikhonov regularization and the truncated singular value decomposition methods, which are appropriated to handle ill-conditioning linear system, were applied in this work to obtain the potential energy surface for an atom-atom short range interaction from second virial coefficient.

Artificial neural network applied for predicting rainbow trajectories in atomic and molecular classical collisions

A simple artificial neural network (ANN) is developed and applied to collision processes. A general discussion of how ANNs can be introduced to study general phenomena in scattering problems is presented and neural networks are proposed to predict classical rainbow trajectories in atomic and molecular collisions. As a result of modeling the collision process, based on the neural network approach, analytical equations were obtained to calculate classical atomic and molecular rainbow trajectories. However, these analytical results just translate the behavior of the input/output data and do not contain any general physical meaning. Although a fitting procedure could be easily used in the present case, the cost of function approximation using ANNs increases only linearly with the number of input variables. This contrasts with classical polynomial fitting procedures for which the computational cost increases exponentially with the input space dimension. This makes the ANN approach worth considering when modeli...

Inversion of Simulated Positron Annihilation Lifetime Spectrum Using a Neural Network

Inversion of positron annihilation lifetime spectroscopy, based on a neural network Hopfield model, is presented in this paper. From a previous reported density function for lysozyme in water a simulated spectrum, without the superposition of statistical fluctuation and spectrometer resolution effects, was generated. These results were taken as the exact results from which the neural network was trained. The precision of the inverted density function was analyzed taking into account the number of neurons and the learning time of the neural network. A fair agreement was obtained when comparing the neural network results with the exact results. For example, the maximum of the density function, with a precision of 0.4% for the percentual relative error, was obtained for 64 neurons.

Hopfield neural network model for calculating the potential energy function from second virial data

Abstract The calculation of the intermolecular potential from the second virial coefficient is treated here by using a Hopfield neural network model. From simulated data for the prototype system HeNe, the repulsive potential was obtained with a desired accuracy. The algorithm used here is general, as it can handle noise in the experimental data and, a neural network of higher dimension can be easily constructed. Although the inversion of the short-range part of the potential was obtained in the present work, the Hopfield neural network under consideration can equally be used to invert virial data to give the long-range part of the potential. The convergence of the states of the neuron and the accuracy of the inverted potential is also discussed.

Probability density function from experimental positron annihilation lifetime spectra

Inversion of experimental positron annihilation lifetime spectra was carried out to obtain the probability density function. Apparatus resolution together with experimental noise was taken into consideration while solving this ill posed problem. The singular value decomposition approach, moving the boundary between the subspaces was the theoretical formulation to calculate the probability density function. For the system considered, the Al(dpm)3 complex, three peaks will be presented in the inverted spectra, indicating the presence of the para-Positronium, the free positron and the ortho-Positronium. The predicted positions were, 0.1042 ns, 0.3542 ns and 1.3958 ns, respectively. Since the present approach gives the distribution of the species, it was possible also to predict the relative importance of each species in the spectra. The areas found correspond to: 13%, 32%, 55%. Both these results, position of the peaks and the areas, together with the half-life distribution can provide important information for experimentalists.

Variable phase equation in quantum scattering

This paper presents the derivation and applications of the variable phase equation for single channel quantum scattering. The approach was first presented in 1933 by Morse and Allis and is based on a modification of the Schrodinger equation to a first order differential equation, appropriate to the scattering problem. The dependence of phase shift on angular momentum and energy, together with Levinsons theorem, is discussed. Because the variable phase equation method is easy to program it can be further explored in an introductory quantum mechanics course.

A critical analysis of the two-dimensional atom ellipsoid model to study rotational collisions

Abstract The two-dimensional (2D) hard ellipsoid model is criticized and the calculations are compared with the 2D classical trajectory results. The scattering angle θ and the final j for a set of initial conditions (α and b ) have been analyzed and it was concluded that the contribution of ∂j / ∂α is the leading term in the Jacobian function. Moreover, the rainbow trajectory calculated by the hard ellipsoid model turned out to be highly accurate for low scattering angles and semi-quantative for the maximum rotational rainbow. For the latter, a relative error of about 10% has been found compared with classical trajectory results. Finally, an inversion procedure based on such a model has also been re-analyzed and better information on the anisotropy of the interaction potential was found using an exact equation rather than an approximate formula for the hard ellipsoid model.

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

This paper focuses on the calculation of the quantum second virial coefficient, under a recently developed potential. This coefficient was determined to within 4-5 significant figures in the temperature range from 3 to 100 K. Our results are within experimental error. The three contributions to the overall value of the coefficient are the quantum scattering (continuum state contribution), the bound state (discrete state contribution) and the quantum ideal gas; we discuss these contributions separately. The most significant contribution is from the scattering states, whereas the smaller contributions are from the discrete states. A sensitivity analysis was performed as a function of temperature for one parameter in the short-range region of the potential and for three parameters in the long-range regions of the potential. For both temperatures considered, 10 and 100 K, the C6 dispersion coefficient was the most significant, and the C10 dispersion term was the least significant to the overall result. In general, the precision required to describe the potential decays as the temperature increases. The overall accuracy and the relationship of the parameters to the experimental errors are discussed.