Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Infinite Transitivity on Affine Varieties

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

Fetal programming of pulmonary vascular dysfunction in mice: role of epigenetic mechanisms.

Insults during the fetal period predispose the offspring to systemic cardiovascular disease, but little is known about the pulmonary circulation and the underlying mechanisms. Maternal undernutrition during pregnancy may represent a model to investigate underlying mechanisms, because it is associated with systemic vascular dysfunction in the offspring in animals and humans. In rats, restrictive diet during pregnancy (RDP) increases oxidative stress in the placenta. Oxygen species are known to induce epigenetic alterations and may cross the placental barrier. We hypothesized that RDP in mice induces pulmonary vascular dysfunction in the offspring that is related to an epigenetic mechanism. To test this hypothesis, we assessed pulmonary vascular function and lung DNA methylation in offspring of RDP and in control mice at the end of a 2-wk exposure to hypoxia. We found that endothelium-dependent pulmonary artery vasodilation in vitro was impaired and hypoxia-induced pulmonary hypertension and right ventricular hypertrophy in vivo were exaggerated in offspring of RDP. This pulmonary vascular dysfunction was associated with altered lung DNA methylation. Administration of the histone deacetylase inhibitors butyrate and trichostatin A to offspring of RDP normalized pulmonary DNA methylation and vascular function. Finally, administration of the nitroxide Tempol to the mother during RDP prevented vascular dysfunction and dysmethylation in the offspring. These findings demonstrate that in mice undernutrition during gestation induces pulmonary vascular dysfunction in the offspring by an epigenetic mechanism. A similar mechanism may be involved in the fetal programming of vascular dysfunction in humans.

Local Stereology of Tensors of Convex Bodies

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝ d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ℝ3, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.

A mixed-integer linear programming approach to the optimization of event-bus schedules: a scheduling application in the tourism sector

This paper deals with “The Enchanted Journey,” which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations in Switzerland; moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour. For operational reasons, however, two or more buses cannot stay at the same location simultaneously. Further operative constraints include time windows for all activities and precedence constraints between some activities. The planning problem is how to compute a feasible schedule for each bus. We implement a two-step hierarchical approach. In the first step, we minimize the total waiting time; in the second step, we minimize the total travel time of all buses. We present a basic formulation of this problem as a mixed-integer linear program. We enhance this basic formulation by symmetry-breaking constraints, which reduces the search space without loss of generality. We report on computational results obtained with the Gurobi Solver. Our numerical results show that all relevant problem instances can be solved using the basic formulation within reasonable CPU time, and that the symmetry-breaking constraints reduce that CPU time considerably.

A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method

We present a novel approach to the reconstruction of depth from light field data. Our method uses dictionary representations and group sparsity constraints to derive a convex formulation. Although our solution results in an increase of the problem dimensionality, we keep numerical complexity at bay by restricting the space of solutions and by exploiting an efficient Primal-Dual formulation. Comparisons with state of the art techniques, on both synthetic and real data, show promising performances.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Index Tracking Using Data-Mining Techniques and Mixed-Binary Linear Programming

Index tracking has become one of the most common strategies in asset management. The index-tracking problem consists of constructing a portfolio that replicates the future performance of an index by including only a subset of the index constituents in the portfolio. Finding the most representative subset is challenging when the number of stocks in the index is large. We introduce a new three-stage approach that at first identifies promising subsets by employing data-mining techniques, then determines the stock weights in the subsets using mixed-binary linear programming, and finally evaluates the subsets based on cross validation. The best subset is returned as the tracking portfolio. Our approach outperforms state-of-the-art methods in terms of out-of-sample performance and running times.