The limit space of a Cauchy sequence of globally hyperbolic spacetimes

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In the second section, I work gradually towards a construction of the limit space. I prove the limit space is unique up to isometry. I als show that, in general, the limit space has quite complicated causal behaviour. This work prepares the final paper in which I shall study in more detail properties of the limit space and the moduli space of (compact) globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this paper a suitable definition of dimension of a Lorentz space in agreement with the one given by Gromov in the Riemannian case.Comment: 31 pages, 5 figures, submitted to Classical and Quantum gravity, seriously improved presentatio

Applications of Abundance Data and Requirements for Cosmochemical Modeling

Understanding the evolution of the universe from Big Bang to its present state requires an understanding of the evolution of the abundances of the elements and isotopes in galaxies, stars, the interstellar medium, the Sun and the heliosphere, planets and meteorites. Processes that change the state of the universe include Big Bang nucleosynthesis, star formation and stellar nucleosynthesis, galactic chemical evolution, propagation of cosmic rays, spallation, ionization and particle transport of interstellar material, formation of the solar system, solar wind emission and its fractionation (FIP/FIT effect), mixing processes in stellar interiors, condensation of material and subsequent geochemical fractionation. Here, we attempt to compile some major issues in cosmochemistry that can be addressed with a better knowledge of the respective element or isotope abundances. Present and future missions such as Genesis, Stardust, Interstellar Pathfinder, and Interstellar Probe, improvements of remote sensing instrumentation and experiments on extraterrestrial material such as meteorites, presolar grains, and lunar or returned planetary or cometary samples will result in an improved database of elemental and isotopic abundances. This includes the primordial abundances of D, ^3He, ^4He, and ^7Li, abundances of the heavier elements in stars and galaxies, the composition of the interstellar medium, solar wind and comets as well as the (highly) volatile elements in the solar system such as helium, nitrogen, oxygen or xenon

Insecurity for compact surfaces of positive genus

A pair of points in a riemannian manifold $M$ is secure if the geodesics between the points can be blocked by a finite number of point obstacles; otherwise the pair of points is insecure. A manifold is secure if all pairs of points in $M$ are secure. A manifold is insecure if there exists an insecure point pair, and totally insecure if all point pairs are insecure. Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds. We prove this for surfaces of genus greater than zero. We also prove that a closed surface of genus greater than one with any riemannian metric and a closed surface of genus one with generic metric are totally insecure.Comment: 37 pages, 11 figure

Gemcitabine and Docetaxel for Epithelioid Sarcoma: Results from a Retrospective, Multi-Institutional Analysis

Objective: Epithelioid sarcoma (ES) presents unique clinical features in comparison to other sarcoma subtypes. Data regarding the benefits of chemotherapy are very limited. Combination regimens using gemcitabine and docetaxel (Gem/Doce) have proven to be effective, especially in uterine and nonuterine leiomyosarcoma. Yet, there is no available data on the efficacy of Gem/Doce in ES. Methods: A retrospective analysis of the three participating institutions was performed. Twenty-eight patients with an ES diagnosis presented at one of the participating institutions between 1989 and 2012. Of this group, 17 patients received chemotherapy. Results: Patients' median overall survival (OS) after the beginning of palliative chemotherapy was 21 months, and the 1-year OS was 87%. Twelve patients received Gem/Doce with a clinical benefit rate of 83%. The median progression-free survival (PFS) was 8 months for all patients receiving Gem/Doce. The best response was complete remission in 1 patient and partial remission in 6 patients. All 6 patients receiving Gem/Doce as a first-line treatment showed measurable responses with a median PFS of 9 months. Conclusions: In this retrospective study, Gem/Doce was an effective chemotherapeutic regimen for ES. Prospective studies are needed to better assess the effects of this combination drug therapy

Postoperative Immune Suppression in Visceral Surgery: Characterisation of an Intestinal Mouse Model

Background: Postoperatively acquired immune dysfunction is associated with a higher mortality rate in case of septic complications. As details of this severe clinical problem are still unknown, animal models are essential to characterise the mechanisms involved. Methods: Mice were laparotomised and the small intestine was pressed smoothly in antegrade direction. For extension of trauma, the intestine was manipulated three times consecutively. Following this, the ex vivo cytokine release of splenocytes was determined. The degree of surgical trauma was analysed by detection of HMGB1 and IL-6 in serum and by neutrophil staining in the muscularis mucosae. Results: We adapted the previously described animal model of intestinal manipulation to provide a model of surgically induced immune dysfunction. Following intestinal manipulation, the mice showed elevated serum levels of HMGB1 and IL-6 and increased infiltration of granulocytes into the muscularis mucosae. Ex vivo cytokine release by splenocytes was suppressed in the postoperative period. The degree of suppression correlated with the extent of surgical trauma. Conclusions: In this study, we describe a surgically induced immune dysfunction animal model, in which a significant surgical trauma is followed by an immune dysfunction. This model may be ideal for the characterisation of the postoperative immune dysfunction syndrome

