PennScience Volume 9 Issue 1

Contents Features 4 The H1N1 Pandemic 7 How Vaccines are Made

Interviews 18 Dr. David Roos 20 Dr. Helen C. Davies

10 Vaccines: Why People Say ‘No’

Research Articles care as seen in foraging bouts of mo22 Parental nogamous owl monkeys (Aotus azarai azarai)

BRIAN LAIDLAW & VARUN PATEL

SANDERS CHANG & ISABEL FAN

SALLY CHU & ANGELO LEE

Research at Penn

14 Understanding the Yersinia pestis bacterium Bacteria in Cholera Patho15 Quorum-Sensing genesis Good Infection: Using Bacteria to Fight 17 ACancer

DEPARTMENT OF BIOLOGY

DEPARTMENT OF MICROBIOLOGY

RACHEL GITTELMAN

Zero-Sum Poker Models with One 26 Two-Player and Two Rounds of Betting HANZHE ZHANG

Energy Ultrasonic Irradiation: Potential 30 Low Applications in Oil Refinement JAMES MANDAGLIO

About PennScience PennScience is a peer reviewed journal of undergraduate research published by the Science and Technology Wing at the University of Pennsylvania. PennScience is an undergraduate journal that is advised by a board of faculty members.

PennScience presents relevant science features, interviews, and research articles from many disciplines including biologial sciences, chemistry, physics, mathematics, geological sciences, and computer sciences.

PennScience is a SAC funded organization.

For additional information about the journal including submission guidelines, visit http://www.pennscience.org.

Journal Staff EXECUTIVE BOARD

GENERAL STAFF

Editors-In-Chief Vishesh Agrawal AJ Argall

Assistant Editing Managers Varun Patel Zhu Wang Emily Xue

Editing Managers Brian Laidlaw Nikhil Shankar Layout Managers Isabel Fan Hijoo Karen Kim Publicity Manager Iris Braunstein Steven Chen Writing Managers Brian Laidlaw Isabel Fan Faculty Advisors Dr. M. Krimo Bokreta Dr. Jorge Santiago-Aviles

Assistant Layout Managers Steven Chen Writing Sanders Chang Sally Chu Angelo Lee Susan Sheng Editing Abraham Chanales Sanders Chang Sally Chu Rachel Grosser Sarah Johnson Jenny Lin Qinnan Lin Susan Sheng Jiaming Zhang Cover Design Maggie Edkins Website Raghav Puranmalka

Research Laboratory at the Hospital of the University of Pennsylvania ca. 1940. Photo courtesy of University Archives.

Copyright Š 2010 PennScience Journal of Undergraduate Research. The authors of the individual research articles published in this journal retain all rights to their work. No part of PennScience Journal of Undergraduate Research may be reprinted, reproduced, or transmitted in any form or by any means without permission in writing from PennScience or the individual authors, whichever is appropriate.

Letter from the Editors Dear Readers, We are proud to introduce you to our 9th volume of PennScience and our first as Editors in Chief. We have dedicated ourselves to continuing the strong tradition of PennScience by further improving upon the quality of the journal and its content in order to better inform our readers about important and interesting topics in science.

The theme of this issue, Infectious Diseases, was inspired by a resurgence of interest following the H1N1 pandemic. Most notably, Vice President Joe Biden encouraged Americans to avoid confined areas, and many Penn upperclassmen will remember long lines of students waiting to get vaccinated. To an extent, this was justified: the WHO approximates 17,000 deaths were caused by the virus. However, H1N1 symptoms rarely exceeded those of the typical seasonal flu.

The PennScience staff decided to examine infectious diseases from a range of viewpoints. We spoke with two Penn faculty members, Professors David Roos and Helen Davies, who are doing groundbreaking research in the field of infectious disease. Additionally, our Writing committee has written a series of compelling articles on the issue. Isabel Fan and Sanders Chang examine how vaccines are made and tested, and why they work. Other articles include an account of the H1N1 pandemic and an analysis of why people are often skeptical of vaccines. We also present a series of features examining the exiciting research happening in the Microbiology Department. Challenging the widespread view that microbes are bad, one article explains a cancer treatment proposal using bacteria to initiate an immune response against tumors. Additional articles delve into the complexities of quorum sensing bacteria and novel ways to prevent the harmful effects of potential bioweapons.

As always, this semester’s PennScience has several terrific undergraduate research papers. Hanzhe Zhang presents an analysis of poker play using game theory. Rachel Gittelman has studied a rare species of owl monkey that exhibits male paternal care. Finally, James Mandaglio presents a review of low energy ultrasonic radiation and how it might be used in oil refinement.

We would like to thank the groups and individuals that make our work at PennScience possible. First, we owe our funding to the Student Activities Council and the Science and Technology Wing, without which we could not publish a high-quality journal in full color. Second, we would like to thank our faculty advisors for their constant support and insight. Lastly, we would like to thank the Penn faculty that took the time to meet with us to discuss their research.

Thank you for reading PennScience, and we hope you enjoy our latest issue!

Sincerely, Arthur Argall and Vishesh Agrawal Co-Editors-in-Chief

Features

The 2009 H1N1 Pandemic BRIAN LAIDLAW & VARUN PATEL • University of Pennsylvania

THE VIRUS EMERGED FROM THE MOUNTAINS OF MEXICO, RAPIDLY DESCENDING ON AN UNSUSPECTING AND VULNERABLE POPULATION. As the virus’ reach extended to more countries, panic spread along with it as governments resorted to quarantines and the mass slaughter of pigs in an attempt to slow the virus down (1). It had begun in April of 2009, a time of year normally associated with the end of flu season, as large numbers of Mexicans suddenly became sick with a flu-like illness (2). However, unlike the seasonal flu, which most people have some immunity against, this flu seemed to be an entirely different strain. By the end of April, 113,000-375,000 Mexicans had already become infected with the new virus, and the number of cases was still increasing (3). Despite the aggressive actions of the Mexican government, which by the end of April had closed all schools and public gathering places in the country, the virus would not be contained. The first cases in the United States were reported as early as late March with confirmed cases in all fifty states by the end of May (4). In June 2009, as the outbreak spread to all corners of the globe and the total number of cases continued to increase, the World Health Organization (WHO) declared the H1N1 influenza outbreak a pandemic, the first since the 1968-69 flu season which claimed an estimated one million people worldwide.

www.pennscience.org

4

Features

T

he H1N1 virus differs from the normal seasonal flu by its genetic makeup. Each flu season, one to two different strains of influenza circulate within the general population causing infections. As the flu season progresses and people gain immunity, the strain loses its ability to infect new individuals. However, through a process known as antigenic drift, the virus is able to mutate itself in such a way that individuals are no longer protected against that strain. It is for this reason that a vaccine against the flu is only effective for one or possibly two years, forcing scientists to constantly develop new vaccines against strains circulating in a given year. Despite this constant mutation, people maintain a certain base level of protection since they have been exposed to a similar strain of the flu, thereby limiting the potential for an outbreak to occur. On rare occasions, however, through a process called antigenic shift, influenza undergoes a complete change in genetic makeup into a strain never exposed to humans and to which we have no immunity. This complete lack of protection leaves people extremely vulnerable to infection and creates the kind of conditions necessary for a pandemic.

It was exactly this type of scenario that occurred in the spring of 2009. Through a gene reassortment between North American and Eurasian swine H1N1 viruses, as well as the avian flu, a novel strain of influenza emerged against which people had very little to no immunity (2). This lack of protection allowed the virus to sweep across the world at a rapid pace, reaching pandemic status within months of its emergence. In addition to this rapid spread, several other disturbing characteristics of the virus soon began to emerge. Typically, influenza heavily affects the young and elderly, leaving those with a strong immune system relatively unaffected. However, H1N1 exhibits the reverse pattern of infection and seems to target those who are most healthy. The unique pathogenesis of the virus became increasingly clear throughout the fall as the pandemic swept through college campuses, infecting students by the hundreds. Another ominous observation was that there already were a high number of cases by November, whereas there are normally few cases during this time. Given that the flu season generally peaks in February, it seemed possible that the situation would continue to worsen. Since a hallmark of the 1918 influenza pandemic, which killed an estimated fifty million people worldwide, was its ability to infect those with healthy immune systems, many were concerned that the virulence of the H1N1 virus could be similar to that strain of influenza (5).

With this concern in mind, many researchers have studied the virulence of the H1N1 virus using animals. Using mammalian models, one group found that H1N1 was more pathogenic than the seasonal flu and had an ability to replicate in the lung and cause appreciable damage, a trait shared by highly pathogenic viruses. It was suggested that sustained person-to-person transmission of the virus could result in the emergence of more pathogenic strains (6). This result was confirmed using ferrets, finding that H1N1-infected ferrets had higher levels of virus then those 5

PennScience Journal of Undergraduate Research

infected with seasonal strains (7). While the ferrets infected with seasonal flu only had viral replication in the nasal cavity, H1N1 infected ferrets had replication in the trachea, bronchi, and bronchioles. Despite this increased virulence compared to the seasonal flu, H1N1 was determined to be a relatively mild virus compared to more pathogenic strains such as the 1918 flu (7).

H1N1 was able to efficiently replicate in human immune cells such as macrophages and primary dendritic cells and displayed an ability to avoid the activation of the innate immune response (1). The replication speed of H1N1 was determined to be comparable to that of the seasonal flu but it failed to generate the type of robust cytokine response that is a distinguishing characteristic of pathogenic strains. For example, it was found that H1N1 in the vast majority of cases only resulted in a mild respiratory tract illness similar to that of the seasonal flu. H1N1 infection did result in gastrointestinal symptoms in a significant number of cases which is atypical in the seasonal flu (2). The mortality rate for H1N1 is comparable to the less than 0.1% rate of the seasonal flu with estimates ranging from 0.4% by the WHO to a more recent estimate by Dr. Marc Lipsitch of Harvard of 0.007-.045% (8).

In addition to the relatively low mortality rate of the virus, the number of new cases has also declined since reaching its peak of about 10,000 new cases per week, reported by the CDC in October 2009. This drop is largely attributable to the introduction of the H1N1 vaccine along with the fact that most of the people susceptible to the virus had already been infected. This allowed the number of positive cases in 2010 to stay below 500 per week as of March 13th (9). The mortality rate due to pneumonia and influenza has also dropped below epidemic threshold and is once again comparable to the seasonal baseline. Considering that the mortality rate before the vaccine was produced was on pace to be well above the epidemic threshold, this result is a testament to the effectiveness of vaccines in limiting the number of new infections (10).

Despite the worst of the H1N1 pandemic seemingly being behind us, there is still cause for concern. Due to influenza’s ability to swiftly mutate, there is a constant threat of the emergence of a more virulent form of the virus. One mutated influenza strain D222G has already been identified and was found in 11 out of 61 severe cases in Norway. This mutation is hypothesized to allow the virus to bind more efficiently to lung cells and cause symptoms similar to those found in infection with the 1918 flu (11). However, doubts remain towards the ability of this mutated strain to allow efficient transmission of the virus. Furthermore, it is unclear whether this mutation is associated with increased virulence, as Dr. Nancy Cox of the CDC commented: “If you look globally you can see that this mutation is neither necessary nor sufficient for a severe or fatal outcome� (12, 13, 14). In addition to this mutation, numerous cases of antiviral resistant H1N1 strains have been found, raising the possibility that our current antivirals VOL 9 ISSUE 1, FALL 2010

FIGURE: Progression of laboratory confirmed H1N1 influenza cases and deaths by May 2009. Courtesy of the World Helath Organization.

may lose much of their potency in treating those infected with H1N1 (15). Thus, while the pandemic seems to have ended, it is still necessary to be vigilant for any changes which might result in the emergence of a new and potentially more virulent form of the virus.

References 1. Ballantyne C. 2010. Will Egypt’s plans to kill pigs protect it from swine-sorry, H1N1 flu? Scientific American. <http:// www.scientificamerican.com/blog/60-second-science/post.cfm?id=willegypts-plans-to-kill-pigs-prot-2009-05-01> 2. Osterlund P, Pirhonen J, Ikonen N, Rönkkö E, Strengell M, Mäkelä SM, et al. 2009. Pandemic H1N1 2009 Influenza A Virus Induces Weak Cytokine Responses in Human Macrophages and Dendritic Cells and Is Highly Sensitive to the Antiviral Actions of Interferons. Journal of Virology.

84(3):1414-22 3. Lipsitch M, Lajous M, O’Hagan JJ, Cohen T, Miller JC, et al. 2009. Use of Cumulative Incidence of Novel Influenza A/H1N1 in Foreign Travelers to Estimate Lower Bounds on Cumulative Incidence in Mexico. PLoS ONE 4: e6895.

4. Fox M, Whitcomb D. 2009. US swine cases hit all 50 states. Reuters. <http://www.reuters.com/article/idUSN01480382> 5. Morens DM, Fauci AS. 2007. The 1918 influenza pandemic: insights for the 21st century. J Infect Dis. 2007 Apr 1;195(7):1018-28.

9. Center for Disease Control. 2009. CDC Estimates of 2009 H1N1 Cases and Related Hospitalizations and Deaths from April 2009 - January 16, 2010, By Age. <http://www.cdc.gov/h1n1flu/estimates_2009_h1n1.htm> 10. Center for Disease Control. 2010. 2009-2010 Influenza Season Week 9 ending March 6, 2010. < http://www.cdc.gov/flu/weekly/> 11. Kiland A, Rykkvin R, Dudman SG, Hungnes O. 2010. Observed association between the HA1 mutation D222G in the 2009 pandemic influenza A(H1N1) virus and severe clinical outcome, Norway 2009-2010. Euro Surveill. 15(9):2 12. World Health Organization. 2009. Preliminary review of D222G amino acid substitution in the haemagglutinin of pandemic influenza A (H1N1) 2009 viruses. <<http://www.who.int/csr/resources/publications/swineflu/cp165_2009_2812_review_d222g_amino_acid_substitution_in_ha_ h1n1_viruses.pdf> 13. Racaniello V. 2009. The D225G change in 2009 H1N1 influenza virus is not a concern. < http://www.virology.ws/2009/11/24/the-d225g-changein-2009-h1n1-influenza-virus-is-not-a-concern/> 14. CIDRAP. 2010. H1N1 mutation’s proposed link to severe illness debated. <http://www.cidrap.umn.edu/cidrap/content/influenza/swineflu/ news/mar0410mutation.html> 15. Janies DA, Voronkin IO, Studer J, Hardman J, Alexandrov BB, Treseder TW, Valson C. 2010. Selection for resistance to oseltamivir in seasonal and pandemic H1N1 influenza and widespread co-circulation of the lineages.

Int J Health Geogr. 9(1):13.

Photo credit: @istockphoto.com/bovinicus

6. Itoh Y, Shinya K, Kiso M, Watanabe T, Sakoda Y, Hatta M, Muramoto Y, et al. 2009. In vitro and in vivo characterization of new swine-origin H1N1 influenza viruses. Nature. 460(7258):1021-5.

7. Munster VJ, de Wit E, van den Brand JM, Herfst S, Schrauwen EJ, Bestebroer TM, van de Vijver D, Boucher CA, Koopmans M, Rimmelzwaan GF, Kuiken T, Osterhaus AD, Fouchier RA. 2009. Pathogenesis and transmission of swine-origin 2009 A(H1N1) influenza virus in ferrets. Science.

325(5939):481-3.

8. Fox M. 2009. Swine flu death rate similar to seasonal flu: expert. Reuters <http://www.reuters.com/article/idUSTRE58E6NZ20090916>

www.pennscience.org

6

Features

How

Vaccines are Made

SANDERS CHANG & ISABEL FAN â&#x20AC;˘ University of Pennsylvania

EVERY YEAR, MILLIONS OF FLU SHOTS ARE ADMINISTERED IN SCHOOLS AND CLINICS. In response to major outbreaks like avian flu, SARS, and H1N1, governments, health organizations, and research institutions collaborate to distribute vaccines to those at risk. Vaccines play a critical role in the wellbeing of countless people each year, whether they are being used to suppress the seasonal flu or prevent a major global epidemic. However, it is crucial that we do not overlook the research and testing involved in vaccine development in order to better appreciate their contributions to global health.

7

PennScience Journal of Undergraduate Research

VOL 9 ISSUE 1, FALL 2010

T

he human body is trained to induce an immune response whenever it comes in contact with a foreign pathogen. Antibodies are synthesized that can specifically bind to the antigens or the surface proteins of the pathogen. These antibodies then mark the pathogen for destruction by white blood cells.

To prepare the body for future invasions of the same pathogen, memory cells are created that can immediately synthesize these antibodies, allowing the body to respond more quickly to infections of this pathogen (1). A vaccine works by introducing a manageable, weakened form of the pathogen to the body. The body responds to the weakened pathogen as if it were an actual infection, producing memory cells that can prepare it from actual infections of the pathogen. Depending on the way they are made and their safety, vaccines are divided into five different categories: attenuated, inactivated, subunit, conjugate, and toxoid.

The attenuated vaccine uses a live, weakened form of the virus. This virus can still reproduce within the body but at a reduced rate. Attenuated vaccines have been used to protect against relatively common diseases such as measles, mumps, and chickenpox. One common way to create this vaccine is to grow generations of it in cultured cells. This environment causes the virus to accumulate a wide range of mutations, which reduces its reproductive capability to the point that it can safely be introduced to the human body (2). An advantage of this vaccine is that with the virus still alive, the body can produce a fullfledged immune response. One or two vaccinations can thereby assure lifelong immunity to the virus. However, the fact that the virus can still reproduce suggests that it can mutate back to its highly virulent form. Therefore, attenuated vaccines are usually not administered to individuals with weakened immune systems.

Used to create immunity against polio, Hepatitis A, and influenza, an inactivated vaccine is composed of a pathogen that has been killed through the use of radiation, heat, or chemicals (2). This process prevents pathogens from mutating back to their virulent forms. Chemi- FIGURE: The process of developing a West Nile Virus Vaccine cal inactivation can also be used to produce immunity Source: National Institute of Allergy and Infectious Diseases (NIAID) against bacteria that secrete toxins . These toxoid vaccines chemically disintegrate the pathogen into its individual parts and utilize bacterial toxins which have been inactivated by an aqeous filter out its antigens. Another way is to manufacture the antigens formaldehyde solution called formalin (2). As a result, the im- separately from the virus via DNA recombination. This method is mune system develops immunity against the active form of the utilized in creating hepatitis B vaccines by genetically transformtoxin as well. These vaccines are used in the immunization of teta- ing yeast with viral genes coding for its antigens. A special type nus and diphteria. of the subunuit vaccine is the conjugate vaccine, which makes use of the sugar coating of the infectious bacteria in question. SomeAnother type of vaccine is the subunit vaccine. The subunit times, immunity against certain bacteria relies on the ability of vaccine is made from the surface antigens of the pathogen (2). the body to recognize this sugar coating of the bacteria (3). HowThere are several ways to create the subunit vaccine. One way is to ever, it is found that the immune systems of infants and children www.pennscience.org

8

Features

“A vaccine works by introducing a manageable, weakened form of the pathogen to the body. The body responds to the weakened pathogen as if it were an actual infection.” are unable to recognize this sugar coating. Scientists devised a way to avoid this problem by creating vaccines that have the sugar coating linked to the antigens and toxins of the bacteria that can be easily recognized by the immune system (2). Some examples of conjugate vaccines include Haemophilius influenza B and pneumococcal vaccines.

Current research is beginning to focus on the DNA vaccine.

This vaccine makes use of the phenomenon that foreign DNA introduced to the body can be taken up by cells. This causes these cells to manufacture and display these antigens on their surfaces, thus inducing an effective immune response (2). This vaccine does away with the need to use the physical form of the pathogen to induce an immune response. Moreover, this vaccine is generally cheaper and easier to make than other vaccines being used. Methods of ensuring that cells in the body take up the DNA include shooting DNA-containing gold particles into the body’s cells or linking the DNA with molecules that can be easily taken up by the cells (2). However, there is still the concern that this method of vaccination can induce an unwanted autoimmune response or mutagenesis of the cells (4).

References 1. “Immune System: Mounting an Immune Response” National Institute for Allergy and Infectious Diseases. Web. 20 Feb 2010. <http://www3. niaid.nih.gov/topics/immuneSystem/response.htm>.

2. “Types of Vaccines” National Institute for Allergy and Infectious Diseases. Web. 1 Mar 2010. <http://www3.niaid.nih.gov/topics/vaccines/ understanding/typesVaccines.htm>.

3. “How Are Vaccines Made?” The Children’s Hospital of Philadelphia. Mar 2008. Web. 20 Feb 2010. <http://www.chop.edu/service/vaccine-education-center/vaccine-science/how-are-vaccines-made.html>.

4. Hunt, Dr. Richard. “Vaccines: Past Successes and Future Prospects.” University of South Carolina School of Medicine. 24 Nov 2009. Web. 1 Mar 2010. <http://pathmicro.med.sc.edu/lecture/vaccines.htm>.

5. “Vaccine Development and Testing” U.S. Department of Health and Human Services. Aug 2001. Web. 10 Mar 2010. <http://www.hhs.gov/nvpo/ factsheets/fs_tableII_doc1.htm>.

6. “Vaccine Safety” Centers for Disease Control and Prevention. 24 Mar 2010. Web. 26 Mar 2010. <http://www.cdc.gov/vaccinesafety/Concerns/ Index.html>.

7. Seppa, Nathan. “What’s Behind Latest Phobia Towards Vaccines?”

Science News. U.S. News and World Report. 4 Nov 2009. 26 Mar 2010. <http://www.usnews.com/science/articles/2009/11/04/whats-behindlatest-phobia-towards-vaccines.html>.

8. “Annual Influenza Vaccine Production Timeline.” Figure. Influenza.com, Flu Information and Influenza Prevention. 09 Mar 2007. Web. 26 Mar 2010.<http://www.influenza.com/Index.cfm?FA=Science_History_6>.

