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Research Projects

Faculty Mentored Research Projects

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  •  2019 HSMC Research Projects

    • Evaluation and Quantification of the Performance of Stream Ciphers - Dylan Dong, Ayush Suresh, Weilun Sun, Michelle Wang, Mentor: Dan Tamir
    • B-Spline Surface Optimization for Sharp Feature Preservation - Daniel Lee, Isabella Quan, Chris Wu, Jason Wu, Mentor: Dan Tamir
    • Student Strategies When Attempting Combinatorial Games - Kiara Chavez, Lino Guajardo, Emma Yu, Mentor: Cody Patterson
    • Epidemic Intervention on Dynamic Metapopulation Networks - Michael Li, Jack Qiao, Stephanie Wang, Jason Yuan, Mentor: Alex White
    • Effects of Varying Subgroup Vaccination Rates on Risk of Herd Immunity Deterioration - Daphne Han, Tara Roshan, Allison Yang, Hannah Zhang, Mentor: Alex White
    • Dynamic Mode Decomposition for a Linear Operator with External Force - Amy Guan, Esther Lee, Helen Wang, Annie Zhu, Mentor Young Ju Lee
    • Lossless Data Compression on Unbounded Integers - Patrick Peng, Samuel Tian, Alvin Xu, Mentor: Dan Tamir
    • Graph Theoretic Algorithms for Social Network Analysis - Sophie Cui, Rachel Laing, Angela Landry, Eileen Li, Mentors: Jelena Tesic and Lucas Rusnak
    • Representable Matroids and Oriented Hypergraphs - Selena Li, Brian Xu, Eric Yan, Shirley Zhu, Mentor: Lucas Rusnak
    • Generalizing the Tutte Polynomial to Hypergraphs - Michelle Li, Elijah Stroud, Michelle Xiang, Mentor: Lucas Rusnak
    • Identifying Knot Structures in Known Protein Diagrams - Andy Iyabor, Subi Kim, Radha Malhotra, Saba Zerefa, Mentor: Timothy Chase
    • A Computational Assessment of the Probability of Knots in Protein Mechanisms - Turner Bumbary, Andy Jiang, Sarah Wei, Sydney Zhou, Mentor: Timothy Chase
    • Circuit-Chip Firing on Graphs - Eli Meyers, Raghav Samavedam, Alex Yi, Mentor: Anton Dochtermann
    • Prime Factors in Dynamical Orbits - Kelly Cui, Jasmine Huang, Josh Kolenbrander, William Wang, Mentor: Wade Hindes
  • 2018 HSMC Research Projects

    • Algebraic Topological Methods for the Analysis and Modeling of Protein Data - Crystal Wang, Jason Yuan, Mentor: Dave Snyder
    • Utility of Wormlike Micellar Fluids in Enhanced Oil Recovery- Pierce Lai, Michael Li, Sydney Zhou, Mentor: Young Ju Lee
    • Correlation between the Tutte Polynomials of Simple Graphs, Bipartite Graphs, and Hypergraphs - Devanshi Gupta, Danika Luo, Michelle Wang, Mentor: Lucas Rusnak
    • A Complete Bound on the Chromatic Number and Index of Hypergraphs Through a Generalization of Vizing's Theorem - Jenny Lu, Eric Wu, Amy Zhou, Mentor: Lucas Rusnak
    • 3D Mesh Generation through Triangle and Curve Algorithms - Naomi Kenyatta, Raymond Suo, Allen Wu, Mentor: Dan Tamir
    • Enhancement of the SLAM Algorithm between Two Autonomous Vehicles - Richard Li, Michael Liu, Mahalet Mekonen, Mentor: Rodion Podorozhny
    • Construction and Enumeration of Minimal Prime Graphs - Josh Kolenbander, Elijah Stroud, Selina Wu, Mentor: Thomas Kellar
    • An Integrative Evaluation of Statistical Tests for Pseudorandomness to Determine Optimum Randomness Criteria - Asha Pereira, Helen Wang, Angela Zhang, Mentor: Dan Tamir
    • Verification for the Correctness of Concurrent Data Structures - Turner Bumbary, Amy Hu, Shilpita Mitra-Behura, Mentor: Rodion Podorozhny
    • A Generalization of Polygonal Sperner's Lemma to Allow Duplicate Labels - Sarah Wei, Alex Yi, Justin Yu, Mentor: Suho Oh

Siemens Competition Results

Returning students in the Honors Summer Math Camp (HSMC) have the opportunity to conduct original math research projects in a team that can be submitted to various contests.  The HSMC has a strong record of producing award-winning research projects.  In 2009, a team from the HSMC won first place at the national level of the Siemens Competition, sharing a $100,000 college scholarship.

