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

Aurelio, Girolamo e Ludovico Lombardi, fratelli scultori del Cinquecento

The PhD thesis, structured in eight chapters and three appendixes, focuses on Aurelio (1502/1504-1563), Girolamo (1506/1507-1584-1589) and Ludovico (about 1510 - 1575) Lombardi. These Venetian-Ferrarese sculptors, known mainly as Antonio Lombardo's sons, were some of the protagonists of the sixteenth century.My manuscript starts analyzing the fortune of the three masters in literature, from Vasari's Lives (1568) up to the most recent printed contributions. The remaining chapters, instead, investigate Lombardi’s entire career, through the various places where they worked. Although there was no total lack of studies on them, a complete catalogue was still missing: so the main purpose of the thesis is to read the single works in relation to the stylistic facts of the time and to define the artistic specimens of the three brothers. This has allowed new additions to Lombardi’s corpus, but also a more precise focus on works so far attributed to them.The second and third chapters are dedicated to the years of their training, spent in Ferrara and Venice: in these interventions the subject is also largely concentrated on the figurative influences in those cities. The fourth and fifth chapters, on the other hand, face the arrival of the three artists in the Marche region towards the end of the fourth decade of sixteenth century, first in Pesaro and then in Loreto, where they worked as official sculptors of the Santa Casa. The sixth chapter examines Ludovico’s activity in Rome, which can be dated between 1545 and 1550, and consists of bronze portrait-busts inspired by antiquities. The seventh and eighth chapters, finally, retrace the last years of the Lombardi’s production, from the bronze Eucharistic Tabernacle set up in the Milan Cathedral to the last, extraordinary works for the Basilica of Loreto.These essays, as partly anticipated, are followed by a list of illustrations, a documentary appendix, bibliography and images.&nbsp

Chemical abundances and properties of the ionized gas in NGC 1705

We obtained [O III] narrow-band imaging and multi-slit MXU spectroscopy of the blue compact dwarf (BCD) galaxy NGC 1705 with FORS2@VLT to derive chemical abundances of PNe and H II regions and, more in general, to characterize the properties of the ionized gas. The auroral [O III]\lambda4363 line was detected in all but one of the eleven analyzed regions, allowing for a direct estimate of their electron temperature. The only object for which the [O III]\lambda4363 line was not detected is a possible low-ionization PN, the only one detected in our data. For all the other regions, we derived the abundances of Nitrogen, Oxygen, Neon, Sulfur and Argon out to ~ 1 kpc from the galaxy center. We detect for the first time in NGC 1705 a negative radial gradient in the oxygen metallicity of -0.24 \pm 0.08 dex kpc^{-1}. The element abundances are all consistent with values reported in the literature for other samples of dwarf irregular and blue compact dwarf galaxies. However, the average (central) oxygen abundance, 12 + log(O/H)=7.96 \pm 0.04, is ~0.26 dex lower than previous literature estimates for NGC 1705 based on the [O III]\lambda4363 line. From classical emission-line diagnostic diagrams, we exclude a major contribution from shock excitation. On the other hand, the radial behavior of the emission line ratios is consistent with the progressive dilution of radiation with increasing distance from the center of NGC 1705. This suggests that the strongest starburst located within the central $\sim$150 pc is responsible for the ionization of the gas out to at least $\sim$1 kpc. The gradual dilution of the radiation with increasing distance from the center reflects the gradual and continuous transition from the highly ionized H II regions in the proximity of the major starburst into the diffuse ionized gas.Comment: Accepted for publication on A

The galaxy-wide distributions of mean electron density in the HII regions of M51 and NGC 4449

Using ACS-HST images to yield continuum subtracted photometric maps in H\alpha of the Sbc galaxy M51 and the dwarf irregular galaxy NGC 4449, we produced extensive (over 2000 regions for M51, over 200 regions for NGC4449) catalogues of parameters of their HII regions: their H\alpha luminosities, equivalent radii and coordinates with respect to the galaxy centers. From these data we derived, for each region, its mean luminosity weighted electron density, , determined from the H\alpha luminosity and the radius, R, of the region. Plotting these densities against the radii of the regions we find excellent fits for varying as R^{-1/2}. This relatively simple relation has not, as far as we know, been predicted from models of HII region structure, and should be useful in constraining future models. Plotting the densities against the galactocentric radii, r, of the regions we find good exponential fits, with scale lengths of close to 10 kpc for both galaxies. These values are comparable to the scale lengths of the HI column densities for both galaxies, although their optical structures, related to their stellar components are very different. This result indicates that to a first approximation the HII regions can be considered in pressure equilibrium with their surroundings. We also plot the electron density of the HII regions across the spiral arms of M51, showing an envelope which peaks along the ridge lines of the arms.Comment: Accepted for publication in ApJ Letters. 5 pages, 5 figures. Formatted with emulateap