Photo credits: @istockphoto/batman2000, @istockphoto/svengine

9

PennScience Journal of Undergraduate Research

Once a vaccine is developed, rigorous testing is conducted that may last from a couple of months to many years before the vaccine can be licensed and provided to the public. The National Institute of Allergy and Infectious Diseases (NIAID), a branch of the National Institutes of Health, oversees the entire process of vaccine testing, monitoring the thousands of individuals who volunteer to be a part of these clinical trials and maintaining effective communication of research laboratories, pharmaceutical companies, and clinics involved (3, 5). The first level of testing is done with a subject pool of around one hundred patients or less who have relatively little susceptibility to the illness. The purpose of this phase is to simply determine whether the vaccine is safe to administer and whether it has any effect on physiological defense mechanisms. Vaccine safety is more firmly validated in the second level of testing, where it is tested by hundreds of people who tend to be at a higher risk of contracting the disease (3).

Rather than just testing whether the vaccine induces a response, the third level truly determines if the vaccine has the expected effects. This phase of testing utilizes thousands of subjects from a large geographic distribution and can take years to verify whether the vaccine successfully results in the correct immune response (3). The Food and Drug Administration (FDA) must confirm the clinical design and the validity of the data (5). The FDA then passes this information to the Advisory Committee on Immunization Practices (ACIP) of the Centers for Disease Control and Prevention (CDC) and other coalitions who then decide whether the vaccine should be licensed, and if so, how it should be distributed (3). If the vaccine receives acknowledgement and validation from the ACIP and the other committees, it can be distributed to the public.

After the vaccine is provided to the public, the Food and Drug Administration along with the Centers for Disease Control and Prevention continue to monitor test subjects from all three levels of testing for any side effects that might arise after testing has concluded. The FDA and CDC also collects reports of adverse responses to the vaccines among the public. Consequently, no matter how many trials of testing are conducted, there always exists the possibility that vaccines go awry (5). People have argued that some vaccines have resulted in detrimental and sometimes fatal effects. For instance, some have argued of a strong link between meningococcal vaccine and Guillain-Barre syndrome, hepatitis B vaccine and multiple sclerosis, and other vaccines to disorders such as autism and even sudden infant death syndrome (6). As a result, there is a significant population who prefer not to receive vaccines and risk contracting infections. (7).

VOL 9 ISSUE 1, FALL 2010

Vaccines:

Why People Say No SALLY CHU & ANGELO LEE â&#x20AC;˘ University of Pennsylvania

IN 1950, THERE WERE 50 MILLION CASES OF SMALLPOX WORLDWIDE. TODAY, THERE ARE NONE. While this may be one of the more striking examples of vaccinesâ&#x20AC;&#x2122; success, it is far from the only one. Vaccines were developed in order to minimize the illness and death that often ravaged unprotected populations. They are able to do this by training the human body to resist a disease through exposure to a weakened or altered form of that disease. This prevents future infections and helps stop the spread of disease. This quest to eradicate disease through vaccination is largely responsible for the increase in life span experienced in most parts of the world during the last century, and is a vast improvement over gaining immunity to a disease by surviving it (2).

www.pennscience.org

10

Features

D

espite the overwhelming success vaccines have had, they are still looked upon with suspicion by many people. This is largely due to misconceptions people hold towards vaccines. One common misconception is that because there is better hygiene in the world today and no recent cases of a disease, vaccines are unnecessary. However, those who believe this tend to neglect to consider that people from other countries could be carriers of the disease, or that the disease could mutate and reemerge (3). As a result, these people are shocked when they find that people are still becoming ill with the disease, and falsely conclude that the vaccine is to blame for the new cases of the disease. They presume that vaccines are 100% effective, even though immunity successfully develops in only 85-95% of the vaccine’s recipients (4). They ignore the fact that in the vast majority of cases vaccines only have temporary or minor side effects, and they focus on a few select cases where side-effects are major or vaccination failed, and therefore they resist getting a vaccine. These exaggerated thoughts may develop from irrational belief persistence.

Irrational belief persistence occurs when people insist on believing something that has been proven to be false. Even workers in health care are prey to this phenomenon. In a survey of physicians, nurses and administrators, respondents “in all three professional groups who were unvaccinated during the current season were significantly more likely than the vaccinated respondents to overestimate several of the surveyed adverse-effect rates” (5).

Similarly, at Penn, although the H1N1 flu vaccine is available to Penn students, not everyone chooses to get it; this may be because of overestimation of the adverse effects of the H1N1 vaccine. In particular, there have been reports linking thimerosal, an ingredient in some vaccines, to autism in children (6). While these reports have since been discredited and the paper withdrawn, people still persist in believing the H1N1 vaccine causes autism, especially due to media coverage and the comments of public figures (7). President Obama announced, “We’ve seen just a skyrocketing autism rate. Some people are suspicious that it’s connected to the vaccines. The science right now is inconclusive, but we have to research.” (8) Since negative statements tend to resonate more with people, the second part of President Obama’s statement is likely overshadowed by the first, thereby fueling the phenomenon known as availability bias. Availability bias is a human cognitive bias in which people overestimate probabilities of events associated with memorable or vivid occurrences (9). People often subconsciously use the availability bias when making decisions by considering the readiness with which similar memorable events come to mind (10). For in-

stance, although plane crashes are exceedingly rare, many people overestimate their occurrence because the media extensively covers such a tragedy when it does occur.

It is true that if a vaccine is given to someone in poor health or someone who has been immunosuppressed, he or she may experience serious side effects. However, that is no reason for those with healthy immune systems to refuse vaccinations. Yet many people still do refuse vaccines because they believe the vaccine will give them the very disease it is protecting them against. Part of the reason for this is because there is no placebo against which vaccines are tested. Also, people tend to learn only some of the facts surrounding vaccines, and thus they are not aware, for instance, of the extent to which the FDA tests every vaccine before permitting its release to the public. According to one survey conducted in Pittsburgh, PA, almost one-third of the health care workers, excluding doctors and nurses, believed that vaccines were not a safe and effective way to prevent infection. 36% of those surveyed believed that vaccines are safe in pregnancy (many are not) (11). In addition, this survey found that in many cases the most experienced nurses were not the people who were most knowledgeable about symptoms of influenza. This proves that within health care, just as in the public, there are some people who are unaware of, or misinformed about, important health information

“Irrational belief persistance occurs when people insist on believing something that has proven to be false. Even workers in health care are prey to this phenomenon.”

11

PennScience Journal of Undergraduate Research

As mentioned earlier, the link between vaccines and thimerosal is an example of people falling victim to misinformation. Despite the paper linking these two being since disproven and withdrawn, there are still many adults who know nothing of the removal of the paper and still tend to believe that thimerosal causes autism. This is due to lack of general public knowledge - while thimerosal has a mercury ingredient in it, it is generally harmless. People know mercury can be harmful to the body, but they don’t know that mercury comes in different types, including methylmercury and ethylmercury. The latter is used in vaccines, and is processed more quickly than the former so that there is minimal accumulation in the body. This greatly reduces the possibility of it having any harmful effect on the body. However, most simply believe that because thimerosal has mercury in it, the vaccine is dangerous and could induce autism in unborn children; thus, many parents allow their children to go unvaccinated.

The media in many cases exacerbates this problem through coverage that employs fear tactics to draw in viewers. As people tend to find negative stories more memorable then positive ones more due to cognitive biases, coverage focusing on the fears about vaccines rather than the facts can result in people perVOL 9 ISSUE 1, FALL 2010

“People seem to put more weight on the consequences of their actions, as opposed to those of their inactions.” validity of the results to real world vaccination is not completely valid. To test the validity of omission bias in the real world, Baron conducted another survey concerning parents’ thoughts in administering the DPT vaccine to their children. Baron also found that some respondents who believed the DPT vaccination was beneficial still resisted vaccination and others resisted vaccination because they believed the vaccine was harmful, proving that “omission bias is not confined to hypothetical cases presented in the laboratory.” (16)

FIGURE: Decline of Scarlet Fever, Diphtheria, Whooping Cough, and Measles

ceiving vaccines as dangerous. This bias against vaccines is what viewers take away from the program causing them to ignore those who encourage people to get vaccinated. People seem to put more weight on the consequences of their actions, as opposed to those of their inactions. This is called the omission bias.

Professor Jonathan Baron of the University of Pennsylvania psychology department defines omission bias as “the tendency to favor omissions (such as letting someone die) over otherwise equivalent commissions (such as killing someone actively).” It seems that parents feel more guilt if their child dies from a vaccination received at their urging than if their child dies from the disease naturally. From a normative standpoint, the parents should feel equal guilt for the death caused by administering or failing to administer the vaccine.

I. Ritov and J. Baron, in an experiment to find the connection between omission bias and vaccination, found that “subjects are reluctant to vaccinate a child when the vaccination itself can cause death, even when vaccine-related mortality is far less likely than death by the would-be-vaccinated disease.” (13) This study was conducted by surveying the responses of 53 undergraduates to situations in which they had a choice between vaccinating their children against dangerous disease using a vaccine which in very rare cases can lead to death, or allowing their children to go unvaccinated. From this, the two concluded that parents would be unwilling to vaccinate their children if the death rate from the disease was less than 10 times higher than the death rate from the vaccine (14). However, since hypothetical questions were used to obtain the results, generalizing the

In order to minimize the number of deaths from viral illnesses, it is important to compare the relative costs and benefits of vaccination and nonvaccination without favoring inaction over action. Perhaps people should heed the advice of Benjamin Franklin. In his autobiography, Franklin said, “In 1736 I lost one of my sons, a fine boy of four years old, by the small-pox, taken in the common way. I long regretted bitterly, and still regret that I had not given it to him by inoculation. This I mention for the sake of parents who omit that operation, on the supposition that they should never forgive themselves if a child died under it; my example showing that the regret may be the same either way, and that, therefore, the safer should be chosen.” (17) References 1. “Disease Decline before Introduction of Immunization.” Vaccination.

Web. 17 Mar. 2010. <http://www.whale.to/vaccines/decline1.html>.

2. “Vaccine Benefits.” National Institute of Allergy and Infectious Diseases. Web. 1 Mar. 2010. <http://www3.niaid.nih.gov/topics/vaccines/ understanding/vaccineBenefits.htm>.

3. “Vaccines: Vac-Gen/Why Immunize?” Centers for Disease Control and Prevention. 6 Aug. 2009. Web. 1 Mar. 2010. <http://www.cdc.gov/vaccines/vac-gen/why.htm>.

4. “Vaccines.” Centers for Disease Control and Prevention. Web. 20 Mar. 2010. <http://www.cdc.gov/vaccines/pubs/vis/default.htm>.

5. Ehrenstein, M.D., Boris P., Frank Hanses, M.D., Stefan Blaas, M.D., Falitsa Mandraka, M.D., Franz Audebert, M.D., and Bernd Salzberger, M.D. “Perceived Risks of Adverse Effects and Influenza Vaccination: a Survey of Hospital Employees.” Oxford Journals | Medicine | European Journal of Public Health. 20 Jan. 2010. Web. 10 Mar. 2010. <http://eurpub.oxfordjournals.org/cgi/content/full/ckp227v1>.

6. Betz, Ph.D., RN, FAAN, Cecily.“Educating the Public About H1N1.”Journal of Pediatric Nursing 24.6 (2009): 445. ScienceDirect. Web. 1 Mar. 2010. <http:// www.sciencedirect.com/science?_ob=Ar ticleURL&_udi=B6WKM4 X R 8 S R H - 5 & _ u s e r = 4 8 9 2 5 6 & _ c ove r D a t e = 1 2 % 2 F 3 1 % 2 F 2 0 0 9 & _ rdoc=1&_fmt=high&_orig=search&_sort=d&_doca Photo credit: @istockphoto.com/markchentx

www.pennscience.org

12

Features

Research at Penn SARS, AVIAN FLU, AND SWINE FLU are just some of the diseases that have hit the news headlines in recent years. Over the years, various infectious diseases have risen to infamy; at the same time, as doctors and scientists study these diseases, some have fallen to obscurity as new treatments and preventative methods are discovered. At the University of Pennsylvania, many researchers are studying different aspects of various disease-causing agents in the hopes of finding vaccines and treatments. Read on to learn more about three of these researchers.

13

PennScience Journal of Undergraduate Research

VOL 9 ISSUE 1, FALL 2010

Understanding the Yersinia pestis bacterium SUSAN SHENG, University of Pennsylvania

S

ince the anthrax attacks in 2001, researchers such as Dr. Dieter Schifferli, Associate Professor of Microbiology at the University of Pennsylvania, have become interested in studying the Yersinia pestis bacterium because of its potential for use as a bioweapon.

Yersinia pestis is perhaps best known for causing the “Black Death” that swept through Europe during the 14th century, killing 25 million people (25% of Europe’s population) over a 5 year period (3). Several centuries earlier, in the 6th century, the plague traveled throughout much of the known world, causing 100 million deaths over a 50 year period. Y. pestis is responsible for causing bubonic, septicemic, and pneumonic plague; the manifestation of the disease is dependent on the method and location in which the bacterium infects the host. With modern antibiotics, individuals with bubonic plague can be treated effectively if the disease is detected early. Primary pneumonic plague however, which results from aerosolized Y. pestis entering the lungs, is much more deadly, and often kills the patient within 3-5 days. Thus, there is much concern currently over the potential weaponization of Y. pestis into an aerosolized form.

The fear of the weaponization of Y. pestis is not without historical precedence. As early as 1346, the bodies of plague victims were being used as weapons as the Tartars catapulted the bodies over the walls of the city now known as Feodosia in a battle against Genoese merchants, hoping to create an epidemic inside the city (6). During World War II, records indicate that the Japanese successfully tested different variations of a “flea bomb” on Chinese villagers and prisoners, with the intent of dropping the bomb – a “ceramic container filled with plague-infested fleas and flour” – on San Diego, California (4). Furthermore, both the United States and Soviet Union experimented with aerosolized Y. pestis during the 1950s and 1960s.

There is currently no licensed vaccine against the disease in the United States. During the Vietnam War, a formalin-killed Y. pestis vaccine was used by the US military. Although effective against bubonic plague, this vaccine did not efficiently protect

against pneumonic plague. A vaccine used in other countries (including the former Soviet Union) is based on an attenuated strain – a strain of the bacteria missing a large region of DNA, which renders it less harmful – but that vaccine is not used in the U.S. due to severe secondary side effects. An experimental vaccine which targets two proteins associated with Y. pestis is currently being developed and tested. While this new vaccine appears promising, Dr. Schifferli and other researchers are working to find additional bacterial proteins to target, which would make a vaccine even more effective in protecting against infection by a greater variety of Y. pestis strains.

The long-term goal of Dr. Schifferli’s lab is to understand how bacterial pathogens initiate their infectious process. The lab studies bacterial ligands that bind the bacteria to receptors on host cells, mediate colonization, host cell signaling, and/or optimal toxin delivery. The hope is that an improved understanding of how bacteria infect the host and promote infection will lead to new targets for prophylactic and therapeutic treatments. For instance, one type of ligand being studied is bacterial fimbriae, which are hair like protein structures on the surface of the bacteria. These structures, which coil in a helical formation, help the bacteria adhere to each other and to host cells. In Y. pestis, the structure of a major type of adhesive fimbriae (designated Psa) is comprised of only one repeating subunit protein. These fimbriae are being examined as a potential target for a vaccine or therapeutic treatment; if the fimbriae are unable to attach to host cells, then infection can be delayed or even prevented.

Using mouse models and attenuated strains of Y. pestis, Dr. Schifferli and his team have been working to develop a method that would target the bacterial fimbriae and improve the prognosis of infected individuals. If the progression of pneumonic disease can be slowed down, then the ability of medical professionals to recognize and treat infected individuals in time is improved. Additionally, Dr. Schifferli has been looking at ways to mimic the specific region of host receptors that are targeted by the bacteria. If successful, therapeutic treatments such as a nasal spray could be developed. The spray could be provided to individuals at high risk for exposure (e.g. soldiers or researchers); in the event of exposure, individuals could quickly use the www.pennscience.org

14

Features spray, which would enter the respiratory system and coat it with molecules mimicking host receptors. Y. pestis would then bind to the mimic receptors instead of host cells, and the severity of infection would be reduced.

Quorum-Sensing Bacteria in Cholera Pathogenesis EMILY XUE, University of Pennsylvania

D

r. Jun (Jay) Zhu, an assistant professor in the Penn Department of Microbiology, is studying the process of “quorum sensing” in bacteria, specifically in Vibrio cholerae, the bacterium responsible for the disease cholera. Research on cholera can have profound and pressing health implications. In addition, the study of quorum sensing can shed light on an important and prevalent function of a wide range of bacteria.

FIGURE: The 987P-like CS18 fimbriae of human enterotoxigenic Escherichia coli ON phase variants. (Molecular Microbiology, Volume 48, Number 1, 2003, cover illustration)

Inevitably as our knowledge of the world increases, the potential for that knowledge to be harnessed for malicious purposes also increases. Fortunately, researchers including Dr. Schifferli are already developing ways to counter these emerging threats.

References 1. Dieter M. Schifferli, Description of Research Expertise. [Internet] Philadelphia (PA): University of Pennsylvania School of Veterinary Medicine; c2010 [cited 2010 March 20] Available from: http://www. vet.upenn.edu/FacultyandDepartments/Faculty/tabid/362/Default. aspx?faculty_id=4382134 2. Division of Vector-Bourne Diseases. Information on Plague. [Internet]. Fort Collins (CO): Center for Disease Control and Prevention; [modified 2005 March 30; cited 2010 March 20]. Available from: http:// www.cdc.gov/ncidod/dvbid/plague/info.htm 3. Douglas Fix, Yersinia [ Internet] Carbondale (IL): Southern Illinois University Carbondale; c1997-2010 [cited 2010 March 20] Available from: http://www.cehs.siu.edu/fix/medmicro/yersi.htm 4. GlobalSecurity.org, Plague (Yersinia pestis) [Internet]. GlobalSecurity.org; c2000-2010 [modified 2007 October 23; cited 2010 March 20] Available from: http://www.globalsecurity.org/wmd/intro/bio_ plague.htm 5. Tami Port, What Are Bacterial Fimbriae? [Internet] Microbiology: Suite10; 2009 March 9 [cited 2010 March 20] Available from: http:// microbiology.suite101.com/article.cfm/what_are_bacterial_fimbriae 6. Thomas Johnson, A History of Biological Warfare from 300B.C.E. to the Present [Internet] Irving (TX): American Association for Respiratory Care; [cited 2010 March 20]. Available from: http://www.aarc.org/ resources/biological/history.asp Photo credits: @istockphoto.com/theasis, @istockphoto.com/janrysavy

15

PennScience Journal of Undergraduate Research

Quorum sensing is not unique to V. cholerae and was in fact first described in V. fischeri, a strain of bacteria that produces bioluminescence only when the bacteria achieves a high density of cells in the light organs of certain species of marine fish. The behavior implies a method of communication between single-celled bacteria, usually through a diffusible molecule produced by the bacteria that “autoinduces” their neighbors. This autoinduction process was discovered in the late 1970’s, but it wasn’t until Dr. Zhu’s mentor, Dr. Steve Winans, a professor at Cornell University, coined the term “quorum sensing” in the 1990’s to describe it, that the process became more widely researched and was found to occur in a number of different bacterial strains.

Dr. Zhu has focused his study of quorum sensing on the bacteria that cause cholera, a disease that poses a serious global health threat even though it is no longer common in the United States (2). Cholera is most often acquired from drinking water contaminated with V. cholerae, especially in developing countries without sophisticated methods of waste treatment. If left untreated, it can lead to death within days from dehydration due to diarrhea and vomiting. Cholera is also a disease particularly prone to epidemics, as waste carrying the V. cholerae bacteria from infected patients can contaminate a local water supply and increase the rate of infection, often to the thousands of cases (3). Partly because of its high pathogenicity, the CDC has listed cholera amongst potential agents of bioterrorism, making understanding its transmission and infectious behavior even more crucial (4).

Dr. Zhu explains that the quorum sensing process employed by V. cholerae is notably different from the system used by other infectious disease-causing bacteria, which do not become pathogenic until a critical mass of the bacteria has been reached in the host.

This is achieved through an auto-inducing molecule produced by the bacteria that in high concentrations activates concentrationdependent gene transcription of a “virulence factor” that actually VOL 9 ISSUE 1, FALL 2010

FIGURE: “We love quorum sensing.” An example of bioluminescent quorum sensing bacteria in vitro (picture provided by Dr. Zhu)

“Dr. Zhu has focused his study of quorum sensing on the bacteria that cause cholera, a disease that poses a serious global health threat...” causes the disease. Though V. cholerae follows the same concentration-dependent model of transcription, its pathogenesis is just the opposite, as quorum sensing is actually used to repress the virulence factor. Due to the relatively fast progression of the disease, the bacteria produce the cholera toxin shortly after colonizing the intestine, sickening the host and allowing the bacteria to multiply rapidly. The resulting high concentration of V. cholerae’s auto-inducing molecules causes these molecules to diffuse back into the bacteria, and quorum sensing deactivates pathogenesis and allows the bacteria to escape from the diseased host. Dr. Zhu notes that this unusual method of quorum sensing behavior could lead to treatments for cholera by targeting the quorum sensing pathway, effectively minimizing the virulence of a V. cholerae infection – though he also notes that such treatments would require more research.

Dr. Zhu’s research focuses on the complex gene regulatory network in V. cholerae as a result of quorum sensing. There are inherent difficulties in studying the behavior of bacteria that cause disease in living organisms, especially because this behavior may be quite different in vitro. Dr. Zhu’s lab uses in vivo models to most accurately reflect the variety of environmental factors that affect bacteria in the host, measuring the expression of genes through a recombinant genetic reporter system.

