This paper deals with mathematical programming based on predictive model. Prediction-based mathematical programming suffers from the problem that the calculated optimal value is biased in the direction suggesting optimistic results. This paper investigates this optimistic bias, and introduces two methods for correcting the bias.

One of the major topics in the structural rigidity theory is the rigidity of graphs, which concerns about the rigidity or the flexibility of abstract models of linkages, truss structures, and so on. This article is an introductory survey about the combinatorial aspect of graph rigidity.