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In this study, effects of high-order interactions on synchronization of the fractional-order Hindmarsh–Rose neuron models have been examined deeply. Three different network situations in which first-order coupling, high-order couplings and first-plus second-order couplings included in the neuron models, have been considered, respectively. In order to find the optimal values of the first- and high-order coupling parameters by minimizing the cost function resulted from pairwise and triple interactions, the particle swarm optimization algorithm is employed. It has been deduced from the numerical simulation results that the first-plus second-order couplings induce the synchronization with both reduced first-order coupling strength and total cost compared to the first-order coupled case solely. When the only first-order coupled case is compared with the only second-order coupled case, it is determined that the neural network with only second-order couplings involved could achieve synchronization with lower coupling strength and, as a natural result, lower cost. On the other hand, solely second- and first-plus second-order coupled networks give very similar results each other. Therefore, high-order interactions have a positive effect on the synchronization. Additionally, increasing the network size decreases the values of the both first- and high-order coupling strengths to reach synchronization. However, in this case, total cost should be kept in the mind. Decreasing the fractional order parameter causes slower synchronization due to the decreased frequency of the neural response. On the other hand, more synchronous network is possible with increasing the fractional order parameter. Thus, the neural network with higher fractional order as well as high-order coupled is a good candidate in terms of the neural synchronization. [ABSTRACT FROM AUTHOR]

For many classification problems, in addition to providing accurate classification results, very often it is equally important to determine which predictors are contributing to the results, and by how much. This motivates this article, where a new sensitivity analysis framework is developed for classification problems to address this issue. The effectiveness of this framework is illustrated through simulation studies and application to real data. Notice that this framework can be coupled with different classification methods. However, in practice it is recommended to pair it with a classification method called Bayesian smoothing spline ANOVA probit regression (BSSANOVA). When compared with other existing methods through numerical experiments, BSSANOVA performs extremely well for both classification and sensitivity analysis. [ABSTRACT FROM AUTHOR]

Background: Most preference-based instruments producing overall values for health states are devised on the simplifying assumption that the overall effect of distinct health-related quality of life domains (attributes) of the instrument equals the sum of the attributes. Nevertheless, health attributes are often inter-related and depend on each other.Objectives: To investigate whether inclusion of second-order interactions in the three-level EuroQol five-dimensional questionnaire (EQ-5D-3L) value function would result in better fit and lead to different health state values than a model with main effects only.Methods: Using an efficient design, 400 pairs of EQ-5D-3L health states were generated in a pairwise choice format. We analyzed responses of 4000 people from the general population using a conditional logit model, and we tested goodness of fit using pseudo R2, Akaike information criterion, differences in log-likelihood, and likelihood ratio. We compared accuracies of models' predictions based on root mean square error and mean absolute error.Results: The interaction-effects model showed systematically lower values than the main-effects model. Inclusion of interactions resulted only in a slightly better model fit. Interactions comprising mobility and self-care were the most salient.Conclusions: For the EQ-5D-3L, a value function based on interactions produces systematically lower values than a main-effects model, meaning that the effect of two or more health problems combined is stronger than the sum of the individual main effects. [ABSTRACT FROM AUTHOR]

Methoxy-ρ-benzoquinone (MBQ) and 2, 6-dimethoxy-ρ-benzoquinone (DMBQ) are two potential anticancer compounds in fermented wheat germ. In present study, modeling and optimization of added macronutrients, microelements, vitamins for producing MBQ and DMBQ was investigated using artificial neural network (ANN) combined with genetic algorithm (GA). A configuration of 16-11-1 ANN model with Levenberg-Marquardt training algorithm was applied for modeling the complicated nonlinear interactions among 16 nutrients in fermentation process. Under the guidance of optimized scheme, the total contents of MBQ and DMBQ was improved by 117% compared with that in the control group. Further, by evaluating the relative importance of each nutrient in terms of the two benzoquinones’ yield, macronutrients and microelements were found to have a greater influence than most of vitamins. It was also observed that a number of interactions between nutrients affected the yield of MBQ and DMBQ remarkably. [ABSTRACT FROM AUTHOR]

A new method for the simulation of nonlinear processes of sum-frequency generation (SFG), difference-frequency generation (DFG) and cascaded SFG/DFG (cSFG/DFG) in complex periodically poled lithium niobate (PPLN) gratings for continuous wave signals is proposed and numerically validated. It is based on the transfer matrix method and shows better performance in comparison with traditional numerical solving methods of ordinary differential equations, in particular when nonuniform PPLN are considered. In addition, a Fourier transform method to compute SFG, DFG, cSFG/DFG, and also some cascaded second-harmonic generation/difference-frequency generation interactions of modulated signals is presented. This new algorithm considerably decreases the computing time in comparison with well-known finite-differences methods. [ABSTRACT FROM PUBLISHER]

In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions ensuring the local exponential stability of 2^N equilibrium points are derived. Secondly, some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region. Thirdly, the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the SOCNNs can have (r+1)^N locally exponentially stable equilibrium points. Even if there is no second-order interactions, the obtained results are less restrictive than those in some recent works. Finally, three examples with their simulations are presented to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

The occurrence of significant second-order interactions for group characteristics was examined using real data in a randomized controlled trial (RCT). The interactions exist in all RCTs; they could be easily overlooked when using the simple randomization or stratification methods, but could become more obvious when minimization methods are used. Using real data from an RCT, the minimization method enabled balancing the distributions of the four selected stratified factors. Analyses for three-way second-order interactions including six additional potential confounding variables (for a total of 10 variables) presented 8 significant second-order interactions with the treatment groups. Interaction effects need to be evaluated when treatment effects are examined to maximize the power of the treatment effects in any RCTs. A stepwise regression method with piecewise linear functions would be useful to select the significant variables with interaction effects affecting the treatment outcomes in RCTs. Additional ways to handle interaction effects in RCTs are presented in this paper. [Copyright &y& Elsevier]