Differential cross sections for excitation to the n=2 states of atomic helium by electrons were computed for incident energies in the range from 30 to 50 eV. The n=2 states excitation cross sections are calculated with the use of closecoupling expansion with a non-orthogonal Laguerre-L2 basis function. The present status of agreement between theory and experiment for excitation of the ground-state was quite satisfactory.
In this paper we present a new line search method known as the HBFGS method, which uses the search direction of the conjugate gradient method with the quasi-Newton updates. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) update is used as approximation of the Hessian for the methods. The new algorithm is compared with the BFGS method in terms of iteration counts and CPU-time. Our numerical analysis provides strong evidence that the proposed HBFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent.
This paper proposes the use of bootstrap, robust and fuzzy multiple linear regressions method in
handling general insurance in order to get improved results. The main objective of bootstrapping is to
estimate the distribution of an estimator or test statistic by resampling one's data or a model estimated
from the data under conditions that hold in a wide variety of econometric applications. In addition,
bootstrap also provides approximations to distributions of statistics, coverage probabilities of confidence
intervals, and rejection probabilities of hypothesis tests that produce accurate results. In this paper, we
emphasize the combining and modelling using bootstrapping, robust and fuzzy regression methodology.
The results show that alternative methods produce better results than multiple linear regressions (MLR)
model.
Clonal selection algorithm and discrete Hopfield neural network are extensively employed for solving higher-order optimization problems ranging from the constraint satisfaction problem to complex pattern recognition. The modified clonal selection algorithm is a comprehensive and less iterative immune-inspired searching algorithm, utilized to search for the correct combination of instances for Very large-scale integrated (VLSI) circuit structure. In this research, the VLSI circuit framework consists of Boolean 3-Satisfiability instances with the different complexities and number of transistors are considered. Hence, a hybrid modified clonal selection algorithm with discrete Hopfield neural network is well developed to optimize the configuration of VLSI circuits with different number of electronic components such as transistors as the instances. Therefore, the performance of the developed hybrid model was assessed experimentally with the standard models, HNNVLSI-3SATES and HNNVLSI-3SATGA in term of circuit accuracy, sensitivity, robustness and runtime to complete the verification process. The results have demonstrated the developed model, HNNVLSI-3SATCSA produced a minimum error (consistently approaching 0), better accuracy (more than 80%) and faster computational time (less than 125 seconds) against changes in the complexity in term of the number of transistors. Furthermore, the developed hybrid model is able to minimize the computational burden and configurational noises for the variant of VLSI circuits.
Maximum k Satisfiability logical rule (MAX-kSAT) is a language that bridges real life application to neural network optimization. MAX-kSAT is an interesting paradigm because the outcome of this logical rule is always negative/false. Hopfield Neural Network (HNN) is a type of neural network that finds the solution based on energy minimization. Interesting intelligent behavior has been observed when the logical rule is embedded in HNN. Increasing the storage capacity during the learning phase of HNN has been a challenging problem for most neural network researchers. Development of Metaheuristics algorithms has been crucial in optimizing the learning phase of Neural Network. The most celebrated metaheuristics model is Genetic Algorithm (GA). GA consists of several important operators that emphasize on solution improvement. Although GA has been reported to optimize logic programming in HNN, the learning complexity increases as the number of clauses increases. GA is more likely to be trapped in suboptimal fitness as the number of clauses increases. In this paper, metaheuristic algorithm namely Artificial Bee Colony (ABC) were proposed in learning MAX-kSAT programming. ABC is swarm-based metaheuristics that capitalized the capability of Employed Bee, Onlooker Bee, and Scout Bee. To this end, all the learning models were tested in a new restricted learning environment. Experimental results obtained from the computer simulation demonstrate the effectiveness of ABC in modelling MAX-kSAT.