Smart grids are re-engineering the electricity transmission and distribution system
throughout the world. It is an amalgam of increased digital information with the electrical …

We show how to extend several basic concentration inequalities for simple random tensors
X=x_1⊗⋯⊗x_d where all x_k are independent random vectors in R^n with independent …

Consider a distributed computing setup consisting of a master node and n worker nodes,
each equipped with p cores, and a function f (x)= g (f 1 (x), f 2 (x),..., fk (x)), where each fi can …

Numerical evaluations of the memory capacity (MC) of recurrent neural networks reported in
the literature often contradict well-established theoretical bounds. In this paper, we study the …

For a random matrix of entries sampled independently from a fairly general distribution in ZZ
we study the probability that the cokernel is isomorphic to a given finite abelian group, or …

We develop a unified approach to bounding the largest and smallest singular values of an
inhomogeneous random rectangular matrix, based on the non-backtracking operator and …

Let M n be an n× n random matrix with independent and identically distributed Bernoulli (p)
entries. We show that there is a universal constant C≥ 1 such that, whenever p and n satisfy …

Let d≥ 3 be a fixed integer, and let A be the adjacency matrix of a random d-regular directed
or undirected graph on n vertices. We show that there exists a constant d> 0 such that P (A is …

For a class of sparse random matrices of the form A n=(ξ i, j δ i, j) i, j= 1 n where {ξ i, j} are iid
centered sub-Gaussian random variables of unit variance, and {δ i, j} are iid Bernoulli …

A simple way to generate a Boolean function is to take the sign of a real polynomial in n
variables. Such Boolean functions are called polynomial threshold functions. How many low …