![]() We propose a probabilistic graphical model to extract global and local topics related to social events in a unified framework at the same time. In this paper, we distinguish global and local topics by associating each tweet with both of them simultaneously. However, most of existent works neglect the difference between them and suffer from the Long Tail Effect, resulting in the inability to detect the. ![]() There are two types of topics, i.e., global topics attracting widespread tweets with larger volume and local topics drawing attention of limited tweets of somewhere. Read moreĭetecting topics from Twitter has been widely studied for understanding social events. Consequently, the second Born approximation is seen to suffer from the same problem as does the first Born approximation, namely, too dominant a contribution of the large bound-state momentum components. It is shown that additional contributions to the amplitude deriving from values of the bound-state momentum in the wings of the distributions are non-negligible and in fact explain the large differences found between exact and linearized-propagator approximation results. lowest-order quantum estimate of the Thomas mechanism by employing initial and final bound-state momentum values around the center of these distributions along with a neglect of the electronic part of the momentum transfer in the two collisions of the mechanism. The plane-wave second Born approximation to the single-electron capture amplitude calculated in a linearized-propagator approximation gives the. The double-scattering mechanism of Thomas represents the dominant means in an ion-atom collision at high velocities for the electron-projectile subsystem to rid itself of its large internal kinetic energy and thus allow the electron to be captured. Treated, as are various types of mean values. Asymptotic formulas for relatively large angles are The distributions of lateral deflections and other characteristics areĬonsidered, but the details of applications to emulsions, cloud and bubbleĬhambers, etc, are not entered into, nor are the electron-penetration and Multiple scattering of polarized electrons is included, with the importantĬorrection that no depolarization appears in the approximation to which they The work of Muhlschlegel and Koppe on the Very thin films are given, as well as a detailed discussion following Lenz on Calculations by Keil, Zeitler, and Zinn for Snyder'sĬalculations are outlined, and previously unpublished work on spatial-angle Nigam is given by the same method with newly computed tables. Moliere's multiple-scatteringĬalculation is presented by an improvement of Bethe's method, and the work of Of them given by Nigam, Sundaresan, and Wu. Single-scattering formulas of Moliere are derived, along with the modifications ![]() Slight attention is given to the less accurate Gaussian approximation. TheĪpproximation considered is that of the Snyder-Scott-Moliere theory, and only The multiple scattering of fast charged particles in the small-angle range. An explicit asymptotic formula for large η is given, showing correction terms to the single scattering formula.Ī systematic unified review is given of the basic statistical theory of The deviations of the new results from each of these limiting values is quite large over a wide range of angle. The matching is shown between the approximately Gaussian result for small angles and the Rutherford single scattering result valid for large angles. Curves are presented for a few values of zλ. ![]() Numerical calculations for values of zλ from 100 to 84,000, and for an adequate range of ηη0, have been carried out, and tables have been made available. The results are expressed in terms of dimensionless variables ηη0 and zλ representing respectively the deflection angle in terms of a small unit determined by the screening, and the foil thickness in terms of the mean free path for scattering. The projection of the scattering on a plane has been used for simplicity. The extension consists of an exact solution of the integral diffusion equation for the correlated probabilities of lateral and angular displacements, and the numerical integration of the resulting expression for the angular distribution. The theory of multiple scattering of charged particles has been extended in the small-angle approximation valid for thin foils and fast particles.
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