Inverse theorem in dynamic programming I

Approximate Dynamic Programming I: Modeling

Stochastic optimization problems pose unique challenges in how they are represented mathematically. These problems arise in a number of different communities, often in the context of problems that introduce specific computational characteristics. As a result, a number of contrasting notational styles have evolved, which complicate our ability to communicate research across communities. This is ...

Dynamic Programming I Parallel and Sequential Data

“An interesting question is, ’Where did the name, dynamic programming, come from?’ The 1950s were not good years for mathematical research. We had a very interesting gentleman in Washington named Wilson. He was Secretary of Defense, and he actually had a pathological fear and hatred of the word, research. I’m not using the term lightly; I’m using it precisely. His face would suffuse, he would t...

Declarative Dynamic Programming as an Alternative Realization of Courcelle's Theorem

Many computationally hard problems become tractable if the graph structure underlying the problem instance exhibits small treewidth. A recent approach to put this idea into practice is based on a declarative interface to specify dynamic programming over tree decompositions, delegating the computation to dedicated solvers. In this paper, we prove that this method can be applied to any problem wh...

Theorem Proving and Programming with Dynamic First Order Logic

An Inverse Spectral Theorem

We prove a substantial extension of an inverse spectral theorem of Ambarzumyan, and show that it can be applied to arbitrary compact Riemannian manifolds, compact quantum graphs and finite combinatorial graphs, subject to the imposition of Neumann (or Kirchhoff) boundary conditions.