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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.
Pizza Race Problem  [PDF]
Keyue Gao
Mathematics , 2012,
Abstract: This paper deals with a problem in which two players share a previously sliced pizza and try to eat as much amount of pizza as they can. It takes time to eat each piece of pizza and both players eat pizza at the same rate. One is allowed to take a next piece only after the person has finished eating the piece on hand. Also, after the first piece is taken, one can only take a piece which is adjacent to already-taken piece. This paper shows that, in this real time setting, the starting player can always eat at least two-fifth of the total size of the pizza. However, this may not be the best possible amount the starting player can eat. It is a modified problem from an original one where two players takes piece alternatively instead.
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.
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.
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.
Colonialidad, Modernidad y representación en el cine latinoamericano contemporáneo: De Memorias del subdesarrollo a Pizza, Birra, Faso
Salinas,Claudio;
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?
Avalia??o de filme incorporado com óleo essencial de orégano para conserva??o de pizza pronta
Botre, Diego Alvarenga;Soares, Nilda de Fatima Ferreira;Espitia, Paula Judith Perez;Sousa, Solange de;Renhe, Isis Rodrigues Toledo;
Revista Ceres , 2010, DOI: 10.1590/S0034-737X2010000300001
Abstract: the consumption of ready-to-eat pizzas has increased in the last years because of the handiness of the product, its low cost, good flavour and nutritional value. however, ready-to-eat pizzas undergo intense manipulation during processing, contributing to spoilage, reducing the quality and increasing the risks of contamination by pathogens. besides convenient products, consumers also seek for safer foods, with increasing demand for the use of natural compounds as food preservatives. among them, the oregano essential oil presents antimicrobial activity and it is a spice used in the cookery of several countries. the objective of this work was to develop a cellulosic film incorporated with oregano essential oil for the conservation of refrigerated ready-to-eat pizza. the oregano essential oil incorporated to the film, in the concentrations of 25% and 50% w/w, showed in vitro inhibitory effect against penicillium spp., and staphylococcus aureus. when the oil was applied to the pizza, it caused a decrease in the compounds ?-cymene and ?-terpinene and a consequent increase in tymol and carvacrol concentrations; however, in an amount probably not enough for the inhibitory effect against microorganisms. the mechanical resistance of the films incorporated with 25% and 50% of oregano essential oil was reduced, and film tenacity increased by 50% compared with the control (0%). the use of films incorporated with oregano essential oil for pizza packaging is of great interest, since the oregano is already an ingredient of the product and therefore it does not compromise the flavour and aroma of the product.
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.
How do drug users define their progress in harm reduction programs? Qualitative research to develop user-generated outcomes
Terry Ruefli, Susan J Rogers
Harm Reduction Journal , 2004, DOI: 10.1186/1477-7517-1-8
Abstract: The study used nominal group technique (NGT) to develop the outcomes (phase 1) and focus group interviews to help validate the findings (phase 2). Study participants were recruited from a large harm-reduction program in New York City and involved approximately 120 clients in 10 groups in phase 1 and 120 clients in 10 focus groups in phase 2.Outcomes of 10 life areas important to drug users were developed that included between 10 to 15 incremental measures per outcome. The outcomes included ways of 1) making money; 2) getting something good to eat; 3) being housed/homeless; 4) relating to families; 5) getting needed programs/benefits/services; 6) handling health problems; 7) handling negative emotions; 8) handling legal problems; 9) improving oneself; and 10) handling drug-use problems. Findings also provided insights into drug users' lives and values, as well as a window into understanding how this population envisions a better quality of life. Results challenged traditional ways of measuring drug users based solely on quantity used and frequency of use. They suggest that more appropriate measures are based on the extent to which drug users organize their lives around drug use and how much drug use is integrated into their lives and negatively impacts other aspects of their lives.Harm reduction and other programs serving active drug users and other marginalized people should not rely on institutionalized, provider-defined solutions to problems in living faced by their clients.Harm reduction programs operate with the assumption that some people who engage in high-risk behaviors are unwilling or unable to abstain. Using a "low-threshold approach," they do not require that clients abstain from drug use in order to gain access to services, nor expect adherence to one service to be eligible for another. Rather than having abstinence goals set for them, clients in such programs take part in a goal-setting process, an approach that has been shown to correlate consistently
Colonialidad, Modernidad y representación en el cine latinoamericano contemporáneo: De Memorias del subdesarrollo a Pizza, Birra, Faso Coloniality, Modernity and Representations in Today's Latin American Cinema: From Memories Of Underdevelopment To Pizza, Beer, Fag  [cached]
Claudio Salinas
Aisthesis , 2012,
Abstract: El artículo pretende revisar y analizar las maneras en que la colonialidad y las modernidades en América Latina han sido representadas, construidas y problematizadas en dos películas importantes para la cinematografía latinoamericana contemporánea: Memorias del Subdesarrollo (Cuba, 1968) y Pizza, Birra, Faso (Argentina, 1998). Dos son las preguntas que articulan el texto: Qué imágenes de la colonialidad y la modernidad se despliegan en estas películas? Cómo se articulan colonialidad y modernidad en las piezas visuales seleccionadas? 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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