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

On the Structure of Equilibria in Basic Network Formation

We study network connection games where the nodes of a network perform edge swaps in order to improve their communication costs. For the model proposed by Alon et al. (2010), in which the selfish cost of a node is the sum of all shortest path distances to the other nodes, we use the probabilistic method to provide a new, structural characterization of equilibrium graphs. We show how to use this characterization in order to prove upper bounds on the diameter of equilibrium graphs in terms of the size of the largest $k$-vicinity (defined as the the set of vertices within distance $k$ from a vertex), for any $k \geq 1$ and in terms of the number of edges, thus settling positively a conjecture of Alon et al. in the cases of graphs of large $k$-vicinity size (including graphs of large maximum degree) and of graphs which are dense enough. Next, we present a new swap-based network creation game, in which selfish costs depend on the immediate neighborhood of each node; in particular, the profit of a node is defined as the sum of the degrees of its neighbors. We prove that, in contrast to the previous model, this network creation game admits an exact potential, and also that any equilibrium graph contains an induced star. The existence of the potential function is exploited in order to show that an equilibrium can be reached in expected polynomial time even in the case where nodes can only acquire limited knowledge concerning non-neighboring nodes.Comment: 11 pages, 4 figure

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

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

A Framework for Global Twenty-First Century Scenarios and Models of Biological Invasions

Biological invasions have emerged as an eminent feature of global change, with substantial impacts on the environment and human livelihoods. Current research demonstrates that the numbers and impacts of alien species are rising unabatedly. At the same time, we lack a thorough understanding of potential future trajectories for the decades to come. With the recent establishment of comprehensive global databases, it is, for the first time, feasible to develop and quantify future scenarios of biological invasions. Therefore, we propose a conceptual framework for how to develop alien species scenarios for the twenty-first century and how to identify relevant steps and challenges along the way. The concept will be important to inform research, policy, stakeholders, and the general public. Furthermore, we call for the scientific community to join forces and to operationalize the framework for scenarios and models of biological invasions to develop an important baseline for understanding and managing future biological invasions

The poleward naturalization of intracontinental alien plants.

Plant introductions outside their native ranges by humans have led to substantial ecological consequences. While we have gained considerable knowledge about intercontinental introductions, the distribution and determinants of intracontinental aliens remain poorly understood. Here, we studied naturalized (i.e., self-sustaining) intracontinental aliens using native and alien floras of 243 mainland regions in North America, South America, Europe, and Australia. We revealed that 4510 plant species had intracontinental origins, accounting for 3.9% of all plant species and 56.7% of all naturalized species in these continents. In North America and Europe, the numbers of intracontinental aliens peaked at mid-latitudes, while the proportion peaked at high latitudes in Europe. Notably, we found predominant poleward naturalization, primarily due to larger native species pools in low-latitudes. Geographic and climatic distances constrained the naturalization of intracontinental aliens in Australia, Europe, and North America, but not in South America. These findings suggest that poleward naturalizations will accelerate, as high latitudes become suitable for more plant species due to climate change

Drivers of the relative richness of naturalized and invasive plant species on Earth

Biological invasions are a defining feature of the Anthropocene, but the factors that determine the spatially uneven distribution of alien plant species are still poorly understood. Here, we present the first global analysis of the effects of biogeographic factors, the physical environment and socio-economy on the richness of naturalized and invasive alien plants. We used generalized linear mixed-effects models and variation partitioning to disentangle the relative importance of individual factors, and, more broadly, of biogeography, physical environment and socio-economy. As measures of the magnitude of permanent anthropogenic additions to the regional species pool and of species with negative environmental impacts, we calculated the relative richness of naturalized (= RRN) and invasive (= RRI) alien plant species numbers adjusted for the number of native species in 838 terrestrial regions. Socio-economic factors (per-capita gross domestic product (GDP), population density, proportion of agricultural land) were more important in explaining RRI (~50 % of the explained variation) than RRN (~40 %). Warm-temperate and (sub)tropical regions have higher RRN than tropical or cooler regions. We found that socio-economic pressures are more relevant for invasive than for naturalized species richness. The expectation that the southern hemisphere is more invaded than the northern hemisphere was confirmed only for RRN on islands, but not for mainland regions nor for RRI. On average, islands have ~6-fold RRN, and >3-fold RRI compared to mainland regions. Eighty-two islands (=26 % of all islands) harbour more naturalized alien than native plants. Our findings challenge the widely held expectation that socio-economic pressures are more relevant for plant naturalization than for invasive plants. To meet international biodiversity targets and halt the detrimental consequences of plant invasions, it is essential to disrupt the connection between socio-economic development and plant invasions by improving pathway management, early detection and rapid response

Enhancement of bichromatic high-harmonic generation with a high-frequency field

Using a high-frequency field superposed to a linearly polarized bichromatic laser field composed by a wave with frequency $\omega$ and a wave with frequency $2\omega$, we show it is possible to enhance the intensity of a group of high harmonics in orders of magnitude. These harmonics have frequencies about 30% higher than the monochromatic-cutoff frequency, and, within the three-step-model framework, correspond to a set of electron trajectories for which tunneling ionization is strongly suppressed. Particular features in the observed enhancement suggest that the high-frequency field provides an additional mechanism for the electron to reach the continuum. This interpretation is supported by a time-frequency analysis of the harmonic yield. The additional high frequency field permits the control of this group of harmonics leaving all other sets of harmonics practically unchanged, which is an advantage over schemes involving only bichromatic fields.Comment: 6 pages RevTex, 5 figures (ps files), Changes in text, figures, references and equations include

