BINGO: A code for the efficient computation of the scalar bi-spectrum

We present a new and accurate Fortran code, the BI-spectra and Non-Gaussianity Operator (BINGO), for the efficient numerical computation of the scalar bi-spectrum and the non-Gaussianity parameter f_{NL} in single field inflationary models involving the canonical scalar field. The code can calculate all the different contributions to the bi-spectrum and the parameter f_{NL} for an arbitrary triangular configuration of the wavevectors. Focusing firstly on the equilateral limit, we illustrate the accuracy of BINGO by comparing the results from the code with the spectral dependence of the bi-spectrum expected in power law inflation. Then, considering an arbitrary triangular configuration, we contrast the numerical results with the analytical expression available in the slow roll limit, for, say, the case of the conventional quadratic potential. Considering a non-trivial scenario involving deviations from slow roll, we compare the results from the code with the analytical results that have recently been obtained in the case of the Starobinsky model in the equilateral limit. As an immediate application, we utilize BINGO to examine of the power of the non-Gaussianity parameter f_{NL} to discriminate between various inflationary models that admit departures from slow roll and lead to similar features in the scalar power spectrum. We close with a summary and discussion on the implications of the results we obtain.Comment: v1: 5 pages, 5 figures; v2: 35 pages, 11 figures, title changed, extensively revised; v3: 36 pages, 11 figures, to appear in JCAP. The BINGO code is available online at http://www.physics.iitm.ac.in/~sriram/bingo/bingo.htm

A study of superstitious beliefs among bingo players

This study was conducted in order to examine the beliefs players have regarding superstition and luck and how these beliefs are related to their gambling behaviour. A self-completion questionnaire was devised and the study was carried out in a large bingo hall in Nottingham, over four nights. 412 “volunteer” bingo players completed the questionnaires. Significant relationships were found in many areas. Many players reported beliefs in luck and superstition; however, a greater percentage of players reported having “everyday” superstitious beliefs, rather than those concerned with bingo

HI intensity mapping with FAST

We discuss the detectability of large-scale HI intensity fluctuations using the FAST telescope. We present forecasts for the accuracy of measuring the Baryonic Acoustic Oscillations and constraining the properties of dark energy. The FAST $19$-beam L-band receivers ($1.05$--$1.45$ GHz) can provide constraints on the matter power spectrum and dark energy equation of state parameters ($w_{0},w_{a}$) that are comparable to the BINGO and CHIME experiments. For one year of integration time we find that the optimal survey area is $6000\,{\rm deg}^2$. However, observing with larger frequency coverage at higher redshift ($0.95$--$1.35$ GHz) improves the projected errorbars on the HI power spectrum by more than $2~\sigma$ confidence level. The combined constraints from FAST, CHIME, BINGO and Planck CMB observations can provide reliable, stringent constraints on the dark energy equation of state.Comment: 7 pages, 3 figures, submitted to "Frontiers in Radio Astronomy and FAST Early Sciences Symposium 2015" conference proceedin

Bingo pricing: a game simulation and evaluation using the derivatives approach

The Bingo game is well known and played all over the world. Its main feature is the sequential drawing without repetition of a set of numbers. Each of these numbers is compared to the numbers contained in the boxes printed on the different rows (and columns) of the score-cards owned by the Bingo participants. The winner will be the participant that firstly is able to check all the boxes (numbers) into a row (Line) or into the entire score-card (Bingo). Assuming that the score-card has a predetermined purchase price and that the jackpot is divided into two shares, respectively for the Bingo and the Line winner, it is evident that all the score-cards show the same starting value (initial price). After each drawing, every score-card will have different values (current price(s)) according with its probability to gain the Line and/or the Bingo. This probability depends from the number of checked boxes in the rows of the score-card and from the number of checked boxes in the rows of all the other playing score-cards. The first aim of this paper is to provide the base data structure of the problem and to formalize the needed algorithms for the initial price and current price calculation. The procedure will evaluate the single score-card and/or the whole set of playing score-cards according to the results of the subsequent drawings. In fact, during the game development and after each drawing, it will be possible to know the value of each score-card in order to choose if maintain it or sell it out. The evaluation will work in accordance to the traditional Galilee's method of "the interrupted game jackpot repartition". This approach has been also mentioned by Blaise Pascal and Pierre de Fermat in their mail exchange about the "jackpot problem". More advanced objective of the paper would be the application of the stock exchange techniques for the calculation of the future price of the score-card (and/or of a set of score-cards) that will have some checked numbers after a certain number of future drawings. In the same way will be calculated the value of the right to purchase or sell a score-card (and/or of a set of score-cards) at a pre-determined price (option price). Especially during the prototyping phase, the modelling and the development of these kind of problems need the use of computational environments able to manage structured data and with high calculation skills. The software that meet these requirements are APL, J and Matlab , as for their capability to use nested arrays and for the endogenous parallelism features of the programming environments. In this paper we will show the above mentioned issues through the use of Apl2Win/IBM . The formalisation of the game structure has been made in a general way, in order to foresee particular cases that act differently from the Bingo. In this way it is possible to simulate the traditional game with 90 numbers in the basket, 3 rows per 10 columns score-cards, 15 number for the Bingo and 5 numbers for the Line but already, for example, the Roulette with 37 (or 38) numbers, score-cards with 1 (or more) row and 1 column and Line with just 1 number.bingo, options, futures, gambling, market, evaluation