Cognitive learning in differential evolution and its application to model order reduction problem for single-input single-output systems

Differential evolution (DE) is a well known and simple population based probabilistic approach for global optimization over continuous spaces. It has reportedly outperformed a few evolutionary algorithms and other search heuristics like the particle swarm optimization when tested over both benchmark and real world problems. DE, like other probabilistic optimization algorithms, has inherent drawback of premature convergence and stagnation. Therefore, in order to find a trade-off between exploration and exploitation capability of DE algorithm, a new parameter namely, cognitive learning factor (CLF) is introduced in the mutation process. Cognitive learning is a powerful mechanism that adjust the current position of individuals by the means of some specified knowledge (previous experience of individuals). The proposed strategy is named as cognitive learning in differential evolution (CLDE). To prove the efficiency of various approaches of CLF in DE,?CLDE is tested over 25 benchmark problems. Further, to establish the wide applicability of CLF,?CLDE is applied to two advanced DE variants. CLDE is also applied to solve a well known electrical engineering problem called model order reduction problem for single input single output systems.     

Fitness based Differential Evolution

Differential Evolution (DE) is a well known and simple population based probabilistic approach for global optimization. It has reportedly outperformed a few Evolutionary Algorithms and other search heuristics like Particle Swarm Optimization when tested over both benchmark and real world problems. But, DE, like other probabilistic optimization algorithms, sometimes exhibits premature convergence and stagnates at suboptimal point. In order to avoid stagnation behavior while maintaining a good convergence speed, a new position update process is introduced, named fitness based position update process in DE. In the proposed strategy, position of the solutions are updated in two phases. In the first phase all the solutions update their positions using the basic DE and in the second phase, all the solutions update their positions based on their fitness. In this way, a better solution participates more times in the position update process. The position update equation is inspired from the Artificial Bee Colony algorithm. The proposed strategy is named as Fitness Based Differential Evolution ( $FBDE$ ). To prove efficiency and efficacy of $FBDE$ , it is tested over 22 benchmark optimization problems. A comparative analysis has also been carried out among proposed FBDE, basic DE, Simulated Annealing Differential Evolution and Scale Factor Local Search Differential Evolution. Further, $FBDE$ is also applied to solve a well known electrical engineering problem called Model Order Reduction problem for Single Input Single Output Systems.     

A novel tetracyclic ring system. 10H-tetrazolo[5′,1′:3,4][1,2,4]triazino[5,6-b]indole

The reaction of 3-hydrazino-1,2,4-triazino[5,6-b]indole with nitrous acid affords a novel tetracyclic ring system: 10H-tetrazolo[5′,1′:3,4][1,2,4]triazino[5,6-b]indole. The mode of cyclization has been discussed.     

A constructive approach to cubic Hermite Fractal Interpolation Function and its constrained aspects

The theory of splines is a well studied topic, but the kinship of splines with fractals is novel. We introduce a simple explicit construction for a -cubic Hermite Fractal Interpolation Function (FIF). Under some suitable hypotheses on the original function, we establish a priori estimates (with respect to the L _p -norm, 1≤p≤∞) for the interpolation error of the -cubic Hermite FIF and its first derivative. Treating the first derivatives at the knots as free parameters, we derive suitable values for these parameters so that the resulting cubic FIF enjoys global smoothness. Consequently, our method offers an alternative to the standard moment construction of -cubic spline FIFs. Furthermore, we identify appropriate values for the scaling factors in each subinterval and the derivatives at the knots so that the graph of the resulting -cubic FIF lies within a prescribed rectangle. These parameters include, in particular, conditions for the positivity of the cubic FIF. Thus, in the current article, we initiate the study of the shape preserving aspects of fractal interpolation polynomials. We also provide numerical examples to corroborate our results.     

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

In this paper, we introduce optimal control algorithm for the design of pulse sequences in NMR spectroscopy. This methodology is used for designing pulse sequences that maximize the coherence transfer between coupled spins in a given specified time, minimize the relaxation effects in a given coherence transfer step or minimize the time required to produce a given unitary propagator, as desired. The application of these pulse engineering methods to design pulse sequences that are robust to experimentally important parameter variations, such as chemical shift dispersion or radiofrequency (rf) variations due to imperfections such as rf inhomogeneity is also explained.     

Electron Paramagnetic Resonance,Optical Spectra and DC Conductivity Studies of Vanadyl Doped Bi2O3 · BaO · B2O3 Glasses

Glasses with composition xBi₂O₃ ·(0.30 - x)BaO · 0.70B₂O₃ have been prepared in the range (0.00 ≤ x ≤ 0.15) containing 2.0 mol% of V₂O₅. Electron paramagnetic resonance (EPR), optical transmission and absorption spectra and DC conductivity of these glasses have been studied. The spin Hamiltonian parameters (SHP) of VO²⁺ ions, dipolar hyperfine coupling parameter P, Fermi contact interaction parameter K, and molecular orbital coefficients (α² and γ²) have been calculated. The SHP arc related with the theoretical optical basicity. A_th. The position of the absorption edge and the values of the optical band gap have also been reported. The effect of addition of Bi₂O₃ on the DC conductivity has also been studied.     

System size and energy dependence of jet-induced hadron pair correlation shapes in Cu+Cu and Au+Au collisions at square root sNN=200 and 62.4 GeV

We present azimuthal angle correlations of intermediate transverse momentum (1-4 GeV/c) hadrons from dijets in Cu+Cu and Au+Au collisions at square root sNN=62.4 and 200 GeV. The away-side dijet induced azimuthal correlation is broadened, non-Gaussian, and peaked away from Delta phi=pi in central and semicentral collisions in all the systems. The broadening and peak location are found to depend upon the number of participants in the collision, but not on the collision energy or beam nuclei. These results are consistent with sound or shock wave models, but pose challenges to Cherenkov gluon radiation models.     

Near-barrier fission of the system12C+232Th

The fission fragment angular distributions for the system¹²C +²³²Th have been measured in the energy range 0.97<>_c.m./V_B<1.22. the=" measured=" anisotropies=" have=" been=" compared=" with=" the=" predictions=" of=" the=" standard=" saddle=" point=" statistical=" model,=" using=" the=" second=" moment=" of=" the=" compound=" nucleus=" spin=" distribution=">l² deduced from a Wong model fit to the fission excitation function. While the measured anisotropies agree with the standard saddle point statistical model for E_c.m./V_B>1.05, they are abnormally large at lower energies. This is also true for the existing measurements of¹⁶O and¹⁹F +²³²Th systems. Since for this system pre-equilibrium fission contributions are not expected, this anomaly indicates strong channel coupling effects leading to an increase in l² at sub-barrier energies.The authors thank Drs. R.K. Choudhury and A. Saxena for useful discussions, Dr. R.J. Singh for making the thorium target and the Pellectron operation staff for excellent operation of the machine.