In addition to the virulence controlled by quorum sensing in Vibrio cholerae, Dr. Zhu also has an interest in biofilm formation, another factor related to quorum sensing. Biofilms can be defined as microorganisms attach to a surface to form 3-D complex structures. Both bacterial biofilms and quorum-sensing systems fundamentally blur the distinction between unicellular and multicellular forms of life. V. cholerae bacteria form biofilms in aquatic environments to help them resist harsh conditions. Biofilms also protect V. cholerae when traveling through the low pH environment of the host’s stomach. Once the bacteria reach the target site, quorum sensing allows the bacteria to detach from the biofilm, aiding colonization of the intestine, an integral step in the progression of the disease.

In gaining a greater understanding of quorum sensing in V. cholerae, Dr. Zhu can shed light on various stages in the course of a cholera infection through knowledge of both pathogenesis and bacterial environmental survival. This understanding may one day lead to novel methods of combating cholera and is increasing our knowledge of an integral and widespread function of bacteria.

References 1. Dr. Jun Zhu. Personal interview. 10 March 2010.

2. National Center for Zoonotic, Vector-borne, and Enteric Diseases. Cholera. [Internet]. Centers for Disease Control and Prevention; [modified 2009 July 17; cited 2010 March 21]. Available from: http://www.cdc.gov/ nczved/divisions/dfbmd/diseases/cholera/ 3. World Health Organization. Global Epidemics and Impact of Cholera.

[Internet]. World Health Organization; [modified 2010; cited 2010 March 21]. Available from: http://www.who.int/topics/cholera/impact/en/index.html 4. National Center for Zoonotic, Vector-borne, and Enteric Diseases. Bacterial Zoonoses Branch. [Internet]. Centers for Disease Control and Prevention; [modified 2009 August 11; cited 2010 March 21]. Available from: http://www.cdc.gov/nczved/divisions/dfbmd/bzb/

www.pennscience.org

16

Features

A Good Infection: Using Bacteria to Fight Cancer VISHESH AGRAWAL, University of Pennsylvania

T

raditional cancer therapies such as chemotherapy and radiation therapy often have detrimental side effects due to the treatments’ lack of specificity. Research conducted by Dr. Yvonne Paterson in the Department of Microbiology at the University of Pennsylvania may present an alternative approach to treating cancer. Instead of using radiation therapy, surgery or chemotherapy, Dr. Paterson’s research seeks to use bacteria to activate the body’s own immune response against cancer cells. Her lab uses the pathogen Listeria monocytogenes to activate the innate immune response toward particular tumor factors.

Listeria is an unusual pathogen that can live and replicate in the cytosol of Antigen Presenting Cells (APCs). APCs are a group of cells that include macrophages, dendritic cells and B cells that can activate CD4+ and CD8+ T cells. Dr. Paterson has genetically engineered these bacteria to preferentially express a tumor antigen after the bacteria have infected cells. Tumor antigens are proteins which are usually expressed at very high levels in cancer cells and include BCR/ABL, Her2-Neu, and HPV-16 oncogenes.

These proteins are often oncogenic and overexpressed, which causes cancerous growth.

When Listeria bacteria produce tumor antigens within the cytosol of APCs, these immunogenic peptides are transported to the endoplasmic reticulum and then exported to the cellular membrane of APCs complexed with Major Histocomptability Complex (MHC) proteins. T-cells bind to the MHC-peptide complex and recognize the tumor antigen as a threat.

tive in treating cancer. This research has also moved into human clinical trials with a Phase I clinical trial using Dr. Paterson’s research having recently been completed. This is the first clinical trial to use live-attenuated Listeria for the treatment of cancer (1). Patients in this study had advanced stage, metastatic, cervical squamous cell carcinoma and had failed to respond to chemotherapy, radiotherapy, and/or surgery. These patients were infected with tumor antigen expressing Listeria. The tumor antigen used in this trial was HPV-16, E7, a protein specific for cervical cancer. Patients in this trial showed an increase in survival with over half showing disease stabilization while a third of the patients showed tumor regression.

This immunotherapy method presents an interesting and novel approach to fighting cancer. It can be used to specifically target cancer and has been shown to be effective in causing tumor regression. An added benefit is that this approach is likely to cost much less than traditional cancer therapies. Additionally, perhaps the most interesting outcome of this research is the relatively decreased severity of side effects. Most patients displayed flu-like symptoms after infection with Listeria, a much less severe side effect than cancer patients normally experience.

References 1. Maciag PC, Radulovic S, Rothman J. (2009). Vaccine. 27(30):3975-83.

2. Personal interview with Dr. Yvonne Paterson.

These T-cells then activate an immune response towards cells that display these proteins. Because tumor cells usually express these proteins at high levels, these peptide MHC complexes are more likely to be found on the surface of cancer cells than on normal human cells. As a result, the immune system is activated to eliminate tumors. This is especially useful because tumors themselves are not particularly immunogenic. Human cells are designed to be recognized as “self” by the immune system and avoid being attacked by immune cells, and because tumors arise from normal humancells, they often do not invoke a strong immune response. However, by infecting a patient with Listeria the immune system is preferentially activated to target cancer cells expressing the antigen expressed by both the cancer cell and the Listeria bacterium.

The use of Listeria for the treatment of cancer has been greatly helped by the work of Dr. Paterson. Experiments done in mice have demonstrated that Listeria-based immunotherapy is effec17

PennScience Journal of Undergraduate Research

FIGURE: Listeria bacteria living inside Antigen Presenting Cells.

Courtesy of the Paterson Lab.

VOL 9 ISSUE 1, FALL 2010

INTERVIEWS

Interview with David S. Roos, Ph.D. Your lab work focuses on host-pathogen interactions, and you also teach a course on infectious disease biology. Can you give us an overview of what your research is about?

My laboratory studies protozoan parasites – unicellular eukaryotes (cells with nuclei) that are responsible for diseases like malaria. While Plasmodium has been eliminated from the US, malaria remains a huge problem globally, causing more than one million deaths each year – and the problem is growing, due to the emergence and spread of drug resistance. Toxoplasma is even more common: about 30% of the U.S. population is thought to be chronically infected.

Unlike malaria, which is transmitted by mosquitoes, Toxoplasma is carried by cats, which shed oocysts in the feces that can survive in the environment for decades. Dogs, pigs, sheep, and other animals get infected by nosing around in contaminated soil. Humans can become infected by playing in sandboxes, gardening, or eating improperly washed vegetables. Infected animals develop a ‘tissue cyst’ form that can be transmitted in undercooked meat – so both vegetarians and carnivores are at risk for infection! Toxoplasmosis isn’t usually a problem in healthy adults, but it’s a serious concern if you are immunosup¬pressed (in AIDS, or for cancer chemotherapy). Toxoplasma is also a notorious congenital pathogen, since primary infections can cross the placenta during pregnancy.

David Roos is the E. Otis Kendall Professor of Biology at Penn, where he runs a research laboratory integrating cell biology, biochemistry, immunology, genomics, and computational approaches to explore eukaryotic evolution and the genetics of host-pathogen interactions. Focusing on the protozoan parasites Plasmodium falciparum (malaria) and Toxoplasma gondii, the Roos lab studies molecular mechanisms of drug action and resistance, the origin of subcellular organelles, immune effector pathways, and comparative genomics. Dr. Roos also directs the Eukaryotic Pathogen Genome Database (EuPathDB. org), one of four national bioinformatics resource centers for biodefense and emerging pathogens, and was Founding Director of the Penn Genomics Institute. Roos graduated from Harvard College in 1979, received his Ph.D. in Virology from The Rockefeller University in 1984, and did post-doctoral work at Stanford University before joining Penn in 1989.

Beyond the clinical importance of these parasites, our research is also driven by the insights that these parasites provide into basic cell biological processes and evolution. We would like to understand the interactions between pathogens and their hosts, and Toxoplasma turns out to be a very convenient experimental system, allowing us to carry out the same kinds of manipulative experiments that biologists use to study E. coli, or fruit flies, or guinea pigs. We can use these parasites to learn what is shared among all eukaryotic cells (including ourselves), and also about the diversity of life … keeping in mind that whatever distinguishes a parasite from its host provides a possible target for killing the pathogen without harming the patient.

Are there clinical applications of your studies on mechanisms of drug action and resistance?

Contrary to popular opinion, there is no shortage of effective treatments for infectious diseases. Thousands of drugs can kill TB, or flu, or malaria – or cancer, for that matter – but they’re not much use if they kill the patient as well! The chalwww.pennscience.org

18

INTERVIEWS lenge is to discriminate between healthy cells and the disease.

What makes penicillin so effective is that it prevents the synthesis of the cell wall that is necessary for bacterial survival, but this structure is completely lacking in humans. Similarly, sulfa drugs inhibit the enzymes used by bacteria to make folic acid – which we eat as a vitamin (as the side of your cereal box will tell you). Sulfonamides are also effective against Toxoplasma and Plasmodium, but unfortunately, their target enzymes can acquire mutations that block drug binding without inhibiting function.

That’s the basis of drug resistance. We are trying to discover what genes are targeted by effective drugs whose mechanism of action is unknown, what mutations might lead to resistance, and ways of combating this, by developing better inhibitors or new treatment strategies.

How do you integrate computational biology into your research?

It turns out that computational approaches aren’t all that different from the many other strategies we pursue in the lab. Immunological, molecular genetic, cell biological and biochemical studies all use distinct techniques to provide complementary answers to biological questions, like the parable of the blind men and the elephant. Technological advances have brought about an information explosion in biology and medicine – as in many other areas of life, from weather forecasting to the financial sector – and advances in computer hardware, software, databases, and algorithm development helps us to make sense of this data, allowing us to conduct experiments in silico. We now know the complete sequence of the human genome, the Toxoplasma genome, the malaria genome, and even the mosquito genome. We are learning where every gene is, when it is turned on, and the distribution of different alleles in individuals from all over the world. That’s a lot of information! And things get even more challenging – and more interesting – when we start to put these pieces together to figure out how entire biological systems operate. I have always been keen to adopt new technologies, and have been interested in computers for a long time, so my lab has used computational approaches to make sense of genomic-scale datasets for the parasites we study, helping to identify genes, determining when and where they are used, developing algorithms to figure out what they might do, and analyzing potential functions in the context of the many other activities taking place simultaneously in the same biological system.

The demand for computational biologists is increasing. Where do you see this area going in the future?

You’re certainly right to notice the increasing demand for computational biologists. We live in a data-rich age, and I don’t see any signs that this is about to change. When I was a gradate student, it was difficult to do experiments, but the results were usually easy 19

PennScience Journal of Undergraduate Research

to understand. Now we can probe all of the genes in a parasite (or a person) in a single afternoon, generating millions of data points.

Instead of spending years trying to figure out how to do an experiment and days figuring out what our data means, we now spend days on the experiment … but months or years in data analysis.

Computational biology provides many challenges, and many opportunities. One challenge is that the scientists most familiar with isolating culturing parasites from an infected animal may be less familiar with statistical and computational approaches … and vice versa. On the positive side, computational experiments have the advantage that they can often be carried out rapidly, and without expensive reagents. It is easy to waste thousands of dollars on an unsuccessful ‘wet’ lab experiment, and changing the parameters means further financial investment, but on the computer, we can simply run the analysis again.

Were you trained as a computational biologist?

No, I wasn’t. This field didn’t really develop as a distinct discipline until fairly recently. We established one of the world’s first programs in computational biology at Penn, in 1993. As it happens, however, I had the good fortune of growing up in an area that was part of a pioneering computer education project developed at Dartmouth College. Local students were introduced to computers in grade school: like many of my classmates, I wrote my first computer program in the second grade, which was unheard of in the 1960s! I wasn’t as heavily into computers as many of my friends, but I certainly developed some familiarity with what computers can do, so that when I was confronted with large-scale datasets in my career as a biologist, I was perhaps more familiar than some of my colleagues with how computers might help us to connect the dots. With a sense of what should be possible, I have been able to assemble a spectacular group of colleagues to help put this vision into practice.

Can you tell us about your decision to go to graduate school? What advice do you have for undergraduates thinking about pursuing a PhD? There are lots of people who have always known that they wanted to go into biomedical research. Not me. I knew something about biology, because my father was an endocrinologist, and I grew up pretty close to nature as a kid in rural New Hampshire, but I had no idea what I wanted to do as an undergraduate. I started out as an art major. Science classes do a great job of teaching a lot of information, but they tend not to be so good at getting students to understand how anyone ever figured all that stuff out. I ended up working in a laboratory almost by accident, and found out that I really enjoy the process of scientific discovery. It’s like a giant puzzle that you get to work on all the time, with a lot of smart people. I think that if you enjoy doing crossword puzzles, or playVOL 9 ISSUE 1, FALL 2010

“I work in infectious disease biology for various reasons: because pathogens provide a fantastic way to explore how biology works, and because they are so important in human health on a global scale.”

Interview with Helen C. Davies, Ph.D.

ing Scrabble, you might find that you are good at science. I try to teach a bit about how scientists think to my students in Biology 406 (Molecular Mechanisms of Infectious Disease Biology).

One of the discoveries that my laboratory is best known for is figuring out that malaria and Toxoplasma parasites harbor a distinctive subcellular organelle that they stole from an ancestral plant, and that this ‘apicoplast’ provides a novel target for drugs that don’t kill people. All of the pieces of this puzzle were already known: the parasite genome, the subcellular organelle, the drugs, but we were able to put these pieces together, which was pretty exciting. Science is full of such discoveries, which help to keep you going in the face of the frustrating fact that most of what we try to do in the lab doesn’t work, and everything takes much longer than expected!

I work in infectious disease biology for various reasons: because pathogens provide a fantastic way to explore how biology works, and because they are so important in human health on a global scale. I have run a five continent lab for many years, and the parasitology area provides plenty of opportunity for travel. One of the unanticipated pleasures of computational biology is that so much of our work is internet-based, so we can easily collaborate with colleagues all over the world.

In the current state of economy, many labs are finding it difficult to find research funding. How do you think this will affect students who are applying to graduate school? And how will it affect their careers?

Based on my own experience, and the many students who have passed through my lab (now quite a large sample: about 50 undergraduates, 20 PhD students, and 30 post-doctoral fellows), I am quite confident in saying that if you work hard, keep your eyes open, and think imaginatively, there are always possibilities and opportunities. It is certainly a time of high anxiety for scientific research, as it is for other areas of the economy. But my experience has been that there has never been anything I felt that we really needed to do for which it hasn’t been possible to obtain the necessary support, sometimes from unexpected sources.

Helen C. Davies, Ph.D. is a professor in the University of Pennsylvania School of Medicine, where she serves as academic coordinator of Microbiology as well as Ombudsman for Graduate and Medical Students. She has been teaching at Penn since 1962, notably in an infectious diseases course that has won praise for her inventive use of music as a memory device. She has been widely acclaimed for her passion and dedication in her work with students, as evidenced by her numerous teaching awards including the Lifetime Mentor Award of the American Association for the Advancement of Science, Penn’s All-University Lindback Award for Distinguished Teaching, and the American Medical Student Association’s National Excellence in Teaching Award.

How did you become interested in the study of infectious diseases? Why study infectious diseases?

When I was in grade school and read books on microbiology, I thought it was fascinating and that’s what I’ve wanted to do since I can remember. It’s important because as diseases emerge, as they become virulent, as we lose the ability to treat them, we will all be dying off.

Interview by Zhu Wang www.pennscience.org

20

INTERVIEWS Would you say there is a disease or group of diseases that pose the most threat?

One is MRSA, which is methicillin resistant staphylococcus aureus; it’s very virulent and we have very few antibiotics that work for it, so it could kill off a large number of people.

There’s ebola, which you may have heard about, where the patient bleeds through every orifice. There are a number of very deadly diseases, and they are extremely important. There are also diseases like C. difficile, which you also may have heard of.

What are some of the things that are being done to combat these diseases?

We keep looking for new antibiotics for those that aren’t viruses, as well as new antivirals, and so far we have managed to keep ahead of the really problematic emerging infectious diseases. But we’ve also seen the emergence of viruses, bacteria, and parasites that have no antivirals, antibacterials, or anti-parasites that will work on these organisms, so that’s our big problem.

Might this have something to do with modern medicine, such as by inadvertently causing resistant strains as we attempt to treat them?

Yes, one of our problems is that we feed animals antiviral, antiparasitic, and antibacterial materials, and this builds up the amount of immunity to these organisms and causes problems for us. Most of the antibacterials that are sold in the United States, for instance, are sold for animal use, and that creates an enormous amount of resistant organisms. If we could stop that from happening, we’d be much better off. But at this point, “big pharma” – that is, the big pharmaceutical companies – don’t seem willing to give that up.

So, you believe that at this point trying prevent these diseases from arising in the first place is more effective than the attempts to combat them after the fact.

What other advances have there been in the field of infectious disease treatment or research?

What we’re looking forward to right now is a kind of personalized way of dealing with infectious diseases. We need to look at each of the infectious diseases, and see how they impinge upon a particular person, and deal with that. For instance, if we have a human being who has a genetic tendency to get a certain disease, we can deal with it for that person differently than we can for other people. So this is a personalized kind of method for dealing with infectious diseases.

For instance, people with Crohn’s disease have a tendency to get C. difficile, and we need to deal with it for those individuals 21

PennScience Journal of Undergraduate Research

in a different way than we do for others. It’s a more personalized way of working, which will be more expensive, but will hit the disease in a more targeted way.

Would that be addressed with medicines? What other aspects are there in considering individuals?

Working with the individual is useful not just for infectious diseases, but for all types of medicine. It’s an exciting field to be in, so if you’re planning on going into medicine now is a great time to do it.

Infectious diseases have been especially prominent in the news lately. What was your take on how some of these issues, such as the recent H1N1 outbreak, were treated?

The whole business of the influenza was carried through pretty well. What happens with different viruses, for instance, is that they can get into a certain species and “mix” there and come out to be much more damaging than they were individually.

What happened with H1N1 was that it started in Mexico and came from there to the US, and we tried very hard to make vaccines for it, and did make some pretty effective vaccines.

But what happened in the mixing of flus is that we had to deal with things such as avian flu, which is much more harmful than swine flu. But we do now have vaccines for many different flu types. I would also urge anyone who hasn’t gotten the vaccine to do so. Another observation is that students of high school age and younger are much more aware of infectious diseases now than they used to be. Students from Sayre High School who come here to Penn and attend lectures in infectious diseases, are fascinated by infectious diseases and they want to know as much as you can tell them about staphylococcus, and streptococcus and various viruses; they are just fascinated and are constantly asking questions. I think infectious diseases have become something that even young kids want to know about, which is great.

Can you describe your teaching interests?

My interest is in teaching about emerging infectious diseases, and teaching in such a way that students will understand and retain the information.

I’ve heard you have some very interesting ways to help your students to remember the things you teach; can you give us some examples?

One thing I do is to teach with music, which is a good thing to use because your brain can remember so much more when it’s set to music.

Interview by Emily Xue

VOL 9 ISSUE 1, FALL 2010

Research Articles

Parental care as seen in foraging bouts of monogamous owl monkeys (Aotus azarai azarai) Rachel Gittelman, University of Pennsylvania Male paternal care is often hard to find in primates. A group of monogamous owl monkeys (aotus azarai azarai), one of the few species that does exhibit male paternal care, was followed for a two month period to document the extent to which each parent babysat their infant during foraging bouts. This data was also compared to the foraging bouts of a group without an infant to determine whether or not foraging behaviors change based on the presence or absence of an infant. The male in the group with an infant was found to babysit the infant significantly more than the female, and positions within the foraging bouts did seem to vary slightly between groups.

Introduction

Male parental care is more commonly seen among primates than in most other mammalian taxa, but is still quite rare when compared to the rest of the animal kingdom (Charpentier et al 2008; Fernandez-Duque et al 2009). It is hypothesized that male parental care will be observed more frequently when paternal certainty is high or as a mating strategy to demonstrate parental ability to a future mate (Fernandez-Duque et al. 2007). Among both human and nonhuman primates, parental care behaviors include carrying, grooming, playing, sharing food, feeding, retrieving, huddling, babysitting, defending and teaching (FernandezDuque et al. 2009). All of these behaviors increase the probability of infant survival and development.

The owl monkeys of the Argentinean Gran Chaco (Aotus azarai azarai) are one taxon of primates that do show intensive male parental care. Owl monkeys are monogamous and live in groups consisting of one pair-bonded adult male and female and two to four young (Fernandez-Duque et al. 2009). For most of the time in the several months after a birth all infants are carried by a parent (ie. the mother and suspected father), with the father shouldering up to 90% of these carrying responsibilities (Fernandez-Duque 2009). Adult males have also been shown to transfer food to juveniles and infants in the group more often than females (Wolovich et al. 2007). While there is strong evidence for paternal care in terms of food sharing and carrying, less evidence has been reported in terms of babysitting, which is another important form of parental care. Additionally, little is known about how the parental responsibilities may shift as the infant gets older. This study examined social interactions during feeding bouts as a way to analyze the roles of adult males and females in the care of infants and older young. Because individuals tend to forage with their groups, the bouts provide a useful opportunity to observe individual relationships and group dynamics, all important factors in studying paternal care.

The groups included in this study reside in the Estancia

Guaycolec, a cattle ranch in the Province of Formosa, Argentina that contains small forested areas in which the monkeys reside. The owl monkeys in this region are cathemeral, meaning that they are most active at dawn and dusk but still show activity, including feeding bouts, throughout the day.

During a feeding bout the group will move from tree to tree feeding on a variety of leaves and fruits. The order in which each monkey in the group enters and leaves the tree may thus become a proxy for babysitting, or in other words the position entering and leaving a tree will be related to the amount of care provided to the infant by that individual. If, for instance, the adult male and infant are typically seen entering and leaving in consecutive order, this may be seen as possible evidence that the male is watching over the infant more than the other members of the group are. Previous studies have shown that during the months when the infant is most dependent and being carried, the parent doing the carrying is most frequently seen traveling in the middle of the group, sometimes first, but rarely last. After several months when the infant is independent but still quite young, it is never observed moving last in the group, but after around five months of age this reverses and it begins to travel last more often than not (Rotundo et al. 2005). The infant observed during the time of the study was well over six months old.

