To motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately log n= log logn with high probability.1 Now suppose instead that the balls are placed sequentiall...

Herbicides are the main type of pesticides causing water contamination. The chloroacetanilide herbicide Smetolachlor is frequently detected in ground and surface waters, and represents a potential source of water pollution. The addition of organic residues to soils to reduce losses of organic pollutants constitutes sometimes an efficient method to control contamination. One of the recent techno...

Distributed voting is a fundamental topic in distributed computing. In the standard model of pull voting, in each step every vertex chooses a neighbour uniformly at random, and adopts the opinion of that neighbour. The voting is said to be completed when all vertices hold the same opinion. On many graph classes including regular graphs, irrespective of the expansion properties, pull voting requ...

We consider the problem of phase retrieval from corrupted magnitude observations. In particular we show that a fixed x0 ∈ Rn can be recovered exactly from corrupted magnitude measurements |〈ai, x0〉|+ ηi, i = 1, 2 . . . m with high probability for m = O(n), where ai ∈ Rn are i.i.d standard Gaussian and η ∈ Rm has fixed sparse support and is otherwise arbitrary, by using a version of the PhaseMax...

The directionality of millimeter-wave (mmWave) communications creates a significant challenge in serving fast-moving mobile terminals on, e.g., high-speed vehicles, trains, and UAVs. This challenge is exacerbated in mmWave systems using analog antenna arrays, because of the inherent non-convexity in the control of the phase shifters. In this paper, we develop a recursive beam tracking algorithm...