Multiplier methods based on augmented Lagrangians are attractive in convex and nonconvex programming for their stabilizing and even convexifying properties. They have widely been seen, however, as incompatible with taking advantage of a block-separable structure. In fact, when articulated in the right way, they can produce decomposition algorithms in which low-dimensional subproblems can be solved…

Modern data sets are often distributed across multiple machines and processors, and bandwidth and energy limitations in networks and within multiprocessor systems often impose significant bottlenecks on the performance of algorithms. Motivated by this trend, we consider the problem of estimating high-dimensional distributions and parameters in a distributed network, where each node in the network…

Computation in the brain has been modeled productively at many scales, ranging from molecules to dendrites, neurons, and synapses, all the way to the whole brain models useful in cognitive science. I will discuss recent work on an intermediate layer, involving assemblies of neurons --- that is to say, sets of neurons firing together in…