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Year in Review, Year II

Global Awareness

Being in a community as large and diverse as the one present at OSU has helped me expand my knowledge of the world and my awareness of global issues. It’s not uncommon to talk with course mates about experiences that we have had living in different countries, and this interchange and debate of views has enriched our conversations and ideas. Everyone brings something different to the table, and whether that is a song, a book, art, political ideas, history, or food, it’s great to be able to share and appreciate them.

Original Inquiry

Having joined a research group on my first semester on campus, I have had a lot of experiences in research since joining the university. This year has been especially fruitful in that regard, as I have passed the initial period of learning the basic tools and methods of the research process, and have been able to make progress in the projects that I have worked on and in my own personal development. Overall, this year in research has been a fantastic experience that has excited me about doing more of it in the future and learning more about how to analyze and study the natural world.

Academic Enrichment

My Honors Contract reflects the rigor that I have attempted to conduct in my courses at university. I have challenged myself and I have pursued my interests, namely the studies of physics and mathematics. The GE’s that I have taken have also been held to the same standard, I tried to expand my knowledge and try new things, such as the studies of sociology, ancient Greek history, holography, etc. Each of them has taught me something new about the world, in each I have found a place and an angle to look intelligently upon it. All of them in a way have supported my main studies by broadening my views and ideas, and ensuring a well-rounded approach to my future career.

Leadership Development

While I don’t participate in many activities that have helped me cultivate my leadership in a direct way, I feel myself growing in confidence and ability to direct people in daily situations. This originates from the accumulation of events that have helped me develop a sense of self and of my abilities, and a growing into a purpose-driven and motivated individual. I have learned to ask for help and give it to others, I have learned to respect and value people’s different approaches and styles and help synthesize them when working as a group.

Service Engagement

The OSU community is truly one of mutual support and respect. Its size and presence of campus are felt everyday, and have helped me feel as part of this larger community, which has inspired me to give back to it everyday.

Holography

A term often used and just as often misunderstood, it traces its origin to Denis Gabor, inventor of holography and recipient of the Nobel Prize in Physics in 1971 for the invention of holography.

A hologram is a piece of film on which the full field of light has been recorded. There are a few ways to achieve this, but generally the method to produce a hologram is to make an interference pattern on the film using a laser with some of its light that is bounced off an object and some that hits the film directly. When suitably lit, the hologram perfectly reproduces the light field: one can move and look around the object as if the object was there.

If one were to cut the hologram in a half, one would be able to view the full image from both pieces of film! It would be like looking through half of a window rather than a full window.

OSU has a unique lab for holography, one of the few in the world, and offers several courses in it, all taught by Dr. Kagan.

It took many, many lab hours to get some results, as there are very specific processes must be followed. For example, when shooting an hologram, the exposure can last up to 20 or 40 seconds, and in that time, the object that is being exposed cannot move for more than a fraction of the wavelength of light, or else the diffraction pattern is ruined and the hologram won’t turn out. I got to work with lasers, optics, and a dark room to produce these.

Here are some, and unfortunately they are not as nice as seen in real life, since normal 2D imagining can’t reproduce the effects of the holograms.

These are videos, which look better, but below are some gifs, and remember, these aren’t boxes with objects in them, they are just 2D pieces of films, like photographs!

IMG_4458_HEVC-1a1d8t3

IMG_4325_HEVC-2g4f6m1

 

 

Linear Algebra Final Project

As mentioned in an earlier post, I worked on a project with a group in my linear algebra class, which we ended up presenting at a poster session with the rest of the class.

Our topic was Game Theory.

This is truly a fascinating subject we learned (and a great application of linear algebra), as it seeks to mathematically describe rational decision making in strategic interactions of ‘games’. This definition allows it to describe games from tic-tac-toe to poker and to chess, but can also be used to describe economic agents in the market or problems like the Prisoner’s Dilemma.

We studied the formalism of the subject in describing such games, and the Minimax Theorem. Briefly, this theorem states (for zero-sum, two person games) that there is an equilibrium between the best mixed strategies of two players which guarantees a certain value of the game, i.e. for player I, there exists a strategy for which the average profits will be at least V, and for player II there exists a strategy for which the average costs will be at most V.  This theorem actually is a case of the LP Duality Theorem, in  which Player I seeks to Minimize costs cx, while Player II seeks to Maximize profits yb, subject to constraints Ax > b, x > o, yA < c, y > 0.

We worked through a simplified version of Poker (the one described by John von Neumann), for which we wrote out all the strategies of each player, eliminated the dominated strategies (i.e. strategies that make no sense), and calculated the payoff matrix. This is a matrix in which the columns represent the pure strategies for one player and the rows the pure strategies for the other, and the entries represent the result of two strategies being played. A pure strategy is essentially a description of how that player would act given any state of the game. This is why often a combination of pure strategies is the optimal solution. E.g. in rock, paper, scissors, each player has 3 pure strategies: rock, paper, scissors, but the optimal solution is an equal distribution of those pure strategies. We then solved the matrix using simply Ax=b, finding the optimal mix of the pure strategies for each player for the poker game.

We also wrote a quick program that uses the simplex method to solve the linear programming problem and find the solution to any payoff matrix that we inputted, returning the optimal strategies for each player and the value of the game.

 

The Dionysian Rites, Their God, and Pentheus in Euripides’ The Bacchae

Literature, philosophy, and the classics have always been an interest of mine. After reading The Bacchae one summer, I wrote this paper for my Classics 2022H course the autumn semester in my first year.

I was honored to receive an award for it, the Undergraduate Award for Excellence – Best Undergraduate Paper in Classics.