Naturalized alien flora of the world: species diversity, taxonomic and phylogenetic patterns, geographic distribution and global hotspots of plant invasion

Using the recently built Global Naturalized Alien Flora (GloNAF) database, containing data on the distribution of naturalized alien plants in 483 mainland and 361 island regions of the world, we describe patterns in diversity and geographic distribution of naturalized and invasive plant species, taxonomic, phylogenetic and life-history structure of the global naturalized flora as well as levels of naturalization and their determinants. The mainland regions with the highest numbers of naturalized aliens are some Australian states (with New South Wales being the richest on this continent) and several North American regions (of which California with 1753 naturalized plant species represents the world's richest region in terms of naturalized alien vascular plants). England, Japan, New Zealand and the Hawaiian archipelago harbour most naturalized plants among islands or island groups. These regions also form the main hotspots of the regional levels of naturalization, measured as the percentage of naturalized aliens in the total flora of the region. Such hotspots of relative naturalized species richness appear on both the western and eastern coasts of North America, in north-western Europe, South Africa, south-eastern Australia, New Zealand, and India. High levels of island invasions by naturalized plants are concentrated in the Pacific, but also occur on individual islands across all oceans. The numbers of naturalized species are closely correlated with those of native species, with a stronger correlation and steeper increase for islands than mainland regions, indicating a greater vulnerability of islands to invasion by species that become successfully naturalized. South Africa, India, California, Cuba, Florida, Queensland and Japan have the highest numbers of invasive species. Regions in temperate and tropical zonobiomes harbour in total 9036 and 6774 naturalized species, respectively, followed by 3280 species naturalized in the Mediterranean zonobiome, 3057 in the subtropical zonobiome and 321 in the Arctic. The New World is richer in naturalized alien plants, with 9905 species compared to 7923 recorded in the Old World. While isolation is the key factor driving the level of naturalization on islands, zonobiomes differing in climatic regimes, and socioeconomy represented by per capita GDP, are central for mainland regions. The 11 most widely distributed species each occur in regions covering about one third of the globe or more in terms of the number of regions where they are naturalized and at least 35% of the Earth's land surface in terms of those regions' areas, with the most widely distributed species Sonchus oleraceus occuring in 48% of the regions that cover 42% of the world area. Other widely distributed species are Ricinus communis, Oxalis corniculata, Portulaca oleracea, Eleusine indica, Chenopodium album, Capsella bursa-pastoris, Stellaria media, Bidens pilosa, Datura stramonium and Echinochloa crus-galli. Using the occurrence as invasive rather than only naturalized yields a different ranking, with Lantana camara (120 regions out of 349 for which data on invasive status are known), Calotropis procera (118), Eichhornia crassipes (113), Sonchus oleraceus (108) and Leucaena leucocephala (103) on top. As to the life-history spectra, islands harbour more naturalized woody species (34.4%) than mainland regions (29.5%), and fewer annual herbs (18.7% compared to 22.3%). Ranking families by their absolute numbers of naturalized species reveals that Compositae (1343 species), Poaceae (1267) and Leguminosae (1189) contribute most to the global naturalized alien flora. Some families are disproportionally represented by naturalized aliens on islands (Arecaceae, Araceae, Acanthaceae, Amaryllidaceae, Asparagaceae, Convolvulaceae, Rubiaceae, Malvaceae), and much fewer so on mainland (e.g. Brassicaceae, Caryophyllaceae, Boraginaceae). Relating the numbers of naturalized species in a family to its total global richness shows that some of the large species-rich families are over-represented among naturalized aliens (e.g. Poaceae, Leguminosae, Rosaceae, Amaranthaceae, Pinaceae), some under-represented (e.g. Euphorbiaceae, Rubiaceae), whereas the one richest in naturalized species, Compositae, reaches a value expected from its global species richness. Significant phylogenetic signal indicates that families with an increased potential of their species to naturalize are not distributed randomly on the evolutionary tree. Solanum (112 species), Euphorbia (108) and Carex (106) are the genera richest in terms of naturalized species; over-represented on islands are Cotoneaster, Juncus, Eucalyptus, Salix, Hypericum, Geranium and Persicaria, while those relatively richer in naturalized species on the mainland are Atriplex, Opuntia, Oenothera, Artemisia, Vicia, Galium and Rosa. The data presented in this paper also point to where information is lacking and set priorities for future data collection. The GloNAF database has potential for designing concerted action to fill such data gaps, and provide a basis for allocating resources most efficiently towards better understanding and management of plant invasions worldwide

IPBES Invasive Alien Species Assessment: Chapter 1. Introducing biological invasions and the IPBES thematic assessment of invasive alien species and their control

Chapter 1: Introducing biological invasions and the IPBES thematic assessment of invasive alien species and their control of the Thematic Assessment Report on Invasive Alien Species and their Control of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services