Switching between two concurrent tasks is an important ability of the mind. In a series of two experiments, we explored the role of activation (arousal and subjective significance) and emotional valence in shaping the effectiveness of switching between two cognitive tasks: gender-marking and emotional categorisations of verbal stimuli. We expected arousal to disrupt and subjective significance to boost the effectiveness of cognitive switching. We employed a paradigm that allowed us to present emotional words and measure the reaction latencies when a task given to the participants was switched; thus, the response was more costly than when continuing to respond to the same task. The first experiment, conducted with neutral words, showed that high subjective significance reduced reaction latencies in comparison with medium subjective significance. The second experiment showed a similar pattern only for neutral stimuli in the emotional categorisation task, but not for negative and positive stimuli. We did not find a clear effect of arousal or valence. The results of our studies suggest that subjective significance is independent of arousal in enhancing the cognitive control resources.

Much research on language control in bilinguals has relied on the interpretation of the costs of switching between two languages. Of the two types of costs that are linked to language control, switching costs are assumed to be transient in nature and modulated by trial-specific manipulations (e.g., by preparation time), while mixing costs are supposed to be more stable and less affected by trial-specific manipulations. The present study investigated the effect of preparation time on switching and mixing costs, revealing that both types of costs can be influenced by trial-specific manipulations.

In this paper we study systems of weakly coupled Hamilton-Jacobi equations with implicit obstacles that arise in optimal switching problems. Inspired by methods from the theory of viscosity solutions and weak $\text{KAM}$ theory, we extend the notion of Aubry set for these systems. This enables us to prove a new result on existence and uniqueness of solutions for the Dirichlet problem, answering a question of F. Camilli, P. Loreti, and N. Yamada.

A collection of jobs is to be processed by a single machine. The amount of processing required by each job is a random variable with a known probability distribution. The jobs must be processed in a manner which is consistent with a precedence relation but the machine is free to switch from one job to another at any time; such switches are costly, however. This paper discusses conditions under which there is an optimal strategy for allocating the machine to the jobs which is given by a fixed permutation of the jobs indicating in which order they should be processed. When this is so, existing algorithms may be helpful in giving the best job ordering.