Interactions of multiple rhythms in a biophysical network of neurons.

Neural oscillations, including rhythms in the beta1 band (12-20 Hz), are important in various cognitive functions. Often neural networks receive rhythmic input at frequencies different from their natural frequency, but very little is known about how such input affects the network's behavior. We use a simplified, yet biophysical, model of a beta1 rhythm that occurs in the parietal cortex, in order to study its response to oscillatory inputs. We demonstrate that a cell has the ability to respond at the same time to two periodic stimuli of unrelated frequencies, firing in phase with one, but with a mean firing rate equal to that of the other. We show that this is a very general phenomenon, independent of the model used. We next show numerically that the behavior of a different cell, which is modeled as a high-dimensional dynamical system, can be described in a surprisingly simple way, owing to a reset that occurs in the state space when the cell fires. The interaction of the two cells leads to novel combinations of properties for neural dynamics, such as mode-locking to an input without phase-locking to it.

Parietal low beta rhythm provides a dynamical substrate for a working memory buffer.

Working memory (WM) is a component of the brain's memory systems vital for interpretation of sequential sensory inputs and consequent decision making. Anatomically, WM is highly distributed over the prefrontal cortex (PFC) and the parietal cortex (PC). Here we present a biophysically detailed dynamical systems model for a WM buffer situated in the PC, making use of dynamical properties believed to be unique to this area. We show that the natural beta1 rhythm (12 to 20 Hz) of the PC provides a substrate for an episodic buffer that can synergistically combine executive commands (e.g., from PFC) and multimodal information into a flexible and updatable representation of recent sensory inputs. This representation is sensitive to distractors, it allows for a readout mechanism, and it can be readily terminated by executive input. The model provides a demonstration of how information can be usefully stored in the temporal patterns of activity in a neuronal network rather than just synaptic weights between the neurons in that network.

Make-or-Break: Chasing Risky Goals or Settling for Safe Rewards?

Humans regularly pursue activities characterized by dramatic success or failure outcomes where, critically, the chances of success depend on the time invested working toward it. How should people allocate time between such make-or-break challenges and safe alternatives, where rewards are more predictable (e.g., linear) functions of performance? We present a formal framework for studying time allocation between these two types of activities, and we explore optimal behavior in both one-shot and dynamic versions of the problem. In the one-shot version, we illustrate striking discontinuities in the optimal time allocation policy as we gradually change the parameters of the decision-making problem. In the dynamic version, we formulate the optimal strategy-defined by a giving-up threshold-which adaptively dictates when people should stop pursuing the make-or-break goal. We then show that this strategy is computationally inaccessible for humans, and we explore boundedly rational alternatives. We compare the performance of the optimal model against (a) a myopic giving-up threshold that is easier to compute, and even simpler heuristic strategies that either (b) only decide whether or not to start pursuing the goal and never give up or (c) consider giving up at a fixed number of control points. Comparing strategies across environments, we investigate the cost and behavioral implications of sidestepping the computational burden of full rationality.