We derive new cut-set bounds on the achievable rates in a general multi-terminal network with finite number of states. Multiple states are common in communication networks in the form of multiple channel and nodes’ states. Our results are broadly applicable and provide much tighter upper bounds than the known single state min-cut max-flow theorem, and hence form an important new tool to bound t...

In this study, the application of gray relational analysis (GRA) and Taguchi method in multi-criteria process parameters selection of turning operation has been investigated. The process responses under study are material removal rate (MRR) and surface roughness (SR); in turn, the input parameters include cutting speed, feed rate, depth of cut and nose radius of the cutting tool. The proposed a...

In this note, we present a simple geometric argument to determine a lower bound on the split rank of intersection cuts. As a first step of this argument, a polyhedral subset of the lattice-free convex set that is used to generate the intersection cut is constructed. We call this subset the restricted lattice-free set. It is then shown that dlog2(l)e is a lower bound on the split rank of the int...

Let [n] = {1, 2, . . . , n} and let 2 be the collection of all subsets of [n] ordered by inclusion. C ⊆ 2 is a cutset if it meets every maximal chain in 2, and the width of C ⊆ 2 is the minimum number of chains in a chain decomposition of C. Fix 0 ≤ m ≤ l ≤ n. What is the smallest value of k such that there exists a cutset that consists only of subsets of sizes between m and l, and such that it...