Thus the position the male takes while traveling may change as an infant becomes more independent.

Methods

The study was conducted between June 3rd and July 31st 2009, with most of the data collected during July. The study site was located within the Estancia Guaycolec, a large ranch just outside Formosa, Argentina. Four habituated groups of owl monkeys were observed for a full day at least twice a week during the month of July. An observer would enter the forest just before sunrise (approximately 7:00 hrs during the winter months) and locate one of the four study groups using radio telemetry equipment. Once located the observer would follow the group for the entire day until sundown, or approximately 18:00 hrs. www.pennscience.org

22

Research Articles While following the group the observer collected many types of data. During foraging bouts the observer noted the tag number of the tree each individual foraged in (nearly all of the trees in each group’s territory were tagged), the beginning and ending time of the foraging bout, the type of tree, the part of the tree being eaten and the order in which each individual entered and left the tree. The times the adult male and adult female entered and left the tree were also noted.

Often times the group would split up and feed in separate trees so there was also an option to record if the record of the bout had a “late start” or an “early end.” Because it was often impossible to collect bout information for multiple individuals in separate trees simultaneously these additional variables were useful when the endpoints of a bout went unseen. Information on the demography and ranging of the group was collected in addition to foraging bouts.

Data Analysis

Several tests were conducted on the data collected. The most frequent position (first, middle or last) was calculated for each individual in each group, except for the juveniles.

Juveniles have only in extremely rare cases been observed to take care of siblings and often lag behind or go off on their own during foraging bouts (Fernandez-Duque, personal communication) so any analysis of group foraging effects, especially for the scope of this study, will simply assume minimal contribution by juveniles. This being said, most bouts included in these analyses involved either all of the members of the group or all of the members of the group minus any or all of the juveniles. Additionally, even if all members were present bouts were still excluded from the analysis if the observer was unable to record the order in which any or all of the monkeys entered (for the most frequent position entering) or left (for the most frequent position leaving) the tree. This frequently occurred because a monkey moved too far from the observer’s view or because a bout was simply too short to reliably and accurately record all of the data.

Only data from two of the four groups was compared (E350 and E500) because very few bouts were observed for the other two. Because each group is different it is important that analysis be done for each group separately and there simply was not enough data to conduct tests for two of the groups. The two groups that were not used, D500 and CC, consist of one adult male, one adult female, one juvenile and one adult male, one adult female and two juveniles, respectively. Of the groups that were used, E500 consists of one adult male, one adult female, one juvenile and one infant.

E350 consists of one adult male, one adult female and one juvenile. Thus E500 was used as the group with an infant and E350 as the group without an infant.

Finally, analysis was also conducted for the group that had an infant (E500) on how often the adult male and female moved from bout to bout in a consecutive position to the

23

PennScience Journal of Undergraduate Research

infant. For instance, if the adult male left the tree third and the infant left the tree last this was used as a data point. This measure was used as a proxy for the degree to which each adult “babysat” or watched the infant.

Results

In total 110 feeding bouts were observed. After excluding bouts for the reasons described above, only 51 bouts were actually used in various parts of the analyses (28 from E500 and 23 from E350).

In group E500, the infant never traveled first and most frequently traveled in the middle of the group, occasionally traveling last. In this group the female traveled first more often than the male (18 of 34 bouts vs. 8 of 34 bouts) while entering or leaving the tree. This difference was statistically significant as indicated by a two sample hypothesis test for proportions which was used for all of the other comparisons conducted as well (α =.05, p=.0075). The male traveled last in 11 of 34 bouts and the female traveled last in 4 of 34 bouts while entering or leaving. These values were also significant (α=.05 and P=.0202). There was, however, no significant dif-

Figure 1: Number of times individuals with an infant entered or left a feeding bout in each position

Figure 2: Number of times individuals without an infant entered or left a feeding bout in each position

VOL 9 ISSUE 1, FALL 2010

Figure 3: Number of times spent in a consecutive position (directly in front of or directly behind) with the infant while entering or leaving a foraging tree

ference between the number of times either traveled in the middle (Figure 1).

In the group without an infant (E350), the female traveled first in 25/41 bouts and the male did so in 17/41 bouts.

The female traveled in the middle less often than the male with 9/41 bouts compared to the male’s 21/41 bouts. There was little difference between the position of the male and female while traveling last, the male traveling last in 3 out of 41 bouts and the female in 7 out of 41 bouts. The differences between male and female were significant for first (α=.05, p=.0384) and middle (α=.05, P=.0030). The last position was not significant with α=.05, p=.0885 (Figure 2).

A comparison of the individuals between both groups suggested that there was no notable difference between the number of times the male with the infant (E500) traveled first or in the middle compared to the male without an infant (E350; first: α=.05, p=.505, middle: α=.05, p=.2709).

The male did, however, travel last more frequently in the group with the infant (11/34 bouts) than the male without the infant (3/41 bouts; α=.05, p=.0028). The female’s position in both groups did not differ significantly (α=.05, first: p=.2420, middle: p=.1210, last: p=.260). These results should certainly be interpreted cautiously because, as mentioned before, there is little reason the female of one group should be compared to the female of the other group. Many reasons besides the presence or absence of an infant may account for differences in the data Regarding the position of the male and female relative to the infant, the adult male spent more time in a consecutive position with the infant (27/28 bouts) than did the adult female (20/28 bouts) while either entering or leaving the tree.

This sex difference was significant with an α value of .05 and a P value of .0054.

Discussion

The results obtained do tend to support the observation that males expend more parental care than females with infants. It has been shown previously that males may carry

the infant more often during the months immediately following its birth (Fernandez-Duque et al 2009) and transfer food more often to infants and juveniles than do females (Wolovich et al. 2007). The data show that during the study the male of E500 traveled in a consecutive position with the infant more often than the female which may be interpreted as indicating that the male is babysitting or watching over the infant to a greater degree than the female.

The other results obtained, simply comparing the frequency of each position held during travel from tree to tree between the sexes, show more mixed results. In both groups the female traveled first more often than the male. If it is true that much of the parental care responsibilities fall on the male it may be that the female then fulfills a leadership position in making decisions on when to leave each tree and which tree to go to next. This division of labor would make sense especially during the harsh winter months which coincide with the mating season (May - September) when a pregnant female would have additional nutritional demands (Rotundo et al 2005). Indeed, one hypothesis for the maintenance of monogamy in these owl monkeys supposes that the female is unable to raise the young on her own and must have the continuing support of the male well after the birth of their young (Fernandez-Duque personal communication). Thus it is possible that the female travels first in both groups regardless of the presence of an infant for both have important nutritional needs. Researchers also suspect that the males and females may have such different needs that they often feed on different foods during separate feeding bouts (Van der Heide personal communication). This may account for why many of the bouts recorded did not contain the entire group.

The results also indicate that the adult male traveled last more often in the group with the infant. Because the infant most often traveled in the middle of the group it would make sense that the male would increase his time spent at the back of the group in order to watch over the infant. Analyzing the middle position is more difficult because E500 consisted of four members at the time of the study and E350 consisted of only three. There are thus twice as many ways to be the “middle” animal entering or leaving for the E500 bouts.

For instance, there was no significant difference between the number of times the adult males of each group traveled in the middle (15/34 bouts for the male with an infant and 21/41 bouts for the male without an infant). However, the fact that the male of E500 is expected to travel more often in the middle simply by chance (50% of the time) than the male in E350 (33% of the time) may have artificially affected the differences between groups. This does, however, also seem to make more robust the result that the male with the infant traveled last more often. This is because the male of E500 would actually be expected to travel last less frequently than the male of E350 simply by random chance. Any future rewww.pennscience.org

24

Research Articles search should aim at correcting this problem by comparing groups of the same size.

Additionally, many bouts were counted twice in the analysis as data were collected for entering and for leaving the tree. If, for instance, the adult female was first in a certain bout to enter and to leave the tree this was counted twice in the analysis. After doing separate analyses for entering and leaving that resulted in similar patterns the two types of data were combined for the presentation of final results here. One potential problem in doing so may be that the entering and leaving events are not independent of each other and thus should not be counted separately. If an individual enters first in to a tree it may then be more likely to leave first as they simply get satiated before the others. Future analysis of this dataset should consider this issue.

The data presented are a preliminary attempt at quantifying the degree to which babysitting changes as an infant ages. Rotundo et al 2005 states that after 5 months of age the infant travels last more frequently than in the middle. This was not the case for the infant of E500 during this study, who traveled last in only 8 out of 34 cases and middle in 24 out of 34 cases despite being over 5 months old. Such discrepancies highlight the dangers of drawing conclusions from small sample sizes. Only one infant was used in this study and simply may not be representative of other individuals of the species. Results should only be seen as a guide for future research.

Sex differences in parental care, as well as the length of the period in which intensive parental care is needed are both important components in investigating the behavioral ecology of nonhuman primates. Such topics also contribute to that study of monogamy and why it is maintained in certain species but not in others. As with much other nonhuman primate research, owl monkeys have close evolutionary ties to humans and any results may eventually give us insight into our own behavioral ecology. In particular, as one of the few monogamous species of primate, owl monkeys offer a unique opportunity to study pair-bonding and bi-parental care, topics with important parallels and contrasts to modern human societies.

and mentoring this project would have never been possible.

References Charpentier M. J. E., Van Horn R. C., J. Altmann, Alberts S. C. (2008).

Paternal effects on offspring fitness in a multimale primate society.

Proceedings of the National Academy of Sciences of the United States of America. 105:1988-1992.

E. Fernandez-Duque, C. Ju谩rez & A. Di Fiore (2008). Adult male replacement and subsequent infant care by male and siblings in socially monogamous owl monkeys (Aotus azarai). Primates 49:81-84.

E. Fernandez-Duque, C. R. Valeggia & S.P. Mendoza (2009). The Biology of Paternal Care. Annual Review of Anthropology, Volume 38: 115-130.

C.K. Wolovich, J.P. Perea-Rodriguez, E. Fernandez-Duque (2008).

Food sharing as a form of paternal care in wild owl monkeys (Aotus azarai). American Journal of Primatology 70:211-221.

Rotundo, M., Fernandez-Duque, E. & Dixson, A.F. (2005). Infant development and parental care in owl monkeys (Aotus azarai azarai) of Formosa, Argentina. International Journal of Primatology: 26 (6): 1459-1473.

Fernandez-Duque, E.; Rotundo, M & Ramirez-Llorens, P. (2002). Environmental determinants of birth seasonality in night monkeys (Aotus azarai) of the Argentinean Chaco. International Journal of Primatology 23 (3), 639-656.

Acknowledgments

The author is greatful to the Center for Undergraduate Research and Fellowships at the University of Pennsylvania for awarding the Pincus-Magaziner Family Undergraduate Research and Travel Award. The project was also supported by a Hewlett Award for Innovation in International Offerings Grant (Provost Office-Penn) and an NSF-REU grant (BCS-0924352) to E. Fernandez-Duque. This research was also made made possible by Fundaci贸n ECO of Formosa, the Estancia Guaycolec of Formasa, Argentina, Griette Van der Heide, Victor Davalos, John Lindo, Claudia Valeggia and Ellie and Arye Gittelman. A special thanks goes to Dr. Eduardo Fernandez-Duque, for without his continual support

25

PennScience Journal of Undergraduate Research

VOL 9 ISSUE 1, FALL 2010

In this paper, in addition to presentation of the original model, it is extended to allow an round of raise by the second player. This modification makes the model closer and more a real poker (Texas Hold’em), and provides more information on optimal players by both playe complicated situation. In addition, discussion on allowing multiple rounds follows.

2 von Neumann’s Model Two-Player Zero-Sum Poker Models with One and Two Rounds of Betting

This section presents the basic model of von Neumann, and definitions and lemmas that are in general. Two players each contribute an ante of $1, and are dealt “hands” x1 and x2 , independent and identically distributed as U (0, 1). Player I can check or bet a predetermin B, and player II can call or fold if player I bets. The only available information for each p Hanzhe Zhang, University of Pennsylvania own hand and the game structure. Strategies for two players are Player I: s1 : x1 → {check, bet}; Player II: s2 : x2 × spoker {call, fold}.

1 (x1 ) →model The paper presents the basic von Neumann’s two-player zero-sum with independent and identically A player’s payoff is dependent of x1 , x2 , s1 (x1 ), s2 (x2 ). Extensive form of the game and optima distributed uniform hands, and extends it by allowing Player II to re-raise. The analysis shows that both models are presented in Figure 1 with player I’s payoffs shown (their reciprocals are player II’s becau favor the player who initially raises, but re-raisingisoption cuts in Player I’s advantage, reducing his expected payoff. zero-sum). want to investigate how players equilibrium.isThey are going and to play a pair “Payoff square”, a square diagram that indicates the We payoffs under different handsplay andinstrategies, introduced strategiesand as defined below.

A strategy is optimalare if given any hand and and the other player’s str used to derive players’ payoffs. Extensions to multiple infinite rounds of betting discussed, optimal is no incentive to deviate to any other strategy.

strategies are conjectured. Related models are reviewed along the way.

Introduction

Definition 2.1. For player i, a strategy s∗i is optimal if given any other strategy s i and ot strategy sj ,

chance and de- ui (xi , xj , s∗i (xi ), sj (xj ))dxj ≥ ui (xi , xj , s i (xi ), sj (xj ))dxj ∀x1 ∈ (0, 1).

Poker is a complex multi-player game of ception. In order to gain insight into different aspects of the xj xj game, mathematical and psychological alike, we∗ To construct whom correspondence should be addressed: hanzhe@sas.upenn.edu. † Submatriculation u Pemantle, Figureof1:Mathematics, Extensive University o Thesis Advisor: Professor simple models of poker by making assumptions about their check u Robin u Department check check form of von Neuhands and restricting rules. Two-player zero-sum poker (1+B)u(1+B)u I I I call call (1+B)u mann’s game, where call models with independent uniform hands are the simplest bet 1 u = 1 if x1 ≥ x2;= −1 bet bet u II non-trivial ones. Von Neumann (1953) discusses his model II check II otherwise. fold 1 I fold 1fold 1 call in Theory of Games and Economic Behaviors (von Neu(1+B)u u check bet mann & Morgenstern, 1953). twoNeumann’s similar hands, Figure 1: Extensive form For of von game,payoff wherefrom u = 1anif optimal x ≥ x ; strategy = −1 otherwise.

II Figure 1: Extensive Figure 1:form Extensive of von form Neumann’s of vonIgame, Neumann’s where game, ucall = 1where if x1(1+B)u ≥u x1=2 ;1=if2−1 x1 otherwise. ≥ x2 ; = −1 oth fold In this paper, in addition to presentation of the original should be the same. Otherwise, there is an incentive to de1 bet model, it is extended to allow an additional round of raise by viate to the strategy played ifIIgiven the other hand. ThereFor two similar hands, payoff from an optimal strategy should be the 1 same. is fold Figure 1:payoff Extensive form offrom vonstrategy Neumann’s game, =yield 1 Otherwise, ifsame. xsimilar x2 ;there = 1 ≥ the second player. This modication makes model closer fore, hands slightly bigger andstrategy slightly smaller For twothe similar For hands, two similar hands, from an payoff optimal an optimal should be thewhere should same.ube Otherwise, the there Otherwise, is −1 an o incentive to deviate to the strategy played if given the other hand. Therefore, hands slightly bigger a incentive to deviate incentive to to the deviate strategy to played the strategy if given played the other if given hand. the Therefore, other hand. hands Therefore, slightly hands biggerslightly and and more applicable to real poker (Texas Hold’em), and propayoffs.

This idea is isembodied the condition slightly smaller yield similar payoffs.

This embodied in in the indifference indifference Figure 1: Extensive form of idea von Neumann’s game, where uindifference = 1 condition if x1 ≥(IC). x2 ;(IC). =For −1 F slightly smaller slightly yield smaller similar yield payoffs. similar This payoffs. idea is embodied This idea in is embodied the indifference in the condition condition vides more information on optimal players byinboth players (IC).

For example inIIan the optimal strategy above, player II isOtherwise example the optimal strategy above, player is optimal indifferent between folding andsame. calling when he For two similar hands, payoff from strategy should be the example in the example optimal in strategy the optimal above, strategy playerabove, II is indifferent player II is between indifferent folding between and calling foldingwhen and calling he is dealt c. discussion in a more complicated situation. In addition, indifferent between folding andthe calling is dealt c. incentive toon deviate to the strategy played if given otherwhen hand.he Therefore, hands slightl dealt c. dealt c. slightly similar payoffs.

This idea in the indifference conditio allowing multiple rounds follows.

For smaller two similar hands, from an s optimal strategy be the same. Otherwis 2.2 (IC).

For *, asisЄembodied →0+, should Lemma 2.2 (IC).

For s∗i yield , as Lemma + →∗ 0+ ,payoff ∗ + i

Lemma 2.2 Lemma (IC).

For2.2 sito,the (IC).

For as optimal → 0tos,ithe ,strategy asstrategy → 0above, ,played example in II isthe indifferent between foldinghands and calling incentive if given other hand.

Therefore, slight player deviate the indifference conditi

∗ ∗ dealt c. slightly smaller yield similar payoffs.

This idea is embodied in

von Neumann’s Model ui xi ,∗xj , si xi − ∗, xj → (2 ui xi ,∗xj , si xi + ∗, xj ∀xi . uiinxxj the , si xuii −x∗strategy si isxuiindifferent x i , x ,x x∀x ∀xiand . (2.1) i , x ,x x xxjji , x→ i. , x j ,II j ,j si between i + j i+− ui,player i+ i , xj optimal j ,j si → example above, folding callin x s , as

→ 0 , This section presents the basic model of vonLemma Neumann, i x x xj 2.2 (IC). xFor j j j dealt c. is presented as follows. Player I chec strategy of von Neumann’s game and denitions and lemmas that are applicable in general.

Theorem 2.3. AnTwo equilibrium as follows.

∗ + ∗ 0 ,of vongame Theorem 2.3.

Anstrategy equilibrium strategy Neumann’s is ∗follows. presented Play Theorem 2.3.

An equilibrium von Neumann’s is presented as I checks Lemma 2.2 bets (IC).

Foruisof → xotherwise; + Player , xjx2 >∀x ui game xplayer ix,B i , xj , si IIxicalls i ,as j , s j →of raise, i xi − in, x whenare a ≤ x1 ≤ b and amount case if ci .and fo players each contribute an ante ofwhen $1, and dealt “hands” Theorem 2.3.

An equilibrium strategy of von Neumann’s ≤ bets x1 ≤amount a ≤ x1when ≤ b a and b and xjbets B otherwise; amount Binotherwise; case of raise, in xcase of raise, II callsplayer if x2 II> calls c andif folds x2 > j player otherwise, wheredistrib Player I checks∗ when a x1 b

x1 and x2, respectively independent and identically otherwise, where otherwise, where game isu presented follows. , s∗i xas von , xj Neumann’s ui xgame xi + , xjas follows. ∀xi . Pla → i , xj , s i − i xi , xjstrategy Theorem 2.3.

An equilibrium of isi presented 2 uted as U(0,1). Player I can check or bet a predetermined andBbets xj j B(B + 3) II calls + 4B +2 2 in xcase amount otherwise; of raise, player 2 BB when a ≤ otherwise; of raise, II 3) calls if x2 > + 3) player B(B. + B b and bets B + 2 B + in 4B a =x1 ≤ ,amount bB= +B4B , case c+=2B(B amount B, and player II can call or fold if player I abets. = The(B + a 1)(B = b= , +b 1)(B = ,+ where c= , +c 1)(B = .+ 4) .

4) (B 4) (B if x2 >,+c+and otherwise, Theorem 2.3.

An strategy Neumann’s is 4) presented follows. P (Bwhere + 1)(B + equilibrium 4) (B 1)(Bfolds + 4) (B + otherwise, 1)(Bof+von 4) (B + 1)(B(B + 4) + game 1)(B + (B + 1)(B as + 4) only available information for each player is hiswhen ownahand ≤ strategies x1 ≤ b and amountinBFigure otherwise; Two players’ optimal arebets illustrated 2. 2 in case of raise, player II calls if x2 > B(B + 3) + 4B players’ Two optimal players’ strategies optimal are strategies illustratedB are in illustrated Figure 2. in B Figure 2.+ 2 and the game structure. StrategiesTwo for two players are otherwise, where a= , b= , c= .

(B + 1)(B + 4) (B + 1)(B + 4) (B + 1)(B + 4) Player I: s1 : x1 → {check, bet}; Player I bet(bluff) check bet 2 B(B + 3) B a check B check + 4B 2 c +bet Player I bet(bluff) Player I abet(bluff) c , ba = in Figure ,c c = bet .

0 a =strategies Player II: s2 : x2 × s1(x1) → {call, fold}.

1 Two players’ 0optimal are illustrated 2.

(B0+ 1)(B + 4) c (B + 1)(B + 4) 1(B + 1)(B +14)

Player II fold c call A player’s payoff is dependent of x1; x2; s1(x1); s2(x2Player ). Extenc call II Player II fold strategies call in Figure 2.

Two fold players’ optimal are illustrated Two players’ optimal strategies are illustrated in Figure 2.

Player I bet(bluff) a check bet sive form of the game and optimal strategies are presented in Figure 2:0Optimal strategies of both playersc 1 2: Optimal Figure strategies 2: Optimal of strategies both players of both players Figure 1 with player I’s payoffs shown (their reciprocals areFigurePlayer c check fold call bet PlayerIII bet(bluff) c a player II’s because the game is zero-sum).

0 1 Proof.

