In planning with partially observable Markov decision processes, pre-compiled policies are often represented as finite state controllers or sets of alpha-vectors, which provide a lower bound on the value of the optimal policy. Some algorithms (e.g., HSVI2, SARSOP, GapMin) also compute an upper bound to guide the search and to offer performance guarantees, but they do not derive a policy from th...

In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the dual simplex method with the most negative pivoting rule for LP. The bound is comparable with the bound given by Kitahara and Mizuno (2010) for the primal simplex method. We apply the result to the maximum flow problem and get a strong polynomial bound.

stability of foundations near slopes is one of the important and complicated problems in geotechnical engineering, which has been investigated by various methods such as limit equilibrium, limit analysis, slip-line, finite element and discrete element. the complexity of this problem is resulted from the combination of two probable failures: foundation failure and overall slope failure. the curr...

it is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...

The band structure for a crystal generally consists of connected components in energy-momentum space, known as complexes. Here, we explore fundamental aspect regarding the maximal number bands that can be accommodated single complex. We show that, principle, complex have no finite upper bound certain space groups. This means infinitely many entangle together, forming pattern stable against symm...