Greedy Selfish Network Creation

We introduce and analyze greedy equilibria (GE) for the well-known model of selfish network creation by Fabrikant et al.[PODC'03]. GE are interesting for two reasons: (1) they model outcomes found by agents which prefer smooth adaptations over radical strategy-changes, (2) GE are outcomes found by agents which do not have enough computational resources to play optimally. In the model of Fabrikant et al. agents correspond to Internet Service Providers which buy network links to improve their quality of network usage. It is known that computing a best response in this model is NP-hard. Hence, poly-time agents are likely not to play optimally. But how good are networks created by such agents? We answer this question for very simple agents. Quite surprisingly, naive greedy play suffices to create remarkably stable networks. Specifically, we show that in the SUM version, where agents attempt to minimize their average distance to all other agents, GE capture Nash equilibria (NE) on trees and that any GE is in 3-approximate NE on general networks. For the latter we also provide a lower bound of 3/2 on the approximation ratio. For the MAX version, where agents attempt to minimize their maximum distance, we show that any GE-star is in 2-approximate NE and any GE-tree having larger diameter is in 6/5-approximate NE. Both bounds are tight. We contrast these positive results by providing a linear lower bound on the approximation ratio for the MAX version on general networks in GE. This result implies a locality gap of $\Omega(n)$ for the metric min-max facility location problem, where n is the number of clients.Comment: 28 pages, 8 figures. An extended abstract of this work was accepted at WINE'1

Probability of local bifurcation type from a fixed point: A random matrix perspective

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectra is considered both numerically and analytically using previous work of Edelman et. al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion is not general, e.g. real random matrices with Gaussian elements with a large positive mean and finite variance.Comment: 21 pages, 19 figure

Selection of reference system elements in the model of PGE - Product generation engineering: Method for the integration of customer and user satisfaction in product planning

In the development of mechatronic systems, it is important to differentiate the products to be developed from those of the competitors, but also from the own product generations already available on the market. However, there are uncertainties regarding the correct features to be differentiated from the customer and user perspective and how these features should be designed. Nevertheless, despite the high impact, decisions must be taken early in the development process. Within this publication, a method to support in this respect was derived based on the findings of the Model of PGE - Product Generation Engineering and the Kano-Model. Therefore, experienceable product features and reference system elements as characteristics of these are evaluated according to the Kano-Model and thus made comparable with regard to the customers and user satisfaction. The objective is to select the product features to be differentiated and the corresponding reference system elements in such a way that a desired level of customer and user satisfaction is achieved. In order to evaluate the method, it was applied in a real development project. It was found that the application of the method led to a reduction of the existing uncertainty

Network Creation Games: Think Global - Act Local

We investigate a non-cooperative game-theoretic model for the formation of communication networks by selfish agents. Each agent aims for a central position at minimum cost for creating edges. In particular, the general model (Fabrikant et al., PODC'03) became popular for studying the structure of the Internet or social networks. Despite its significance, locality in this game was first studied only recently (Bil\`o et al., SPAA'14), where a worst case locality model was presented, which came with a high efficiency loss in terms of quality of equilibria. Our main contribution is a new and more optimistic view on locality: agents are limited in their knowledge and actions to their local view ranges, but can probe different strategies and finally choose the best. We study the influence of our locality notion on the hardness of computing best responses, convergence to equilibria, and quality of equilibria. Moreover, we compare the strength of local versus non-local strategy-changes. Our results address the gap between the original model and the worst case locality variant. On the bright side, our efficiency results are in line with observations from the original model, yet we have a non-constant lower bound on the price of anarchy.Comment: An extended abstract of this paper has been accepted for publication in the proceedings of the 40th International Conference on Mathematical Foundations on Computer Scienc

A variational approach to Givental's nonlinear Maslov index

In this article we consider a variant of Rabinowitz Floer homology in order to define a homological count of discriminant points for paths of contactomorphisms. The growth rate of this count can be seen as an analogue of Givental's nonlinear Maslov index. As an application we prove a Bott-Samelson type obstruction theorem for positive loops of contactomorphisms.Comment: 14 page

