Local theory of projection methods for Cauchy singular integral equations on an interval

We consider a finite section (Galerkin) and a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polymoninals, where the coefficients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra techniques, where also the system case is mentioned. With the help of appropriate Sobolev spaces a result on convergence rates is proved. Computational aspects are discussed in order to develop an effective algorithm. Numerical results, also for a class of nonlinear singular integral equations, are presented

Local theory of a collocation method for Cauchy singular integral equations on an interval

We consider a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polynomials , where the coefficients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra methods, and numerical results are given

Assessment of reward-related brain function after a single-dose of oxytocin in autism: A randomized controlled trial

Background Autism spectrum disorder (ASD) is characterized by difficulties in social communication and interaction, which have been related to atypical neural processing of rewards, especially in the social domain. Since intranasal oxytocin has been shown to modulate activation of the brain’s reward circuit, oxytocin might ameliorate the processing of social rewards in ASD and thus improve social difficulties. Methods In this randomized, double-blind, placebo-controlled, crossover fMRI study, we examined effects of a 24 IU dose of intranasal oxytocin on reward-related brain function in 37 men with ASD without intellectual impairment and 37 age- and IQ-matched control participants. Participants performed an incentive delay task that allows the investigation of neural activity associated with the anticipation and receipt of monetary and social rewards. Results Non-significant tests suggested that oxytocin did not influence neural processes related to the anticipation of social or monetary rewards in either group. Complementary Bayesian analyses indicated moderate evidence for a null model, relative to an alternative model. Our results are inconclusive regarding possible oxytocin effects on amygdala responsiveness to social rewards during reward consumption. There were no significant differences in reward-related brain function between the two groups under placebo. Conclusions Our results do not support the hypothesis that intranasal oxytocin generally enhances activation of reward-related neural circuits in men with and without ASD