In daily life the brain is exposed to a large amount of external signals that compete for processing resources. The attentional system can select relevant information based on many possible combinations of goal-directed and stimulus-driven control signals. Here, we investigate the behavioral and physiological effects of competition between distinctive visual events during free-viewing of naturalistic videos. Nineteen healthy subjects underwent functional magnetic resonance imaging (fMRI) while viewing short video-clips of everyday life situations, without any explicit goal-directed task. Each video contained either a single semantically-relevant event on the left or right side (Lat-trials), or multiple distinctive events in both hemifields (Multi-trials). For each video, we computed a salience index to quantify the lateralization bias due to stimulus-driven signals, and a gaze index (based on eye-tracking data) to quantify the efficacy of the stimuli in capturing attention to either side. Behaviorally, our results showed that stimulus-driven salience influenced spatial orienting only in presence of multiple competing events (Multi-trials). fMRI results showed that the processing of competing events engaged the ventral attention network, including the right temporoparietal junction (R TPJ) and the right inferior frontal cortex. Salience was found to modulate activity in the visual cortex, but only in the presence of competing events; while the orienting efficacy of Multi-trials affected activity in both the visual cortex and posterior parietal cortex (PPC). We conclude that in presence of multiple competing events, the ventral attention system detects semantically-relevant events, while regions of the dorsal system make use of saliency signals to select relevant locations and guide spatial orienting.

A method of choice for the long-time integration of constrained Hamiltonian systems is the Rattle algorithm. It is symmetric, symplectic, and nearly preserves the Hamiltonian, but it is only of order two and thus not efficient for high accuracy requirements. In this article we prove that certain symmetric linear multistep methods have the same qualitative behavior and can achieve an arbitrarily high order with a computational cost comparable to that of the Rattle algorithm.

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