Selfish Network Creation with Non-Uniform Edge Cost

Network creation games investigate complex networks from a game-theoretic point of view. Based on the original model by Fabrikant et al. [PODC'03] many variants have been introduced. However, almost all versions have the drawback that edges are treated uniformly, i.e. every edge has the same cost and that this common parameter heavily influences the outcomes and the analysis of these games. We propose and analyze simple and natural parameter-free network creation games with non-uniform edge cost. Our models are inspired by social networks where the cost of forming a link is proportional to the popularity of the targeted node. Besides results on the complexity of computing a best response and on various properties of the sequential versions, we show that the most general version of our model has constant Price of Anarchy. To the best of our knowledge, this is the first proof of a constant Price of Anarchy for any network creation game.Comment: To appear at SAGT'1

An Oscillating MinD Protein Determines the Cellular Positioning of the Motility Machinery in Archaea.

MinD proteins are well studied in rod-shaped bacteria such as E. coli, where they display self-organized pole-to-pole oscillations that are important for correct positioning of the Z-ring at mid-cell for cell division. Archaea also encode proteins belonging to the MinD family, but their functions are unknown. MinD homologous proteins were found to be widespread in Euryarchaeota and form a sister group to the bacterial MinD family, distinct from the ParA and other related ATPase families. We aimed to identify the function of four archaeal MinD proteins in the model archaeon Haloferax volcanii. Deletion of the minD genes did not cause cell division or size defects, and the Z-ring was still correctly positioned. Instead, one of the deletions (ΔminD4) reduced swimming motility and hampered the correct formation of motility machinery at the cell poles. In ΔminD4 cells, there is reduced formation of the motility structure and chemosensory arrays, which are essential for signal transduction. In bacteria, several members of the ParA family can position the motility structure and chemosensory arrays via binding to a landmark protein, and consequently these proteins do not oscillate along the cell axis. However, GFP-MinD4 displayed pole-to-pole oscillation and formed polar patches or foci in H. volcanii. The MinD4 membrane-targeting sequence (MTS), homologous to the bacterial MinD MTS, was essential for the oscillation. Surprisingly, mutant MinD4 proteins failed to form polar patches. Thus, MinD4 from H. volcanii combines traits of different bacterial ParA/MinD proteins

Disgust sensitivity is not associated with health in a rural Bangladeshi sample.

Disgust can be considered a psychological arm of the immune system that acts to prevent exposure to infectious agents. High disgust sensitivity is associated with greater behavioral avoidance of disease vectors and thus may reduce infection risk. A cross-sectional survey in rural Bangladesh provided no strong support for this hypothesis. In many species, the expression of pathogen- and predator-avoidance mechanisms is contingent on early life exposure to predators and pathogens. Using childhood health data collected in the 1990s, we examined if adults with more infectious diseases in childhood showed greater adult disgust sensitivity: no support for this association was found. Explanations for these null finding and possible directions for future research are discussed

The role of the g9/2 orbital in the development of collectivity in the A = 60 region: The case of 61Co

An extensive study of the level structure of 61Co has been performed following the complex 26Mg(48Ca, 2a4npg)61Co reaction at beam energies of 275, 290 and 320 MeV using Gammasphere and the Fragment Mass Analyzer (FMA). The low-spin structure is discussed within the framework of shell-model calculations using the GXPF1A effective interaction. Two quasi-rotational bands consisting of stretched-E2 transitions have been established up to spins I = 41/2 and (43/2), and excitation energies of 17 and 20 MeV, respectively. These are interpreted as signature partners built on a neutron {\nu}(g9/2)2 configuration coupled to a proton {\pi}p3/2 state, based on Cranked Shell Model (CSM) calculations and comparisons with observations in neighboring nuclei. In addition, four I = 1 bands were populated to high spin, with the yrast dipole band interpreted as a possible candidate for the shears mechanism, a process seldom observed thus far in this mass region