The cluster population of the irregular galaxy NGC 4449 as seen by the Hubble Advanced Camera for Surveys

We present a study of the star cluster population in the starburst irregular galaxy NGC 4449 based on B, V, I, and Ha images taken with the Advanced Camera for Surveys on the Hubble Space Telescope. We derive the cluster properties such as size, ellipticity, and total magnitudes. Cluster ages and masses are derived fitting the observed spectral energy distributions with different population synthesis models. Our analysis is strongly affected by the age-metallicity degeneracy; however, if we assume a metallicity of ~1/4 solar, as derived from spectroscopy of HII regions, we find that the clusters have ages distributed quite continuously over a Hubble time, and they have masses from ~10^3 M_sun up to ~2 x 10^6 M_sun, assuming a Salpeters' IMF down to 0.1 M_sun. Young clusters are preferentially located in regions of young star formation, while old clusters are distributed over the whole NGC 4449 field of view, like the old stars (although we notice that some old clusters follow linear structures, possibly a reflection of past satellite accretion). The high SF activity in NGC 4449 is confirmed by its specific frequency of young massive clusters, higher than the average value found in nearby spirals and in the LMC (but lower than in other starburst dwarfs such as NGC 1705 and NGC 1569), and by the flat slope of the cluster luminosity function (dN(L_V)\propto L_V^{-1.5} dL for clusters younger than 1 Gyr). We use the upper envelope of the cluster log(mass) versus log(age) distribution to quantify cluster disruption, and do not find evidence for the high (90%) long-term infant mortality found by some studies. For the red clusters, we find correlations between size, ellipticity, luminosity and mass: brighter and more massive clusters tend to be more compact, and brighter clusters tend to be also more elliptical.Comment: Accepted for publication on AJ, one data point changed in Fig. 1

Prevention of neurological injuries during mandibular third molar surgery: technical notes

Surgery to the mandibular third molar is common, and injuries to the inferior alveolar nerve and the lingual nerve are well-recognized complications of this procedure. The aim of these technical notes is to describe operative measures for reducing neurological complications during mandibular third molar surgery. The following procedure should be used to prevent damage to the inferior alveolar nerve: a well-designed mucoperiosteal flap, to obtain appropriate access to the surgical area; a conservative ostectomy on the distal and distal-lingual side; tooth sectioning, to facilitate its removal by decreasing the retention zones; tooth dislocation in the path of withdrawal imposed by the curvature of the root apex; and careful socket debridement, when the roots of the extracted tooth are in intimate contact with the mandibular canal. To prevent injury to the lingual nerve, it is important (I) to assess the integrity of the mandibular inner cortex and exclude the presence of fenestration, which could cause the dislocation of the tooth or its fragment into the sublingual or submandibular space; (II) to avoid inappropriate or excessive dislocation proceedings, in order to prevent lingual cortex fracture; (III) to perform horizontal mesial-distal crown sectioning of the lingually inclined tooth; (IV) to protect the lingual flap with a retractor showing the cortical ridge; and (V) to pass the suture not too apically and from the inner side in a buccal-lingual direction in the retromolar are

Performance of mesenchymal cell-scaffold constructs in human oral reconstructive surgery: a systematic review

Background: Different sources of cultured cells combined with different scaffolds (allogenic, xenogeneic, alloplastic or composite materials) have been tested extensively in vitro and in preclinical animal studies, but there have been only a few clinical trials involving humans. Aim: This study reviewed all of the English language literature published between January 1990 and December 2015 to assess the histological performance of different mesenchymal cell-scaffold constructs used for bone regeneration in human oral reconstructive procedures. Methods: An electronic search of the MEDLINE and Cochrane Central Register of Controlled Trials databases complemented by manual searching was conducted to identify studies involving histological evaluation of mesenchymal cell-scaffold constructs in human oral surgical procedures. The methodological quality of randomized controlled clinical trials and controlled clinical trials was assessed using the Cochrane Collaboration tool for assessing the risk of bias. Heterogeneity was assessed using Review Manager software. Considering the heterogeneity, the data collected were reported by descriptive methods and a meta-analysis was applied only to the articles that reported the same outcome measures. The articles were classified and described based on the material scaffolds used. Results: The search identified 1030 titles and 287 abstracts. Full-text analysis was performed for 32 articles, revealing 14 studies that fulfilled the inclusion criteria. Three randomized controlled clinical trials were identified as potentially eligible for inclusion in a meta-analysis. The studies were grouped according to the scaffold materials used: bone allograft (three studies), polyglycolic-polylactic scaffold (four studies), collagen sponge (two studies), and bovine bone matrix (five studies). The stem cells used in these studies had been sourced from the iliac crest, periosteum, dental pulp and intraoral sites. Conclusions: The very small amount of available data makes it impossible to draw any firm conclusions regarding the increase in bone formation in human oral reconstructive procedures when using graft materials engineered with autogenous stem cells