By CAMDEN CARMICHAEL, Apex, North Carolina, the United States

By ASHWIN SIVAKUMAR, Bangalore, India

Abstract: In this paper, the author describes various new and easier methods for finding the gap between two consecutive square numbers.

By ARPAN SAHOO, JONATHAN SHEN, DARREL D’SOUZA, JOHN REZK, Morganville, USA

ABSTRACT

Parkinson’s disease is a neurological disorder that affects movement (Mayo Clinic Staff, 2015). Current solutions include surgical therapy or medications, but these solutions are not fully effective. Our solution treats Parkinson’s at its source. Lewy bodies are clumps of alpha-synuclein common to Parkinson’s. Lewy bodies have been shown to cause neurons to die, impairing the nervous system ("Alpha-Synuclein and Parkinson's Disease"). Our solution uses the enzyme NEDD4, which degrades alpha-synuclein, in order to degrade the build-up and allow for recovery. To deliver NEDD4 to the alpha-synuclein, it will be attached to aptamers. Aptamers are RNA nanostructures that bind to specific targets by forming hydrogen bonds. The aptamer will be modified by adding polyethylene glycol (a high density polymer) so that the aptamer will not be affected by nuclease degradation and kidney filtration. By injecting a modified aptamer carrying NEDD4, alpha-synuclein will be destroyed, leading to an effective treatment of Parkinson’s.

By IMANI BECKETT, Los Angeles, California, the USA

Okun’s Law is an empirically observed relationship between changes in unemployment and changes in national output. This experiment used quarterly unemployment, GNP, and GDP data between 2000-2016 to find if Okun's Law held in the 21st century. Since studies supported the theory that the relationship held up in recent times, the hypothesis was that Okun’s Law would hold in the 21st century. A regression analysis was done on the data to see how much it fit with the equation y=1-0.4x, where y is the change in the unemployment rate and x is the change in output. Overall, the data did not fit into the equation when GNP or GDP was the output, from there I concluded that Okun's Law did not hold in the 21st century.

Read more here: https://drive.google.com/file/d/0B6fYIQxjoVuTaTFFTmdFM0tRdE0/view?usp=sharing

Works cited: ​https://drive.google.com/open?id=0B6fYIQxjoVuTWDVyTmswbGVjd1E

By DRIPTO BISWAS, Kolkata, India

By AHIT KAAN TARHAN, Istanbul, Turkey
Mentor: James Butterworth

By SPANDAN SENGUPTA, Kolkata, India
​
ACKNOWLEDGMENTS: Mrs. Manjuli Mukherjee, Class teacher & Biology teacher at St James’ School; Ms. Amrita Nandy, Asst. Manager in Quality Assurance Dept., Apollo Gleneagles Hospitals, Kolkata; Ms. Shilpi Aurora Kundu, Regional Manager, Schülke India Ltd

By THEODORE BAAS, Michigan, the USA

By PRANAV JAIN, Pune, India

Abstract
 
This paper serves to outline and describe a previously unexplored relationship between four “equidistant numbers”, a term that here means four numbers chosen such that each one is separated from the previous term by a constant numerical difference. The idea emerged from observing patterns within the number plates of cars, and has been generalized to encompass any 4 equidistant real numbers. The theorem states: “The absolute difference between the product of the first and last term, and the second and third term of a sequence of four equidistant real numbers is always equal to two times the numerical distance squared.” This paper proves the relationship for all real numbers. It was found that this relationship holds true for the set of real numbers.
This concept is related to Number Theory, the study of relationships of numbers. The primary method of proving the theorem is multi-dimensional induction.
 

By SHIVAM AGARWAL and NABEEL QURYSHI, Pasadena, USA

By JIAYI (VIVIAN) LI, Shanghai, China
​Dr. Mary J. Barnett, Georgetown University

​Othello was written between 1603 and 1604; its first recorded performance was in 1604, with Richard Burbage playing Othello (Swindall 11). Undoubtedly, Burbage played Othello in blackface. It was not until over 200 years later, in 1833 that the first black actor played Othello in London. Since then, most actors playing Othello have been black, although scholars like Peter Ackroyd argue that Shakespeare intended him to be a Spanish Moor (Arogundade). Recently some scholars began to argue about the ethnicity of Othello. Some scholars even suggest that Othello should be played by a white actor of blackface, like hundreds of years ago. After all, one of Othello’s main themes is racial discrimination. Othello is a play focusing on the issue of racial discrimination that offers unlimited possibilities for new interpretations. Spectators, critics and directors in different time have tended to think differently about the most proper race to play Othello because as time goes by, more and more people can accept racial diversity in the society.

By RAYMOND XU, San Jose, California, USA
​Stanford Summer Humanities Institute, 2016
Master Thinkers of the 19th Century: Marx, Nietzsche, Freud
Professor: Adrian Daub

By ZACK LIGHT, Ridgefield, USA
Stanford Summer High School College
Professor: Robert Leeson
​Teaching Assistants: Kevin Hoan Nguyen and Guido Alejo Martirena

By JIAXUAN LU, China
Advisor: Minxia Zhang
​First prize, Boxue History Paper Competition

