Local Algorithms for Finding Interesting Individuals in Large Networks

We initiate the study of local, sublinear time algorithms for finding vertices with extreme topological properties — such as high degree or clustering coefficient — in large social or other networks. We introduce a new model, called the Jump and Crawl model, in which algorithms are permitted only two graph operations. The Jump operation returns a randomly chosen vertex, and is meant to model the ability to discover “new” vertices via keyword search in the Web, shared hobbies or interests in social networks such as Facebook, and other mechanisms that may return vertices that are distant from all those currently known. The Crawl operation permits an algorithm to explore the neighbors of any currently known vertex, and has clear analogous in many modern networks. We give both upper and lower bounds in the Jump and Crawl model for the problems of finding vertices of high degree and high clustering coefficient. We consider both arbitrary graphs, and specializations in which some common assumptions are made on the global topology (such as power law degree distributions or generation via preferential attachment). We also examine local algorithms for some related vertex or graph properties, and discuss areas for future investigation

Private and Third-Party Randomization in Risk-Sensitive Equilibrium Concepts

We consider risk-sensitive generalizations of Nash and correlated equilibria in noncooperative games. We prove that, except for a class of degenerate games, unless a two-player game has a pure Nash equilibrium, it does not have a risksensitive Nash equilibrium. We also show that every game has a risk-sensitive correlated equilibrium. The striking contrast between these existence results is due to the different sources of randomization in Nash (private randomization) and correlated equilibria (third-party randomization)

Behavioral Experiments on a Network Formation Game

We report on an extensive series of behavioral experiments in which 36 human subjects collectively build a communication network over which they must solve a competitive coordination task for monetary compensation. There is a cost for creating network links, thus creating a tension between link expenditures and collective and individual incentives. Our most striking finding is the poor performance of the subjects, especially compared to our long series of prior experiments. We demonstrate that the subjects built difficult networks for the coordination task, and compare the structural properties of the built networks to standard generative models of social networks. We also provide extensive analysis of the individual and collective behavior of the subjects, including free riding and factors influencing edge purchasing decisions

Behavioral Conflict and Fairness in Social Networks

We report on a series of behavioral experiments in social networks in which human subjects continuously choose to play either a dominant role (called a King) or a submissive one (called a Pawn). Kings receive a higher payoff rate, but only if all their network neighbors are Pawns, and thus the maximum social welfare states correspond to maximum independent sets. We document that fairness is of vital importance in driving interactions between players. First, we find that payoff disparities between network neighbors gives rise to conflict, and the specifics depend on the network topology. However, allowing Kings to offer tips or side payments to their neighbors substantially reduces conflict, and consistently increases social welfare. Finally, we observe that tip reductions lead to increased conflict. We describe these and a broad set of related findings

Learning and Predicting Dynamic Behavior with Graphical Multiagent Models

Factored models of multiagent systems address the complexity of joint behavior by exploiting locality in agent interactions. History-dependent graphical multiagent models (hGMMs) further capture dynamics by conditioning behavior on history. The challenges of modeling real human behavior motivated us to extend the hGMM representation by distinguishing two types of agent interactions. This distinction opens the opportunity for learning dependence networks that are different from given graphical structures representing observed agent interactions. We propose a greedy algorithm for learning hGMMs from time-series data, inducing both graphical structure and parameters. Our empirical study employs human-subject experiment data for a dynamic consensus scenario, where agents on a network attempt to reach a unanimous vote. We show that the learned hGMMs directly expressing joint behavior outperform alternatives in predicting dynamic human voting behavior, and end-game vote results. Analysis of learned graphical structures reveals patterns of action dependence not directly reflected in the original experiment networks

Fossilized skin reveals coevolution with feathers and metabolism in feathered dinosaurs and early birds

Feathers are remarkable evolutionary innovations that are associated with complex adaptations of the skin in modern birds. Fossilised feathers in non-avian dinosaurs and basal birds provide insights into feather evolution, but how associated integumentary adaptations evolved is unclear. Here we report the discovery of fossil skin, preserved with remarkable nanoscale fidelity, in three non-avian maniraptoran dinosaurs and a basal bird from the Cretaceous Jehol biota (China). The skin comprises patches of desquamating epidermal corneocytes that preserve a cytoskeletal array of helically coiled α-keratin tonofibrils. This structure confirms that basal birds and non-avian dinosaurs shed small epidermal flakes as in modern mammals and birds, but structural differences imply that these Cretaceous taxa had lower body heat production than modern birds. Feathered epidermis acquired many, but not all, anatomically modern attributes close to the base of the Maniraptora by the Middle Jurassic

Next nearest neighbour Ising models on random graphs

This paper develops results for the next nearest neighbour Ising model on random graphs. Besides being an essential ingredient in classic models for frustrated systems, second neighbour interactions interactions arise naturally in several applications such as the colour diversity problem and graphical games. We demonstrate ensembles of random graphs, including regular connectivity graphs, that have a periodic variation of free energy, with either the ratio of nearest to next nearest couplings, or the mean number of nearest neighbours. When the coupling ratio is integer paramagnetic phases can be found at zero temperature. This is shown to be related to the locked or unlocked nature of the interactions. For anti-ferromagnetic couplings, spin glass phases are demonstrated at low temperature. The interaction structure is formulated as a factor graph, the solution on a tree is developed. The replica symmetric and energetic one-step replica symmetry breaking solution is developed using the cavity method. We calculate within these frameworks the phase diagram and demonstrate the existence of dynamical transitions at zero temperature for cases of anti-ferromagnetic coupling on regular and inhomogeneous random graphs.Comment: 55 pages, 15 figures, version 2 with minor revisions, to be published J. Stat. Mec