The n-step mixed integer rounding (MIR) inequalities of Kianfar and Fathi (Math Program 120(2):313–346, 2009) are valid inequalities for the mixedinteger knapsack set that are derived by using periodic n-step MIR functions and define facets for group problems. The mingling and 2-step mingling inequalities of Atamtürk and Günlük (Math Program 123(2):315–338, 2010) are also derived based on MIR a...

Mixed-integer rounding (MIR) is a simple, yet powerful procedure for generating valid inequalities for mixed-integer programs. When used as cutting planes, MIR inequalities are very effective for mixed-integer programming problems with unbounded integer variables. For problems with bounded integer variables, however, cutting planes based on lifting techniques appear to be more effective. This i...

Many macro systems, especially for Lisp and Scheme, allow macro transformers to perform general computation. Moreover, the language for implementing compile-time macro transformers is usually the same as the language for implementing run-time functions. As a side effect of this sharing, implementations tend to allow the mingling of compile-time values and run-time values, as well as values from...

Some people perceive colours when they hear words--a phenomenon known as synaesthesia. Brain imaging techniques have revealed the areas of the cortex involved in this rare mingling of the senses.