We study solution sets to systems of generalized linear equations of the form ℓi(x1, x2, · · · , xn) ∈ Ai (mod m) where ℓ1, . . . , ℓt are linear forms in n Boolean var...
One can reduce the problem of proving that a polynomial is nonnegative, or more generally of proving that a system of polynomial inequalities has no solutions, to finding polynomi...
We study the intrinsic difficulty of solving linear parabolic initial value problems numerically at a single point. We present a worst case analysis for deterministic as well as fo...
We transform the outputs of each hidden neuron in a multi-layer perceptron network to have zero output and zero slope on average, and use separate shortcut connections to model th...
This paper analyzes and improves the linearized Bregman method for solving the basis pursuit and related sparse optimization problems. The analysis shows that the linearized Bregma...