We examine primitive roots modulo the Fermat number Fm = 2 2m + 1. We show that an odd integer n ≥ 3 is a Fermat prime if and only if the set of primitive roots modulo n is equal to the set of quadratic non-residues modulo n. This result is extended to primitive roots modulo twice a Fermat number.
In this paper, a necessity measure optimization model of linear programming problems with fuzzy oblique vectors is discussed. It is shown that the problems are reduced to linear fractional programming problems. Utilizing a special structure of the reduced problem, we propose a solution algorithm based on Bender's decomposition. A numerical example is given.
The telecommunication and Ethernet trafic prediction problem is studied. Network traffic prediction is an important problem of telecommunication and Ethernet congestion control and network management. In order to improve network traffic prediction accuracy, a network traffic hybrid prediction model was proposed by using the advantages of grey model and Elman neural network, grey model and Elman neural network predictive values were independently obtained, the different weight coefficients of two prediction models were given. In terms of weight coefficients optimization, an improved harmony search algorithm with better convergence speed and accuracy was proposed, the optimal weight coefficients of network traffic hybrid prediction model were determined through this algorithm, two prediction models results were multiplied by the weight coefficients to obtain the final prediction value. The network traffic sample data from an actual telecommunication network was collected as simulation object. The simulation results verified that the proposed network traffic hybrid prediction model based on improved harmony search algorithm has higher prediction accuracy.
This study aimed to determine grip strength data for Turkish dentistry students and developed prediction models that allow: i) investigation of the relationship between grip strength and hand anthropometry using artificial neural networks (ANNs) and stepwise regression analysis, ii) prediction of the grip strength of Turkish dentistry students, and iii) assessment of the potential impact of hand anthropometric variables on grip strength. The study included 153 right-handed dentistry students, consisting of 81 males and 72 females. From 44 anthropometric and biomechanical measurements obtained from the right hands of the participants; five anthropometric measurements were selected for ANN and regression modeling using stepwise regression analysis. We included stepwise regression analysis results to assess the predictive power of the neural network approach, in comparison to a classical statistical approach. When the model accuracy was calculated based on the coefficient of determination (R2), the root mean squared error (RMSE) and the mean absolute error (MAE) values for each of the models, ANN showed greater predictive accuracy than regression analysis, as demonstrated by experimental results. For the best performing ANN model, the testing values of the models correlated well with actual values, with a coefficient of determination (R2) of 0.858. Using the best performing ANN model, sensitivity analysis was applied to determine the effects of hand dimensions on grip strength and to rank these dimensions in order of importance. The results suggest that the three most sensitive input variables are the forearm length, the hand breadth and the finger circumference at the first joint of digit 5 and that the ANNs are promising techniques for predicting hand grip strength based on hand breadth, finger breadth, hand length, finger circumference and forearm length.
We propose a neural network approach for global optimization with applications to nonlinear least square problems. The center idea is defined by the algorithm that is developed from neural network learning. By searching in the neighborhood of the target trajectory in the state space, the algorithm provides the best feasible solution to the optimization problem. The convergence analysis shows that the convergence of the algorithm to the desired solution is guaranteed. Our examples show that the method is effective and accurate. The simplicity of this new approach would provide a good alternative in addition to statistics methods for power regression models with large data.
Genetic algorithms (GAs) are stochastic methods that are widely used in search and optimization. The breeding process is the main driving mechanism for GAs that leads the way to find the global optimum. And the initial phase of the breeding process starts with parent selection. The selection utilized in a GA is effective on the convergence speed of the algorithm. A GA can use different selection mechanisms for choosing parents from the population and in many applications the process generally depends on the fitness values of the individuals. Artificial neural networks (ANNs) are used to decide the appropriate parents by the new hybrid algorithm proposed in this study. And the use of neural networks aims to produce better offspring during the GA search. The neural network utilized in this algorithm tries to learn the structural patterns and correlations that enable two parents to produce high-fit offspring. In the breeding process, the first parent is selected based on the fitness value as usual. Then it is the neural network that decides the appropriate mate for the first parent chosen. Hence, the selection mechanism is not solely dependent on the fitness values in this study. The algorithm is tested with seven benchmark functions. It is observed from results of these tests that the new selection method leads genetic algorithm to converge faster.