From 2001-2017, students' team entries have achieved the following in the Siemens Competition in Math, Science, and Technology:

  • National Finalist: 5 teams
  • Regional Finalist: 25 teams
  • Semifinalist: 73 teams

This includes 192 students named as semifinalists, 72 regional finalists, and 14 national finalists.

    • Regional Finalist- "Criteria for Determining Concordance in Positroids"
      • Team: Andrew Lu, Claire Zhou, Brandon Chen
      • Mentor: Suho Oh
    • Semifinalist- "Algebraic Topological Applications in Data Modeling and Analysis"
      • Team: Jenny Lu, Elijah Stroud, Rachel Laing
      • Mentor: David Snyder
    • Semifinalist: "A Predictive Model of the Spontaneous Segregation of Spherical Nanoparticles Due to Force Imbalances"
      • Team: William Wang, Kyle Wang, Lucy Xu
      • Mentor: Gary Beall
    • Semifinalist- "A Complete Characterization of Oriented Hypergraphs with Singular Laplacians"
      • Team: Junu Lee, Elizabeth Guo, Saba Zerefa
      • Lucas Rusnak
    • Semifinalist- "A Numerical Study of Floating Drops"
      • Team: Eric Wu, Josh Kolenbrander, Grace Zhang
      • Mentor: Ray Treinen
    • Semifinalist- "Integrated Analysis of Gene Expression and Methylation Data for Breast Cancer Cell Lines"
      • Team: Juyon Lee, Catherine Li, Jessica Ding
      • Mentor: Shuying Sun
    • Semifinalist- "Topological Characterization of Graph Study"
      • Team: William Wang, Linda Yu, Kathleen Zhang
      • Mentor: Tim Chase
    • Semifinalist- "A Novel Algorithm for Enhancing the naïve Bayes Spam Filter Through Text Modification Detection"
      • Team: Linda Huang, Julia Jia, Emma Ingram
      • Mentor: Wuxu Peng
    • Semifinalist- "A Three Species Model for Wormlike Micellar Fluids in Porous Media and its Applications"
      • Team: Jonathan Shoemaker, Ethan Nolen
      • Mentor: Young Ju Lee
    • Semifinalist - "Applications of Grassmann Algebra on Laplacian Matrices and Their Properties"
      • Team: Junu Lee, Andrew Lu, and Sophia Sun
      • Mentor: Eugene Curtin
    • Semifinalist - "A Generalization of Structural Degree of Imbalance and Complexity in Oriented Hypergraphs"
      • Team: Gina Chen, Vivian Liu, and Kyle Wang
      • Mentor: Lucas Rusnak
    • Semifinalist - "DNA Co-Methylation Patterns in Cancerous and Normal Tissues"
      • Team: Emily Chen, Surya Namboodiri, and Lillian Sun
      • Mentor: Shuying Sun
    • Semifinalist - "Exploring Energy Efficient Query Optimization Techniques for Databases Without Degrading Performance"
      • Team: Julia Jia, Catherine Li, and Angela Zhang
      • Mentor: Ziliang Zong
    • Regional Finalist - "Signed Path Matrices and Oriented Hypergraphic Generalizations"
      • Team: Eric Li, David Xiang, and Amber Lu
      • Mentor: Lucas Rusnak
    • Semifinalist - "Clusters of Floating and Sessile Drops in the Absence of Gravity"
      • Team: Christine Jou and Yagmur Yuksel
      • Mentor: Ray Treinen
    • Semifinalist - "A Combinatorial Proof for the Rank-Unimodality of Poset Order Ideals"
      • Team: Hans Li, William Liu, and Kevin Rao
      • Mentor: Edward Early
    • Semifinalist - "Energy-Aware Deep Learning for Image Recognition"
      • Team: Lillian Bu, Michelle Hamilton, and Nina Osipova
      • Mentor: Ziliang Zong
    • Regional Finalist - "Identifying DNA Methylation Variation Patterns For Breast Cancer Biomarker Genes"
      • Team: Brandon Alston, Lily Xu, Simantini Mitra-Behura
      • Mentors: Shuying Sun and Ziliang Zong
    • Semifinalist - "Improvements In 3D Volumetric Displays"
      • Team: Wilbur Li, YingYan Ho, Eric Gao
      • Mentor: Matt Gately
    • Regional Finalist - "Maximizing the Number Of K-Sets"
      • Team: Weiwei Chen, Patrick Guo, and Jessica Yu
      • Mentor: Edward Early
    • Regional Finalist - "A Characterization of Balance in Oriented Hypernetworks via Generalized Signed Walks"
      • Team: Angie Rao, Alex Yang, and Vinci Chen
      • Mentor: Lucas Rusnak
    • Semifinalist - "Generating Molecular Solubility Predictors Using Quantitative Structure Activity Relationships"
      • Team: Justin Zhang, Amber Guo, and Angela Feng
      • Mentor: Carl Fisher and Eumi Pyun
    • Semifinalist - "A Game of Tri: A Graph Theoretic Generalization of Hex"
      • Team: Leslie Tu, Selcen Yuksel, and Michaela Taylor-Williams
      • Mentor: Eugene Curtin
    • Semifinalist - "On the synthesis and predictive modeling of stable pigments utilizing silica extracted from rice husk biowastes"
      • Team: Caroline Gao, Susan Xu, and Lily Xu
      • Mentor: Luyi Sun
    • Regional Finalist - "A Novel Approach To Estimating Survival Functions For Interval Censored Data With STD Behavioral Diary Information"
      • Team: George Qi, Vinciane Chen, Robert Tung
      • Mentor: Qiang Zhao
    • Semifinalist - "On The Ratios Of Binomial Coefficients"
      • Team: Leslie Tu, Catherine Yip, Aditya Jain
      • Mentor: Edward Early
    •  
    •  5th Place National Finalist - "Determining the Existence of Graceful Valuations of Various Families of Graphs"
      • Team: Kevin Tian, Kevin Chang, Andrew Xu
      • Mentor: Edward Early
    • Regional Finalist - "On the Acyclic Subgraphs of k-Majority Tournments"
      • Team: Alexandra Ilic, Bobby Shen, and Lilly Shen
      • Mentor: Jian Shen
    •  Semifinalist- "A Generalization of Sperner's Theorem for Multisets"
      • Team: Steven Chen, Amy Kang, and Jeremy Kalas
      • Mentor: Eugene Curtin
    • Semifinalist- "Computing Spatio-Temporal Data with Applications to Hurricane Analysis"
      • Team: Ding Zhou and Jessica Wang
      • Mentor: Mark McKenney
    • Semifinalist - "A Mathematical Model of Structural Behaviors and Physical Properties of Polymer Nanocomposites"
      • Team: George Qi, Catherine Liu, and Linda Zhang
      • Mentor: Gary Beall