Optimal strategies are Player found by backward induction.

Player II’s optimal strategy is found fir We want to investigate how players play in equilibrium. c II’s optimal IIFigure fold call 2: backward Optimal strategies of both players Proof. Optimal Proof. strategies Optimal arestrategies found by are backward found by induction.

Player induction.

Player strategy II’s optimal is found strategy first.is Whenstrategies Player I raises, player II calls if his expected payoff is greater than −1, which is his payoff fro They are going to play a pair of When optimal asplayer dePlayer When I raises, Player I raises, II callsplayer if his II expected calls if his payoff expected is greater payoff than is greater −1, which than is −1, his payoff which from is his p Figure 2: Optimal strategies of both Since his payoff depends piecewise-linearly on his hand strength x2both , uplayers 2 (x 1 , x2 ), player II’s payo Figure 2: his Optimal strategies players scribed below. A strategy is optimal iffolding. given hand andhis payoff folding.

Sinceany folding. his payoff Since depends piecewise-linearly depends piecewise-linearly on hand strength on his hand x2 , of x2player ustrength , u2 (x1II’s , x2payoff, ), player 2 (x1 , x2 ), is a monotonic function ofstrategies x2 if he calls.

Therefore, player II’s optimalPlayer strategy isoptimal to call when x2 > Optimal byplayer backward induction. monotonic isProof. afunction monotonic ofto x2function of xare if he calls. if found he calls.

Therefore, II’s optimal strategy II’s optimal is II’s tostrategy call when isstrategy to x2 call > c wi 2Therefore, the other player’s strategy, there isisnoa incentive to deviate Proof.

Optimal strategies areplayer found bygreater backward inducand to foldWhen otherwise.

Player I raises, player II calls if his expected payoff is than −1, which is his and to fold otherwise. and to fold otherwise. any other strategy.

Given player II’s optimal strategy, player I should bet if his expected payoff ofII’s betting is1 ,greater th tion.

Player II’s optimal strategy is found first.

When Player folding.

Since his payoff depends piecewise-linearly on his hand strength x , u (x x ), playe Proof.

Optimal strategies are found by backward induction.

Player optimal strategy 2 2 2 Given player Given II’s optimal playerstrategy, II’s optimal player strategy, I should player bet ifI his should expected bet if payoff his expected of betting payoff is greater of betting than is g ofs ichecking (Tie situations need not be considered because theplayer density function isstrategy non-atomic).

Play Denition 2.1. For player i, a strategy * is optimal if given is a monotonic function of x if he calls.

Therefore, II’s optimal is to call When Player I raises, player II calls if his expected payoff is greater than −1, which is 2 I raises, Player II calls if his expected payoff is greater than of checking (Tie of checking situations (Tie need situations not be considered need not bebecause considered the density becausefunction the density is non-atomic). function is non-atom Player hi I’s payoff sgiven tox1fold otherwise.

Since his payoff depends piecewise-linearly on his hand strength x , u (x , x2 ), play any other strategy si’ and other player’s strategy ,jfolding.

2 2 1 I’s payoff given I’sand xpayoff given x 1 1 −1, which is his payoff from folding. Since his payoff depends player II’s optimal player I should bet if his expected of betting is aGiven monotonic of+xstrategy, if he· (1 calls.

Therefore, player II’s optimalpayoff strategy is to call 2 • from is checking is (+1)function · (x − 0) (−1) − x ) = 2x − 1.

1 1 hand 1 on his x1.2, density u2(x1, xfunction ), playeris non-ato • from checking • checking from is (+1) checking · (x1piecewise-linearly −is0) (+1) + (−1) · (x (1not 0) −+ xbe )= 2x · (1 −1. x1strength )because = 2x1 −the 2 1· − 1(−1) 1 − ofand (Tie situations need considered to fold otherwise.

• fromI’s betting isgiven Given playerx1is II’s optimal strategy, player I should bet if his expected payoff of betting is • from betting • payoff from is betting situations

www.pennscience.org 26 of checking (Tie not be considered because the density function is non-ato c 1 ·1need c • from checking c 1 is (+1) (x1 − 0) + (−1) · (1 − x1 ) = 2x1 − 1. (+1)dx + x (−1 − B)dx = c + (−1 − B)(1 − c) = (B + 2)c − B − 1, x < c, I’s payoff given

et(bluff) yer I bet(bluff) check bet B(B + 3) .

B 2 +bet 4B + 2 c a a = (Bcheck aB , cb = , c= + 1)(B + 4) (B + 1)(B + 4) 0 1 (B + 1)(B1+ 4) Articles c c call foldoptimal strategies yer IIResearch fold call Two playersâ&#x20AC;&#x2122; are illustrated in Figure 2.

I bet(bluff) check players re 2: Figure Optimal strategies of botha players 2:Player Optimal strategies of both c 0 payoff, Player II is

bet

a(1 + B) + (1 â&#x2C6;&#x2019; b)(â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; B) 2b â&#x2C6;&#x2019; 1

=

( (2.5)

Solve Equations 2.4strategy and 2.5should give values a and b and substitute into Equation 2.6, c = B(B + 3) (B optimal Player IIâ&#x20AC;&#x2122;s obey the indifference condition, 1)(B + 4) . a and b as functions of B are obtained by re-substitution.

a(1 + B) + (1 â&#x2C6;&#x2019; b)(â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; B)

1

a + 1 â&#x2C6;&#x2019; b = â&#x2C6;&#x2019;1

(B + 1)(2b â&#x2C6;&#x2019; c â&#x2C6;&#x2019; 1) + c

a + 1 â&#x2C6;&#x2019; b = â&#x2C6;&#x2019;1

(2.6)

Payoffs of both players can be determined. In addition, given that player I determines his bet amo

before are assigned, that maximizes isB(B of interest. pay Solvehands Equations 2.4 and 2.5the giveoptimal values aBand b and substitutethe intoexpected Equationpayoff 2.6, c = + 3) (BFirst, +

There-squares Corollary 2.6. Given that both players followarethe optimal strategies payoffs of players introduced.

1)(B + that 4) . adescribe and b as functions of and B arecorresponding obtained by re-substitution.

IIâ&#x20AC;&#x2122;s a monotonic x2 if he calls. cfunction ofcall fold 2.4. payoff is a two-dimensional square diagram withishis hands fore, player IIâ&#x20AC;&#x2122;s optimal strategy is to call when x2 > c and toDefinition strategies in Theorem 2.3,given Player Iâ&#x20AC;&#x2122;s ubet (x1of, player I in Payoffs of bothAdescribed players cansquare be determined.

In addition, that player Ipayoff determines 1 amount Figure 2: Optimal strategies of both players nd are by backward induction.

Player IIâ&#x20AC;&#x2122;s optimal strategy isstrategy found first. ies found by backward induction.

Player IIâ&#x20AC;&#x2122;s optimal is found first. axis, andhands player in y-axis.

A point the square indicatespayoff a hand pair (x1First, , x2 ),payoff and the pay before are IIâ&#x20AC;&#x2122;s assigned, the optimal B thatin maximizes the expected is of interest. , s2describe ), x=2 ),a.

Optimal bet amount isisofB * = 2.are fold otherwise. x22, ,ss1that squares strategies corresponding payoffs players introduced. u1 (x s2 (x indicated at the point resulted from the strategies played correspond 1, x 1 (x1 1 , x2 )), and alls if his expected is greater â&#x2C6;&#x2019;1, which is his payoff from player II calls if his payoff expected payoff than is greater than â&#x2C6;&#x2019;1, which is his payoff from the hands. 2.4. A payoff square is a two-dimensional square diagram with hands of player I in xDefinition Given player IIâ&#x20AC;&#x2122;s optimal I 2should bet iftopayoff, piecewise-linearly on are hisfound hand ,strategy, u2 (x1Player , x2 ), player payoff, ffProof. depends piecewise-linearly on his handx strength ,player uIIâ&#x20AC;&#x2122;s ),strategy player 2 2 (x 1 , xIIâ&#x20AC;&#x2122;s Optimal strategies bystrength backward induction. optimal isIIâ&#x20AC;&#x2122;s found first.and player IIâ&#x20AC;&#x2122;s in y-axis. A point in the square indicates a hand pair (x , x ), and the payoff, axis, Remark 2.5. Payoffs of any strategy set can be depicted byIthe payoff square. can also be general he Therefore, player IIâ&#x20AC;&#x2122;s optimal strategy is to call when x > c payoff from player checking all Ithands his expected payoff of betting is greater than of checking n ofcalls. xPlayer if he calls.

Therefore, player IIâ&#x20AC;&#x2122;s optimal strategy is to call when x > When I raises, player II calls if his expected payoff is greater than â&#x2C6;&#x2019;1, which is his payoff 2 2 2ufrom (x c , xProof. , s (x , x Expected ), s (x , x )), indicated at the point is resulted from the strategies played corresponding n-dimension, which is equivalent to taking multiple integrals of n variables (Besides the payoff squ olding. Since his payoff depends piecewise-linearly on his hand strength x2 , u2 (x1 , x2 ), player IIâ&#x20AC;&#x2122;stopayoff, to the hands.

(Tie situations need not be considered because the densityx2 >aiscpayoff 0, +1â&#x20AC;&#x153;cubeâ&#x20AC;? below x1 = axthree-player and â&#x2C6;&#x2019;1 above x1 = x2. Equivalently, the depicting is beneficial).

2 set can be game s a monotonic function of x2 if he calls. Therefore, player IIâ&#x20AC;&#x2122;s optimal strategy is to call whenonly Remark 2.5. Payoffs of any strategy depicted by the payoff square. It can also be generalized egy, player I should if his expected payoff betting is greater timal strategy, player Inon-atomic). should bet if his expected payoffgiven of betting is greater than nd to fold otherwise.

Corollary 2.6.differential Givenisthat both players follow the optimal described Theorem function isbet Player Iâ&#x20AC;&#x2122;sofpayoff x1 than payoff from this strategy illustrated and ex-square,2.3, pla to n-dimension, which equivalent to taking multiple integrals ofisnstrategies variables (Besides thein payoff not be considered because the density function is non-atomic).

Player ons need notIIâ&#x20AC;&#x2122;sbeoptimal considered the bet density function is non-atomic).

Player Given player strategy,because player I should if his expected payoff of betting is greater than only a payoff a three-player is beneficial).

Iâ&#x20AC;&#x2122;s payoff is u1â&#x20AC;&#x153;cubeâ&#x20AC;? (x1 , x2depicting , s1 , s2 ) = a. Optimalgame bet amount is B â&#x2C6;&#x2014; = 2. pected payoff would be the same overall, so we add 1 above f checking (Tie situations need not be considered because the density function is non-atomic). Player Corollary 2.6. Given that both players follow the optimal strategies described in Theorem 2.3, player Expected payoff Icancel checking all hands below x1on = xthe â&#x2C6;&#x2019;1 above x1 = 2 andtop â&#x20AC;&#x2122;s payoff given xâ&#x20AC;˘ 1 Iâ&#x20AC;&#x2122;s x payoff , x , s from , s ) 1, =player a.and Optimal bet amount isaBsquare =is2.0, +1region from checking is (+1) â&#x2C6;&#x2122; (x1 â&#x2C6;&#x2019; 0) + (â&#x2C6;&#x2019;1) â&#x2C6;&#x2122; (1 â&#x2C6;&#x2019; x1) = 2xProof. = xis 2u, (x subtract out 1 1 Equivalently, the payoff differential from this strategy is illustrated and expected payoff would be â&#x2C6;&#x2019;+1) 0) + (â&#x2C6;&#x2019;1) (1+â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1) x1 ) ¡= 2x ¡ (x â&#x2C6;&#x2019; ¡0) ¡(x(1 â&#x2C6;&#x2019; x ) = 2x 1.

10)â&#x2C6;&#x2019; 1 1.

1â&#x2C6;&#x2019;â&#x2C6;&#x2019; â&#x20AC;˘ from 1checking is (+1) â&#x2C6;&#x2019; + (â&#x2C6;&#x2019;1) ¡ (1 x ) = 2x â&#x2C6;&#x2019; 1.

1 1 Proof.

Expected checking all hands issquare 0, cancel +1 below x a= x and â&#x2C6;&#x2019;1 above x =top x . of +B â&#x2C6;&#x2019; 1. 1 of +B soand â&#x2C6;&#x2019;B1from to player get the on the right.

The same overall, wepayoff add above x1 I= x2 , resulting subtract 1, and out square region on the the payoff square differential fromright. this strategy is illustrated and expected payoff as would â&#x2C6;&#x2019;BEquivalently, to get the resulting on the The original, complete payoff square wellbe as the its geome â&#x20AC;˘ from bettingâ&#x20AC;˘ is from betting is original, complete square well its geometric same overall, so we add 1 above xpayoff = x , subtract 1, andas cancel out as a square region on the topand of +B and and algebraic manipulation are shown in Figure 3.

1 â&#x2C6;&#x2019;B to get the resulting square on the right. The original, complete payoff square as well as its geometric 1 c manipulation shown in Figure 3. (+1)dx2 + (â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; B)dx2 = c + (â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; B)(1 â&#x2C6;&#x2019; c) = (B + 2)c â&#x2C6;&#x2019; B â&#x2C6;&#x2019; 1, x1 < c, andalgebraic algebraic manipulation are shown inare Figure 3.

1

1

1

2

1

1

1

2

1

2

2

1

1

â&#x2C6;&#x2014;

2

1

1

12 â&#x2C6;&#x2019; + (â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; B)(1 â&#x2C6;&#x2019; c) (B â&#x2C6;&#x2019; + c) 2)c=â&#x2C6;&#x2019;(B B+ â&#x2C6;&#x2019; 2)c 1, â&#x2C6;&#x2019;xB + B)dx (â&#x2C6;&#x2019;1 + (â&#x2C6;&#x2019;1 â&#x2C6;&#x2019;= B)(1 â&#x2C6;&#x2019;c, 1, 2 0=â&#x2C6;&#x2019;cB)dx 1 < 2 = c c orc

c

x1

x1 < c,

x2

1

(+1)dx2 + (1 + B)dx2 + (â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; B)dx2 = (B + 1)(2x1 â&#x2C6;&#x2019; 1) â&#x2C6;&#x2019; Bc, x1 â&#x2030;Ľ c.

x1 1 1 c 0 x1 + B)dx + (â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; B)dx = (B + 1)(2x â&#x2C6;&#x2019; Bc, x1â&#x2C6;&#x2019;â&#x2030;ĽBc, c. x1 â&#x2030;Ľ c. + (1 + B)dx + (â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; B)dx 1)(2x 2 1 â&#x2C6;&#x2019;+1) 2 2 = (B 1 â&#x2C6;&#x2019; 1) Then

by IC2 in Equation22.1, x1

c

x1 â&#x2C6;&#x2019; 1

x1 â&#x2C6;&#x2019; 1

2x1 â&#x2C6;&#x2019; 1

=

(B + 1)(2x1 â&#x2C6;&#x2019; c â&#x2C6;&#x2019; 1) + c

= Bâ&#x2C6;&#x2019; 2x1 2c â&#x2C6;&#x2019; 1+ Bc = â&#x2C6;&#x2019; 2c + 1, Bc â&#x2C6;&#x2019; B â&#x2C6;&#x2019; 1,

= â&#x2C6;&#x2019; 1) + c c â&#x2C6;&#x2019; 1) + c 2x1 (B â&#x2C6;&#x2019; 1+ 1)(2x = (B 1 â&#x2C6;&#x2019;+c 1)(2x 1 â&#x2C6;&#x2019;

1

2

0

-1-B

x2

0

-1-B

x1

1 = 2c +2.1, Bc â&#x2C6;&#x2019; B â&#x2C6;&#x2019; 1, Then by IC2xin1 â&#x2C6;&#x2019;Equation

n 2.1,

x2

0

2

2

x2

0

2

2

(2.2)

-1-B -1-B

(2.2)

(2.3) c c (2.2)

(2.3)

(2.3)

-1 -1 1+B 1+B

b -B

c

c

-B B

+2

+1

+1

b

+1

B

+2

+1

2

Since Player Iâ&#x20AC;&#x2122;s payoff is also piecewise linear with respect 0 0 a b 1 a b 1 x 0 a b a b 1 x1 to x1, Player Iâ&#x20AC;&#x2122;s optimal strategy is to bet if x1 < a or x1 > b, 0 Figure 3: Illustration of Player Iâ&#x20AC;&#x2122;s payoff by payoff square. and to check if a â&#x2030;¤2 x1 â&#x2030;¤ b. Then x1 â&#x2030;¤ c in Equation 2.2, and x1 2 respect Figure square.

Figure3: 3:Illustration Illustration of of Player Player Iâ&#x20AC;&#x2122;s Iâ&#x20AC;&#x2122;spayoff payoff by by payoff payoff square. ecewise inear with linear respect with to x1 , player to x1Iâ&#x20AC;&#x2122;s , player optimal Iâ&#x20AC;&#x2122;s strategy optimal strategy is to bet isif to x1 bet < aif x1 < a Expected payoff of player I is 2.3, fâ&#x2030;¤ab.â&#x2030;¤ Then x1 â&#x2030;¤â&#x2030;Ľ b. xc1in Then â&#x2030;¤ Equation c inx1Equation â&#x2030;¤ c in Equation 2.2, and 2.2, x1 â&#x2030;Ľand c inx1Equation â&#x2030;Ľ c in Equation 2.3, 2.3,

B(1 â&#x2C6;&#x2019; of b)(bplayer â&#x2C6;&#x2019; c) â&#x2C6;&#x2019;IB(a)(1 â&#x2C6;&#x2019; c) + (2)(1/2)(c u also inearpiecewise with respect lineartowith x1 , player respectIâ&#x20AC;&#x2122;s tooptimal x1 , player strategy Iâ&#x20AC;&#x2122;s optimal is to bet strategy if x1 < is a to bet Expected if x1 Expected < =apayoff isof Player payoff I is + c â&#x2C6;&#x2019; a)(a) = B (B + 1)(B + 4) = a.

1

x1

1

x1

1

2 heck â&#x2030;¤ if1 a 2a â&#x2030;¤ â&#x2030;¤ cb.= in Then Equation â&#x2030;¤ 2.2, cB in â&#x2C6;&#x2019; and Equation in Equation and x1 â&#x2030;Ľ 2.3, c in Equation 1â&#x2030;¤+ 2cB +xâ&#x2C6;&#x2019; Bc 1 x1 â&#x2030;Ľ c2.2, (2.4) 2ab.â&#x2C6;&#x2019;Then =xxâ&#x2C6;&#x2019; Bc â&#x2C6;&#x2019; 1â&#x2C6;&#x2019; (2.4) 2.3, 112c 1 B, 4 â&#x2C6;&#x2019;â&#x2C6;&#x2019; B 2c) +(B a =+1/9, = a. + 1)2 (B + 4) = 0, B â&#x2C6;&#x2014; ==2.Bu1 (2) Maximizing 1 (B) u = uB(1 â&#x2C6;&#x2019;with b)(brespect â&#x2C6;&#x2019; c) â&#x2C6;&#x2019;toB(a)(1 (2)(1/2)(c +câ&#x2C6;&#x2019; a)(a) (B=+1/9, 1)(B 4) b = 1

2b â&#x2C6;&#x2019; 1 2a â&#x2C6;&#x2019; 1

2b 1 +=1)(2b (Bâ&#x2C6;&#x2019; +c1)(2b = â&#x2C6;&#x2019;(B â&#x2C6;&#x2019; 1) â&#x2C6;&#x2019; + c â&#x2C6;&#x2019; 1) + c = 2c2a +â&#x2C6;&#x2019; Bc 1 â&#x2C6;&#x2019;= B â&#x2C6;&#x2019;2c 1 + Bc â&#x2C6;&#x2019; B â&#x2C6;&#x2019; 1

(2.5) (2.4)

7/9, c = 5/9.

(2.5) (2.4) Maximizing u1 (B) with respect to B, 4 â&#x2C6;&#x2019; B 2 (B + 1)2 (B + 4)2 = 0, B â&#x2C6;&#x2014; = 2. u1 (2) = 1/9, a = 1/9, 2 7/9, c = 5/9.

Maximizing u (B) with respect to B, (4â&#x2C6;&#x2019;B )â&#x2C6;&#x2022;[(B+1)2(B+4)2 ] 1 (2.5) 3

â&#x2C6;&#x2019; 1 the =obey (B2b +â&#x2C6;&#x2019;1)(2b 1 condition, =â&#x2C6;&#x2019; c(B â&#x2C6;&#x2019; 1) +condition, + 1)(2b c â&#x2C6;&#x2019; c â&#x2C6;&#x2019; 1) + c (2.5) ld2bobey indifference egy should the indifference Player IIâ&#x20AC;&#x2122;s optimal strategy should obey the indierence = 0; B* = 2: u1(2) = 1â&#x2C6;&#x2022;9; a = 1â&#x2C6;&#x2022;9; b = 7â&#x2C6;&#x2022;9; c = 5â&#x2C6;&#x2022;9.

obey the should indifference condition, indifference condition, +ldstrategy B) + (1 â&#x2C6;&#x2019; b)(â&#x2C6;&#x2019;1 B)the a B) + 1 â&#x2C6;&#x2019; ba += (2.6) a(1 + B) + (1obey â&#x2C6;&#x2019; b)(â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; 1â&#x2C6;&#x2019;1 â&#x2C6;&#x2019; b = â&#x2C6;&#x2019;1 (2.6) The result deserves some discussion. Player Iâ&#x20AC;&#x2122;s payoff, condition, 3

2 Bâ&#x2C6;&#x2022;(B +5B +4) is positive for all B > 0, and it achieves its maxi

a(1 + (1 b)(â&#x2C6;&#x2019;1 a+ 1 â&#x2C6;&#x2019; bc ==2.6, â&#x2C6;&#x2019;1 c+=3)B(B +2.5 B)give + (1 â&#x2C6;&#x2019; b)(â&#x2C6;&#x2019;1 â&#x2C6;&#x2019;+substitute B) asubstitute +into 1â&#x2C6;&#x2019; â&#x2C6;&#x2019;B) bEquation =into â&#x2C6;&#x2019;1 (2.6) values a values and b and 2.6, B(B (B aB)and bâ&#x2C6;&#x2019; and Equation ++3) (B + (2.6)

mum at B * = 2, the pot size. This means that the game favors

of B are of obtained by re-substitution. nctions B are obtained by re-substitution.

