Extended Formulations for Packing and Partitioning Orbitopes

We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in (Kaibel and Pfetsch, 2008). These polytopes are the convex hulls of all 0/1-matrices with lexicographically sorted columns and at most, resp. exactly, one 1-entry per row. They are important objects for symmetry reduction in certain integer programs. Using the extended formulations, we also derive a rather simple proof of the fact that basically shifted-column inequalities suffice in order to describe those orbitopes linearly.Comment: 16 page

On largest volume simplices and sub-determinants

We show that the problem of finding the simplex of largest volume in the convex hull of $n$ points in $\mathbb{Q}^d$ can be approximated with a factor of $O(\log d)^{d/2}$ in polynomial time. This improves upon the previously best known approximation guarantee of $d^{(d-1)/2}$ by Khachiyan. On the other hand, we show that there exists a constant $c>1$ such that this problem cannot be approximated with a factor of $c^d$, unless $P=NP$. % This improves over the $1.09$ inapproximability that was previously known. Our hardness result holds even if $n = O(d)$, in which case there exists a \bar c\,^{d}-approximation algorithm that relies on recent sampling techniques, where $\bar c$ is again a constant. We show that similar results hold for the problem of finding the largest absolute value of a subdeterminant of a $d\times n$ matrix

Extension complexity of stable set polytopes of bipartite graphs

The extension complexity $\mathsf{xc}(P)$ of a polytope $P$ is the minimum number of facets of a polytope that affinely projects to $P$. Let $G$ be a bipartite graph with $n$ vertices, $m$ edges, and no isolated vertices. Let $\mathsf{STAB}(G)$ be the convex hull of the stable sets of $G$. It is easy to see that $n \leqslant \mathsf{xc} (\mathsf{STAB}(G)) \leqslant n+m$. We improve both of these bounds. For the upper bound, we show that $\mathsf{xc} (\mathsf{STAB}(G))$ is $O(\frac{n^2}{\log n})$, which is an improvement when $G$ has quadratically many edges. For the lower bound, we prove that $\mathsf{xc} (\mathsf{STAB}(G))$ is $\Omega(n \log n)$ when $G$ is the incidence graph of a finite projective plane. We also provide examples of $3$-regular bipartite graphs $G$ such that the edge vs stable set matrix of $G$ has a fooling set of size $|E(G)|$.Comment: 13 pages, 2 figure

Cargo Integration

This paper discusses aspects of cargo integration as applied to the shuttle transportation system and is intended to familiarize the STS user with the applicable, significant features of the integration process. The development of the mixed cargo carrying capability and extended orbit time of the STS has introduced a variety of new aspects to the processing and integration of cargos at the launch and landing site. STS cargo integration and flight operations dictate that the integration process for each cargo validates compliance with the established requirements. All payloads assigned to fly in the shuttle orbiter as cargo must be designed to fit the cargo bay envelope, and each must conform to the STS capabilities and limitations as described in the STSprovided standard handbooks and user guides

Valutazioni sperimentali di probabilità di occorrenza dei terremoti utilizzando metodologie non parametriche applicate a zonazioni diverse

In 2003 a new building code for Italy has been released. Subsequently a new seismic hazard reference map of Italy (MPS04) have been compiled for definition of seismic zones. In order to define priority area for any short-term policy in loss reduction in Italy, different approach have been followed and compared. One of this approach is based on the clustered feature of the earthquake occurrence for events greater than M5.5, according to the Proportional Hazard Model. The analysis of the distribution of large events is composed by several ingredients. In fact, besides the statistical distribution of events, the catalogue and the zonation play an important role. In this work the same input data used for the MPS04 have been introduced in the model, in order to investigate its sensitivity and the stability of the results and to check the influence into the probability distribution of factors like the catalogues, the zonations and the magnitude-temporal completeness. Then, the predictive ability of this model has been tested and compared to the one of the Poisson distribution, which is used in standard hazard analysis. The results show the same pattern for earthquake occurrence in all the applications, indicating a cluster properties for earthquake occurrence. The cluster characteristic, in terms of time duration and intensity, may change adopting a different catalogue, but it is not significantly influenced by the three zonations adopted in the test

Regression analysis of MCS Intensity and ground motion parameters in Italy and its application in ShakeMap

In Italy, the Mercalli-Cancani-Sieberg, MCS, is the intensity scale in use to describe the level of earthquake ground shaking, and its subsequent effects on communities and on the built environment. This scale differs to some extent from the Mercalli Modified scale in use in other countries and adopted as standard within the USGS-ShakeMap procedure to predict intensities from observed instrumental data. We have assembled a new PGM/MCS-intensity data set from the Italian database of macroseismic information, DBMI04, and the Italian accelerometric database, ITACA. We have determined new regression relations between intensities and PGM parameters (acceleration and velocity). Since both PGM parameters and intensities suffer of consistent uncertainties we have used the orthogonal distance regression technique. The new relations are IMCS = 1.68 ± 0.22 + 2.58 ± 0.14 log P GA, σ = 0.35 and IMCS = 5.11 ± 0.07 + 2.35 ± 0.09 log P GV , σ = 0.26. Tests designed to assess the robustness of the estimated coefficients have shown that single-line parameterizations for the regression are sufficient to model the data within the model uncertainties. The relations have been inserted in the Italian implementation of the USGS-ShakeMap to determine intensity maps from instrumental data and to determine PGM maps from the sole intensity values. Comparisons carried out for earthquakes where both kinds of data are available have shown the general effectiveness of the relations