    • Regional Finalist - " On the Power Dominating Set of Various Classes of Graphs"
      • Team: Alexandra Ilic, Ignacio Ramirez, and Kevin Tian
      • Mentor: Nathaniel Dean
    • Regional Finalist - " Attainability of the chromatic numbers of functigraphs"

    Team: George Qi and Daniel (Shenghao) Wang

    Mentor: Weizhen Gu

     

    • Semifinalist - " An Application of Subsampling Quantile Estimators to Image Denoising"

    Team:  Sophia (Wen) Chu and Sumit Gogia

    Mentor: Alex White

    • Semifinalist - " On Relating the Prime-counting and Totient Functions to Pigeonhole Goldbach Partitions"

    Team:  Patrick Kim and Michael Proulx

    Mentor: Edward Early 

    • First Place Overall - "Relating Missing and Decycling Edges in Directed Graphs"

    Team:  Dan Liu, Kevin Chen, Sean Karson

    Mentor:  Jian Shen

    • Regional Finalist - "A Prediction of Nanocomposite Permeability from Monte Carlo Simulations and the Implications of the Constrained Polymer Region"

    Team: Patrick Kim, Sumit Gogia, Vincent Yu

    Mentor: Gary Beall

    • Semifinalist - "Creating and Deducing Structure using Domination Numbers in Permutation Graphs"

    Team:  Max Wimberley, Millie Shi

    Mentor: Weizhen Gu

    • Semifinalist - "The Rank Generating Function for Partially Ordered Rb(n)"

    Team:  Fan-Hal Koung, Jennifer Hu, Rebecca Salinas

    Mentor: Edward Early

    • 5th Place National Finalist - "Previously Unknown Parts of the Greene-Kleitman Partition for the Tamari Lattice"

    Team:  Mark Zhang, R-J Lim 

    Mentor: Edward Early

    • Regional Finalist - "Survival Analysis of Gene Expression Data using Dimension Reduction Techniques"

    Team:  Alicia Zhang, Jeffrey Chan, Sameer Deshpande 

    Mentor: Qiang Zhao

    • Semifinalist - "Analysis of Non-Static Two-Person Poker Models"

    Team: Fan-Hal Koung, Jack Geller, Rick Bhattacharya

    Mentor: Eugene Curtin

    • Semifinalist - “The Effect of Different Air Bubble Arrangements on the Dielectric Constant of Teflon”

    Team:  Eunice Alade, Jennifer Hu, Scarrlett Yin 

    Mentor: Gary Beall

    • Semifinalist - “A Model to compute Settling Velocities of Non-Spherical Nanoparticles in a Centrifuge”

