On the construction of discrete approximations to linear differential expressions

Algorithm for generating discrete approximations in terms of ordinates for linear differential expression

Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases

We prove tight entropic uncertainty relations for a large number of mutually unbiased measurements. In particular, we show that a bound derived from the result by Maassen and Uffink for 2 such measurements can in fact be tight for up to sqrt{d} measurements in mutually unbiased bases. We then show that using more mutually unbiased bases does not always lead to a better locking effect. We prove that the optimal bound for the accessible information using up to sqrt{d} specific mutually unbiased bases is log d/2, which is the same as can be achieved by using only two bases. Our result indicates that merely using mutually unbiased bases is not sufficient to achieve a strong locking effect, and we need to look for additional properties.Comment: 9 pages, RevTeX, v3: complete rewrite, new title, many new results, v4: minor changes, published versio

Who Contributes to the Knowledge Sharing Economy?

Information sharing dynamics of social networks rely on a small set of influencers to effectively reach a large audience. Our recent results and observations demonstrate that the shape and identity of this elite, especially those contributing \emph{original} content, is difficult to predict. Information acquisition is often cited as an example of a public good. However, this emerging and powerful theory has yet to provably offer qualitative insights on how specialization of users into active and passive participants occurs. This paper bridges, for the first time, the theory of public goods and the analysis of diffusion in social media. We introduce a non-linear model of \emph{perishable} public goods, leveraging new observations about sharing of media sources. The primary contribution of this work is to show that \emph{shelf time}, which characterizes the rate at which content get renewed, is a critical factor in audience participation. Our model proves a fundamental \emph{dichotomy} in information diffusion: While short-lived content has simple and predictable diffusion, long-lived content has complex specialization. This occurs even when all information seekers are \emph{ex ante} identical and could be a contributing factor to the difficulty of predicting social network participation and evolution.Comment: 15 pages in ACM Conference on Online Social Networks 201

Multiphase Plasma in Sub-Damped Lyman Alpha Systems: A Hidden Metal Reservoir

We present a VLT/UVES spectrum of a proximate sub-damped Lyman-alpha (sub-DLA) system at z=2.65618 toward the quasar Q0331-4505 (z_qso=2.6785+/-0.0030). Absorption lines of O I, Si II, Si III, Si IV, C II, C III, C IV, Fe II, Al II, and O VI are seen in the sub-DLA, which has a neutral hydrogen column density log N(H I)=19.82+/-0.05. The absorber is at a velocity of 1820+/-250 km/s from the quasar; however, its low metallicity [O/H]=-1.64+/-0.07, lack of partial coverage, lack of temporal variations between observations taken in 2003 and 2006, and non-detection of N V imply the absorber is not a genuine intrinsic system. By measuring the O VI column density and assuming equal metallicities in the neutral and ionized gas, we determine the column density of hot ionized hydrogen in this sub-DLA, and in two other sub-DLAs with O VI drawn from the literature. Coupling this with determinations of the typical amount of warm ionized hydrogen in sub-DLAs, we confirm that sub-DLAs are a more important metal reservoir than DLAs, in total comprising at least 6-22% of the metal budget at z~2.5.Comment: 5 pages, 3 color figures, accepted for publication in ApJ

Automated data reduction workflows for astronomy

Data from complex modern astronomical instruments often consist of a large number of different science and calibration files, and their reduction requires a variety of software tools. The execution chain of the tools represents a complex workflow that needs to be tuned and supervised, often by individual researchers that are not necessarily experts for any specific instrument. The efficiency of data reduction can be improved by using automatic workflows to organise data and execute the sequence of data reduction steps. To realize such efficiency gains, we designed a system that allows intuitive representation, execution and modification of the data reduction workflow, and has facilities for inspection and interaction with the data. The European Southern Observatory (ESO) has developed Reflex, an environment to automate data reduction workflows. Reflex is implemented as a package of customized components for the Kepler workflow engine. Kepler provides the graphical user interface to create an executable flowchart-like representation of the data reduction process. Key features of Reflex are a rule-based data organiser, infrastructure to re-use results, thorough book-keeping, data progeny tracking, interactive user interfaces, and a novel concept to exploit information created during data organisation for the workflow execution. Reflex includes novel concepts to increase the efficiency of astronomical data processing. While Reflex is a specific implementation of astronomical scientific workflows within the Kepler workflow engine, the overall design choices and methods can also be applied to other environments for running automated science workflows.Comment: 12 pages, 7 figure