On the computation of zone and double zone diagrams

Classical objects in computational geometry are defined by explicit relations. Several years ago the pioneering works of T. Asano, J. Matousek and T. Tokuyama introduced "implicit computational geometry", in which the geometric objects are defined by implicit relations involving sets. An important member in this family is called "a zone diagram". The implicit nature of zone diagrams implies, as already observed in the original works, that their computation is a challenging task. In a continuous setting this task has been addressed (briefly) only by these authors in the Euclidean plane with point sites. We discuss the possibility to compute zone diagrams in a wide class of spaces and also shed new light on their computation in the original setting. The class of spaces, which is introduced here, includes, in particular, Euclidean spheres and finite dimensional strictly convex normed spaces. Sites of a general form are allowed and it is shown that a generalization of the iterative method suggested by Asano, Matousek and Tokuyama converges to a double zone diagram, another implicit geometric object whose existence is known in general. Occasionally a zone diagram can be obtained from this procedure. The actual (approximate) computation of the iterations is based on a simple algorithm which enables the approximate computation of Voronoi diagrams in a general setting. Our analysis also yields a few byproducts of independent interest, such as certain topological properties of Voronoi cells (e.g., that in the considered setting their boundaries cannot be "fat").Comment: Very slight improvements (mainly correction of a few typos); add DOI; Ref [51] points to a freely available computer application which implements the algorithms; to appear in Discrete & Computational Geometry (available online

Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds

We apply compensated convex transforms to define a multiscale Hausdorff stable method to extract intersections between smooth compact manifolds represented by their characteristic functions or as point clouds embedded in Rn. We prove extraction results on intersections of smooth compact manifolds and for points of high curvature. As a result of the Hausdorff–Lipschitz continuity of our transforms, we show that our method is stable against dense sampling of smooth manifolds with noise. Examples of explicitly calculated prototype models for some simple cases are presented, which are also used in the proofs of our main results. Numerical experiments in two- and three-dimensional space, and applications to geometric objects are also shown

Surgical Trauma and Postoperative Immune Dysfunction

Background: In postoperative sepsis, mortality is increased due to the surgically induced immune dysfunction. Further causes of this traumatic effect on the immune system include burn injuries and polytrauma, as well as endogenous traumata like stroke. Several animal models have been defined to analyse the characteristics of trauma-induced immune suppression. This article will correlate our results from animal studies and clinical observations with the recent literature on postoperative immune suppression. Methods: The previously described model of surgically induced immune dysfunction (SID) was performed in mice by laparotomy and manipulation of the small intestine in the antegrade direction. Blood samples were collected 6 and 72 h following SID to analyse the white blood cell count and corticosterone levels. To assess the postoperative immune status in humans, we analysed expression of HLA-DR on monocytes of 118 patients by flow cytometry prior to and 24, 48 and 72 h after surgery. Results: The postoperative immune suppression in our SID model is characterised by lymphocytopenia and significantly increased corticosterone levels in mice dependent on the degree of surgical trauma. This is comparable to the postoperative situation in humans: major and especially long-lasting surgery results in a significantly reduced expression of HLA-DR on circulating monocytes. Previous studies describe a similar situation following burn injury and endogenous trauma, i.e. stroke. Conclusions: We suggest the completion of our previously published sepsis classification due to the immune status at the onset of sepsis: type A as the spontaneously acquired sepsis and type B as sepsis in trauma-induced pre-existing immune suppression

The moduli space of isometry classes of globally hyperbolic spacetimes

This is the last article in a series of three initiated by the second author. We elaborate on the concepts and theorems constructed in the previous articles. In particular, we prove that the GH and the GGH uniformities previously introduced on the moduli space of isometry classes of globally hyperbolic spacetimes are different, but the Cauchy sequences which give rise to well-defined limit spaces coincide. We then examine properties of the strong metric introduced earlier on each spacetime, and answer some questions concerning causality of limit spaces. Progress is made towards a general definition of causality, and it is proven that the GGH limit of a Cauchy sequence of $\mathcal{C}^{\pm}_{\alpha}$, path metric Lorentz spaces is again a $\mathcal{C}^{\pm}_{\alpha}$, path metric Lorentz space. Finally, we give a necessary and sufficient condition, similar to the one of Gromov for the Riemannian case, for a class of Lorentz spaces to be precompact.Comment: 29 pages, 9 figures, submitted to Class. Quant. Gra