Compressed sensing (or compressive sensing) refers to the recovery of high-dimensional
but low-complexity objects from a limited number of measurements. Two canonical …

We prove the cohomological version of the Sarnak-Xue Density Hypothesis for $ SO_5 $
over a totally real field and for inner forms split at all finite places. The proof relies on recent …

In their seminal paper, Lubotzky, Phillips and Sarnak (LPS) defined the notion of regular
Ramanujan graphs and gave an explicit construction of infinite families of $(p+ 1) $-regular …

We construct explicitly an infinite family of Ramanujan graphs which are bipartite and
biregular. Our construction starts with the Bruhat–Tits building of an inner form of SU 3 (ℚ p) …

Let $ G $ be a topological group acting on a simplicial complex $\mathcal {X} $ satisfying
some mild assumptions. For example, consider a $ k $-regular tree and its automorphism …

We prove that there exist bipartite, biregular Ramanujan graphs of every degree and every
number of vertices provided that the cardinalities of the two sets of the bipartition divide each …

The objectives of this article are threefold. Firstly, we present for the first time explicit
constructions of an infinite family of unbalanced Ramanujan bigraphs. Secondly, we revisit …

Graphs with large isoperimetric constants play an important role in cryptography because
one can utilize such graphs to construct cryptographic hash functions. Ramanujan graphs …

The objectives of this article are three-fold. Firstly, we present for the first time explicit
constructions of an infinite family of\textit {unbalanced} Ramanujan bigraphs. Secondly, we …

In this paper, we study the matrix completion problem: Suppose X∈ ℝ nr× nc is unknown
except for an upper bound r on its rank. By measuring a small number m≪ nrnc of elements …