It is well known that the convergence of Gaussian belief propagation (BP) is not guaranteed in loopy graphs. The classical convergence conditions, including diagonal dominance, walk-summability, and convex decomposition, are derived under pairwise factorizations of the joint Gaussian distribution. However, many applications run Gaussian BP under high-order factorizations, making the classical results not applicable.

Spike estimation from calcium (Ca 2+ ) fluorescence signals is a fundamental and challenging problem in neuroscience. Several models and algorithms have been proposed for this task over the past decade. Nevertheless, it is still hard to achieve accurate spike positions from the Ca 2+ fluorescence signals. While existing methods rely on data-driven methods and the physiology of neurons for modeling the spiking process, this paper exploits the nature of the fluorescence responses to spikes using signal processing.

This paper introduces a node-asynchronous communication protocol in which an agent in a network wakes up randomly and independently, collects states of its neighbors, updates its own state, and then broadcasts back to its neighbors. This protocol differs from consensus algorithms and it allows distributed computation of an arbitrary eigenvector of the network, in which communication between agents is allowed to be directed.

In this paper, we study the problem of recovering a group sparse vector from a small number of linear measurements. In the past, the common approach has been to use various “group sparsity-inducing” norms such as the Group LASSO norm for this purpose. By using the theory of convex relaxations, we show that it is also possible to use 1 -norm minimization for group sparse recovery.