Optimal Crowdsourcing Contests

We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as all-pay auctions because entrants must exert effort up-front to enter. Unlike all-pay auctions where a usual design objective would be to maximize revenue, in crowdsourcing contests, the principal only benefits from the submission with the highest quality. We give a theory for optimal crowdsourcing contests that mirrors the theory of optimal auction design: the optimal crowdsourcing contest is a virtual valuation optimizer (the virtual valuation function depends on the distribution of contestant skills and the number of contestants). We also compare crowdsourcing contests with more conventional means of procurement. In this comparison, crowdsourcing contests are relatively disadvantaged because the effort of losing contestants is wasted. Nonetheless, we show that crowdsourcing contests are 2-approximations to conventional methods for a large family of "regular" distributions, and 4-approximations, otherwise.Comment: The paper has 17 pages and 1 figure. It is to appear in the proceedings of ACM-SIAM Symposium on Discrete Algorithms 201

Auditing: Active Learning with Outcome-Dependent Query Costs

We propose a learning setting in which unlabeled data is free, and the cost of a label depends on its value, which is not known in advance. We study binary classification in an extreme case, where the algorithm only pays for negative labels. Our motivation are applications such as fraud detection, in which investigating an honest transaction should be avoided if possible. We term the setting auditing, and consider the auditing complexity of an algorithm: the number of negative labels the algorithm requires in order to learn a hypothesis with low relative error. We design auditing algorithms for simple hypothesis classes (thresholds and rectangles), and show that with these algorithms, the auditing complexity can be significantly lower than the active label complexity. We also discuss a general competitive approach for auditing and possible modifications to the framework.Comment: Corrections in section

Time-reversal in dynamically-tuned zero-gap periodic systems

We show that short pulses propagating in zero-gap periodic systems can be reversed with 100% efficiency by using weak non-adiabatic tuning of the wave velocity at time-scales that can be much slower than the period. Unlike previous schemes, we demonstrate reversal of {\em broadband} (few cycle) pulses with simple structures. Our scheme may thus open the way to time-reversal in a variety of systems for which it was not accessible before.Comment: Accepted for publication in Phys. Rev. Letter

Spatio-Temporal Low Count Processes with Application to Violent Crime Events

There is significant interest in being able to predict where crimes will happen, for example to aid in the efficient tasking of police and other protective measures. We aim to model both the temporal and spatial dependencies often exhibited by violent crimes in order to make such predictions. The temporal variation of crimes typically follows patterns familiar in time series analysis, but the spatial patterns are irregular and do not vary smoothly across the area. Instead we find that spatially disjoint regions exhibit correlated crime patterns. It is this indeterminate inter-region correlation structure along with the low-count, discrete nature of counts of serious crimes that motivates our proposed forecasting tool. In particular, we propose to model the crime counts in each region using an integer-valued first order autoregressive process. We take a Bayesian nonparametric approach to flexibly discover a clustering of these region-specific time series. We then describe how to account for covariates within this framework. Both approaches adjust for seasonality. We demonstrate our approach through an analysis of weekly reported violent crimes in Washington, D.C. between 2001-2008. Our forecasts outperform standard methods while additionally providing useful tools such as prediction intervals

Properties of low-lying states in a diffusive quantum dot and Fock-space localization

Motivated by an experiment by Sivan et al. (Europhys. Lett. 25, 605 (1994)) and by subsequent theoretical work on localization in Fock space, we study numerically a hierarchical model for a finite many-body system of Fermions moving in a disordered potential and coupled by a two-body interaction. We focus attention on the low-lying states close to the Fermi energy. Both the spreading width and the participation number depend smoothly on excitation energy. This behavior is in keeping with naive expectations and does not display Anderson localization. We show that the model reproduces essential features of the experiment by Sivan et al.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev. Let

Energy Level Alignment at Molecule-Metal Interfaces from an Optimally-Tuned Range-Separated Hybrid Functional

The alignment of the frontier orbital energies of an adsorbed molecule with the substrate Fermi level at metal-organic interfaces is a fundamental observable of significant practical importance in nanoscience and beyond. Typical density functional theory calculations, especially those using local and semi-local functionals, often underestimate level alignment leading to inaccurate electronic structure and charge transport properties. In this work, we develop a new fully self-consistent predictive scheme to accurately compute level alignment at certain classes of complex heterogeneous molecule-metal interfaces based on optimally-tuned range-separated hybrid functionals. Starting from a highly accurate description of the gas-phase electronic structure, our method by construction captures important nonlocal surface polarization effects via tuning of the long-range screened exchange in a range-separated hybrid in a non-empirical and system-specific manner. We implement this functional in a plane-wave code and apply it to several physisorbed and chemisorbed molecule-metal interface systems. Our results are in quantitative agreement with experiments, both the level alignment and work function changes. Our approach constitutes a new practical scheme for accurate and efficient calculations of the electronic structure of molecule-metal interfaces.Comment: 15 pages, 8 figure

Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach

The problem of electron--electron lifetime in a quantum dot is studied beyond perturbation theory by mapping it onto the problem of localization in the Fock space. We identify two regimes, localized and delocalized, corresponding to quasiparticle spectral peaks of zero and finite width, respectively. In the localized regime, quasiparticle states are very close to single particle excitations. In the delocalized state, each eigenstate is a superposition of states with very different quasiparticle content. A transition between the two regimes occurs at the energy $\simeq\Delta(g/\ln g)^{1/2}$, where $\Delta$ is the one particle level spacing, and $g$ is the dimensionless conductance. Near this energy there is a broad critical region in which the states are multifractal, and are not described by the Golden Rule.Comment: 13 pages, LaTeX, one figur