Design of wavelet neural networks based on symmetry fuzzy C-means for function approximation

Specifying the number and locations of the translation vectors for wavelet neural networks (WNNs) is of paramount significance as the quality of approximation may be drastically reduced if initialization of WNNs parameters was not done judiciously. In this paper, an enhanced fuzzy C-means algorithm, specifically the modified point symmetry–based fuzzy C-means algorithm (MPSDFCM), was proposed, in order to determine the optimal initial locations for the translation vectors. The proposed neural network models were then employed in approximating five different nonlinear continuous functions. Assessment analysis showed that integration of the MPSDFCM in the learning phase of WNNs would lead to a significant improvement in WNNs prediction accuracy. Performance comparison with the approaches reported in the literature in approximating the same benchmark piecewise function verified the superiority of the proposed strategy

Thermodynamics and relativistic kinetic theory for q-generalized Bose-Einstein and Fermi-Dirac systems

The thermodynamics and covariant kinetic theory have been elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics have been established for a grand canonical system having q-generalized BE/FD degrees of freedom. The many particle kinetic theory has been set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws have been realized in terms of appropriate moments of the transport equation. The thermodynamic quantities have been obtained in weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the q-modified effective coupling have been estimated for a quark-gluon system.by Sukanya Mitr