We study several network design problems with degree constraints. For the degree-constrained 2-connected subgraph problem we obtain a factor 6 violation for the degrees with 4 approximation for the cost. This improves upon the logarithmic degree violation and no cost guarantee obtained by Feder, Motwani, and Zhu (2006). Then we consider the problem of finding an arborescence with at least k ter...

Split cuts constitute a class of cutting planes that has been successfully employed by the majority of Branch-and-Cut solvers for Mixed Integer Linear Programs. Given a basis of the LP relaxation and a split disjunction, the corresponding split cut can be computed with a closed form expression. In this paper, we use the Lift-and-Project framework [10] to provide the basis, and the Reduce-andSpl...

{(f1(x), . . . , fm(x)) : x ∈ T } for quadratic polynomials f0, . . . , fm and a subset T of R . This paper studies semidefinite representation of the convex hull conv(V ) or its closure, i.e., describing conv(V ) by projections of spectrahedra (defined by linear matrix inequalities). When T is defined by a single quadratic constraint, we prove that conv(V ) is equal to the first order moment t...

Introduction: A promising approach for the simultaneous quantification of proton density, T1 and T2 is the IR TrueFISP sequence proposed by Schmitt et al. [1]. This sequence consists of an inversion pulse followed by a series of TrueFISP acquisitions, observing a quasirelaxation towards the steady-state. However, this sequence requires a delay between individual segments in order to allow the m...

In order to understand the origin of stock price jumps, we crosscorrelate high-frequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and around news are quite different: jumps are followed by increased volatility, wher...

The spin-lattice relaxation times for the In isotope in liquid indium embedded into artificial opals and porous glass were found to be shortened remarkably compared to the bulk indium melt. The spin relaxation acceleration was ascribed mainly to the enhancement of the quadrupole contribution caused by the translational diffusion in liquid indium; the magnetic contribution was implied unchanged ...

A computational scheme for fitting smoothing spline ANOVA models to large data sets with a (near) tensor product design is proposed. Such data sets are common in spatial-temporal analyses. The proposed scheme uses the backfitting algorithm to take advantage of the tensor product design to save both computational memory and time. Several ways to further speed up the backfitting algorithm, such a...

The last twenty years have seen many attempts to calculate formation energies and formation volumes of vacancies and interstitials in facecentred cubic metals. (Johnson [l] has given an authoritative review; for recent developments see refs. [2,3] .) Judged by the effort spent, however, the progress achieved must be considered small. The majority of the model calculations on point-defects in Cu...

The Thesis is devoted to investigating the problem of computing the norm ‖A‖E,F = max x∈E:‖x‖E≤1 ‖Ax‖F of a linear mapping x 7→ Ax acting from a finite-dimensional normed space (E, ‖ · ‖E) to a finite-dimensional normed space (F, ‖ · ‖F ). This problem is important and interesting by its own right and especially due to its role in Robust Optimization. We mainly focus on the case where (E, ‖ · ‖...

We consider some generalizations of the Asymmetric Traveling Salesman Path problem. Suppose we have an asymmetric metric G = (V,A) with two distinguished nodes s, t ∈ V . We are also given a positive integer k. The goal is to find k paths of minimum total cost from s to t whose union spans all nodes. We call this the k-Person Asymmetric Traveling Salesmen Path problem (k-ATSPP). Our main result...