The Price of Anarchy for Selfish Ring Routing is Two

We analyze the network congestion game with atomic players, asymmetric strategies, and the maximum latency among all players as social cost. This important social cost function is much less understood than the average latency. We show that the price of anarchy is at most two, when the network is a ring and the link latencies are linear. Our bound is tight. This is the first sharp bound for the maximum latency objective.Comment: Full version of WINE 2012 paper, 24 page

A simulation method for the wetting dynamics of liquid droplets on deformable membranes

Biological cells utilize membranes and liquid-like droplets, known as biomolecular condensates, to structure their interior. The interaction of droplets and membranes, despite being involved in several key biological processes, is so far little understood. Here, we present a first numerical method to simulate the continuum dynamics of droplets interacting with deformable membranes via wetting. The method combines the advantages of the phase-field method for multi-phase flow simulation and the arbitrary Lagrangian-Eulerian (ALE) method for an explicit description of the elastic surface. The model is thermodynamically consistent, coupling bulk hydrodynamics with capillary forces, as well as bending, tension, and stretching of a thin membrane. The method is validated by comparing simulations for single droplets to theoretical results of shape equations, and its capabilities are illustrated in 2D and 3D axisymmetric scenarios

On Linear Congestion Games with Altruistic Social Context

We study the issues of existence and inefficiency of pure Nash equilibria in linear congestion games with altruistic social context, in the spirit of the model recently proposed by de Keijzer {\em et al.} \cite{DSAB13}. In such a framework, given a real matrix $\Gamma=(\gamma_{ij})$ specifying a particular social context, each player $i$ aims at optimizing a linear combination of the payoffs of all the players in the game, where, for each player $j$, the multiplicative coefficient is given by the value $\gamma_{ij}$. We give a broad characterization of the social contexts for which pure Nash equilibria are always guaranteed to exist and provide tight or almost tight bounds on their prices of anarchy and stability. In some of the considered cases, our achievements either improve or extend results previously known in the literature

Extended Smoothed Boundary Method for Solving Partial Differential Equations with General Boundary Conditions on Complex Boundaries

In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original differential equations such that the equations are solved in the region where a domain parameter takes a specified value while boundary conditions are imposed on the region where the value of the domain parameter varies smoothly across a short distance. The mathematical derivations are straightforward and generically applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples herein: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions; (2) the diffusion equation with both surface diffusion and reaction; (3) the mechanical equilibrium equation; and (4) the equation for phase transformation with the presence of additional boundaries. The solutions for several of these cases are validated against corresponding analytical and semi-analytical solutions. The potential of the approach is demonstrated with five applications: surface-reaction-diffusion kinetics with a complex geometry, Kirkendall-effect-induced deformation, thermal stress in a complex geometry, phase transformations affected by substrate surfaces, and a self-propelled droplet.Comment: This document is the revised version of arXiv:0912.1288v

Greek diminutives in Gothic

Investigation of the outcomes of Greek diminutive nouns in the Gothic New Testament reveals a variety of translation strategies. The Gothic Version does not automatically carry over a word’s diminutive character. Most cases of Greek diminutives translated with Gothic diminutives are part of a Gothic pattern, centred on children. In other cases, the usual range of Gothic translation decisions are found, ranging from subtle discriminations to elisions of distinction.PostprintPeer reviewe

Evaluation of the uncertainty in an EBT3 film dosimetry system utilizing net optical density

Radiochromic film has become an important tool to verify dose distributions for intensity-modulated radiotherapy (IMRT) and quality assurance (QA) procedures. A new radiochromic film model, EBT3, has recently become available, whose composition and thickness of the sensitive layer are the same as those of previous EBT2 films. However, a matte polyester layer was added to EBT3 to prevent the formation of Newton’s rings. Furthermore, the symmetrical design of EBT3 allows the user to eliminate side-orientation dependence. This film and the flatbed scanner, Epson Perfection V750, form a dosimetry system whose intrinsic characteristics were studied in this work. In addition, uncertainties associated with these intrinsic characteristics and the total uncertainty of the dosimetry system were determined. The analysis of the response of the radiochromic film (net optical density) and the fitting of the experimental data to a potential function yielded an uncertainty of 2.6%, 4.3%, and 4.1% for the red, green, and blue channels, respectively. In this work, the dosimetry system presents an uncertainty in resolving the dose of 1.8% for doses greater than 0.8 Gy and less than 6 Gy for red channel. The films irradiated between 0 and 120 Gy show differences in the response when scanned in portrait or landscape mode; less uncertainty was found when using the portrait mode. The response of the film depended on the position on the bed of the scanner, contributing an uncertainty of 2% for the red, 3% for the green, and 4.5% for the blue when placing the film around the center of the bed of scanner. Furthermore, the uniformity and reproducibility radiochromic film and reproducibility of the response of the scanner contribute less than 1% to the overall uncertainty in dose. Finally, the total dose uncertainty was 3.2%, 4.9%, and 5.2% for red, green, and blue channels, respectively. The above uncertainty values were obtained by minimizing the contribution to the total dose uncertainty of the film orientation and film homogeneity

A modification of Honoré's triple-link model in the synoptic problem

In New Testament studies, the synoptic problem is concerned with the relationships between the gospels of Matthew, Mark and Luke. In an earlier paper a careful specification in probabilistic terms was set up of Honoré's triple-link model. In the present paper, a modification of Honoré's model is proposed. As previously, counts of the numbers of verbal agreements between the gospels are examined to investigate which of the possible triple-link models appears to give the best fit to the data, but now using the modified version of the model and additional sets of data

Nash Social Welfare in Selfish and Online Load Balancing

In load balancing problems there is a set of clients, each wishing to select a resource from a set of permissible ones, in order to execute a certain task. Each resource has a latency function, which depends on its workload, and a client's cost is the completion time of her chosen resource. Two fundamental variants of load balancing problems are {\em selfish load balancing} (aka. {\em load balancing games}), where clients are non-cooperative selfish players aimed at minimizing their own cost solely, and {\em online load balancing}, where clients appear online and have to be irrevocably assigned to a resource without any knowledge about future requests. We revisit both selfish and online load balancing under the objective of minimizing the {\em Nash Social Welfare}, i.e., the geometric mean of the clients' costs. To the best of our knowledge, despite being a celebrated welfare estimator in many social contexts, the Nash Social Welfare has not been considered so far as a benchmarking quality measure in load balancing problems. We provide tight bounds on the price of anarchy of pure Nash equilibria and on the competitive ratio of the greedy algorithm under very general latency functions, including polynomial ones. For this particular class, we also prove that the greedy strategy is optimal as it matches the performance of any possible online algorithm