On Elo based prediction models for the FIFA Worldcup 2018

We propose an approach for the analysis and prediction of a football championship. It is based on Poisson regression models that include the Elo points of the teams as covariates and incorporates differences of team-specific effects. These models for the prediction of the FIFA World Cup 2018 are fitted on all football games on neutral ground of the participating teams since 2010. Based on the model estimates for single matches Monte-Carlo simulations are used to estimate probabilities for reaching the different stages in the FIFA World Cup 2018 for all teams. We propose two score functions for ordinal random variables that serve together with the rank probability score for the validation of our models with the results of the FIFA World Cups 2010 and 2014. All models favor Germany as the new FIFA World Champion. All possible courses of the tournament and their probabilities are visualized using a single Sankey diagram.Comment: 22 pages, 7 figure

Branching Random Walks on Free Products of Groups

We study certain phase transitions of branching random walks (BRW) on Cayley graphs of free products. The aim of this paper is to compare the size and structural properties of the trace, i.e., the subgraph that consists of all edges and vertices that were visited by some particle, with those of the original Cayley graph. We investigate the phase when the growth parameter $\lambda$ is small enough such that the process survives but the trace is not the original graph. A first result is that the box-counting dimension of the boundary of the trace exists, is almost surely constant and equals the Hausdorff dimension which we denote by $\Phi(\lambda)$. The main result states that the function $\Phi(\lambda)$ has only one point of discontinuity which is at $\lambda_{c}=R$ where $R$ is the radius of convergence of the Green function of the underlying random walk. Furthermore, $\Phi(R)$ is bounded by one half the Hausdorff dimension of the boundary of the original Cayley graph and the behaviour of $\Phi(R)-\Phi(\lambda)$ as $\lambda \uparrow R$ is classified. In the case of free products of infinite groups the end-boundary can be decomposed into words of finite and words of infinite length. We prove the existence of a phase transition such that if $\lambda\leq \tilde\lambda_{c}$ the end boundary of the trace consists only of infinite words and if $\lambda>\tilde\lambda_{c}$ it also contains finite words. In the last case, the Hausdorff dimension of the set of ends (of the trace and the original graph) induced by finite words is strictly smaller than the one of the ends induced by infinite words.Comment: 39 pages, 4 figures; final version, accepted for publication in the Proceedings of LM

The Economic Growth Debate - Geography versus Institutions: Is There Anything Really New?

International analysis of economic growth has confirmed the theoretical assumption that international variations in per capita income can to a large extent be explained by differences in the accumulation of capital and human capital and by differing rates of technological progress. However, these results do not provide an answer to the question as to what causes trans-national variations in accumulation rates and technological progress. In searching for the ultimate drivers of economic growth, three competing lines of explanation have emerged: ? The geography-hypothesis which assumes that economic growth is ultimately determined by geographical characteristics ? The institutions-hypothesis which views the quality of institutions as a fundamental driver of growth ? The policy-hypothesis which emphasises the importance of economic policy This paper provides an overview over these three hypotheses and revisits the debate over their empirical relevance. Comparing the three approaches leads to the conclusion that none of them is really new and that many of their findings have already been incorporated into the strategies for international development assistance. Furthermore, the three hypotheses are not as exclusive as the debate on geography versus institutions would suggest but are indeed interconnected and complementary. --

Evaluating one-loop string amplitudes

We evaluate one-loop open-string amplitudes at finite $\alpha'$ for the first time. Our method involves a deformation of the integration contour over the modular parameter $\tau$ to a fractal contour introduced by Rademacher in the context of analytic number theory. This procedure leads to explicit and practical formulas for the one-loop four-point amplitudes in type-I superstring theory, amenable to numerical evaluation. We plot the amplitudes as a function of the Mandelstam invariants $s$ and $t$ and directly verify long-standing conjectures about their behaviour at high energies.Comment: 101 pages, many figure

A Novel Fenestration Technique for Abdominal Aortic Dissection Membranes Using a Combination of a Needle Re-entry Catheter and the "Cheese-wire” Technique

Purpose: This study was designed to demonstrate the applicability of a combined needle-based re-entry catheter and "cheese-wire” technique for fenestration of abdominal aortic dissection membranes. Methods: Four male patients (mean age: 65years) with acute complicated aortic type B dissections were treated at our institution by fenestrating the abdominal aortic dissection membrane using a hybrid technique. This technique combined an initial membrane puncture with a needle-based re-entry catheter using a transfemoral approach. A guidewire was passed through the re-entry catheter and across the membrane. Using a contralateral transfemoral access, this guidewire was then snared, creating a through-and-through wire access. The membrane was then fenestrated using the cheese-wire maneuver. Results: We successfully performed: (a) membrane puncture; (b) guidewire passage; (c) guidewire snaring; and (d) cheese-wire maneuver in all four cases. After this maneuver, decompression of the false lumen and acceptable arterial inflow into the true lumen was observed in all cases. The dependent visceral arteries were reperfused. In one case, portions of the fenestrated membrane occluded the common iliac artery, which was immediately and successfully stented. In another case, long-standing intestinal hypoperfusion before the fenestration resulted in reperfusion-related shock and intraoperative death of the patient. Conclusions: The described hybrid approach for fenestration of dissection membranes is technically feasible and may be established as a therapeutic method in cases with a complicated type B dissectio

Recent advances in crystalline and amorphous particulate protein formulations for controlled delivery

AbstractThe number of particulate delivery systems for biologics is negligible compared to liquid dosage forms, signifying the complications associated with development of solid protein delivery systems. Particulate protein delivery systems can improve stability, reduce viscosity of suspensions at high protein concentration and allow for controlled drug release. This review discusses current advances in controlled delivery of particulate protein formulations. While the focus lies on protein crystals and delivery systems employing protein crystals, amorphous protein particles will also be addressed. Crystallization and precipitations methods and modifications allowing controlled delivery with and without encapsulation are summarized and discussed