A cluster expansion approach to exponential random graph models

The exponential family of random graphs is among the most widely-studied network models. We show that any exponential random graph model may alternatively be viewed as a lattice gas model with a finite Banach space norm. The system may then be treated by cluster expansion methods from statistical mechanics. In particular, we derive a convergent power series expansion for the limiting free energy in the case of small parameters. Since the free energy is the generating function for the expectations of other random variables, this characterizes the structure and behavior of the limiting network in this parameter region.Comment: 15 pages, 1 figur

Incentivizing High Quality Crowdwork

We study the causal effects of financial incentives on the quality of crowdwork. We focus on performance-based payments (PBPs), bonus payments awarded to workers for producing high quality work. We design and run randomized behavioral experiments on the popular crowdsourcing platform Amazon Mechanical Turk with the goal of understanding when, where, and why PBPs help, identifying properties of the payment, payment structure, and the task itself that make them most effective. We provide examples of tasks for which PBPs do improve quality. For such tasks, the effectiveness of PBPs is not too sensitive to the threshold for quality required to receive the bonus, while the magnitude of the bonus must be large enough to make the reward salient. We also present examples of tasks for which PBPs do not improve quality. Our results suggest that for PBPs to improve quality, the task must be effort-responsive: the task must allow workers to produce higher quality work by exerting more effort. We also give a simple method to determine if a task is effort-responsive a priori. Furthermore, our experiments suggest that all payments on Mechanical Turk are, to some degree, implicitly performance-based in that workers believe their work may be rejected if their performance is sufficiently poor. Finally, we propose a new model of worker behavior that extends the standard principal-agent model from economics to include a worker's subjective beliefs about his likelihood of being paid, and show that the predictions of this model are in line with our experimental findings. This model may be useful as a foundation for theoretical studies of incentives in crowdsourcing markets.Comment: This is a preprint of an Article accepted for publication in WWW \c{opyright} 2015 International World Wide Web Conference Committe

Observation of giant positive magnetoresistance in a Cooper pair insulator.

Ultrathin amorphous Bi films, patterned with a nanohoneycomb array of holes, can exhibit an insulating phase with transport dominated by the incoherent motion of Cooper pairs (CP) of electrons between localized states. Here, we show that the magnetoresistance (MR) of this Cooper pair insulator (CPI) phase is positive and grows exponentially with decreasing temperature T, for T well below the pair formation temperature. It peaks at a field estimated to be sufficient to break the pairs and then decreases monotonically into a regime in which the film resistance assumes the T dependence appropriate for weakly localized single electron transport. We discuss how these results support proposals that the large MR peaks in other unpatterned, ultrathin film systems disclose a CPI phase and provide new insight into the CP localization

Interactions and Scaling in a Disordered Two-Dimensional Metal

We show that a non-Fermi liquid state of interacting electrons in two dimensions is stable in the presence of disorder and is a perfect conductor, provided the interactions are sufficiently strong. Otherwise, the disorder leads to localization as in the case of non-interacting electrons. This conclusion is established by examining the replica field theory in the weak disorder limit, but in the presence of arbitrary electron-electron interaction. Thus, a disordered two-dimensional metal is a perfect metal, but not a Fermi liquid.Comment: 4 pages, RevTe

A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page