During the second industrial revolution, scientists invented numerous means of transportation, such as aircraft, automobiles and tanks. The prevalence of these novel vehicles in the beginning of twentieth century accelerated the development of the oil industry because operating them required petroleum, one of the rarest but most powerful fuels at that time. The subsequent fierce competition for petroleum, as a result of its scarcity, caused the great warfare in the 1930s. Petroleum was one of the most essential factors that determined whether Germany and Japan could triumph over the Allies and propagate their ideologies throughout the world. Some historians, such as Yehuda Bauer, consider that World War Two was a war caused by the clash of ideologies.[1] Other political scientists, such as Robert Paxton, believe that World War Two was caused by unfair treaties after World War One, such as the Treaty of Versailles and the League of Nations.[2] Their hypotheses come from superficial facts: in the European theater of World War Two, Germany and Italy carved spheres of influence; in the Pacific theater, Japan desired to become a hegemonic power in Asia. Their focus on ideology and nationalisms are correct but neglect one of the most important causes, economics. Specifically speaking, it was petroleum. For the sake of petroleum, the separated theaters of Asia and Europe connected with one another as Germany attacked both France and USSR, and Japan attacked both China and the US. Unfortunately, the core conflicts of this war were still overshadowed by the conflicts of ideology after the failure of the Axis. It is only through exploring petroleum in World War II that we can truly understand German and Japanese strategy during a war heightened by ideologies and nationalism.

By OSAMA HASAN MUSTAFA HASAN ABDALLA, Doha, Qatar

Abstract

We shall come up with two formulae, one for odd and another for even, to calculate the maximum number of central hexagons that are formed by section-ing an equilateral triangle’s lengths equally into any given parity number and then connecting each of the sections made to their opposite vertex. We shall also construct several area-ratio generalizations between the different central hexagons and their triangle with use of the number of odd or even-sections made to the triangle. Finally, we shall make use of such generalizations to craft two final formulae that can calculate the area-ratio of any specified central hexagon in comparison to the triangle through which they are occupying, provided the number of odd or even-sections made is given.

1991 Mathematics Subject Classification. Primary: 52C99, Secondary: 51M05 51M15 51D20
51M20.

This paper may be accessed via Google Drive: https://drive.google.com/file/d/0B6fYIQxjoVuTMnQ3ckxvUWFzMDQ/view?usp=sharing

By YUNZHI PAN, Beijing, China
​Pan delivered a presentation on the subject at the Speaker Series during the Yale Young Global Scholars (Politics, Law and Economics) Program, 2016

By HYUN JOON CHOI, Richmond Hill, Canada
​The ​Stanford Summer Humanities Institute (2016): "Marx, Nietzsche, Freud: The Master Thinkers of the Nineteenth Century."

By DALIA, Kielce, Poland
Supervision: Dr Paul Hoff Backe & Prof Magnar Bjoras
Finalist of the Intel International Science and Engineering Fair (Intel ISEF); Issuer: Society for Science and the Public, May 2015
Finalist in The E(x)plory Scientific Competition 2015; Issuer: Fundacja Zaawansowanych Technologii, March 2015
The Talent of Swietokrzyskie, Marshal Office of the Swietokrzyskie Voivodeship, October 2014
Let's Talk about [X] Multidisciplinary Student Research Conference - University of Glasgow, February 2015

By MARY MARKATOU, Kefalonia, Ionian Islands, Greece

By MIN CHAN-HONG, Seoul, South Korea

By MARGARET HEINZ, East Dundee, Illinois, the USA

By JOHANNES LANG, Vienna, Austria
Mentor: Ruth Schabauer (Department of English, Neulandschule Grinzing)

​This work examines the impact of Europeans’ commercial expansion into the Indian Ocean on the local Asian and African economies between 1600 and 1650. By studying this historically important period of time, we can also gain a deeper understanding of modern globalization and of Europe’s continuing political and economic influence today. The different consequences for the various regions bordering the Indian Ocean are compared, contrasted, and evaluated. For my research I use primarily books and articles but also rely on the analysis of economic data. Epic poems from Mughal writers as well as modern studies are included so that the reader may gain thorough insights into the topic. As I try to tell history from an Afro-Asian perspective, I let both 17th century and contemporary voices native to the Indian Ocean have their say.
I conclude in my study that the consequences of trade with the Europeans differed greatly between the heterogeneous regions. The nature of these consequences depended on the socioeconomic structure as well as on the environmental particularities of the regions in question. Some economies profited from the new situation; others suffered from the altered trade system. Interestingly, many effects of 17th century globalization, such as increased competition with countries far away and a heightened reliance on foreign trade, are visible also in today’s process of globalization.   

By HANI CHOKSI, Brampton, Canada

​After graduating from high school, students are expected to make a vital decision about what they want to pursue as a career and even more importantly, how they want to pursue it. There are four main pathways that are considered while making this choice – College, University, Apprenticing, and directly joining the workforce. Many believe that the key to a successful future is attending a post-secondary institution and getting a degree, and also that simply by doing so one will instantly land a job in their desired field of work and live a financially stable life. This may have stood true in the past but with the skyrocketing tuition, the stress, and the thousands of other people getting similar degrees, the value of post-secondary education is on the decline.

By ANJALI BHAVAN, New Delhi, India

Worldwide, millions of women are subjected to the practice of Female Genital Mutilation/Cutting (FGM/C) every year, every month, every day. This practice of cutting up female genitalia for a variety of reasons either around birth or puberty violates child and women rights to their very core and has consequences, both immediate and long-term, on the mental, physical and emotional health and well-being of many women across the world—even claiming the lives of many women and children, who die from the pain or subsequent onset of sepsis or reproductive illnesses. Such mutilation is steeped in tradition, religion and culture, often attributed to religion and performed as a rite of purification, and this superstition is passed on for generations, thus perpetrating a vicious cycle. This research aims to assess this practice—that is, delve on its history, both social and cultural, the current scenario and the impact of such mutilation on women and children, examined through the life story of victims of such mutilation. This research also hopes to spread awareness to mitigate the problem at hand and provide relief to countless women who undergo this ritual as a mark of womanhood.​