Polynomiality for Bin Packing with a Constant Number of Item Types

We consider the bin packing problem with d different item sizes s_i and item multiplicities a_i, where all numbers are given in binary encoding. This problem formulation is also known as the 1-dimensional cutting stock problem. In this work, we provide an algorithm which, for constant d, solves bin packing in polynomial time. This was an open problem for all d >= 3. In fact, for constant d our algorithm solves the following problem in polynomial time: given two d-dimensional polytopes P and Q, find the smallest number of integer points in P whose sum lies in Q. Our approach also applies to high multiplicity scheduling problems in which the number of copies of each job type is given in binary encoding and each type comes with certain parameters such as release dates, processing times and deadlines. We show that a variety of high multiplicity scheduling problems can be solved in polynomial time if the number of job types is constant

The Commercial Music Industry in Atlanta and the State of Georgia: An Economic Impact Study

This study was prepared to ascertain the magnitude of the commercial music industry's economic impact on Atlanta and its surrounding areas. Report #8

Comments on lattice gauge theories with infrared-attractive fixed points

Theories of interacting gauge fields and fermions can possess a running gauge coupling with an infrared attractive fixed point (IRFP). We present a minimal description of the physics of these systems and comment on some simple expectations for results from lattice simulations done within the basin of attraction of the IRFP in these theories.Comment: 10 pages, 2 figures. Published version, fixed typos in version

Fault reactivation by fluid injection: Controls from stress state and injection rate

We studied the influence of stress state and fluid injection rate on the reactivation of faults. We conducted experiments on a saw-cut Westerly granite sample under triaxial stress conditions. Fault reactivation was triggered by injecting fluids through a borehole directly connected to the fault. Our results show that the peak fluid pressure at the borehole leading to reactivation depends on injection rate. The higher the injection rate, the higher the peak fluid pressure allowing fault reactivation. Elastic wave velocity measurements along fault strike highlight that high injection rates induce significant fluid pressure heterogeneities, which explains that the onset of fault reactivation is not determined by a conventional Coulomb law and effective stress principle, but rather by a nonlocal rupture initiation criterion. Our results demonstrate that increasing the injection rate enhances the transition from drained to undrained conditions, where local but intense fluid pressures perturbations can reactivate large faults