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

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

Prefactorized subgroups in pairwise mutually permutable products

The final publication is available at Springer via http://dx.doi.org/10.1007/s10231-012-0257-yWe continue here our study of pairwise mutually and pairwise totally permutable products. We are looking for subgroups of the product in which the given factorization induces a factorization of the subgroup. In the case of soluble groups, it is shown that a prefactorized Carter subgroup and a prefactorized system normalizer exist.Aless stringent property have F-residual, F-projector and F-normalizer for any saturated formation F including the supersoluble groups.The first and fourth authors have been supported by the grant MTM2010-19938-C03-01 from MICINN (Spain).Ballester-Bolinches, A.; Beidleman, J.; Heineken, H.; Pedraza Aguilera, MC. (2013). Prefactorized subgroups in pairwise mutually permutable products. Annali di Matematica Pura ed Applicata. 192(6):1043-1057. https://doi.org/10.1007/s10231-012-0257-yS104310571926Amberg B., Franciosi S., de Giovanni F.: Products of Groups. Clarendon Press, Oxford (1992)Ballester-Bolinches, A., Pedraza-Aguilera, M.C., Pérez-Ramos, M.D.: Totally and Mutually Permutable Products of Finite Groups, Groups St. Andrews 1997 in Bath I. London Math. Soc. Lecture Note Ser. 260, 65–68. Cambridge University Press, Cambridge (1999)Ballester-Bolinches A., Pedraza-Aguilera M.C., Pérez-Ramos M.D.: On finite products of totally permutable groups. Bull. Aust. Math. Soc. 53, 441–445 (1996)Ballester-Bolinches A., Pedraza-Aguilera M.C., Pérez-Ramos M.D.: Finite groups which are products of pairwise totally permutable subgroups. Proc. Edinb. Math. Soc. 41, 567–572 (1998)Ballester-Bolinches A., Beidleman J.C., Heineken H., Pedraza-Aguilera M.C.: On pairwise mutually permutable products. Forum Math. 21, 1081–1090 (2009)Ballester-Bolinches A., Beidleman J.C., Heineken H., Pedraza-Aguilera M.C.: Local classes and pairwise mutually permutable products of finite groups. Documenta Math. 15, 255–265 (2010)Beidleman J.C., Heineken H.: Mutually permutable subgroups and group classes. Arch. Math. 85, 18–30 (2005)Beidleman J.C., Heineken H.: Group classes and mutually permutable products. J. Algebra 297, 409–416 (2006)Carocca A.: p-supersolvability of factorized groups. Hokkaido Math. J. 21, 395–403 (1992)Carocca, A., Maier, R.: Theorems of Kegel-Wielandt Type Groups St. Andrews 1997 in Bath I. London Math. Soc. Lecture Note Ser. 260, 195–201. Cambridge University Press, Cambridge, (1999)Doerk K., Hawkes T.: Finite Soluble Groups. Walter De Gruyter, Berlin (1992)Maier R., Schmid P.: The embedding of quasinormal subgroups in finite groups. Math. Z. 131, 269–272 (1973

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

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

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

Estimating the spectrum of a density matrix with LOCC

The problem of estimating the spectrum of a density matrix is considered. Other problems, such as bipartite pure state entanglement, can be reduced to spectrum estimation. A local operations and classical communication (LOCC) measurement strategy is shown which is asymptotically optimal. This means that, for a very large number of copies, it becomes unnecessary to perform collective measurements which should be more difficult to implement in practice.Comment: 12 pages, uses iopart.cls and iopart10.clo. Improved version. v3: Reference updated, added journal referenc

On a theorem of Kang and Liu on factorised groups

[EN] Kang and Liu ['On supersolvability of factorized finite groups', Bull. Math. Sci. 3 (2013), 205-210] investigate the structure of finite groups that are products of two supersoluble groups. The goal of this note is to give a correct proof of their main theorem.The first author was supported by the grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union, and a project of Natural Science Foundation of Guangdong Province (No. 2015A030313791).Ballester-Bolinches, A.; Pedraza Aguilera, MC. (2018). On a theorem of Kang and Liu on factorised groups. Bulletin of the Australian Mathematical Society. 97(1):54-56. https://doi.org/10.1017/S0004972717000363S5456971Ezquerro, L. M., & Soler-Escrivà, X. (2003). On MutuallyM-Permutable Products of Finite Groups. Communications in Algebra, 31(4), 1949-1960. doi:10.1081/agb-120018515Kang, P., & Liu, Q. (2013). On supersolvability of fatorized finite groups. Bulletin of Mathematical Sciences, 3(2), 205-210. doi:10.1007/s13373-013-0032-4Ballester-Bolinches, A., Esteban-Romero, R., & Asaad, M. (2010). Products of Finite Groups. de Gruyter Expositions in Mathematics. doi:10.1515/9783110220612Ballester-Bolinches, A., Cossey, J., & Pedraza-Aguilera, M. C. (2001). ON PRODUCTS OF FINITE SUPERSOLUBLE GROUPS. Communications in Algebra, 29(7), 3145-3152. doi:10.1081/agb-501