Fibrational induction rules for initial algebras

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of particular syntactic forms. We establish the correctness of our generic induction rule by reducing induction to iteration. We show how our rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The former lies outside the scope of Hermida and Jacobs’ work because it is not polynomial; as far as we are aware, no induction rules have been known to exist for the latter two in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set

On Online Labeling with Polynomially Many Labels

In the online labeling problem with parameters n and m we are presented with a sequence of n keys from a totally ordered universe U and must assign each arriving key a label from the label set {1,2,...,m} so that the order of labels (strictly) respects the ordering on U. As new keys arrive it may be necessary to change the labels of some items; such changes may be done at any time at unit cost for each change. The goal is to minimize the total cost. An alternative formulation of this problem is the file maintenance problem, in which the items, instead of being labeled, are maintained in sorted order in an array of length m, and we pay unit cost for moving an item. For the case m=cn for constant c>1, there are known algorithms that use at most O(n log(n)^2) relabelings in total [Itai, Konheim, Rodeh, 1981], and it was shown recently that this is asymptotically optimal [Bul\'anek, Kouck\'y, Saks, 2012]. For the case of m={\Theta}(n^C) for C>1, algorithms are known that use O(n log n) relabelings. A matching lower bound was claimed in [Dietz, Seiferas, Zhang, 2004]. That proof involved two distinct steps: a lower bound for a problem they call prefix bucketing and a reduction from prefix bucketing to online labeling. The reduction seems to be incorrect, leaving a (seemingly significant) gap in the proof. In this paper we close the gap by presenting a correct reduction to prefix bucketing. Furthermore we give a simplified and improved analysis of the prefix bucketing lower bound. This improvement allows us to extend the lower bounds for online labeling to the case where the number m of labels is superpolynomial in n. In particular, for superpolynomial m we get an asymptotically optimal lower bound {\Omega}((n log n) / (log log m - log log n)).Comment: 15 pages, Presented at European Symposium on Algorithms 201

Constraints on the Ultra High Energy Photon flux using inclined showers from the Haverah Park array

We describe a method to analyse inclined air showers produced by ultra high energy cosmic rays using an analytical description of the muon densities. We report the results obtained using data from inclined events (60^{\circ}<\theta<80^{\circ}) recorded by the Haverah Park shower detector for energies above 10^19 eV. Using mass independent knowledge of the UHECR spectrum obtained from vertical air shower measurements and comparing the expected horizontal shower rate to the reported measurements we show that above 10^19 eV less than 48 % of the primary cosmic rays can be photons at the 95 % confidence level and above 4 X 10^19 eV less than 50 % of the cosmic rays can be photonic at the same confidence level. These limits place important constraints on some models of the origin of ultra high-energy cosmic rays.Comment: 45 pages, 25 figure

The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Application

A New Measurement of Kaonic Hydrogen X rays

The $\bar{K}N$ system at threshold is a sensitive testing ground for low energy QCD, especially for the explicit chiral symmetry breaking. Therefore, we have measured the $K$-series x rays of kaonic hydrogen atoms at the DA$\Phi$NE electron-positron collider of Laboratori Nazionali di Frascati, and have determined the most precise values of the strong-interaction energy-level shift and width of the $1s$ atomic state. As x-ray detectors, we used large-area silicon drift detectors having excellent energy and timing resolution, which were developed especially for the SIDDHARTA experiment. The shift and width were determined to be $\epsilon_{1s} = -283 \pm 36 \pm 6 {(syst)}$ eV and $\Gamma_{1s} = 541 \pm 89 {(stat)} \pm 22 {(syst)}$ eV, respectively. The new values will provide vital constraints on the theoretical description of the low-energy $\bar{K}N$ interaction.Comment: 5 figures, submitted to Physics Letters

Transforming data by calculation

Thispaperaddressesthefoundationsofdata-modeltransformation.A catalog of data mappings is presented which includes abstraction and representa- tion relations and associated constraints. These are justified in an algebraic style via the pointfree-transform, a technique whereby predicates are lifted to binary relation terms (of the algebra of programming) in a two-level style encompassing both data and operations. This approach to data calculation, which also includes transformation of recursive data models into “flat” database schemes, is offered as alternative to standard database design from abstract models. The calculus is also used to establish a link between the proposed transformational style and bidi- rectional lenses developed in the context of the classical view-update problem.Fundação para a Ciência e a Tecnologia (FCT

Measurement of the Bs0→J/ψKS0B_s^0\to J/\psi K_S^0 branching fraction

The $B_s^0\to J/\psi K_S^0$ branching fraction is measured in a data sample corresponding to 0.41$fb^{-1}$ of integrated luminosity collected with the LHCb detector at the LHC. This channel is sensitive to the penguin contributions affecting the sin2$\beta$ measurement from $B^0\to J/\psi K_S^0$ The time-integrated branching fraction is measured to be $BF(B_s^0\to J/\psi K_S^0)=(1.83\pm0.28)\times10^{-5}$. This is the most precise measurement to date

Measurement of the CP-violating phase \phi s in Bs->J/\psi\pi+\pi- decays

Measurement of the mixing-induced CP-violating phase phi_s in Bs decays is of prime importance in probing new physics. Here 7421 +/- 105 signal events from the dominantly CP-odd final state J/\psi pi+ pi- are selected in 1/fb of pp collision data collected at sqrt{s} = 7 TeV with the LHCb detector. A time-dependent fit to the data yields a value of phi_s=-0.019^{+0.173+0.004}_{-0.174-0.003} rad, consistent with the Standard Model expectation. No evidence of direct CP violation is found.Comment: 15 pages, 10 figures; minor revisions on May 23, 201

Measurement of the ratio of branching fractions BR(B0 -> K*0 gamma)/BR(Bs0 -> phi gamma) and the direct CP asymmetry in B0 -> K*0 gamma

The ratio of branching fractions of the radiative B decays B0 -> K*0 gamma and Bs0 phi gamma has been measured using an integrated luminosity of 1.0 fb-1 of pp collision data collected by the LHCb experiment at a centre-of-mass energy of sqrt(s)=7 TeV. The value obtained is BR(B0 -> K*0 gamma)/BR(Bs0 -> phi gamma) = 1.23 +/- 0.06(stat.) +/- 0.04(syst.) +/- 0.10(fs/fd), where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is associated with the ratio of fragmentation fractions fs/fd. Using the world average value for BR(B0 -> K*0 gamma), the branching fraction BR(Bs0 -> phi gamma) is measured to be (3.5 +/- 0.4) x 10^{-5}. The direct CP asymmetry in B0 -> K*0 gamma decays has also been measured with the same data and found to be A(CP)(B0 -> K*0 gamma) = (0.8 +/- 1.7(stat.) +/- 0.9(syst.))%. Both measurements are the most precise to date and are in agreement with the previous experimental results and theoretical expectations.Comment: 21 pages, 3 figues, 4 table