Convergence of some leader election algorithms

We start with a set of n players. With some probability P(n,k), we kill n-k players; the other ones stay alive, and we repeat with them. What is the distribution of the number X_n of phases (or rounds) before getting only one player? We present a probabilistic analysis of this algorithm under some conditions on the probability distributions P(n,k), including stochastic monotonicity and the assumption that roughly a fixed proportion alpha of the players survive in each round. We prove a kind of convergence in distribution for X_n-log_a n, where the basis a=1/alpha; as in many other similar problems there are oscillations and no true limit distribution, but suitable subsequences converge, and there is an absolutely continuous random variable Z such that the distribution of X_n can be approximated by Z+log_a n rounded to the nearest larger integer. Applications of the general result include the leader election algorithm where players are eliminated by independent coin tosses and a variation of the leader election algorithm proposed by W.R. Franklin. We study the latter algorithm further, including numerical results.Comment: 27 pages, 13 figures, 5 table

High-contrast Imaging with Spitzer: Deep Observations of Vega, Fomalhaut, and epsilon Eridani

Stars with debris disks are intriguing targets for direct imaging exoplanet searches, both due to previous detections of wide planets in debris disk systems, as well as commonly existing morphological features in the disks themselves that may be indicative of a planetary influence. Here we present observations of three of the most nearby young stars, that are also known to host massive debris disks: Vega, Fomalhaut, and eps Eri. The Spitzer Space Telescope is used at a range of orientation angles for each star, in order to supply a deep contrast through angular differential imaging combined with high-contrast algorithms. The observations provide the opportunity to probe substantially colder bound planets (120--330 K) than is possible with any other technique or instrument. For Vega, some apparently very red candidate point sources detected in the 4.5 micron image remain to be tested for common proper motion. The images are sensitive to ~2 Mjup companions at 150 AU in this system. The observations presented here represent the first search for planets around Vega using Spitzer. The upper 4.5 micron flux limit on Fomalhaut b could be further constrained relative to previous data. In the case of eps Eri, planets below both the effective temperature and the mass of Jupiter could be probed from 80 AU and outwards, although no such planets were found. The data sensitively probe the regions around the edges of the debris rings in the systems where planets can be expected to reside. These observations validate previous results showing that more than an order of magnitude improvement in performance in the contrast-limited regime can be acquired with respect to conventional methods by applying sophisticated high-contrast techniques to space-based telescopes, thanks to the high degree of PSF stability provided in this environment.Comment: 11 pages, 12 figures, accepted for publication in A&

Imaging correlated wave functions of few-electron quantum dots: Theory and scanning tunneling spectroscopy experiments

We show both theoretically and experimentally that scanning tunneling spectroscopy (STS) images of semiconductor quantum dots may display clear signatures of electron-electron correlation. We apply many-body tunneling theory to a realistic model which fully takes into account correlation effects and dot anisotropy. Comparing measured STS images of freestanding InAs quantum dots with those calculated by the full configuration interaction method, we explain the wave function sequence in terms of images of one- and two-electron states. The STS map corresponding to double charging is significantly distorted by electron correlation with respect to the non-interacting case.Comment: RevTeX 4.0, 5 pages, 3 B/W figures, 1 table. This paper is based on an invited talk presented by the authors at the 28th International Conference on the Physics of Semiconductors, which was held 24-28 July 2006, in Vienna, Austri

SPOTS: The Search for Planets Orbiting Two Stars: II. First constraints on the frequency of sub-stellar companions on wide circumbinary orbits

A large number of direct imaging surveys for exoplanets have been performed in recent years, yielding the first directly imaged planets and providing constraints on the prevalence and distribution of wide planetary systems. However, like most of the radial velocity ones, these surveys generally focus on single stars, hence binaries and higher-order multiples have not been studied to the same level of scrutiny. This motivated the SPOTS (Search for Planets Orbiting Two Stars) survey, which is an ongoing direct imaging study of a large sample of close binaries, started with VLT/NACO and now continuing with VLT/SPHERE. To complement this survey, we have identified the close binary targets in 24 published direct imaging surveys. Here we present our statistical analysis of this combined body of data. We analysed a sample of 117 tight binary systems, using a combined Monte Carlo and Bayesian approach to derive the expected values of the frequency of companions, for different values of the companion's semi-major axis. Our analysis suggest that the frequency of sub-stellar companions in wide orbit is moderately low ($\lesssim$13% with a best value of 6% at 95% confidence level) and not significantly different between single stars and tight binaries. One implication of this result is that the very high frequency of circumbinary planets in wide orbits around post-common envelope binaries, implied by eclipse timing (up to 90% according to Zorotovic & Schreiber 2013), can not be uniquely due to planets formed before the common-envelope phase (first generation planets), supporting instead the second generation planet formation or a non-Keplerian origin of the timing variations.Comment: 21 pages, 3 figure

Access Control in Publicly Verifiable Outsourced Computation

Publicly Verifiable Outsourced Computation (PVC) allows devices with restricted re-sources to delegate expensive computations to more powerful external servers, and to verify the correctness of results. Whilst highlybeneficial in many situations, this increases the visi-bility and availability of potentially sensitive data, so we may wish to limit the sets of entities that can view input data and results. Additionally, it is highly unlikely that all users have identical and uncontrolled access to all functionality within an organization. Thus there is a need for access control mechanisms in PVC environments. In this work, we define a new framework for Publicly Verifiable Outsourced Computation with Access Control (PVC-AC). We formally define algorithms to provide different PVC functionality for each entity within a large outsourced computation environment, and discuss the forms of access control policies that are applicable, and necessary, in such environments, as well as formally modelling the resulting security properties. Finally, we give an example instantiation that (in a black-box and generic fashion) combines existing PVC schemes with symmetric Key Assignment Schemes to cryptographically enforce the policies of interest.

Hybrid Publicly Verifiable Computation

Publicly Verifiable Outsourced Computation (PVC) allows weak devices to delegate com-putations to more powerful servers, and to verify the correctness of results. Delegation and verification rely only on public parameters, and thus PVC lends itself to large multi-user systems where entities need not be registered. In such settings, individual user requirements may be diverse and cannot be realised with current PVC solutions. In this paper, we in-troduce Hybrid PVC (HPVC) which, with a single setup stage, provides a flexible solution to outsourced computation supporting multiple modes: (i) standard PVC, (ii) PVC with cryptographically enforced access control policies restricting the servers that may perform a given computation, and (iii) a reversed model of PVC which we call Verifiable Delegable Computation (VDC) where data is held remotely by servers. Entities may dynamically play the role of delegators or servers as required