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Graph games and the pizza problem  [PDF]
Daniel E. Brown,Lawrence G. Brown
Mathematics , 2015,
Abstract: We propose a class of two person perfect information games based on weighted graphs. One of these games can be described in terms of a round pizza which is cut radially into pieces of varying size. The two players alternately take pieces subject to the following rule: Once the first piece has been chosen, all subsequent selections must be adjacent to the hole left by the previously taken pieces. Each player tries to get as much pizza as possible. The original pizza problem was to settle the conjecture that Player One can always get at least half of the pizza. The conjecture turned out to be false. Our main result is a complete solution of a somewhat simpler class of games, concatenations of stacks and two-ended stacks, and we provide a linear time algorithm for this. The algorithm and its output can be described without reference to games. It produces a certain kind of partition of a given finite sequence of real numbers. The conditions on the partition involve alternating sums of various segments of the given sequence. We do not know whether these partitions have applications outside of game theory. The algorithm leads to a quadratic time algorithm which gives the value and an optimal initial move for pizza games. We also provide some general theory concerning the semigroup of equivalence classes of graph games.
Solution of Peter Winkler's Pizza Problem  [PDF]
Josef Cibulka,Jan Kyn?l,Viola Mészáros,Rudolf Stola?,Pavel Valtr
Computer Science , 2008, DOI: 10.1007/978-3-642-13580-4_4
Abstract: Bob cuts a pizza into slices of not necessarily equal size and shares it with Alice by alternately taking turns. One slice is taken in each turn. The first turn is Alice's. She may choose any of the slices. In all other turns only those slices can be chosen that have a neighbor slice already eaten. We prove a conjecture of Peter Winkler by showing that Alice has a strategy for obtaining 4/9 of the pizza. This is best possible, that is, there is a cutting and a strategy for Bob to get 5/9 of the pizza. We also give a characterization of Alice's best possible gain depending on the number of slices. For a given cutting of the pizza, we describe a linear time algorithm that computes Alice's strategy gaining at least 4/9 of the pizza and another algorithm that computes the optimal strategy for both players in any possible position of the game in quadratic time. We distinguish two types of turns, shifts and jumps. We prove that Alice can gain 4/9, 7/16 and 1/3 of the pizza if she is allowed to make at most two jumps, at most one jump and no jump, respectively, and the three constants are the best possible.
The fair and random maximal division of "pizza"  [PDF]
Floyd E. Brown,Anant P. Godbole
Mathematics , 2005,
Abstract: Consider n straight line cuts of a circular pizza made so as to maximize the number of pieces. We investigate how fair such a maximal division may be and how many slices are obtained if the cuts are successfully made with a certain probability.
How to eat 4/9 of a pizza  [PDF]
Kolja Knauer,Piotr Micek,Torsten Ueckerdt
Computer Science , 2008,
Abstract: Given two players alternately picking pieces of a pizza sliced by radial cuts, in such a way that after the first piece is taken every subsequent chosen piece is adjacent to some previously taken piece, we provide a strategy for the starting player to get 4/9 of the pizza. This is best possible and settles a conjecture of Peter Winkler.
The impact of beer type, pizza spiciness and gender on match perceptions  [PDF]
Harrington, Robert J.,Miszczak, Daniel C.,Ottenbacher, Michael C.
PASOS : Revista de Turismo y Patrimonio Cultural , 2008,
Abstract: This exploratory study surveys preferences of participants towards pairing three categories of beer (lager, ale and stout) with a non-spicy and spicy pizza. The goals of this study are to determine the level of a ‘just right’ match of pizza style with each beer type, determine any differences by gender, and to explore if spice has an impact on participants’ beer selection and beer preference. Implications of this research apply to restaurateurs’ ability to appropriately cater their beer and pizza offerings in terms of menu design and pro-duct delivery.
Anti-staphylococcal effectiveness of nisaplin in refrigerated pizza doughs
Freitas, Wilma Carla de;Souza, Evandro Leite de;Sousa, Cristina Paiva de;Travassos, Ant?nio Eustáquio Resende;
Brazilian Archives of Biology and Technology , 2008, DOI: 10.1590/S1516-89132008000300021
Abstract: this study evaluated the effectiveness of nisaplin, commercial product having nisin as active component, in decreasing the staphylococcal population in refrigerated pizza doughs. the refrigerated pizza dough pieces randomly chosen were dipped in the solutions with nisaplin concentrations of 1.0 x 10-3 g and 1.0 x 10-2 g nisaplin/ml named for the treatment a and b and kept under refrigeration (7 °c ± 1 °c). on times 0, 15 and 30 days post treatment the staphylococcus spp. count was carried out. the results showed that both nisaplin treatments were able to reduce the staphylococcus spp. count (cfu/g) in the refrigerated pizza doughs. however, only treatment b showed statistically significant reducer effect (p < 0.05) on the count providing a decrease of 1.0 and 0.98 log cycles, respectively, after 15 and 30 days post treatment. these data suggest that nisin could appear as promising alternative to control the survival of the pathogen microorganisms in the foods, particularly, staphylococcus in the refrigerated pizza doughs.