4values and 2.5 giveb values a and b and = B(B (B +I who is given the chance to raise, and he maximizes a and and substitute intosubstitute Equation into 2.6, cEquation = B(B +2.6, 3) c (B + + 3)player Inofaddition, given that player I2.5 determines his bet can be obtained determined.

In addition, given that player his bet amount bsdetermined. as Bby arere-substitution. obtained by re-substitution. of B functions are Solving Equations 2.4 and givesI determines values a amount and b and his payoff to be 1â&#x2C6;&#x2022;9 by betting pot size every time. Player I timal that maximizes the expected payoff ofB(B interest.

First, d, the B optimal B that maximizes the expected is 3)â&#x2C6;&#x2022; of interest.

First, payoff substituting into Equation 2.6, cis=payoff + [(B + payoff 1)(B + 4)]. has an advantage because he can bluff with his worst hands. players can Inplayers addition, given thatintroduced. playerhis I determines determined.

Indetermined. addition, thatofplayer I determines bet amounthis bet amount and corresponding payoffsgiven ofpayoffs are introduced. rategies andbe corresponding players are a and b as functions of B are obtained by re-substitution. ssigned, B that the expected payoffFirst, is of interest. payoffimportantly, for real poker perhaps, he must bluff with timal B the thatoptimal maximizes the maximizes expected payoff is of interest. payoff First, More are isstrategies a two-dimensional square diagram with playerof I player in x-that off is a two-dimensional square diagram with I in xPayoffs of both players behands determined.

Given his worst but not mediocre hands. ribe and corresponding payoffs of players areofhands introduced. andsquare corresponding payoffs of players arecan introduced.

A point A in point the square a hand pair (x1 ,pair x2 ), (x and payoff, the payoff, y-axis. in theindicates square indicates a hand 1 , xthe 2 ), and Player Iatisdetermines his betstrategies amount before hands as- I inInx-contrast to von Neumannâ&#x20AC;&#x2122;s model in which the bet A payoff square a resulted two-dimensional square diagram hands of are is a at two-dimensional square diagram with of with player I corresponding inare x- player ndicated the point the is point is from resulted the from thehands strategies played corresponding played 1 , x2 )), indicated signed, the optimal B athat maximizes Iâ&#x20AC;&#x2122;s in y-axis. point in the square indicates pair the (x1 ,payoff, A point in theAsquare indicates hand pair (xa1 ,hand xthe and xpayoff payoff, is pre-determined and fixed, Donald Newman pres2 ), expected 2 ), andisthe amount ), ndicated s2 (x1 , xat the indicated point isFirst, resulted at thepayoff point fromis the resulted strategies fromdescribe played the strategies corresponding playedand corresponding 2 )), of interest. squares that strategies ents a model that has the same game structure but allows ategy f any set strategy can be setdepicted can be depicted by the payoff by thesquare. payoff It square. can also It can be generalized also be generalized corresponding payoffs of players are introduced. any bet amount (Newman, 1959). Set Ξ = 2â&#x2C6;&#x2022;(B + 2). The optint equivalent to takingtomultiple taking multiple integrals integrals of n variables of n variables (Besides(Besides the payoff thesquare, payoff square, yoffs ategy of set any can strategy be depicted set can by be the depicted payoff square. by the payoff It can square. also be generalized It can also be generalized Definition A payoff square is a two-dimensional mal strategy is that Player I checks when 1â&#x2C6;&#x2022;7 â&#x2030;¤ x1 â&#x2030;¤ 4â&#x2C6;&#x2022;7, bets three-player icting a three-player game is beneficial). game 2.4. is beneficial). hich nt toistaking equivalent multiple to taking integrals multiple of n variables integrals (Besides of n variables payoff (Besides square, the payoff square, square diagram with hands of player I inthex-axis, player B with hands (1 â&#x2C6;&#x2019; 3Ξ2 + 2Ξ3)â&#x2C6;&#x2022;7, or 1 â&#x2C6;&#x2019; 3Ξ2 â&#x2C6;&#x2022;7; Player II calls if hat players both follow players the follow optimal the strategies optimal strategies described described in Theorem in Theorem 2.3,and player 2.3, player eâ&#x20AC;? three-player depicting game a three-player is beneficial). game is â&#x2C6;&#x2014;beneficial). â&#x2C6;&#x2014; , sOptimal Optimal bet in amount bet is amount B point = 2. is B = 2.square indicates a hand pair (x1, and only if x2 > 1 â&#x2C6;&#x2019;6Ξ â&#x2C6;&#x2022;7. In this game, Player Iâ&#x20AC;&#x2122;s value is 1â&#x2C6;&#x2022;7 y-axis.

A in the 2 ) = a. IIâ&#x20AC;&#x2122;s Given players thatfollow both players the optimal follow strategies the optimal described strategies in Theorem in player Theorem 2.3, player x2),I checking and the all payoff, u below (x0, , x+1 , s1= (x1x, xxand ), s described (x , and x2)),2.3, indicated at because Player I bluffs 1â&#x2C6;&#x2022;7 of time. Optimality of the strategy â&#x2C6;&#x2014; 1 is 2x yer player allOptimal handsis isB hands 0, +12.1is x21 above â&#x2C6;&#x2019;1 x1above = x2 . x1 = x2 . .rom xOptimal = a.amount bet = amount B1â&#x2C6;&#x2014;below = 2.

2 2 1 =2â&#x2C6;&#x2019;1 2 ,Ischecking 1 , s2 ) bet the point is resulted from the strategies played corresponding is proven by showing that the given pure strategy is a saddle ial differential from thisfrom strategy this strategy is illustrated is illustrated and expected and expected payoff would payoffbewould the be the yer ayoff I checking from player all hands I checking is 0, all +1 hands below is x 0, +1 below x = x and â&#x2C6;&#x2019;1 above = x and x = â&#x2C6;&#x2019;1 x . above x . all strategies.

1 2 1 2 1 2 1 = x2of to the hands. point above x = x , subtract = x , subtract 1, and cancel 1, and out cancel a square out a region square on region the top on of the +B top and of +B and 1 2 1 2 payoff ial differential this strategy from isthis illustrated strategy isany illustrated expected payoff and expected be payoff the would quare thefrom right. on the The right. original, The original, complete complete payoff square payoff assquare well as aswould its well as its geometric Remark 2.5.

Payoffs ofand strategy set can begeometric depicted by be the add xin =are x12in ,above subtract = 1, xand cancel out 1, and a square cancelregion out aon square the top region of +B on the and top of +B and 1 1 3.

2 , subtract hown on shown Figure Figure 3.

Extension: Re-raise by player II theon payoff square.

It canpayoff also be generalized to n-dimension, nlting the right. squareThe the original, right.complete The original, complete square as payoff well as square its geometric as well as its geometric The key extension to the previous model is allowing Playwhich is equivalent to taking multiple integrals of n variables hown ipulation in Figure are shown 3. in Figure 3.

1-B

1-B27

x2 payoff x2 square, only a payoff â&#x20AC;&#x153;cubeâ&#x20AC;? depicting a (Besides the three-player x20 game is x2 0 beneficial).

-1-B

0

0

PennScience Journal of Undergraduate Research -1-B

b

er II to re-raise B2 after calling Player Iâ&#x20AC;&#x2122;s bet B1, and Player I either calls or folds. This model is discussed in Fergusonâ&#x20AC;&#x2122;s

-B b

-B

VOL 9 ISSUE 1, FALL 2010

eves3 its maximum at player I who is giventhe antes contributed by the players by treating them as sunk costs.

2 B = 2, the pot size. This means that the game favors Now suppose weI’signore 2 2ξ )/7, or 1 − 3ξhe /7; II calls if only x21/9 > B/(B 1 −betting 6ξ/7.

In4)this game, player value The result deserves some discussion.

Player I’sifbe payoff, + 5B + is positive for all BPlayer > 0, and ance to raise, and maximizes hisand payoff to by pot size every time.

I has is 1/7 optimal strategy, and player I has hand x , I’s “gain” that Player II that uses the conjectured 1 ayer I bluffs time. of the strategy is the proven showing given it achieves its 1/7 maximum at B ∗Optimality = 2, the size.

This means game by favors player I whoperhaps, isthe given antage because he of can bluff with his pot worst hands.

Morethat importantly, for real poker he pure chance toworst raise, and maximizes payoff to be 1/9 by betting pot size every time.

Player I has athe saddle point of but all he strategies. luff with his not mediocrehis hands.

• from checking is 2x1 . an advantage because he can bluff with his worst hands. More importantly, for real poker perhaps, he contrast to von Neumann’s model in which the bet amount is pre-determined and fixed, Donald • from bet-folding is 2a if 0 < x < e; 2a + 2(1 + B)(x − e) if e < x < f , and 2a + 2(1 + B1 )(f must bluff with his worst but not mediocre hands. an presents a model that has the same in game structure but allows any bet amount [Newman, 1959] In contrast to von Neumann’s model which the bet amount is pre-determined f <2007). xand < fixed, 1. Donald works (Ferguson & Ferguson, 2003, Ferguson et al., We can verify that at every critical point, the payoffs from ξ = 2/(B + 2).

The optimal strategy is that I checks when 1/7 ≤ x ≤ 4/7, bets B with hands 1 Newman presents a model that has the same game structure but allows any bet amount [Newman, 1959] 2 3 2 d) if 0 noting < x < d;that 2a − the 2(1 +payoff B1 + Bfunc• from bet-calling is 2a − 2(1 + Bare + 2ξ )/7, or 1 − 3ξ /7; II calls if and only if x > 1 − 6ξ/7.

In this game, player I’s value is 1/7 The strategies given hands x , x ~ U(0, 1), are two strategies equal.

1 +B 2 )(e − Then 2 )(e − x) if d < . Set ξ = 2/(B + 2). The optimal strategy is that 1 2I2 checks when 1/7 ≤ x1 ≤ 4/7, bets B with hands 3 e (1 player bluffs Optimality the ifstrategy is6ξ/7. proven by game, showing given pure + that 2(1I’s +the B1tion )(x − is e) piecewise ifI’s e< x < f linear, ; and 2awe + 2(1 + B )(f − e) + 2(1 + B + B )(x is − f ) if f < − 3ξ 2 I+to 2ξthe )/7,1/7 or 1of−time.

3ξ 2 /7; II callsisifallowing andofonly x2 > 1 −II In this value is 1/7 xtension previous model player to re-raise B22aplayer after calling player bet 1 1 2 verify that Player I’s strategy Player s1strategies. : xmodel × s2Optimality (sis1) discussed → {check, bet B1} ×is {fold, call} =[Ferguson {bet-fold, player Ifolds. bluffs 1/7 of time. of thein strategy proven by showing that the&given pure ybecause is a saddle of I: all 1 either calls orpoint This Ferguson’s works Ferguson, 2003],

tension: Re-raise by player II

We can verify that atsix every critical point, the Player payoffs from twowestrategies equal. notin optimal.

Similarly given I’s optimal and PlaySolving linearly independent equations of six unknowns, getstrategy results asare presented in Then the theorem.

check}, et al., 2007]. bet-raise, The strategies given hands x1 , x2 ∼ U (0, 1), arethe payoff function Now is suppose welinearly ignore antes contributed by players byget treating them as sunk costs.

Given piecewise linear, we verify that I’s strategy is optimal.

Similarly given Solving six equations ofplayer six the unknowns, we results as presented in the theorem. ,the Player II’s expected payoff from er II’s hand x2independent Player II: s : x2 ×bet {check, bet} → {bet B2, check, fold} .

I: s : x × s (s ) → {check, B1 }×{fold, call}={bet-fold, check}, that Player II suppose uses thewe conjectured optimal strategy, and I payoff has handfrom x1them , I’s “gain” 1 1 2 1 Now ignore the antes contributed theplayer players by treating as sunk costs. Given 2 I’sbet-raise, optimal strategy and Player II’s hand x2 , Player II’sby expected Extension: Re-raise by player II Re-raise player II • IIfolding is 0 if 0optimal < y <strategy, a, 2(yand − a) if aI has < yhand < b, 2(b − that Player uses the conjectured player x1 , and I’s “gain” II:3 s2 :Extension: x2 × {check, bet} → {bet Bby 2 , check, fold}.

• from checking is 2x1 . strategy is a saddle point of all strategies.

folding is 0player if 0• < y< a, if 2(y b, and 2(b − a) if b < y < 1. yThe extension to thetoprevious model is allowing player B22 •after after calling I’s bet from checking is − a) <if1a) y0. <<ifx1.a<<e; y2a<+ 2(1 key extension the previous model is allowing playerIIIIto tore-raise re-raise B calling player I’sbet-folding bet • from is b 2a2x + B)(x − e) if e < x < f , and 2a + 2(1 + B1 )(f − e) if dB I 1either calls or folds.

This model is discussed in Ferguson’s works [Ferguson & Ferguson, 2003], if • from bet-folding is 2a if 0 < x < e; 2a +− 2(1 e)yy if< e< < f , and 2a By1 )(f − y) if is 0< y <+a;B2(y ififa0− << b; 2(b −+if a)2(1 +−Be)1 )(y • calling is −2(1 +< , and I either calls or folds. This model is discussed in(1+B Ferguson’s & Ferguson, f < 2003], x 1.

1)u works [Ferguson 1 )(a check )(a −a)+y)B)(x < a;xand 2(y − a) a++<2(1 • B calling −2(1 1 II f < x < 1. son et al., 2007].

The strategies given hands x1 ,xx UU(0, [Ferguson et al., 2007].

The strategies given hands (0,1), 1), are are 1 ,2x∼ 2 ∼ b < y < 1. fold • from bet-calling is 2a − 2(1 + B1 + B2 )(e − d) if 0 < x < d; 2a − 2(1 + B1 + B2 )(e − x) if d < x < e; bet 1 < b; ande2(b − a) ++B2(1 +d)B+if10B)(y b) if2(1 b2(1+<+ByB1< ) → {check, B1 }×{fold, call}={bet-fold, bet-raise, <)(f x− <−d; +1.

B2 )(e − x) if d < x < e; from − 2(1 yer I:Player s1 : xI:1 s×1 :s2x(s bet bet B1 }×{fold, call}={bet-fold, bet-raise,check}, check}, 2a +• 2(1 1 × 2 (s1{check, 2 )(e 1 )s→ + bet-calling B1 )(x − e)isif2a < x <+fB; 1and 2a +−2(1 e)2a +− 1 1 + B2 )(x − f ) if f < x < 1. fold • raising is 0 if 0 < y < a, 2(y −a) if a < y < b; 2(b−a) if b < y < c; and 2(b−a)+(1+B 2a + 2(1 + B )(x − e) if e < x < f ; and 2a + 2(1 + B )(f − e) + 2(1 + B + B2 )(x f ) if < 1. 2 ) Player II: s : x × {check, bet} → {bet B , check, fold}.

1 1 1 -(1+B 1 ) 2 2 2 I yer II: s2 : x2 × {check, bet} → {bet bet B2 , check, fold}.

• raising is 0 if 0 < y < a, 2(y − a) if a < y < b; 2(b −−a) iff < 1x +B

u

that at every critical point, the payoffs from two strategies are equal. Then noting that if c < yWe < can 1.Weverify can verify that at every critical point, the payoffs from two strategies are equal. Then noting that I the payoff functionbis<piecewise we verify that player strategy y < c; linear, and 2(b − a)+(1 + B1I’s+ B2)(y is−isoptimal. c) if c Similarly < y < 1.given player (1+B1)u (1+B1+B2)u check the payoff function is piecewise linear, we verify that player I’s strategy optimal. Similarly given player call IIcheck fold(1+B1)u I’s optimal strategy and Player II’s II’s hand xplayer expected payoff from Then with II’s boundary conditions verified, IIII’s is proven to play an optimal 2 , Player I’s optimal strategy and Player hand x , Player II’s expected payoff from II 2 Then with II’s boundary conditions verified, player II isstrategy a bet 1 with Player I’s payoffs.

Figure 4: Extensive two players bet form of the fold Complicated operations were done by Maple 11.

1 • folding is 0 if 0 < y < a, 2(y − a) if a < y < b, and 2(b − a) if b < y < 1. fold • folding is 0 < yan < a,optimal 2(y − a) if astrategy < y < b, andas 2(bwell. − a) if bComplicated < y < 1.

-(1+B1) I Figure 4: Extensive form of the players with I’s payoffs. proven to0 ifplay opbet twofold -(1+Bplayer 1) I u )(a − y) if 0 < y < a; 2(y − a) if a < y < b; and 2(b −∗ a) + 2(1√ +BB11)(y )(y−−b)b)if if • calling is −2(1 + B1+ I • calling is −2(1 Bplayer check bet 1 )(a − y) if 0 < y < a; 2(y − a) if a < y < b; and 2(b − Corollary 3.2.

Expected payoff of I is a.

Optimal bet for player I, B1 a) =+12(1 + + 13/3.

Optim (1+B1+B2)u call erations were done by Maple 11. √ u I b < y < 1. b < y < 1. check Є (0, a] U (b, c], Theorem 3.1. Player I bet-folds when x ∗ ∗ 1 1+B 2)uII is B = 2B + 2 = 4 + 2 13/3.

(1+B call for 2 1 +B22)(y )(y−c) −c) raising is 0 ifis0 0< if a if<ay<<y b; if if b< •bet-calls raising ify0 < < a, y <2(y a, −a) 2(y −a) < 2(b−a) b; 2(b−a) b <y y<<c;c;and and2(b−a)+(1+B 2(b−a)+(1+B11+B 3.1. Player IFigure bet-folds when xform ∈ (0, a] ∪ (b,players c], checks when x ∈ (a, b],II•and when 1 b], checks when x1 Є (a, and bet-calls when x1 > I’s c.1 payoffs.

Player 4: Extensive of the two with player ify c<<1.y < 1. if ∈ c <(d, Player IIFigure folds when x ≤ d, calls when x ∈ (e, f ], and re-raises when x e] ∪ (f, 1].

2 2 1 Proof.

Applying modified payoff square as illustrated 6, I is a. Optimal Corollary 3.2.

Expected payoffinofFigure Player Extensive the two I’s payoffs. folds 4: when x2 d,form callsofwhen x2 players Є (e, f],with and player re-raises when x1 the withboundary II’s boundary conditions verified, player proventotoplay play an an optimal optimal strategy with II’s conditions verified, player II IIis isproven aswell. well. ≤Theorem b ≤ c ≤ f3.1. ≤ 1Player and I0bet-folds ≤ d ≤ when e (d xcan be larger or smaller than a), whereThen Then * * as when bet for Player I, B = 1 + √13∕3.

Optimal bet for IIb)(b is B−2*e)= strategy 2B 1 ∈ (0, a] ∪ (b, c], checks when x1 ∈ (a, b], and bet-calls Complicated operations were done by Maple 11. Є (d, e] U (f, 1].

0 ≤ a ≤ e ≤ b ≤ c ≤ f ≤ 1 and 0 ≤ d ≤ e (d can Complicated operations were done Maple 11.

1− by 1 = B − a(1 − d) − (c b)(e − d) + (1 − c)(e − d) + (1 − + u 1 1 x1 > c. Player II folds when x2 ≤ d, calls when x2 ∈ (e, f ], and re-raises when x1 ∈ (d, e] ∪ (f, 1]. √

Optimal bet for player I, B∗∗ = 1 + √13/3. Optimal

em 3.1. Player I bet-folds when x ∪ (b, c], checks when x1 ∈ (a, b], and bet-calls +2 2(2d =when 43.2. + 2√13∕3.

1 ∈ (0, Corollary Expected of player I a. is a. bet be larger or smaller than a),a]where 0≤a≤e≤ √player Corollary 3.2.− Expected payoff I isd) Optimal for player I, − B11(f =− 1 +c)(1 13/3. bet a)(a −payoff (cof− b)(e − + B2 (1bet− c)(e − d) − fOptimal ) ∗ 2) 2 b ≤ c ≤ f ≤ 1 and 20 ≤ d ≤ e (d can be larger or smaller than a), where √ II is(f, B2∗ 1]. = c. PlayerBII folds when x21 ∈ (e, f ], and ∈1II(d, e] ∗∪ ∗ 2B1 + 2 = 4 + 2 13/3.

2Bre-raises + 2B B22 )≤ d, calls when )(2 +x2B +for B ) 2+B 1for 1 +x 1 (2 + B1when 2 1 (2

Proof.

Applying the modied payoff square as illustrated is B2 = 2B1 + 2 = 4 + 2 13/3.

a, c = 1 − a = , b = 1 − , 2 2 ≤ e ≤ b ≤ c ≤ (1 f≤ and 0 ≤ d ≤ e2 (d can be larger or smaller than a), where B12 Applying B1 (4 + B1 )square + (1 as +illustrated B1 )(2 +inBFigure {(1 + B +B1B B ∆ + B )= Proof.

