Limitations of the Hyperplane Separation Technique for Bounding the Extension Complexity of Polytopes

We illustrate the limitations of the hyperplane separation bound, a non-combinatorial lower bound on the extension complexity of a polytope. Most notably, this bounding technique is used by Rothvo{\ss} (J ACM 64.6:41, 2017) to establish an exponential lower bound for the perfect matching polytope. We point out that the technique is sensitive to the particular choice of slack matrix. For the canonical slack matrices of the spanning tree polytope and the completion time polytope, we show that the lower bounds produced by the hyperplane separation method are trivial. These bounds may, however, be strengthened by normalizing rows and columns of the slack matrices.Comment: 10 page

Organisational slack, corporate reputation and financial performance

This discussion paper aims to fill the gap left by the latest research on organisational slack that has been focused on emerging economies or on a single company or on a single industry. Senior executives’ perceptions that contribute to a measure of corporate reputation are tested as a proxy measure of unabsorbed slack. Disaggregating the components that make up reputation enables the perceptions of a company’s ‘ability to innovate’ and how efficiently they ‘use their corporate assets’ to also be tested as measures of unabsorbed, perceptual or discretionary slack. The impact of these variables is considered in terms of company performance

The Anomaly of U-3: Why the Unemployment Rate is Overstating the Strength of Today's Labor Market

By examining the historical relationship between the unemployment rate and alternative measures of labor market slack, it is determined that today's labor market has far more slack than is typically associated with an unemployment rate of 5.0 percent. It is therefore unlikely that the economy is at or near full employment

Approximate cone factorizations and lifts of polytopes

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 efficient representations using second order cones. We establish a direct relationship between the quality of the factorization and the quality of the approximations, and our results extend to generalized slack matrices that arise from a polytope contained in a polyhedron

The effect of contextual variables in the relationship between CSR and CFP: Evidence from Indonesian companies

The objectives of this study is to investigate whether business environment, business strategy, formalization, decentralization, reliance on combination of belief & boundary system, reliance on combination of diagnostic & interactive control system, reliance on interactive control system moderate the relationship between CSR and CFP under the slack resource and good management theories. 220 respondents from manufacturing companies listed on the Jakarta Stock Exchange were selected and two regression models were developed to examine the relationship between the related variables. The findings show that business environment has moderated the CSR-CFP link under good management theory, decentralization has moderated the CSR-CFP link under slack resource theory, and reliance on combination of diagnostic and interactive control system has moderated the CSR and CFP link based on slack resource theory

Inflation, slack, and Fed credibility

It is generally agreed that slack has some impact on inflation. There is much less agreement on what form the relationship takes and whether it is stable enough to reliably help predict inflation. This analysis focuses on the Great Moderation period. We find that slack (as measured by the unemployment rate) and changes in slack are negatively correlated with changes in inflation and also deviations of inflation from long-forward inflation expectations.> ; These relationships could have been exploited to produce forecasts of trimmed mean PCE inflation more accurate than rule-of-thumb forecasts. Forecasts of trimmed mean PCE inflation also serve well as predictions of GDP inflation and headline PCE inflation. Our analysis suggests that currently high levels of slack should hold inflation below two percent over 2012.Price levels ; Forecasting