Arabidopsis PIZZA Has the Capacity to Acylate Brassinosteroids  [PDF]
Katja Schneider, Christian Breuer, Ayako Kawamura, Yusuke Jikumaru, Atsushi Hanada, Shozo Fujioka, Takanari Ichikawa, Youichi Kondou, Minami Matsui, Yuji Kamiya, Shinjiro Yamaguchi, Keiko Sugimoto
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0046805
Abstract: Brassinosteroids (BRs) affect a wide range of developmental processes in plants and compromised production or signalling of BRs causes severe growth defects. To identify new regulators of plant organ growth, we searched the Arabidopsis FOX (Full-length cDNA Over-eXpressor gene) collection for mutants with altered organ size and isolated two overexpression lines that display typical BR deficient dwarf phenotypes. The phenotype of these lines, caused by an overexpression of a putative acyltransferase gene PIZZA (PIZ), was partly rescued by supplying exogenous brassinolide (BL) and castasterone (CS), indicating that endogenous BR levels are rate-limiting for the growth of PIZ overexpression lines. Our transcript analysis further showed that PIZ overexpression leads to an elevated expression of genes involved in BR biosynthesis and a reduced expression of BR inactivating hydroxylases, a transcriptional response typical to low BR levels. Taking the advantage of relatively high endogenous BR accumulation in a mild bri1-301 background, we found that overexpression of PIZ results in moderately reduced levels of BL and CS and a strong reduction of typhasterol (TY) and 6-deoxocastasterone (6-deoxoCS), suggesting a role of PIZ in BR metabolism. We tested a set of potential substrates in vitro for heterologously expressed PIZ and confirmed its acyltransferase activity with BL, CS and TY. The PIZ gene is expressed in various tissues but as reported for other genes involved in BR metabolism, the loss-of-function mutants did not display obvious growth phenotypes under standard growth conditions. Together, our data suggest that PIZ can modify BRs by acylation and that these properties might help modulating endogenous BR levels in Arabidopsis.
Effect of Gamma Radiation and Low Temperature on Pathogenic Staphylococcus aureus Isolated from Pizza  [PDF]
H. Arzina,Md. Zahid Hasan,Abdullah- Al-Mahin,Harun- Or-Rashid
American Journal of Food Technology , 2012,
Abstract: Staphylococcus aureus, a common human pathogen, produces enterotoxin and causes intoxication when ingested through contaminated food. The aim of the present study was to investigate microbiological quality of pizza and to detect the presence of the pathogenic S. aureus in this food. Moreover, effects of gamma radiation and low temperature on inoculated pathogenic S. aureus in pizza were examined. For this purpose, 20 pizza samples were collected from 5 different shops to check the microbiological quality and the presence of S. auresu. Isolated S. aureus were then checked for toxin production by mice assay. Pre-sterilized pizza samples inoculated with toxin producing isolate were then subjected to different gamma radiation doses and kept at refrigerator followed by detecting the presence of viable S. aureus. Among the collected pizza samples, 18 samples showed the presence of high number of total bacterial count, coliform count and staphylococcal count. Microwave heating could completely eliminate the viable counts only after 2 min. Among the isolated Staphylococcus spp., 13 isolates were identified as pathogenic S. aureus and one isolate produced deadly toxin. Radiation dose of 8 kGy resulted in the total elimination of S. aureus inoculated in pizza samples. However, low temperature (4C) storage after gamma radiation showed a drastic change on the growth of the organism. The shelf life of these pizza samples was also extended up to 14 days. Thus, irradiation at 8 kGy with combination of storage at 4C could be the suggested treatment for the storage of such ready-to-eat food without presence of pathogenic S. aureus.
Race and Policy  [cached]
Ernest R. House
Education Policy Analysis Archives , 1999,
Abstract: Beliefs about race have played a central role in American history, literature, and education. Racial beliefs are embedded in the national identity in complex and disguised ways. These beliefs attribute presumed character traits to African Americans and other minorities, who are thought of as different in character and ability, especially the ability to govern themselves. These beliefs lead to education policies which separate, differentiate, and mandate different curricula and treatment for minorities, policies justified as being fair and democratic. These beliefs influence not only curriculum content, but how the schools are organized, financed, and administered at a deeper level than is commonly understood.
Colonialidad, Modernidad y representación en el cine latinoamericano contemporáneo: De Memorias del subdesarrollo a Pizza, Birra, Faso
Aisthesis , 2012, DOI: 10.4067/S0718-71812012000100008
Abstract: the following paper aims to review and analyze how latin america's colonialism and modernity have been represented, built and interrogated in two major films of regional contemporary cinema: memorias del subdesarrollo (memories of underdevelopment) cuba, 1968 and pizza, birra, faso (pizza, beer, fag), argentina, 1998. we have two questions to answer: what images of coloniality and modernity are pictured in these films? how are ?coloniality? and ?modernity? articulated in the selected films?
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