In the previous lecture, we introduced linear programming using slack form, and we showed how to solve an LP assuming that we have a black box for solving an LP starting from a feasible solution (SimplexInner). In this lecture, we would present SimplexInner. Slack form-a tuple (N, B, A, b, c, v) is an LP. The feasible solution is generated by assigning all the Nonbasic variables the value zero....

Bus schedules cannot be easily maintained on busy lines with short headways: Experience shows that buses offering this type of service usually arrive irregularly at their stops, often in bunches. Although transit agencies build slack into their schedules to alleviate this problem, their attempts often fail because practical amounts of slack cannot prevent large localized disruptions from spread...

Recent research into the problem of jointly scheduling tasks with both hard and soft time constraints has focused on the development of optimal slack stealing algorithms. Theoretically, these optimal algorithms offer significant performance improvements over previous bandwidth preserving algorithms such as the Sporadic Server or Extended Priority Exchange algorithm. However, there are problems ...

In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral lifts of a polytope are controlled by (exact) nonnegative factorizations of its slack matrix. Our approximations behave well under polarity and have efficien...

The Slack and Slick genes encode potassium channels that are very widely expressed in the central nervous system. These channels are activated by elevations in intracellular sodium, such as those that occur during trains of one or more action potentials, or following activation of non-selective cationic neurotransmitter receptors such as AMPA receptors. This review covers the cellular and molec...

The pressing demands of improving energy efficiency for high performance scientific computing have motivated a large body of software-controlled hardware solutions that strategically switch hardware components to a low-power state, when the peak performance of the components is not necessary. Although OS level solutions can effectively save energy in a black-box fashion, for applications with r...

In this work, we derive second-order optimality conditions for nonlinear semidefinite programming (NSDP) problems, by reformulating it as an ordinary nonlinear programming problem using squared slack variables. We first consider the correspondence between Karush-Kuhn-Tucker points and regularity conditions for the general NSDP and its reformulation via slack variables. Then, we obtain a pair of...

Virtual “slack” strings are designed for and employed by the Laptop Orchestra of Louisiana. These virtual strings are “slack” in the sense that they can be very easily displaced, bent, tugged upon, etc. This enables force-feedback control of widely ranging pitch glides, by as much as an octave or more, simply by bending the virtual string. To realize a slack string design, a virtual spring with...

Though the logical correctness of an asynchronous circuit is independent of implementation delays, the cycle time of an asynchronous circuit is of great importance to the designer. Oftentimes, the insertion of buffers to such circuits reduces the cycle time of the circuit without affecting the logical correctness of the circuit. This optimization is called slack matching. In this thesis the sla...

We aimed to investigate the joint effect of type incentive and stakeholder on acceptance budgetary slack examine rankings five needs in Maslow’s pyramid. Using experimental research we demonstrated that motivational interacted affect slack. Management accountants experiencing non-monetary incentives a situation where internal stakeholders’ expectations can be met with slack, showed highest Resp...