    Team:  Aman Sharma, Manos Souganidis, Veronica Ray

    Mentor: Gary Beall

    • Regional Finalist - “On Winning Strategies for General Two- and Three-Person Vertex Geography and the Characterization of Ck2 Games”

    Team:  Jon Gonzales, Mark Zhang, Wesley Chen 

    Mentor: Nathaniel Dean

    • Regional Finalist - “Risk Neutral Exchange Options in Energy Markets”

    Team:  Aman Sharma, Jean Shiao, Jeffrey Chan 

    Mentor: Thaleia Zariphopoulou and Eugene Curtin

    •  Semifinalist - “General Properties of Partisan Subtraction Games”

    Team:  Jeffrey Chen, R-J Lim, Stephanie Chan 

    Mentor: Nathaniel Dean

    • Semifinalist - “L(321) Labeling in Graphs"

    Team:  Amy Proctor, Jasmine Thum, Kimberly Yeh

    Mentor: Jian Shen

    • Semifinalist - “Modeling Gas Diffusion through Nanocomposites”

    Team:  Bryan Wigianto, Faith Chan, Kevin Luecke 

    Mentor: Gary Beall

    • Regional Finalist - “On Free Minimal Edge Control Sets of Digraphs"

    Team: Kimberly Yeh, Tiffany Tsang 

    Mentor: Xingde Jia

    • Regional Finalist - “Mathematical Developments of the Contact Network Model” 

    Team:  Stephanie Chan, Jacob Shapiro, David Price 

    Mentors: Alex White and Lauren Ancel-Meyers

    • Semifinalist - “Characterization of Maximal Antichains in Posets”

    Team:  R-J Lim, Tal Einav, Wesley Chen 

    Mentor: Edward Early

    • Semifinalist - “Character Tables of the Symmetric Group"

    Team:  Diana Lee, Jasmine Thum, Zijie Zhou 

    Mentor: Edward Early

    • Regional Finalist - “Error Correction in Searching and Sorting Algorithms”

    Team:  Edward Schmerling, Jennifer Schmerling, Erik Feng 

    Mentor: Jian Shen

    • Regional Finalist - “Eccentricity Sequences of Graphs”

    Team:  Alisha Seam, Stephanie Chan, Wesley Chen 

    Mentor: Daniela Ferrero

    • Semifinalist - “Extremal Cayley Graphs of Finite Cyclic Groups”

    Team:  Elysia Sheu, Joseph Lee 

    Mentor: Xingde Jia

    • Regional Finalist - “The Power Domination Problem in Trees and other Bipartite Graphs” 

    Team:  Edward Schmerling, Jennifer Schmerling, Sarah Spikes 

    Mentor: Daniela Ferrero

    • Semifinalist - “Counting Maximal Triangle Free Graphs”

    Team:  Elysia Sheu, Helen Zhang 

    Mentor: Susan Morey

    • Semifinalist - “Variations of the Four-Post Tower of Hanoi Puzzle”

    Team:  Erica Rew, Erik Feng, Jonathan Einav 

    Mentor: Eugene Curtin

    • Semifinalist - “A Coloring on Graphs: The L(2,1) Labeling Problem”

    Team:  Jeff Nanney, Joshua Lim, Kris Kazlowski 

    Mentor: Jian Shen

    • National Finalist 6th Place - "Eccentric Graphs of Block Graphs and Trees"

    Team:  Araceli Fernandez, Hannah Chung, Yiduo Wang

    Mentor: Weizhen Gu

    • Regional Finalist - "Various Cases of Seymour’s 2nd Neighborhood Conjecture for Directed Graphs"

    Team:  Diya Banerjee, Helen Zhang, Jeff Nanney 

    Mentor: Jian Shen

    • Semifinalist - "Domination of Permutation Graphs"

    Team:  Allyson Ho, Chong Jiang, Soham Banerjee 

    Mentor: Weizhen Gu

    • Regional Finalist - "Diameter of Path Graphs"

    Team:  Alan Taylor, Hannah Chung, Jeremy Warshauer 

    Mentor: Daniela Ferrero

    • Semifinalist - "Dominant Planar Graphs"

    Tam:  Araceli Fernandez, Diya Banerjee, Syed Ashrafulla 

    Mentor: Daniela Ferrero

    • Semifinalist - "Examining Four-Player Fair Division Algorithms"

    Team:  Andrew Hsiau, Felicia Alderete, Will Boney 

    Mentors: Eugene Curtin and Cody Patterson

    • National Finalist 4th Place - "The Generalization of the De Bruijn Edge Sums"

    Team:  Charles Hallford, Cynthia Chi, Rebecca Williams

    Mentor: Daniela Ferrero

    • Semifinalist - "Game, Set, Match"

    Team:  Alex Wright, Betty Yang, Yeeland Chen

    Mentor: Eugene Curtin