 

For context,

In The Bacchae, the last play written by Euripides before his death, Dionysius seeks to punish the tyrant of Thebes, Pentheus, for not welcoming the god’s rites into the city and for denying his divine nature. Pentheus is eventually torn apart by his own mother and the other women of the city who had been driven crazy by the god, a cruelty which culminates in his mother’s slow coming to senses, and her horror at the realization of what had happened as she holds the severed head of her son on her thyrsus.

 

My argument,

With several themes arising throughout the play, a wide range of interpretations surround the conflict between the tyrant and the god, in which the antagonists often serve as ideological counterparts, and their confrontation as a symbol of the clash between consistent rationalized philosophies or ways of life. It is the focus of this essay to analyze Euripides’ portrayal of Dionysius and his rites and the mortal reaction to them, of which the two antagonists are symbolic, and of which two views generally form in scholars’ interpretations of the play: either that Dionysius and the rites are depicted as destructive and cruel forces on the mortal sufferers, or liberating in their punishment of human pride and of those who question the gods. I will argue that in truth Pentheus and Dionysius are presented as complex, internally ambivalent characters who come to resemble each other in many aspects, revealing the internal dichotomies of each: the human duality of Pentheus in his faults and merits, and the duality of Dionysius and his rites as both liberating and destructive, which are consistent with what the characters symbolize.

 

The whole paper,

Luca Long Paper V3-22vp3kr

 

 

MilliQan – June 2018

The summer was a great opportunity to dedicate more time to the research group I had joined. The undergraduates and I presented twice to online meetings of the collaboration, and attended many of the weekly meetings that during the year are harder to follow due to conflicts with courses.

One thing I worked on was a closure test in single-channel trigger runs. Measuring the event rate for single coincidence events (one hit in the demonstrator, a hit is the detection of a particle), one can calculate the expected double coincidence rate (two hits in the demonstrator, so a particle hitting two of sensors or two particles hitting two sensors), and then measure it to check discrepancies between calculation and observed. This included developing a lot of ‘vetos’, which means selecting what we consider to be useful data and sorting it out from all the noise. The demonstrator is very sensitive, and though it is shielded, cosmic particles and thermal background noise are constantly showing up, and we learned to measure and remove them as much as we can. I also used geometry and timing, since we were calculating events from muons coming from CMS (where they are generated), I can exclude a lot of particles by tracing their paths and seeing that they are not in a straight line pointing towards CMS, or that the timing between straight line paths is not consistent with what we expect the speed of muons to be.

My experiences in the group have encouraged me to continue trying to work in physics research, which I continuously found interesting, fulfilling, and challenging.

Some of the graphs from the study. In the first is a comparison between calculated double coincidence rates and observed (blue) after the vetoes had been implemented. In the second two is an example of a veto on two runs (run is defined a certain time in which we were collecting data, each run’s graph is normalized to total run duration), showing the removal of afterpulses between the first picture (pre-veto) with the afterpulses and the second (post-veto) without that peak at the left that were the afterpulses.


 

Linear Algebra — Final Project Ideas

My Linear Algebra course this year had the unique feature that aside a final exam, we are responsible for a final project, which will involve studying in depth an application or topic in linear algebra that was not studied for the course.

There were several topics that had peaked my interest throughout the class, here are some that are candidates for my project:

  • Fourier Series: turns out an orthogonal inner product basis for L2(R) is {sin nx} U {cos mx} (n = 1, 2, 3…, m = 0, 1, 2 …), which allows us to write functions as series of sinusoidal functions. A lot of signal detection can be done with this as waves can be well approximated with this series, things like voice recognition, music encoding, etc. and then all we need to do is save the coefficients of all the sines and cosines and we can reproduce/identify sounds.
  • Vandermonde Matrices: an easier way to approach statistics problems, we can use these matrices to find the best fitting curve through a data set by finding the minimization of the least square solution. Would be interesting to write a quick program that does this!
  • Lagandre Polynomials: being orthogonal is useful for calculation, and these give us an orthonormal basis for the span of {1, t, t^2, …}. We can also use these for curve fitting, simply by projecting the polynomial onto their span, which is computationally easier it’s an orthonormal set. They are also pretty useful in multiple expansions for 1/r potentials, which are very common in physics.

First Year in Physics — Helen Cowan Book Award for Physics Undergraduates

Pretty nice surprise to have received this award at the end of my first year of university!
I had greatly enjoyed studying various fields in physics in the introductory sequence courses, with topics ranging from quantum mechanics and thermodynamics to the more traditional first-year-level classical mechanics. The variety of topics really inspired my curiosity and interest in studying the natural world and showed me the beautiful realizations of the physics we use to model it. This confirmed and encouraged my decision of studying physics which, like for most first-year students picking their majors with only high school level experience in a certain field, wasn’t too certain at the beginning of the year. In the end, the fascination that most physics majors have towards it is enough to convince them to stay in the field. For all of this I can only thank my professors, Dr. Mathur and Dr. Connolly, who were fantastic guides to the beginning of my physics experience in university. Receiving this award at the end of the year was greatly rewarding, and gave me confidence heading off to the courses and experiences that lay ahead.

G.O.A.L.S.

Global Awareness: Students cultivate and develop their appreciation for diversity and each individual’s unique differences. For example, consider course work, study abroad, involvement in cultural organizations or activities, etc .
Original Inquiry: Honors & Scholars students understand the research process by engaging in experiences ranging from in-class scholarly endeavors to creative inquiry projects to independent experiences with top researchers across campus and in the global community. For example, consider research, creative productions or performances, advanced course work, etc.
Academic Enrichment: Honors & Scholars students pursue academic excellence through rigorous curricular experiences beyond the university norm both in and out of the classroom.
Leadership Development: Honors & Scholars students develop leadership skills that can be demonstrated in the classroom, in the community, in their co-curricular activities, and in their future roles in society.
Service Engagement: Honors & Scholars students commit to service to the community.