Communication cost of consensus for nodes with limited memory.

Motivated by applications in wireless networks and the Internet of Things, we consider a model of n nodes trying to reach consensus with high probability on their majority bit. Each node i is assigned a bit at time 0 and is a finite automaton with m bits of memory (i.e., [Formula: see text] states) and a Poisson clock. When the clock of i rings, i can choose to communicate and is then matched to a uniformly chosen node j. The nodes j and i may update their states based on the state of the other node. Previous work has focused on minimizing the time to consensus and the probability of error, while our goal is minimizing the number of communications. We show that, when [Formula: see text], consensus can be reached with linear communication cost, but this is impossible if [Formula: see text] A key step is to distinguish when nodes can become aware of knowing the majority bit and stop communicating. We show that this is impossible if their memory is too low.

Cortical representation of ipsilateral arm movements in monkey and man.

A fundamental organizational principle of the primate motor system is cortical control of contralateral limb movements. Motor areas also appear to play a role in the control of ipsilateral limb movements. Several studies in monkeys have shown that individual neurons in primary motor cortex (M1) may represent, on average, the direction of movements of the ipsilateral arm. Given the increasing body of evidence demonstrating that neural ensembles can reliably represent information with a high temporal resolution, here we characterize the distributed neural representation of ipsilateral upper limb kinematics in both monkey and man. In two macaque monkeys trained to perform center-out reaching movements, we found that the ensemble spiking activity in M1 could continuously represent ipsilateral limb position. Interestingly, this representation was more correlated with joint angles than hand position. Using bilateral electromyography recordings, we excluded the possibility that postural or mirror movements could exclusively account for these findings. In addition, linear methods could decode limb position from cortical field potentials in both monkeys. We also found that M1 spiking activity could control a biomimetic brain-machine interface reflecting ipsilateral kinematics. Finally, we recorded cortical field potentials from three human subjects and also consistently found evidence of a neural representation for ipsilateral movement parameters. Together, our results demonstrate the presence of a high-fidelity neural representation for ipsilateral movement and illustrates that it can be successfully incorporated into a brain-machine interface.