For many types of learning, spaced training, which involves repeated long inter-trial intervals, leads to more robust memory formation than does massed training, which involves short or no intervals. Several cognitive theories have been proposed to explain this superiority, but only recently have data begun to delineate the underlying cellular and molecular mechanisms of spaced training, and we review these theories and data here. Computational models of the implicated signalling cascades have predicted that spaced training with irregular inter-trial intervals can enhance learning. This strategy of using models to predict optimal spaced training protocols, combined with pharmacotherapy, suggests novel ways to rescue impaired synaptic plasticity and learning.
Learning and memory are influenced by the temporal pattern of training stimuli. The mechanisms that determine the effectiveness of a particular training protocol are not well understood, however. The hypothesis that the efficacy of a protocol is determined, in part, by interactions among biochemical cascades that underlie learning and memory was examined. Previous studies suggest that the PKA and ERK cascades are necessary to induce long-term synaptic facilitation (LTF) in Aplysia, a neuronal correlate of memory. A computational model of the PKA and ERK cascades was developed, and used the model to identify a novel training protocol that maximized PKA/ERK interactions. In vitro studies confirmed that the protocol enhanced LTF. Moreover, the protocol enhanced levels of phosphorylation of the transcription factor CREB1. Behavioral training confirmed that long-term memory also was enhanced by the protocol. These results illustrate the feasibility of using computational models to design training protocols that improve memory.
The MAPK isoforms ERK and p38 MAPK are believed to play opposing roles in long-term synaptic facilitation (LTF) induced by serotonin (5-HT) in Aplysia. To fully understand their roles, however, it is necessary to consider the dynamics of ERK and p38 MAPK activation. Previous studies determined that activation of ERK occurred ∼45 min after a 5-min pulse of 5-HT treatment. The dynamics of p38 MAPK activation following 5-HT are yet to be elucidated. Here, the activity of p38 MAPK was examined at different times after 5-HT, and the interaction between the ERK and p38 MAPK pathways was investigated. A 5-min pulse of 5-HT induced a transient inhibition of p38 MAPK, followed by a delayed activation between 25 and 45 min. This activation was blocked by a MAPK kinase inhibitor, suggesting that similar pathways are involved in activation of ERK and p38 MAPK. ERK activity decreased shortly after the activation of p38 MAPK. A p38 MAPK inhibitor blocked this decrease in ERK activity, suggesting a causal relationship. The p38 MAPK activity ∼45 min after different stimulus protocols was also characterized. These data were incorporated into a computational model for the induction of LTF. Simulations and empirical data suggest that p38 MAPK, together with ERK, contributes to the efficacy of spaced stimulus protocols to induce LTF, a correlate of long-term memory (LTM). For example, decreased p38 MAPK activity ∼45 min after the first of two sensitizing stimuli might be an important determinant of an optimal interstimulus interval (ISI) for LTF induction.
For the problem of prediction with expert advice in the adversarial setting with geometric stopping, we compute the exact leading order expansion for the long time behavior of the value function. Then, we use this expansion to prove that as conjectured in Gravin et al. [12], the comb strategies are indeed asymptotically optimal for the adversary in the case of 4 experts.
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