2 1 )∆ 1 )modified 1 ) B26,/(2 + 2B1 + B2 ) } = a. the payoff 2B (2 + B )(2 + 2B (2 + 2B + B ) 21 +B

d

check

2 in Figure 6, payoff square as illustrated in Figure 6, Proof. , Applying the modified

u1 = B1 − a(1 − d) − (c − b)(e − d) + (1 − c)(e − d) + (1 − b)(b − e) + − c)(e − d) + (1 − b)(b − e) + u1 = B1 − a(1 − d) − (c − b)(e − d) + (1 2) − (c − b)(e − d) + B 2 (1 − c)(e − d) − (f − c)(1 − f ) 2 (2d − a)(a

a a)(a 2) − (c − b)(e − d) + B2 (1 − c)(e − d) − (f − c)(1 − f ) 2 (2d − (1 2++BB11)∆ B1 1 + B1 ∆ ∆ 2 2 2

= B ) B1 (4 + B1 ) + (1 {(1 + B 1 1 2 2

2 strategies are illustrated 2 + B1 )(2 + B12) B2 /(2 + 2B1 + B2 ) 2 } = a.

2 B )(2 + 2B +1+(2 BB+ optimal in-(1+B1+B2) 2 + B1 )(2B 1 (4 + B1B 1 +B 21) + (1 1 ) 2BB 2 . The )(2 + 2B + B ) B + 2a = B {(1 + B ) B (4 + B ) + (1 + B )(2 + B ) B /(2 + 2B + B ) } = a.

1 1 2 1 1 1 1 1 1 2 1 2 1 where ∆ = B (4 + B )(2 + 2B + B ) + (1 + B )(2 ) B .

The optimal strategies are illustrated in 1 1 1 2 a, f = 1 − 1 1 2 d = ,e = − 1 1 1+B1+B2 1 + B1 ∆ Figure 5. 2 + B1 2 2

a

=

=

1

1

2

,b = 1 −

1

1

a, c = 1 −

1

1

(1 + B B1B1 (2 + B1 )(2 + 2B1 + ∆ B2 ) B1 + 2a B11)∆ ,e + =12a+ B2 )2 B− a, f =2 + 1− 2B∆ B12B(21 + B1B)(2 B1 B1 (2 + B1 )(2 1 (2 + 2B+ B12B 1 + 2 ) + 2B1 + B2 ) 1 1 + B 2 + 1 = d = , , e = , b = 1−− a, f = 1 −a, c = 1 −

x

x

where Δ = B (4 + B )(2 + 2B + B ) + (1 + B )(2 + B ) B . The

1 2 1 1 22 1 x2 f1 2 ∆ = B1 (4 + B1 )(2Player + strategies 2B1I + Bbet-fold + (1illustrated + B1check )(2 + Bin B2 . The5.optimal strategies are illustrated in 2 ) are 1 )bet-fold optimal Figure bet-call x2 1 Player I bet-fold check bet-fold bet-call 5. c a b c c 0 a b 1 1 0 -1-B1 1 -1f f d e f c PlayerPlayer I IIbet-fold bet-call bf fold d check raisee bet-foldcall raise

Player II

a 0 fold

c call

raise b

Figure 5: Optimal Strategies of both players.f e d e

raise 1

b

Player IIFigurefold raise 5: Optimalraise Strategies of call both players.

Proof. First, apply the ICs for 5: Optimal Strategies of both players.

Figure

d

Figure 5: Optimal Strategies of both players. a st, apply the2BICs for • I at b: 1 b + (2 + B1 )d + (−2B1 − 2)e = B1 ; • I at a: −2a + (−2 − B1 )d = B1 ;

Proof.

First, the ICs for • Iapply at (−2 c: (−2 −= B2B )d1apply + ; (2 + 2B a:First, −2a + −−ICs B2B 1for 1 + B2 )e + B2 f 1 )d the

+1

= B2 ;

a: −2a )d = B ; II at d: (2 B1I)aat − (2 + (−2 (2 + − 2BB 1 )b+ 1 + 1 ; B2 )c = 1B1 + B2 ; )d =+BB a:• 1−2a + (−2 B1+ :at2B b + (2 +• + B− (−2B 1 ;1 − 2)e = B1 1 )d

0

c

a

b

d

d

+1 a

a

+1

-1-B1 1+B1

b f

1+B1

-1-B1 1+B1+B2

a

e

b

b

e

d

c

f

+1

c

1 -B2

f

-B1 c

-B2

-B1

B1 B1 -2-B1

d

+2 a d a+2

+1

+1

+1

d e

-1-B1 1+B1+B2

+1

-B2

x2

c b -B1 b e

e

1+B1

+1

x2

c 1

-1-B1

-1-B1

-1

1+B1+B2

1+B1+B2

-1-B1 1+B1+B2

0

d

-(1+B1+B2)

-1-B1

-1

e

f

-(1+B1+B2)

-1-B1

-1-B1

-1-B1

e

-1-B1

f

x1

1

x1

1

0

a

B1+B2

-2-B1

B1 B1+B2

-2-B1

B1+B2

+2 0

a

a

d

d

e

e

b

c

f

b

c

x1

1

1

f

6: 1Payoffofof Player by apayoff payoff Figure square.

0 0 IIby a xPlayer x1 b Figure b c c 6:f Payoff d e d square. e f 1 (−2B − 2)e = B1; 1 • II at f : −c + 2fI = 1.c: (−2 − 2B − B )d + (2 + 2B + B )e + B f = B ; • at Figure 6: Payoff of Player I by payoff square.

Minimizing u with Figure respect to while B Player is fixed, to maximizing B /(2 + 2B + B ) , 2 2 2 at c: 2B1 − B2 )d + (2 + 2B1 +1 B2 )e 2+ B2 f = B2 ; 1 6: BPayoff of I isbyequivalent payoff square. d: (2 (−2 + B− 1 )a − (2 + B1 )b + (2 + 2B1 + B2 )c = B1 + B2 ; Minimizing u1(2B with respect to B2 while B1 is fixed, is • II at d: (2 + B )a − (2 + B )b + (2 + 2B + B )c = B + B ; + 2 + B ) − 2B 1 1 2 1 2 I at d: (2 + B1 )a − (2 + B1 )b + (2 +1 2B1 + B2 )c = = 0 ⇒ B = 2B 2 + 2. e: (−2 − 2B1 )b + (2 + 2B1 + B2 )c = B2 ; 4 B1 + B2 ; equivalent to maximizing B 2B1 +B2to )to,maximizing + 12BisB+ B= ) (2 u1 with to respect to B2(2while is fixed, is equivalent B2 /(2 2B1+ +2B B2 )12 ,+ 1 u1 with respect B B fixed, is + equivalent maximizing B2+/(2 2 while • 1 )b +II(2at+e:2B(−2 − 2B )b + (2 + 2B1 + B2)c = B2; Minimizing Minimizing 2 I at e: (−2 − 2B 1 + B2 )c 1= B2 ; f : −c + 2f = 1.

(2B + 2 + B ) − 2B (2B1 + 2 +1 B2 ) − 22B22 2 = 0 ⇒ B∗2∗ = 2B1∗∗+ 2.

I at f : −c + 2f• = 1.II at f: −c + 2f = 1.

• II at e: (−2 + (2 + 2B B2+ )c B =B 1 )b b: 1 +(2 • − 2B I at 2B b+ )d2 ; +

b: 2B b +1(2 +(2 (−2B B11+ ; B2 f = B1 2 ; 1 )d+ 1 − :at(−2 −12B −+BB2 )d + 12B + B=2 )e 1 2)e

1

2

1

1

2

2

1

(2 + 2B1 + B2 )

(2 + 2B1 + B2 )2

2

2

2

∗ 2

1

2

2

∗ 1

= 0 ⇒ B2 = 2B1 + 2.

5 Solving six linearly independent equations of six un44 2 Substitute in, u = 8B ⁄ [(1+B )(9B12 + 36B1 +4)]. Then knowns, we get results as presented in the theorem. Now 1 1 1 u1 with respect to5B yields 9B 3 − 40B − 8 = 0. suppose we ignore the antes contributed by the Substitute players byin, umaximizing 2 1 1 1 . Then maximizing u1 with respect t (1 + B1 )(9B12 + 36B1 + 4) 1 = 8B1 √ Clearly, treating them as sunk costs. Given that Player 3II uses the Three roots are B1 = −2, 1 + √13∕3, 5 √ 1 − √13∕3.

9B1 − 40B1 − 8 = 0. Three roots are B1 = −2, 1 + 13/3, 1 − 13/3. Clearly, conjectured optimal strategy, and Player I has hand x1, I’s √ √ B1∗ = 1 + 13/3 ≈ 2.202, B2∗ = 4 + 2 13/3 ≈ 6.404 “gain” • from checking is 2x1.

Substituting in B1∗ and B2∗ , a = 0.0955, b = 0.8178, c = 0.909, d = 0.569, e = 0.592, f = 0.954. in B1*I,and B2*, a (0.0955) = 0.0955;is blower = 0.8178; c = in the o still favors player its payoff than that • from bet-folding is 2a if 0 < x < e; 2a + 2(1 Though + B)(x −the e) gameSubstituting Neumann model (1/9).

This shows that allowing player II to re-raise restricts player I’s 0.909; d = 0.569; e = 0.592; f = 0.954. if e < x < f, and 2a + 2(1 + B1)(f − e) if f < x < 1. bluffing, thus decreasing his advantage and profit.

Obviously player I always has Though the game still favors Player I, its payof (0.0955) isadvantage • from bet-calling is 2a − 2(1 + B1 + B2)(e he − d) if 0 < x < makes a voluntary decision first because he can always checks to yield an expected payoff lower than that in the original von Neumann model (1∕9). d; 2a − 2(1 + B1 + B2)(e − x) if d < x < e; note 2a +that 2(1 +player B1) I’s optimal bet is a little over the pot size, and player II is little under the This that allowing Player to re-raisetorestricts Player (x − e) if e < x < f; and 2a + 2(1 + B1)(f −size, e) +however 2(1 + Bvery close.shows This gives some insight and II justification bet by pot size in real p 1 I’s audacity of bluffing, thus decreasing his advantage and In addition, player II can bluff with his “good” hands.

This is justified as follows.

Playe + B2)(x − f) if f < x < 1.

his worst hands because he is caught bluffing, and fold some of his good hands because player raise with his best hands. However, if player II simply calls, he has higher chance of losing t hands that player I has raised with. Folding is even morewww.pennscience.org disastrous as he is bluffed by 28 the w of Player I.

Research Articles

prot. Player I always has advantage given that he makes a tio to win an equivalent amount when he calls. voluntary decision first because he can always check to yield an expected payoff of 0. Also note that Player I’s optimal bet Conclusion

We investigated von Neumann’s model to see that bluffa 2little over the 2pot size, and Player II is little under the e in, u1 =is8B (1 + B1 )(9B 1 1 + 36B1 + 4) . Then maximizing u1 with respect to B1 yields √ close. This √ gives some insight ing is an important strategy to gain advantage. Giving Playadded pot size, however very − 8 = 0. Three roots are B1 = −2, 1 + 13/3, 1 − 13/3. Clearly, er II’s option to re-raise, thus option to bluff after possible and justification to bet by pot size in real √ poker. ∗ ∗ √ B = 1 + 13/3 ≈ 2.202, B = 4 + 2 13/3 ≈ 6.404 2 2 II can 2 1 8B addition, bluff with his “good” hands. bluff after Player I, eliminates some of Player I’s advantage.

Substitute in, u1In = (1 + BPlayer 1 )(9B1 + 36B1 + 4) . Then maximizing u1 with respect to B1 yields 1 √ √ ∗ ∗ is justified as follows. Player I will fold his worst hands This − − 8 =B0.2 ,Three roots areb B = −2, 1 +c =13/3, 1 −d = 13/3.

Clearly, in40B B11 and a = 0.0955, =1 0.8178, 0.909, 0.569, e = 0.592, f = 0.954. Findings in this paper may be applied to real poker. The √ I, itsbluffing, √is lower shows ∗ ∗ and fold he is caught some of histhat good the game because still favors player payoff (0.0955) than in thepaper original vonthat in optimal strategies, a player should bluff B1 = 1 + 13/3 ≈ 2.202, B2 = 4 + 2 13/3 ≈ 6.404 odel (1/9).

This shows that allowing player II to re-raise restricts player I’s audacity of with their worst hands, but not mediocre hands, because hands because Player II will also raise with his best hands. in B1∗ and B2∗ , a = 0.0955, b = 0.8178, c = 0.909, d = 0.569, e = 0.592, f = 0.954. sstituting decreasing his advantage and profit.

Obviously player I always has advantage given that there if Player he ishas higher chance Though theHowever, game still favors playerIII, simply its payoffcalls, (0.0955) lower than that in theoforiginal vonis slim hope of winning with their worst hands. Howvoluntary decision first shows because he can always checks to yield an expected payoff ofof 0. Also mann model (1/9). to This that allowing player II to re-raise restricts player I’s audacity ever, when one raises with a mediocre hand, the opponent is losing the good hands that Player I has raised with.

Foldayer thus I’s optimal bet a little and overprofit. the pot size, and player II is undergiven the that added pot ffing, decreasing his isadvantage Obviously player I always haslittle advantage ingThis isdecision even more disastrous as he is bluffed the size worst makes voluntary because he can checks toto yield payoff of likely 0.poker.

Alsoto call with a better hand and fold worse hands. Thus verya close. givesfirst some insight andalways justification betanby byexpected pot in real that playerhands optimal bet is aI.his little“good” over thehands. pot size,This and player II is little under thePlayer added pot raising byfold the first player magnifies his loss by losing more of Player on, player III’scan bluff with is justified as follows.

I will however very he close.

This gives some insight and justification togood bet byhands pot size in real poker. nds because isboth caught bluffing, and fold some of Ihis because player II will also hands and gaining none from the other player from inferior In models, payoffs for Player are both a which corn addition, player II can bluff with his “good” hands. This is justified as follows. Player I will fold s best hands.

However, if player II and simply calls, he has higher chance of losing toalso the worse good hand. In addition, if the player is re-raised, folding the initial bluff Player I in the player first worst handsresponds because he isto caught bluffing, foldregion some of by his good hands because II will I has raised with.

Folding is even more disastrous as he is bluffed bytothe worst hands elayer with his best hands.

However, if player II simply calls, he has higher chance of losing the good round. This fact needs to be further investigated in order he would have a hard time deciding whether to fold or call ds that player I has raised with. Folding is even more disastrous as he is bluffed by the worst hands withbya Player mediocre hand, because he could falsely think that to determine of Player I is always allowing layer I. payoffs models, for player whether I are bothvalue a which corresponds to the ainitial bluff region nround. both models, payoffs for player I are both a which corresponds to the initial bluff region by Player the opponent additional re-raises.

This fact needs to be further investigated in order to determine whether value of is bluffing him. However, calling would result the first round. This fact needs to be further investigated in order to determine whether value of in even bigger loss. Checking in the beginning could avoid ways a allowing additional re-raises. er I is always a allowing additional re-raises.

Multiple Re-raises such a situation.

The game tree allowing two raises by each player is illusSince unlimited number of raises are allowed in real Multiple Re-raises ltiple Re-raises trated in Figure 7, and model of more raises can be extended poker, extension to more rounds is important too. The exgame tree allowing two raises by each playerisisillustrated illustrated ininFigure 7, and model of more can ee allowing raises by each player Figure 7, and model of raises more raises can can help us to conclude about players’ optimal bytwo adding more “branches”. tensions nded by adding more “branches”. adding more “branches”. strategies corresponding to different regions of cards, and whether Player I’s expected payoff from optimal strategy is check/call always a, the proportion of hands he has bluffed in initial foldcheck/call raise. In addition, it gains insight whether there is a better I II I I II betfold equilibrium play for either player. The paper also introduces I II I I II bet the payoff square, which could be of important use for more Figure 7: Game tree of two raises. complicated hand distributions in games of two or three Figure 7: Game tree of two raises.

By forward induction, we conjectured the optimal strate- players because of its straightforward presentation of payfor both players to optimal be tree as follows.

For player i, ito=be1,as2,follows. offs.For By forward gies induction, weFigure conjectured the strategies for both players 7: Game of two raises. er i, i = 1,in 2, in round j, threshhold, ci,j the calling round j, let letfi,j fi,j be bethe thefolding folding threshhold, ci,j thethreshold, callingand ri,j the ng threshold. fi,j < ci,j < ri,j < 1, dividing the hands into four intervals. Then player i in round j threshold, and ri,j the fi,j <both ci,j <players ri,j < 1,todird induction, we conjectured theraising optimalthreshold. strategies for be asReferences follows. For Cutler, H. (1975). The American Mathematical Monthly 82-4, ∈ (0, f ] fold if x  i i,j vidingj, the into four intervals.

Then player i in round  1, 2, in round let hands fi,j be the folding threshhold, c the calling threshold, and rW. i,j i,j the  raise if xi ∈ (fi,j , ci,j ] 368{376. hold. fi,j j<will ci,j < ri,j < 1, dividing the hands into four intervals. Then player i in round j   call/check if xi ∈ (ci,j , ri,j ]

Ferguson, C. & Ferguson, T. S. (2003). In Game Theory and Applica  raise if xi ∈ (ri,j , 1] if xi ∈ (0, fi,j ]  vol. 9, pp. 17{32. Nova Science Publisher New York, NY.  nofold hand will be folded by player I. Furthermore, 0 < fi,j , ci,j , ri,jtions < fi,J I,1 = 0 in this model because  raiseinterval of ifremaining xi ∈ (fi,j , ci,j ]Relationship of inequalities between ll J > j, producing strictly smaller hands.

Ferguson, C., Ferguson, T. S. & Garaway, C. (2007). In Game Theory call/check if xi ∈ (ci,j , ri,j ]  players’ folding, calling and  raising thresholds needs to be investigated. We can apply indifference and Applications vol. 12, pp. 17{37. Nova Science Publisher New ditions to each of the thresholds and solve for conditions, but it will be complicated raise if xequilibrium i ∈ (ri,j , 1] York, NY. braically. n this model because no hand will be folded by player I. Furthermore, 0 < fi,j , ci,j , ri,j < fi,J f the bet amount is restricted to be pot size, with unlimited number of bets and forbiddingNewman, checkD. J. (1959). Operational Research 7, 557{560. producing strictly ofbecause remaining Relationship of inequalities es, Cutler solves using recursion [Cutler, 1975]. feasible because eachbetween 0smaller in thisinterval model nohands. handRecursion will be isfolded by fI,1an=equilibrium folding, calling thresholds indifference Smith, G., Levere, M. & Kurtzman, R. (2009). Management Science a player pays the and same raising ratio to win an equivalent when calls.

Player I. Furthermore, 0 < needs fi,j , amount ci,jto, rbe <investigated. fi,Jhefor all J We > j, can pro-apply i,j conditions, o each of the thresholds and solve for equilibrium but it will be55-9, complicated 1547{1555.

ducing strictly smaller interval of remaining hands. Rela-

von Neumann, J. & Morgenstern, O. (1953). Theory of Games and Conclusion of to inequalities two players’ amount tionship is restricted be pot size,between with unlimited numberfolding, of bets calland forbidding checkEconomic Behavior pp. 186{219. Princeton, NJ: Princeton University r solves an equilibrium using recursion [Cutler, 1975].

Recursion istofeasible because each investigated von Neumann’s model to see thatneeds bluffing an important strategy gain advantage. ing and raising thresholds tois be investigated.

We can Press. player option to re-raise, option to bluff after possible bluff after player I, eliminates rngpays theII’s same ratio to win thus an equivalent amount when calls. apply indifference conditions to each of thehe thresholds and

e of player I’s advantage.

solve for equilibrium conditions, but it will be complicated algebraically. nclusion 6 If the bet amount is restricted to be pot size, with unted von Neumann’s model to is an check-raises, important strategy to gain advantage. limited number of see betsthat andbluffing forbidding Cutler r II’s option to re-raise, thus option to bluff after possible bluff after player I, eliminates solves an equilibrium using recursion (Cutler, 1975). Recurer I’s advantage. sion is feasible because each time a player pays the same ra29

6 PennScience Journal of Undergraduate Research

VOL 9 ISSUE 1, FALL 2010

Low Energy Ultrasonic Irradiation: Potential Applications in Oil Refinement James P. Mandaglio, Johns Hopkins University Demand for heavy crudes is increasing as lighter crudes become more costly. Compared with light petroleum products, heavy crude is hydrogen deficient and contains a larger fraction of asphaltenes. Asphaltenes are complex mixtures of polyaromatic molecules containing most of the metals, sulfur, and nitrogen within crude oil.

These molecules are difficult to convert to lighter fractions, and the metals within these molecules foul catalysts.

In addition, asphaltenes adversely affect viscosity, and thereby cause clogging during production, refinement, and transport. There is great demand within the oil refinement industry for a cost sensitive method that can efficiently convert heavy crudes into lower sulfur products through catalysts, including biocatalysts and other processes. Recent research suggests that ultrasonic irradiation with frequencies in the range of 15 kHz to 1 MHz are known to cause a variety of chemical transformations (1) that could prove useful in oil refinement. The present paper investigates this potential utility of ultrasonic irradiation and concludes that sonic energy could be useful for catalytic refinement.

Refinement Catalysts: Characteristics of Ultrasonic Irradiation/Rectified Diffusion

There are a variety of microorganisms, catalysts, and combinations thereof that could potentially be suitable for use in oil refinement systems. Studies suggest that extremophilic microorganisms and their enzymes (extremozymes) are attractive catalysts for use in petroleum refining. The enzymes isolated from extremophilic microorganisms possess unique properties that can be used for industrial applications; they are extremely thermostable (i.e. not prone to structural changes both chemically and physically at high temperatures) and are generally resistant to organic solvents, high pressures, and extreme pH environments (2).

Different extremophilic bacterial genera such as Thiobacillus, Achromobacter, Pseudomonas, and Sulfolubus have been utilized in the process of converting heavy crudes into lighter fractions (3). It is clear that a multiplicity of potential bioremediators exist that can be used to degrade sulfur rich asphaltenes within heavy crude. It still remains to be seen which of these catalysts, in the presence of ultrasound and cavitation inception, will show increased reactivity and ashpaltene degradation rate.

