Some Mathematical Structures Underlying Efficient Planning

On the Foundations of Classical Planning: Some Algebraic and Topological Structures

This paper is an attempt to introduce mathematical structures for classical planning. It is rst shown that the set-based structures underlying classical planning are unable to build more than a monoid. Consequently, an appropriate structure is presented (that of the incidence algebra of a partial plan) and used to build the partial plan space as an algebraic eld. A vector space, an aane space a...

Multi-stage Stochastic Programming Models in Production Planning

Production planning is a key area of operations management. An important methodology for production planning is mathematical programming. Traditional mathematical programming models for production planning are deterministic, and cannot provide robust production plans in the presence of uncertainty. As such, deterministic planning models may yield unsatisfactory decisions. Stochastic programming...

[en-023] Mathematical Models for Aircraft Trajectory Design : a Survey

Air traffic management ensure the safety of flight by optimizing flows and maintaining separation between aircraft. After giving some definitions, some typical feature of aircraft trajectories are presented. Trajectories are objects belonging to spaces with infinite dimensions. The naive way to address such problem is to sample trajectories at some regular points and to create a big vector of p...

A Survey on Omega Polynomial of Some Nano Structures

Spaces in the Brain: From Neurons to Meanings

Spaces in the brain can refer either to psychological spaces, which are derived from similarity judgments, or to neurocognitive spaces, which are based on the activities of neural structures. We want to show how psychological spaces naturally emerge from the underlying neural spaces by dimension reductions that preserve similarity structures and the relevant categorizations. Some neuronal repre...