On Lattice-Free Orbit Polytopes

Given a permutation group acting on coordinates of $\mathbb{R}^n$, we consider lattice-free polytopes that are the convex hull of an orbit of one integral vector. The vertices of such polytopes are called \emph{core points} and they play a key role in a recent approach to exploit symmetry in integer convex optimization problems. Here, naturally the question arises, for which groups the number of core points is finite up to translations by vectors fixed by the group. In this paper we consider transitive permutation groups and prove this type of finiteness for the $2$-homogeneous ones. We provide tools for practical computations of core points and obtain a complete list of representatives for all $2$-homogeneous groups up to degree twelve. For transitive groups that are not $2$-homogeneous we conjecture that there exist infinitely many core points up to translations by the all-ones-vector. We prove our conjecture for two large classes of groups: For imprimitive groups and groups that have an irrational invariant subspace.Comment: 27 pages, 2 figures; with minor adaptions according to referee comments; to appear in Discrete and Computational Geometr

Exploring core points for fun and profit: A study of lattice-free orbit polytopes

This thesis studies minimal lattice-free symmetric polytopes. Lattice-free means that the only integral points in the polytope are its vertices. Symmetric in context of the thesis means that all vertices lie in one single orbit under a group action. The thesis focuses on groups that are permutation groups acting on R^n by permuting coordinates. If a symmetric polytope is lattice-free, its vertices are called core points. Methods to construct core points and applications in symmetric integer linear programming are explored.Diese Arbeit behandelt gitterpunkt-freie symmetrische Polytope. Gitterpunkt-frei heißt, dass die Ecken des Polytops die einzigen enthaltenen ganzzahligen Punkte sind. Symmetrisch im Kontext dieser Arbeit meint, dass alle Ecken in einem einzigen Orbit einer Gruppenwirkung liegen. Diese Arbeit beschäftigt sich besonders mit Gruppen, die als Permutationsgruppen auf R^n wirken, indem sie Koordinaten permutieren. Die Ecken eines gitterpunkt-freien symmetrischen Polytops werden core points genannt. Es werden Methoden entwickelt, core points zu finden und in ganzzahliger Optimierung anzuwenden

Computing symmetry groups of polyhedra

Knowing the symmetries of a polyhedron can be very useful for the analysis of its structure as well as for practical polyhedral computations. In this note, we study symmetry groups preserving the linear, projective and combinatorial structure of a polyhedron. In each case we give algorithmic methods to compute the corresponding group and discuss some practical experiences. For practical purposes the linear symmetry group is the most important, as its computation can be directly translated into a graph automorphism problem. We indicate how to compute integral subgroups of the linear symmetry group that are used for instance in integer linear programming.Comment: 20 pages, 1 figure; containing a corrected and improved revisio

Inter-hospital transfer: the crux of the trauma system, a curse for trauma registries

The inter-hospital transfer of patients is crucial to a well functioning trauma system, and the transfer process may serve as a quality indicator for regional trauma care. However, the assessment of the transfer process requires high-quality data from various sources. Prospective studies and studies based on single-centre trauma registries may fail to capture an appropriate width and depth of data. Thus the creation of inclusive regional and national trauma registries that receive information from all of the services within a trauma system is a prerequisite for high quality inter-hospital transfer studies in the future.publishedVersio

Inter-hospital transfer: the crux of the trauma system, a curse for trauma registries

The inter-hospital transfer of patients is crucial to a well functioning trauma system, and the transfer process may serve as a quality indicator for regional trauma care. However, the assessment of the transfer process requires high-quality data from various sources. Prospective studies and studies based on single-centre trauma registries may fail to capture an appropriate width and depth of data. Thus the creation of inclusive regional and national trauma registries that receive information from all of the services within a trauma system is a prerequisite for high quality inter-hospital transfer studies in the future

Synaptophysin and synaptoporin expression in the developing rat olfactory system

The expressions of two closely related synaptic vesicle antigens synaptophysin and synaptoporin were examined in the olfactory system of the adult rat and during pre- and postnatal development. In the adult, immunocytochemistry showed that the continuously regenerating olfactory receptor neurons (primary neurons) produce both synaptophysin and synaptoporin which were localized in the cell bodies of the receptor neurons in the olfactory epithelium, their dendrites, axonal processes in the olfactory nerve and their terminals in the olfactory bulb glomeruli. Furthermore, ultrastructural analysis revealed synaptophysin- and synaptoporin-immunore activities associated with synaptic vesicles in most olfactory receptor axonal terminals impinging on dendrites of the mitral and tufted neurons (secondary neurons in the olfactory bulb circuitry) in the olfactory glomeruli. In like manner, tufted neurons, granule and periglomerular neurons (interneurons in the olfactory bulb circuitry) express both synaptophysin and synaptoporin. In contrast, mitral neurons expressed only the synaptophysin antigen which was likewise associated with mitral axonal terminals in their target the olfactory cortex. The patterns of synaptophysin and synaptoporin expressions in mitral neurons (synaptophysin only) and tufted neurons (synaptophysin and synaptoporin) were similar in prenatal, postnatal and adult rats as revealed by immunocytochemistry and in situ hybridization. However, the biosynthesis of synaptophysin and synaptoporin by granule and periglomerular neurons, olfactory bulb interneurons, occurred mainly postnatally

Trauma systems and early management of severe injuries in scandinavia: review and current status

publishedVersio