Sensitivity to switching rates in stochastically switched ODEs

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press.

The spatiotemporal dynamics of autobiographical memory: neural correlates of recall, emotional intensity, and reliving.

We sought to map the time course of autobiographical memory retrieval, including brain regions that mediate phenomenological experiences of reliving and emotional intensity. Participants recalled personal memories to auditory word cues during event-related functional magnetic resonance imaging (fMRI). Participants pressed a button when a memory was accessed, maintained and elaborated the memory, and then gave subjective ratings of emotion and reliving. A novel fMRI approach based on timing differences capitalized on the protracted reconstructive process of autobiographical memory to segregate brain areas contributing to initial access and later elaboration and maintenance of episodic memories. The initial period engaged hippocampal, retrosplenial, and medial and right prefrontal activity, whereas the later period recruited visual, precuneus, and left prefrontal activity. Emotional intensity ratings were correlated with activity in several regions, including the amygdala and the hippocampus during the initial period. Reliving ratings were correlated with activity in visual cortex and ventromedial and inferior prefrontal regions during the later period. Frontopolar cortex was the only brain region sensitive to emotional intensity across both periods. Results were confirmed by time-locked averages of the fMRI signal. The findings indicate dynamic recruitment of emotion-, memory-, and sensory-related brain regions during remembering and their dissociable contributions to phenomenological features of the memories.

Stability in autobiographical memories.

A total of 30 undergraduates recalled the same 20 autobiographical memories at two sessions separated by 2 weeks. At each session they dated their memories and rated them on 18 properties commonly studied in autobiographical memory experiments. Individuals showed moderate stability in their ratings on the 18 scales (r approximately .5), with consistency of dating being much higher (r = .96). There was more stability in the individuals' average rating on each scale (r approximately .8), even when the averages were calculated on different memories in the different sessions. The results are consistent with a constructive view of autobiographical memory, in which stable individual differences in cognitive style are important.