Counting Hamilton cycles in sparse random directed graphs

Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if $p\ge(\log n+\omega(1))/n$ then D(n,p) typically has a directed Hamilton cycle, and this is best possible. In this paper, we obtain a strengthening of this result, showing that under the same condition, the number of directed Hamilton cycles in D(n,p) is typically $n!(p(1+o(1)))^{n}$. We also prove a hitting-time version of this statement, showing that in the random directed graph process, as soon as every vertex has in-/out-degrees at least 1, there are typically $n!(\log n/n(1+o(1)))^{n}$ directed Hamilton cycles

The universal K3 surface of genus 14 via cubic fourfolds

Using the isomorphism between the moduli space of polarized K3 surfaces of genus 14 and the moduli space of special cubic fourfolds of discriminant 26, we establish the rationality of the universal K3 surface of genus 14. Precisely, we show that the universal K3 surface of genus 14 is a projective bundle over a certain moduli space of nodal scrolls in P^5, whose rationality we prove using a degenerate version of Mukai's structure theorem for curves of genus 8.Comment: 20 pages. Final version, to appear in the Journal de Mathematiques Pures et Appliquee

Sustainable seabed mining: guidelines and a new concept for Atlantis II Deep

The feasibility of exploiting seabed resources is subject to the engineering solutions, and economic prospects. Due to rising metal prices, predicted mineral scarcities and unequal allocations of resources in the world, vast research programmes on the exploration and exploitation of seabed minerals are presented in 1970s. Very few studies have been published after the 1980s, when predictions were not fulfilled. The attention grew back in the last decade with marine mineral mining being in research and commercial focus again and the first seabed mining license for massive sulphides being granted in Papua New Guinea’s Exclusive Economic Zone.Research on seabed exploitation and seabed mining is a complex transdisciplinary field that demands for further attention and development. Since the field links engineering, economics, environmental, legal and supply chain research, it demands for research from a systems point of view. This implies the application of a holistic sustainability framework of to analyse the feasibility of engineering systems. The research at hand aims to close this gap by developing such a framework and providing a review of seabed resources. Based on this review it identifies a significant potential for massive sulphides in inactive hydrothermal vents and sediments to solve global resource scarcities. The research aims to provide background on seabed exploitation and to apply a holistic systems engineering approach to develop general guidelines for sustainable seabed mining of polymetallic sulphides and a new concept and solutions for the Atlantis II Deep deposit in the Red Sea.The research methodology will start with acquiring a broader academic and industrial view on sustainable seabed mining through an online survey and expert interviews on seabed mining. In addition, the Nautilus Minerals case is reviewed for lessons learned and identification of challenges. Thereafter, a new concept for Atlantis II Deep is developed that based on a site specific assessment.The research undertaken in this study provides a new perspective regarding sustainable seabed mining. The main contributions of this research are the development of extensive guidelines for key issues in sustainable seabed mining as well as a new concept for seabed mining involving engineering systems, environmental risk mitigation, economic feasibility, logistics and legal aspects

Business Cycles, Exchange Rates, and Commodity Prices in Transition Economies

My dissertation studies macroeconomic connectedness in the transition economies through the business cycle and exchange rate channels and the downside risk relationship between commodity prices and exchange rates of developing economies. My first two chapters focus on the transition economies of the Commonwealth of Independent States, the CIS, a group of former Soviet republics, and my third chapter considers other developing countries too. The first chapter examines macroeconomic connectedness in the CIS region through business cycle synchronization. I investigate the role of the global factor and the CIS factor in evolution of business cycles in the CIS countries by applying a dynamic factor model. In addition I also examine whether the role of these two factors has changed over time. Results indicate that overall business cycle synchronization of these countries within the region and globally is low. Russia is the most globally integrated CIS country and Belarus displays the highest degree of comovement with the CIS factor. The results show that 2014 Russo-Ukrainian conflict and subsequent Russian sanctions had a profound effect on the region leading to an increase in synchronization within the CIS and decline in the role of the global factor. The second chapter estimates macroeconomic connectedness in the CIS countries through risk spillovers via the exchange rates. I collect high frequency daily data on exchange rates from January 2006 to July 2020 and use the Diebold-Yilmaz method of variance decomposition, as well as the Barunik-Krehlik method of frequency variance decomposition, for the analysis. I find that macroeconomic risk in the region has maintained a higher average level since 2015, a difficult year full of regional and global challenges. Currencies managed by more flexible exchange rate regimes (the Euro, Russian ruble, Armenian dram, Georgian lari, Ukranian hryvnia) on average transmit risk in the region. Time-frequency decomposition signifies that while the majority of risk transmission is smaller-scale and short-lived, spillovers from main regional and global crises are bigger and more persistent. The third chapter evaluates the impact of commodity price changes on the exchange rate changes for developing countries that are major exporters of selected globally important commodities. In particular, I focus on the tail behavior of this relationship since extreme events often have undesirable macroeconomic consequences such as inflationary pressure. I achieve this by estimating quantile regressions and subsequently using them to calculate tail risk measures of expected shortfall and longrise. My findings show that commodity price changes are negatively impactful on the exchange rate changes during depreciation episodes. Moreover, tail risk magnitudes have increased since the Great Recession. The results obtained in this chapter show that commodity dependent economies have been exposed to more macroeconomic risk through the exchange rate channel and that commodity price changes could be an associated signal of downside risk to exchange rate changes