A new upper bound on the game chromatic index of graphs

We study the two-player game where Maker and Breaker alternately color the edges of a given graph $G$ with $k$ colors such that adjacent edges never get the same color. Maker's goal is to play such that at the end of the game, all edges are colored. Vice-versa, Breaker wins as soon as there is an uncolored edge where every color is blocked. The game chromatic index $\chi'_g(G)$ denotes the smallest $k$ for which Maker has a winning strategy. The trivial bounds $\Delta(G) \le \chi_g'(G) \le 2\Delta(G)-1$ hold for every graph $G$, where $\Delta(G)$ is the maximum degree of $G$. In 2008, Beveridge, Bohman, Frieze, and Pikhurko proved that for every $\delta>0$ there exists a constant $c>0$ such that $\chi'_g(G) \le (2-c)\Delta(G)$ holds for any graph with $\Delta(G) \ge (\frac{1}{2}+\delta)v(G)$, and conjectured that the same holds for every graph $G$. In this paper, we show that $\chi'_g(G) \le (2-c)\Delta(G)$ is true for all graphs $G$ with $\Delta(G) \ge C \log v(G)$. In addition, we consider a biased version of the game where Breaker is allowed to color $b$ edges per turn and give bounds on the number of colors needed for Maker to win this biased game.Comment: 17 page

Development of a prototype plastic space erectable satellite Quarterly report, Sep. - Nov. 1965

Test program for cap section mesh fabrication in prototype space erectable satellite developmen

Sampling Geometric Inhomogeneous Random Graphs in Linear Time

Real-world networks, like social networks or the internet infrastructure, have structural properties such as large clustering coefficients that can best be described in terms of an underlying geometry. This is why the focus of the literature on theoretical models for real-world networks shifted from classic models without geometry, such as Chung-Lu random graphs, to modern geometry-based models, such as hyperbolic random graphs. With this paper we contribute to the theoretical analysis of these modern, more realistic random graph models. Instead of studying directly hyperbolic random graphs, we use a generalization that we call geometric inhomogeneous random graphs (GIRGs). Since we ignore constant factors in the edge probabilities, GIRGs are technically simpler (specifically, we avoid hyperbolic cosines), while preserving the qualitative behaviour of hyperbolic random graphs, and we suggest to replace hyperbolic random graphs by this new model in future theoretical studies. We prove the following fundamental structural and algorithmic results on GIRGs. (1) As our main contribution we provide a sampling algorithm that generates a random graph from our model in expected linear time, improving the best-known sampling algorithm for hyperbolic random graphs by a substantial factor O(n^0.5). (2) We establish that GIRGs have clustering coefficients in {\Omega}(1), (3) we prove that GIRGs have small separators, i.e., it suffices to delete a sublinear number of edges to break the giant component into two large pieces, and (4) we show how to compress GIRGs using an expected linear number of bits.Comment: 25 page

The Optimal Intertemporal Management of the Soil and Phosphorus and the Equilibrium in Economic and Biophysical Models

The paper proposes the use of meta models to determine the optimal intertemporal management of soil and phosphorus losses from agricultural land. This approach allows finding a equilibrium of the economic and biophysical system simultaneously. In contrast to the existing literature the model takes account of nonlinear relationships and of a large number of agricultural activities. The mathematical problems arising from this complex setup are addressed and the model is solved numerically. The results show that the second best policy in form of soil protection scores is highly inefficient, while another second best policy in form of land-use taxes is nearly as efficient as the first best policy.Soil erosion, Phosphorus runoffs, Land-use tax, Soil protection scores, Dynamic optimization, Resource /Energy Economics and Policy,

Development of a prototype plastic space erectable satellite

Prototype erectable communications satellite of spherical design using plastic memory effec

Development of a prototype plastic space erectable satellite Quarterly report, Dec. 1965 - Feb. 1966

Plastic space erectable satellit

Introduction: The Fogarty International Research Ethics Education and Curriculum Development Program in Historical Context

In response to the increasing need for research ethics expertise in low and middle income countries (LMICs), the NIH's Fogarty International Research Ethics Education and Curriculum Development Program has provided grants for the development of training programs in international research ethics for LMIC professionals since 2000. This collection of papers draws upon the combined expertise of Fogarty grantees, trainees, and other experts to assess the state of research ethics in LMICs, and the lessons learned over 12 years of international research ethics education; to assess future needs; and to chart a way forward to meet those needs. In this introductory paper we briefly sketch the evolution of research ethics as applied to LMIC research, the underpinning and evolution of the Fogarty bioethics program, and summarize key conclusions from the other papers in the collection

An investigation of the basic properties of irradiated polyethylene memory materials

Properties of irradiated polyethylene memory material