A potentially viable solution to increase the longevity and reactivity of these catalysts is the implementation of ultrasonic irradiation within the refinement process. The propagation of low energy ultrasound (i.e. greater than 20 kHz but less than 1 MHz) through a heterogeneous solid-liquid mixture (i.e. heavy crude and some other hydrocarbon solvent) in a manner such that it does not adversely affect the refinement process or produce any unwanted byproducts through a secondary reaction mechanism, can induce cavitation inception through rectified diffusion. Cavitation inception refers to the process by which the liquid pressure in a liquid flow system drops below the vapor pressure of the operating

fluid at some locations, resulting in unplanned vaporization (4). The vapor bubbles (called cavitation bubbles because they form â&#x20AC;&#x153;cavitiesâ&#x20AC;? in the liquid) collapse as they are swept away from the low-pressure regions, generating extremely high-pressure waves (5). Under ideal conditions or those that best lower the cavitation number (Ď&#x192;) of the system, cavitation inception can potentially increase the reactivity, catalytic capability, and lifespan of these micro-organisms.

This concept seeks to utilize the high energy output in the form of extreme pressure and temperature gradients (previously mentioned) that occur during bubble collapse. The manner by which cavitation might enhance the catalytic reactivity of extremophilic microorganisms within the refinement process draws upon knowledge from a variety of fields of research such as sonochemistry and biology, and will be discussed later in this article following a brief description of the process of cavitation inception via ultrasonic irradiation.

The presence of cavitation nuclei and the advent of cavitation inception can be triggered through various means.

When refining heavy crudes into lighter fractions, ultrasonic irradiation within the heterogeneous solid-liquid mixture will promote cavitation nuclei and future inception. When a sound wave propagates through a heterogeneous mixture, the waveform is comprised of two half cycles. The first half cycle, called rarefaction, produces a negative pressure front that is capable of overcoming the adhesion and cohesion forces of the liquid itself. If this half cycle produces enough negative pressure, cavitation nuclei will form. After the negative pressure rarefaction front, the second half cycle passes, producing a positive pressure front through the system. This positive pressure causes bubbles within the bulk liquid to collapse inward (6). During implosion, a tremendous amount of heat and pressure are released into the system (7). At lower acoustic intensities (i.e. low energy ultrasound), cavitation www.pennscience.org

30

Research Articles inception can occur through diffusion. When the bubble is subjected to an oscillating pressure field there is a net inflow of gas into the bubble (8). During the positive half cycle, gas diffuses out of the bubble. Conversely, during the following negative half cycle (rarefaction), gas flows back in (9). The surface area of the bubble is larger during the negative half cycle due to the pressure decease in the surrounding bulk liquid so that there is, over a number of cycles, a net inflow of gas (10). This process is known as rectified diffusion (11).

In essence, rectified diffusion is the manner by which cavitation occurs in ultrasonically irradiated fluids. After the bubble has reached a critical radius, the tensile strength of the bubble is no longer able to overcome the forces it is subjected to during the positive pressure cycle (12). Its surface then tears and the bubble collapses (13). During the compression cycle all bubbles will be made to contract and collapse (14). If during growth, some gas or vapor has diffused into the void or bubble, complete collapse may not occur (15). Those bubbles which collapse completely are considered transient and those which do not are considered stable (16). The objective is to manipulate the refinement environment such that rectified diffusion is complete and transient cavitation occurs.

The efficiency of cavitation inception and collapse depends on a variety of variables. Certain experimental variables such as the bulk temperature and the viscosity of the system can be manipulated to improve the quantity of cavitation nuclei and energy output during bubble collapse.

The bulk temperature of the system as well as its viscosity are both integral in the quantity and energy of cavitation inception. As the bulk temperature of the system increases, surface tension and viscosity decrease and cavitation is more readily achieved (17). As the bulk temperature of the system increases, the vapor pressure also increases (18). This spike in vapor pressure creates a cushioning effect that will inhibit the high energy output that is typically associated with a normal bubble collapse thus inhibiting transient rectified diffusion (19). Therefore, due to the extreme temperatures associated with the refinement process and the accompanying spike in vapor pressure described above, the operating liquid must have a high bulk boiling point. If the liquid’s boiling point is too low, cavitation inception will be futile due to large vapor pressures in the flow (remember, cavitation occurs only when the flow vapor pressure drops below that of the operating fluid). Therefore, uncovering a combination of temperatures and pressures that maximize catalytic reactivity and cavitation inception at a given ultrasonic energy level is vital.

Potential Method for Enhancing Rectified Diffusion and Catalytic Reactivity

While attempting to refine heavy crude through ultrasonic irradiation, one must utilize the “cleansing” characteristics of cavitation to help increase the reactivity and life spans of chosen catalysts and extremophilic micro-organ-

31

PennScience Journal of Undergraduate Research

isms that degrade the sulfur rich asphaletenes commonly found within heavy crude. Distinct evidence or experimental data suggesting that a technique is energetically feasible has yet to be found. However, one option for success might be to continuously implement low energy ultrasound (i.e. to instigate cavitation via rectified diffusion) so that refinement of heavy crude can occur at the wellhead, and that this useful crude can then be injected into existing oil pipelines. The efficiency of rectified diffusion and the quantity of cavitation nuclei may also be enhanced through hydrodynamical cavitational technique.

Hydrodynamical cavitation occurs when a liquid undergoes a dynamic pressure reduction due to the constriction of devices like venturi or orifice plates (20). In a recent textile wastewater study, researchers assessed the efficiency of this technique by comparing results with “. . . the cavitation generated by ultrasound” (21). Researchers observed: “[T]here is a substantial enhancement in the extent of degradation of this dye using hydrodynamic cavitation for the same level of energy dissipation. Thus, the present set-up of hydrodynamic cavitation using multiple hole orifice plates has been found to give cavitational yields, which are two times higher than the best acoustic cavitation device, tested earlier. Moreover, the capacity of the reactor in the present case (50 l) is also 66 times higher as compared to the largest ultrasonic equipment tested. In case of hydrodynamic cavitation, the efficiency of the pump is also likely to increase with an increase in the scale of the operation, which promises an effective scale-up of the reactor with the same or even better cavitational yields for a larger scale” (22).

Although this study suggests no means by which ultrasonic irradiation and hydrodynamical cavitation can be coupled to enhance rectified diffusion, it seems logical that utilization of the two methods would help ensure higher cavitation rates. Furthermore, the study also demonstrates that cavitation is a viable way to implement large scale refinement, and that the output of this process can be utilized in the commercial realm.

As previously mentioned, a tremendous quantity of energy is exerted into the experimental system during bubble collapse. This energy includes shockwaves created during bubble implosion, high temperatures reaching nearly 5000 K, extremely high pressures (around 2000 Atm), and water jets (23). In a heterogeneous solid-liquid mixture, this energy output can be utilized to perform useful work. In the case of liquid-powder slurries, the shock waves created by homogeneous cavitation can create high-velocity inter-particle collisions. Such inter-particle collisions are capable of inducing striking changes in the surface texture and reactivity of the microorganisms used to refine the heavy crude. Reactivity rate enhancements of more than 10-fold are common, yields are often substantially improved, and unwanted by-products avoided (24). The mechanism of the rate enhancements in reactions of metals has been unveiled by monitoring the efVOL 9 ISSUE 1, FALL 2010

fect of ultrasonic irradiation on the kinetics of the chemical reactivity of the solids, examining the effects of irradiation on surface structure and size distributions of powders and solids, and determining depth profiles of the surface elemental composition (25). The power of this “three-pronged approach” has been proved in studies of the sonochemistry of transition metal powders (26). Doktycz and Suslick found that ultrasonic irradiation of liquid compositions of nickel, zinc, and copper powders leads to dramatic changes in structure (27). The high-velocity interparticle collisions produced in such slurries can cause smoothing of individual particles and agglomeration of particles into extended aggregates (28). Surface composition was probed by Auger electron spectroscopy and mass spectrometry to generate depth profiles of these powders (29). The profiles revealed that ultrasonic irradiation effectively removed the inactive surface oxide coating (30). The removal of such passivating coatings dramatically improves reaction rates (31).

Utilization of Ultrasonic Irradiation and Cavitation in Asphaltene Decomposition

In the case of bioremediation and asphaltene breakdown, which occurs during the refinement of heavy crude, ultrasonic irradiation can capitalize on the possibilities bred by the high energy output associated with a typical bubble collapse. This energy can be utilized in a heterogeneous solidliquid mixture to increase the reactivity, lifespan, and overall efficiency of any catalyst present in the experimental system.

The “smoothing” of the surface of these catalysts is primarily caused by inter-particle collisions created by shockwaves produced in the system during bubble collapse. When these micromolecules strike each other directly, they bind together due to the high temperatures and form agglomerates with larger surface areas. These agglomerates will have more binding sites and be potentially more reactive in nature because of their larger surface areas. If the micromolecules do not strike each other directly, but rather ‘nick’ each other, they will not bind but will chip away at each other’s surfaces.

This process will rid the microorganisms of protein membranes that encapsulate the species and mar their reactivity and catalytic nature. In this way the implementation of low energy ultrasound will have advantages that are two-fold.

First, the high energy output associated with cavitation inception and bubble collapse will enable the emulsification of micro-molecules due to inter- particle collisions that are spurred on by shock waves produced within the system during bubble collapse. These agglomerates will have larger surface areas and more active sites, thus enhancing their reactive capabilities and ability to decompose asphaletenes.

Second, indirect inter-particle collisions will cause gradual cleansing and removal of protein rich membranes that surround the surfaces of the microorganisms and inhibit life spans and reactivity. This will increase the overall capability of the microorganisms introduced to the refining environ-

ment, and will allow for larger quantities of heavy crude to be refined (via asphaletene decomposition) in shorter periods of time. Furthermore, cavitation inception is not typically characterized by singular bubble formation and collapse.

That is, usually, one is left with a remnant cloud of small bubbles that will continue to collapse collectively. Though no longer a single bubble, this remnant cloud will still exhibit the same qualitative dynamic behavior, including the possible production of a shock wave following the point of minimum cavity volume (32). Studies have been performed that have tried to quantitatively measure that amount of energy that is released during bubble collapse within the remnant cloud. Kimoto (1987) was able to observe stress pulses that resulted both from microjet impingement and from the remnant cloud collapse shock. Typically, the impulsive pressures from the latter are 2 to 3 times larger than those due to the microjet, but it would seem that both may contribute to the impulsive loading of the surface [e.g of solid in heterogeneous solid-liquid system] (33). Remnant cloud formation can be utilized during the refinement process. By initiating cavitation and varying the frequency of the ultrasonic irradiation, optimal levels of remnant cloud inception can be achieved. It has been shown that the cumulative implosion of the bubbles within these clouds can create shock waves and microjets, which cause cavitational erosion, pitting, and inter-particle collisions. Christopher Earls Brennen suggests that remnant cloud formation can be maximized when the frequency of the ultrasound is close to the natural frequency of a significant fraction of the nuclei present in the liquid.

Under such conditions, one might be able to increase the rate of “cleansing” by increasing the quantity of inter-particle collisions that occur in the heterogeneous fluid.

A byproduct of the utilization of cavitation in heterogeneous solid-liquid systems such as those at the wellhead is the process of intercalation. Chemical intercalation is defined as the insertion or reversible inclusion of a “molecule (or group) between two other molecules or groups” (34). Suslick suggests that organic or inorganic compounds can be inserted into the atomic sheets of layered solid hosts. Intercalation permits the systematic change of optical, electronic, and catalytic properties (35). This process is especially useful when working with asphaltenes. Asphaltenes have a chemical structure that can be described as “sheet-like” in nature (36). In the crude, the asphaltene sheets remain dispersed (37). However, they have the tendency to be attracted towards each other thus resulting in the formation of an agglomeration (38). The structure of the agglomeration is similar to that of a book: a compact stack of thin sheets (39). The possibility therefore exists that ultrasonic irradiation could be able to inject certain catalysts or micro-molecules into the “sheet” structure of the asphaltenes present within the heavy crude. These molecules, once secured within the benzene ring structure, may help in further breakdown of the www.pennscience.org

32

Research Articles asphaltene structure. Coupled with the processes describe above, this could increase the rate and quantity of heavy crude refinement. Studies have suggested that intercalation is a slow process that typically requires high energy inputs.

Even the use of high-intensity ultrasonic irradiation might produce only modest results over long periods of time.

A variety of patents are currently available that utilize low and high energy sonochemistry to drive chemical reactions. Of particular interest is a sonochemical reactor that has been developed under USPC class 20415715, which comprises of a scaled-up reaction chamber with a plurality of physically coupled externally mounted transducers. Externally mounted transducers overcome the many disadvantages that stem from directly initiating excitations within the fluid (40). That is, the externally mounted transducers simplify the delivery of electric power and avert the potential damage resulting from cavitation inception or from the fluid itself (41). Furthermore, such a configuration proves advantageous when trying to induce cavitation in heterogeneous mixtures, because there can be variations in the acoustic impedance of the mixture within the reaction chamber which can significantly mar the control of internally mounted transducers (42). The patent claims that substantial uniform radial excitation ensures that input energy is focused near the center of the reaction chamber, and the intensity of the resulting cavitation is determined by the input power.

The claim in also made that the device can be operated in a continuous mode that proves advantageous for water purification, sewage sludge processing, and even hydrocarbon “cracking” and dispersal of nano-particles in fluid. The reaction chamber, which is in the form of a thin-walled right circular cylinder, also permits cleaning and maintenance (43).

The concepts exhibited by the patent described above might bridge the gap between small scale laboratory sonochemical reactions and the much larger industrial sonochemical reactions needed to refine heavy crude at the wellhead. As previously mentioned, the efficiency of the refinement process will depend on a combination of the rate of cavitation inception and intensity of bubble collapse. Since both are highly dependent on environmental conditions, a device allowing for some control over ultrasonic intensity and the refinement environment (the reaction chamber is a closed cylindrical vessel) is beneficial. Furthermore, it might be possible to couple multiple devices together and place them in the wellhead. From here, heavy crude can be pumped through each system and further refined sequentially. Having multiple devices enables us to support the needs of multiple customers who might desire varying levels of refined crude. Pumping crude through a system such as this will also enable us to capitalize on enhanced asphaltene decomposition by combining ultrasonic irradiation with hydrodynamic induced cavitation. If we, for instance, insert venturis or orifice plates within the sonochemical reactor 33

PennScience Journal of Undergraduate Research

and pump the heterogeneous mixture through these structures, hydrodynamical cavitation will occur. Combining this with the ultrasonic irradiation will increase the quantity of cavitation nuclei and enhance the rate of refinement.

The aforementioned device is promising in that it has demonstrated the feasibility and validity of inducing cavitation for prolonged periods of time in heterogeneous mixtures similar to those present during heavy crude refinement. The efficacy of asphaltene decomposition (and crude refinement) instigated by ultrasonic and hydrodynamically induced cavitation suggests that ultrasonically generated cavitation might be an economically viable way to refine crude oil.

References

Brennen, Earls Christopher. (1995) Cavitation and Bubble Dynamics.

Oxford University Press.

Çengel, Yunus A, Cimbala, John M. (2010) Fluid Mechanics Fundamentals and Applications. 2nd ed. Boston: McGraw-Hill Higher Education.

Gallaher, Amanda B, Hannon, Dominic B. Hardie and David John Webster (USPC Class 20415715). Sonochemistry. 24 May 2009. http://www.faqs.org/pate nts/app/20080217160.

Hoffmann, Michael R., Inez Hua, and Ralf Hochemer. “Application of Ultrasonic Irradiation for the Degradation of Chemical Contaminants in Water.” Ultrasonics Sonochemistry 3.3 (1996): S163-172. ScienceDirect. Elsevier Science B.V., 11 Feb. 1999. Web. 26 Mar. 2010.

“Intercalation (chemistry).” Wikipedia: The Free Encyclopedia. Accessed August 15, 2008. http://en.wikipedia.org/wiki/Intercalation_ (chemistry).

Le Borgne, Sylvie and Rodolfo Quintero. Biotechnological Processes for the Refining of Petroleum, Programa de Biotecnologia del Petroleo, Instituto Mexicano del Petroleo 81: 15 May 2003: http:// www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TG348FCG111&_user=1082852&_rdoc=1&_fmt=&_orig=search&_ sort=d&view=c&_version=1&_urlVersion=0&_userid=1082852&md 5=70a4508fccdc19e36428e35038490f7c.

Lickiss, D. Paul. (2000) The New Chemistry. Ultrasound in Chemical Synthesis. Cambridge University Press.

Mason, J. Timothy and John P. Lorimer. (2002) Applied Sonochemistry: The Uses of Power Ultrasound in Chemistry and Processing.

Wiley-VCH Verlag GmbH, Weinheim.

OTS Heavy Oil Learning Centre, Lloydminster Oilfield Technical Society. “What Are Asphaltenes?.” http://www.lloydminsterheavyoil. com/asphaltenes.htm.

Sivakumar, Manickam and Aniruddha B. Pandit. 2002. “Waste Water Treatment: A Novel Energy Efficient Hydrodynamic Cavitational Technique.” Ultrasonics Sonochemistry 9, no. 3 (July 2002), http://www.sciencedirect.com/science?_ob=Art icleURL&_ udi=B6T W344GM2JG2&_user=1082852&_rdoc=1&_fmt=&_ orig=search&_sort=d&view=c&_acct=C000051401&_version=1&_ urlVersion=0&_userid=1082852&md5=274acc4a4536576a351abc6 26f688f27 (accessed August 24, 2008).

Suslick, S. Kenneth. (1994) “The Chemistry of Ultrasound,” The Yearbook of Science & the Future, 138-155. Encyclopedia Britannica: Chicago.

Trevena, D. H. (1987) Cavitation And Tension In Liquids, 63. IOP Publishing Ltd.

VOL 9 ISSUE 1, FALL 2010

Notes 1.

2.

Hoffmann, Michael R., Inez Hua, and Ralf Hochemer. “Application of Ultrasonic Irradiation for the Degradation of Chemical Contaminants in Water.” Ultrasonics Sonochemistry 3.3 (1996): S163-172. ScienceDirect. Elsevier Science B.V., 11 Feb. 1999. Web. 26 Mar. 2010.

Sylvie Le Borgne and Rodolfo Quintero. Biotechnological Processes for the Refining of Petroleum, Programa de Biotecnologia del Petroleo, Instituto Mexicano del Petroleo 81: (15 May 2003): 155-169.

3.

Le Borgne and Quintero, 2003, 155-169.

4.

Çengel, Yunus A, Cimbala, John M. (2010) Fluid Mechanics Fundamentals and Applications. (2nd ed. Boston: McGraw-Hill Higher Education), 42.

31. Suslick, 1994, 138-155.

32. Brennen, Earls Christopher. Cavitation and Bubble Dynamics (Oxford University Press, 1995), 79.

33. Brennen, 1995, 79-80.

34. “Intercalation (chemistry).” Wikipedia: The Free Encyclopedia.

Accessed August 15, 2008. http://en.wikipedia.org/wiki/Intercalation_(chemistry).

35. Suslick, 1994, 138-155.

36. OTS Heavy Oil Learning Centre. “What Are Asphaltenes?,” Lloydminster Oilfield Technical Society. http://www.lloydminsterheavyoil.com/asphaltenes.htm.

37. OTS Heavy Oil Learning Centre.

38. OTS Heavy Oil Learning Centre.

5.

Çengel, Yunus A, Cimbala, John M. 2010, 42.

6.

D.H. Trevena, D. H. Cavitation And Tension In Liquids. (IOP Publishing Ltd, 1987), 63.

7.

Trevena, 1987, 63.

40. Amanda B. Gallaher, Dominic B. Hannon, and David John Webster Hardie (USPC Class 20415715). Sonochemistry. 24 May 2009. http://www.faqs.org/pate nts/app/20080217160.

8.

Trevena, 1987, 63.

41. Gallaher, Hannon, and Hardie, 2009.

9.

Trevena, 1987, 63.

42. Gallaher, Hannon, and Hardie, 2009.

10. Trevena, 1987, 63.

43. Gallaher, Hannon, and Hardie, 2009.

39. OTS Heavy Oil Learning Centre.

11. Trevena, 1987, 63.

12. Trevena, 1987, 63.

13. Trevena, 1987, 63.

14. Trevena, 1987, 63.

15. Timothy J. Mason and John P. Lorimer. Applied Sonochemistry: The Uses of Power Ultrasound in Chemistry and Processing. Wiley-VCH Verlag GmbH, Weinheim, 2002), 44.

16. Mason and Lorimer, 2002, 44.

17. Paul D. Lickis, The New Chemistry. Ultrasound in Chemical Synthesis (Cambridge University Press, 2000), 79.

18. Lickis, 2000, 79.

19. Lickis, 2000, 79.

20. Manickam Sivakumar, and Aniruddha B. Pandit. “Waste Water Treatment: A Novel Energy Efficient Hydrodynamic Cavitational Technique.” Ultrasonics Sonochemistry 9, no. 3 (July 2002): 123-131, http://www.sciencedirect.com/science?_ob=Art icleURL&_udi=B6TW344GM2JG2&_user=1082852&_rdoc=1&_ fmt=&_orig=search&_sort=d&view=c&_acct=C00005140&_ version=1&_urlVersion=0&_userid=1082852&md5=274acc4a4 536576a351abc626f688f27 21. Sivakumar and Pandit, 2002, 123-131.

22. Sivakumar and Pandit, 2002, 123-131.

23. Kenneth S. Suslick, “The Chemistry of Ultrasound,” The Yearbook of Science & the Future, (Encyclopedia Britannica: Chicago, 1994), 138-155.

24. Suslick, 1994, 138-155.

25. Suslick, 1994, 138-155.

26. Suslick, 1994, 138-155.

27. Suslick, 1994, 138-155.

28. Suslick, 1994, 138-155.

29. Suslick, 1994, 138-155.

30. Suslick, 1994, 138-155. www.pennscience.org

34