The literature on sparse recovery often adopts the “norm” ( ) as the penalty to induce sparsity of the signal satisfying an underdetermined linear system. The performance of the corresponding minimization problem can be characterized by its null space constant. In spite of the NP-hardness of computing the constant, its properties can still help in illustrating the performance of minimization. I...

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a b...

Abstract—In system identification of structured models, the prediction error method provides asymptotically efficient estimates under mild assumptions, but in general it requires solving a non-convex optimization problem. An alternative class of methods uses a non-parametric model as intermediate step to obtain the model of interest. The weighted null-space fitting (WNSF) method belongs to this...

In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems arise, e.g., from the outer convexification of integer control decisions. We treat this optimal control problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using sequen...

A uniqueness theorem for Minkowski space and de Sitter space associated with the occurrence of null lines (inextendible globally achronal null geodesics) is presented. This result is obtained as a consequence of the null splitting theorem, which is also discussed.

In a randomized experiment with noncompliance, scientific interest is often in testing whether the treatment exposure X has an effect on the final outcome Y [2, 1]. We have proposed a finite-population significance test of the sharp null hypothesis that X has no effect on Y , within the principal stratum of compliers, using a generalized likelihood ratio test [4]. As both the null and alternati...