Optimal path for a quantum teleportation protocol in entangled networks

Bellman's optimality principle has been of enormous importance in the development of whole branches of applied mathematics, computer science, optimal control theory, economics, decision making, and classical physics. Examples are numerous: dynamic programming, Markov chains, stochastic dynamics, calculus of variations, and the brachistochrone problem. Here we show that Bellman's optimality principle is violated in a teleportation problem on a quantum network. This implies that finding the optimal fidelity route for teleporting a quantum state between two distant nodes on a quantum network with bi-partite entanglement will be a tough problem and will require further investigation.Comment: 4 pages, 1 figure, RevTeX

Analysis of a convenient information bound for general quantum channels

Open questions from Sarovar and Milburn (2006 J.Phys. A: Math. Gen. 39 8487) are answered. Sarovar and Milburn derived a convenient upper bound for the Fisher information of a one-parameter quantum channel. They showed that for quasi-classical models their bound is achievable and they gave a necessary and sufficient condition for positive operator-valued measures (POVMs) attaining this bound. They asked (i) whether their bound is attainable more generally, (ii) whether explicit expressions for optimal POVMs can be derived from the attainability condition. We show that the symmetric logarithmic derivative (SLD) quantum information is less than or equal to the SM bound, i.e.\ $H(\theta) \leq C_{\Upsilon}(\theta)$ and we find conditions for equality. As the Fisher information is less than or equal to the SLD quantum information, i.e. $F_M(\theta) \leq H(\theta)$, we can deduce when equality holds in $F_M(\theta) \leq C_{\Upsilon}(\theta)$. Equality does not hold for all channels. As a consequence, the attainability condition cannot be used to test for optimal POVMs for all channels. These results are extended to multi-parameter channels.Comment: 16 pages. Published version. Some of the lemmas have been corrected. New resuts have been added. Proofs are more rigorou

HST/STIS Optical Transit Transmission Spectra of the hot-Jupiter HD209458b

We present the transmission spectra of the hot-Jupiter HD209458b taken with the Space Telescope Imaging Spectrograph aboard the Hubble Space Telescope. Our analysis combines data at two resolutions and applies a complete pixel-by-pixel limb-darkening correction to fully reveal the spectral line shapes of atmospheric absorption features. Terrestrial-based Na I and H I contamination are identified which mask the strong exoplanetary absorption signature in the Na core, which we find reaches total absorption levels of ~0.11% in a 4.4 Ang band. The Na spectral line profile is characterized by a wide absorption profile at the lowest absorption depths, and a sharp transition to a narrow absorption profile at higher absorption values. The transmission spectra also shows the presence of an additional absorber at ~6,250 Ang, observed at both medium and low resolutions. We performed various limb-darkening tests, including using high precision limb-darkening measurements of the sun to characterize a general trend of Atlas models to slightly overestimate the amount of limb-darkening at all wavelengths, likely due to the limitations of the model's one-dimensional nature. We conclude that, despite these limitations, Atlas models can still successfully model limb-darkening in high signal-to-noise transits of solar-type stars, like HD209458, to a high level of precision over the entire optical regime (3,000-10,000 Ang) at transit phases between 2nd and 3rd contact.Comment: 18 pages, 11 figures, Accepted to Ap

Io: IUE observations of its atmosphere and the plasma torus

Two of the main components of the atmosphere of Io, neutral oxygen and sulfur, were detected with the IUE. Four observations yield brightnesses that are similar, regardless of whether the upstream or the downstream sides of the torus plasma flow around Io is observed. A simple model requires the emissions to be produced by the interaction of O and S columns in the exospheric range with 2 eV electrons. Cooling of the 5 eV torus electrons is required prior to their interaction with the atmosphere of Io. Inconsistencies in the characteristics of the spectra that cannot be accounted for in this model require further analysis with improved atomic data. The Io plasma torus was monitored with the IUE. The long-term stability of the warm torus is established. The observed brightnesses were analyzed using a model of the torus, and variations of less than 30 percent in the composition are observed, the quantitative results being model dependent