Astro-Medina
My Projects
Illinois High Mileage Vehicle Competition
As the captain, I led a talented team in designing an aerodynamic car aimed at achieving maximum fuel efficiency. Our focus was on creating a vehicle that not only performed well but also adhered to the strict competition guidelines.
The project provided an incredible opportunity to refine my technical skills under the subject of computer integrated manufacturing. I became proficient in 3D modeling using Autodesk Inventor and worked hands-on with advanced machinery. My experience included:
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Welding
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Plasma Cutting
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Laster Cutting
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Sawmills
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CNC Machines
The process involved:
1. Designing an aerodynamic model and testing with computer-based physics simulations
2. Rendering the model in 3D
3. Constructing the model out of PVC pipes to ensure it fits standard guidelines
4. Construct a metal frame with the aforementioned techniques
5. Adding individual components like the wheels, engine, and brakes
6. Wrapping and decals
These skills and project culminated in the Illinois High Mileage Vehicle competition. Competing against other teams, we demonstrated the capabilities of our vehicle, such that, our vehicle used a few grams of oil over a two-mile course track and placing third in the brake test for the best brakes in the competition.
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Feel free to contact me for more visual and details about this project.
Electrodynamics I - Final Project
Throughout the semester, we covered various topics, however, the primary objective was to familiarize ourselves with relevant mathematical notation and intuition that will be applied to relevant topics in electrodynamics. The sort of subjects we covered during this class ranged from Einstein notation, tensor formalism, special relativity, and Fourier analysis. For reference, this course covered most of Classical Theory of Fields Vol. 2, from Landau & Lifshitz.
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Part of the goal of the final project was to find a way to use the knowledge used in this course and apply it to an alternative topic. For example, an alternative derivation of the Lagrangian of a free particle in an electromagnetic field, or explaining the Van Allen radiation belt via adiabatic process of the magnetic field, or even the discovery of the fine structure constant.
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As an applied math major, derivations have been my bread and butter since high school, hence I was particularly attached to the work from Helmut Haberzettl in his paper, Using gauge invariance to symmetrize the energy-momentum tensor of electrodynamics. While we learned the derivation, it was very hand wavey as covered in our textbook, and this was a more formal derivation. Haberzettl uses a textbook structure but similarly dismisses a lot fo the gaps using words like , "obviously," or "you can see that," etc. In the following paper, I attempt to clarify the work of Haberzettl, deriving most, if not all, of the quantities and filling in the gaps.
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You can view project here:
Machine Learning and Tennis
My years in applied mathematics culminated in a team project where I applied machine learning to predict tennis match outcomes. This project involved using logistic regression models to analyze historical match data and predict the probability of a player winning a match.
Logistic regression is a statistical modeling technique used for classification and predictive analytics. Unlike linear regression, which predicts continuous outcomes, logistic regression predicts the probability of an event occurring. In this project, we aimed to predict the probability of winning or losing a tennis match based on various player statistics and match conditions.
We utilized a comprehensive dataset containing individual match details from major tennis tournaments since 1968. Our dataset included features such as player ages, ranks, handedness, and more. We focused on matches from the US Open, extracting relevant data for our analysis.
My role in the project, involved optimization, applying ML in comparison to basic predictive models like the Markov chain which was implemented by my teammate. We employed logistic regression to model the probability of a player winning a match. Key features of the model included:
1. Sigmoid Function: Transforming real-valued inputs into probabilities.
2. Likelihood Function: Maximizing the likelihood of our training data to uncover model parameters that best fit the data.
3. Negative Log-Likelihood (NLL): Converting the maximization problem into a minimization problem for easier optimization.
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We used hyperparameter tuning through RandomizedSearchCV to optimize the model's performance, evaluating it using metrics such as accuracy, precision, recall, and the Area Under the ROC Curve (AUC).
Our logistic regression model provided a clear and easy-to-understand output, modeling the probability of a player winning a match. This approach allowed us to handle changes over time, such as player performance evolution, and consider various factors influencing match outcomes.
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Despite some limitations, such as the need for a large sample size and sensitivity to outliers, logistic regression proved to be a powerful tool for this application. Our initial exploration with a Markov Chain model showed limitations, prompting a shift to logistic regression for enhanced predictive accuracy.
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You can view the presentation here:
Abundance Properties with APOGEE
As part of a group project in a course on Modern Stellar Astrophysics, we were tasked with analysis of APOGEE data, a large-scale stellar spectroscopic survey.
APOGEE employs two 300-fiber cryogenic spectrographs to detect light from stars, even those situated in the dusty regions of the Milky Way. This allows us to gather detailed chemical and kinematic information about target stars in the Galactic disk and bulge; precisely the data we need to understand the chemical composition of stars and thusly providing insights into the formation and evolution of galaxies.
The survey initially consisted of 733,901 stars. By refining our search criteria to typical red giant stars in the Galactic disk, we narrowed our dataset to 221,244 stars. This involved excluding unreliable measurements and focusing on stars with specific parallax and metallicity values. For these stars, we extracted chemical abundances, parallax measurements, and galactic coordinates, enabling us to calculate their galactocentric radius.
Our analysis revealed complex patterns of chemical abundance in the Galactic disk. Notably, we found that the radial gradients of metallicity and elemental abundance ratios varied significantly with age, indicating that the chemical evolution of the galaxy has not been smooth or continuous. For example, the radial gradient of six alpha elements (O, Mg, Si, S, Ca, and Ti) over iron steepened with increasing age, suggesting non-continuous star formation and chemical enrichment in the inner regions of the galaxy.
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You can read our paper here:
