The title of this session pitting Dynamic Programming against Control Theory is misleading since dynamic programming (DP) is an integral part of the discipline of control theory. However, it is timely to discuss the relative merits of DP and other empirical solution approaches to control problems in agricultural economics, and equally importantly, how control theory can be used to pose more use...

General relativity (GR) is a covariant theory of gravity on curved spacetime (general covariance) which, however, denies a covariant Hamiltonian. Most alternative works of gravity on flat spacetime present non-covariant Lagrangians which treat time t as a parameter entirely distinct from the spatial coordinates. A covariant formulation would require that space and time be considered as entirely...

Abstract. A sign-linear one bit map from the d-dimensional sphere S to the n-dimensional Hamming cube H = {−1,+1}n is given by x 7→ {sign(x · zj) : 1 ≤ j ≤ n} where {zj} ⊂ S. For 0 < δ < 1, we estimate N(d, δ), the smallest integer n so that there is a sign-linear map which has the δ-restricted isometric property, where we impose normalized geodesic distance on S, and Hamming metric on H. Up to...

The general problem of reconstructing an unknown function from a finite collection of samples is considered, in case the position of each input vector in the training set is not fixed beforehand, but is part of the learning process. In particular, the consistency of the Empirical Risk Minimization (ERM) principle is analyzed, when the points in the input space are generated by employing a purel...

1 Discrepancy principle for the dynamical systems method Abstract Assume that Au = f, (1) is a solvable linear equation in a Hilbert space, ||A|| < ∞, and R(A) is not closed, so problem (1) is ill-posed. Here R(A) is the range of the linear operator A. A DSM (dynamical systems method) for solving (1), consists of solving the following Cauchy problem: ˙ u = −u + (B + (t)) −1 A * f, u(0) = u 0 , ...

Straightforward solution of discrete ill-posed least-squares problems with errorcontaminated data does not, in general, give meaningful results, because propagated error destroys the computed solution. Error propagation can be reduced by imposing constraints on the computed solution. A commonly used constraint is the discrepancy principle, which bounds the norm of the computed solution when app...