The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

SrAl4O7 : Eu2+ nanocrystals: synthesis and fluorescence properties

Divalent europium doped strontium di-aluminate (SrAl4O7 : Eu2+) nanocrystals have been synthesized using a facile sol–gel polymer thermolysis method. The photoluminescence characteristics of smaller particles (φ ∼ 15 nm) show a significant difference with respect to their bulk counterpart. In this nanocrystalline system, the electronic structure of the Eu2+ excited state seems to undergo considerable modification induced by the surface states involved in slow relaxation kinetics that mimic phosphorescence like features

Checking Progress with Action Priority: Is it Fair?

The liveness characteristics of a system are intimately related to the notion of fairness. However, the task of explicitly modelling fairness constraints is complicated in practice. To address this issue, we propose to check LTS (Labelled Transition System) models under a strong fairness assumption, which can be relaxed with the use of action priority. The combination of the two provides a novel and practical way of dealing with fairness. The approach is presented in the context of a class of liveness properties termed progress, for which it yields a particularly efficient modelchecking algorithm. Progress properties cover a wide range of interesting properties of systems, while presenting a clear intuitive meaning to users