In this report we show, that an arbitrary MinSum problem (i.e. a MinSum problem with an arbitrary finite set of states) can be adequately transformed into a binary one (i.e. into a MinSum problem with only two states). Consequently all known results for binary MinSum problems can be easily extended to the general case. For instance it gives the possibility to solve exactly submodular MinSum pro...

The following equivalent results in the Boolean lattice 2 are proven. (a) Every fibre of 2 contains a maximal chain. (b) Every cutset of 2 contains a maximal antichain. (c) Every red-blue colouring of the vertices of 2 produces either a red maximal chain or a blue maximal antichain. (d) Given any n antichains in 2 there is a disjoint maximal antichain. Statement (a) is then improved to: (a') Ev...

It is well-know that the Chvátal-Gomory (CG) closure of a rational polyhedron is a rational polyhedron. In this paper, we show that the CG closure of a bounded full-dimensional ellipsoid, described by rational data, is a rational polytope. To the best of our knowledge, this is the first extension of the polyhedrality of the CG closure to a nonpolyhedral set. A key feature of the proof is to ver...

A set function is a function defined on a set family. It is said to be symmetric if the value for each set coincides with that for its complement. A cut capacity function of an undirected graph or hypergraph is a fundamental example of symmetric set functions, and is also submodular if the capacity on each edge or hyperedge is nonnegative. Fujishige and Patkar (2001) provided necessary and suff...

BACKGROUND AND STUDY AIMS With the success of peroral endoscopic myotomy (POEM) in treatment of achalasia, its successful application to other spastic esophageal motility disorders such as Jackhammer esophagus has been noted. The question of whether the lower esophageal sphincter (LES) should be included in the myotomy for Jackhammer esophagus is a topic of current debate. Here, we report our e...

We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family P is affinely reduced to a family Q if for every pol...

The traditional adaptive cruise system is responsible for delay in recognizing the cut-in/cut-out behaviour of front vehicle, and there significant longitudinal acceleration vehicle fluctuation leading to reduced driver’s comfort level even dangerous situation. In this paper, next generation simulation data set back propagation (BP) neural network are used train lane change recognition model re...