Research

Ongoing Work:

• Graphical Economics with Resale
  Team Members: Gabriel P. Andrade, Prof. Rafael Frongillo, Elliot Gorokhovsky, and Sharadha Srinivasan
  

  ^{We extend the Kakade, Kearns, and Ortiz (KKO) graph-theoretic generalization of the classic Arrow--Debreu (AD) exchange economy, by allowing agents to purchase goods on credit in order to resell them. Our model interpolates between AD and KKO through the credit parameter, with zero credit giving KKO and infinite (or sufficiently high) credit giving AD. Via a reduction to a special case of AD with production, we prove the existence of equilibria for general conditions and adapt existing convex programs for AD with production to our setting.}

Past Work:

• Hierarchical Network Structure and Dynamics Motivated by Brains
  Team Members: Gabriel P. Andrade
  Advised By: Prof. Robert Kozma & Prof. Miklós Ruszinkó
  

  ^{I conducted this work in the BINDS lab as part of the DARPA funded project entitled “Superior AI”. We aimed to encode associative memories into the dynamic regimes of hierarchical networks. The system we studied is most easily described as a percolation cellular automaton that has been repurposed with rules and connectivity structures gleaned from biological insights on the cerebral cortex. This simple neuron model is incredibly flexible and produces a diverse array of distinct dynamic behaviours throughout its phase space. More information on this work can be found on the project's research page here. In addition, technical details are described in this manuscript. For information on project "Superior AI" in general, please consult the project website.}

• Recurrent Systems for EMG-based Hand Gesture Recognition
  Team Members: Connor Amorin, Gabriel P. Andrade, Chris Brissette, Matthew Gagnon, Brandon Iles, Jimmy Smith, and Lance Wrobel
  Advised By: Prof. Qian-Yong Chen
  

  ^{This was the second project of the yearly projects required for my M.S. degree. We compared models for classifying electromyography (EMG) signals. Particular emphasis was placed on recurrent neural networks (RNNs) and Reservoire Computing. Slides about this work are found here.}

• Deep Neural Networks for Classifying Breast Masses From Mammograms
  Team Members: Gabriel P. Andrade, Dean Katsaros, Oliver Spiro
  Advised By: Prof. Nathaniel Whitaker
  

  ^{This was the first of the yearly projects that are part of my M.S. requirements. During this project, all 12 of the Applied Math M.S. students worked together to develop an autonomous end-to-end system for breast mass detection and diagnosis. Along with two team members, I was tasked with evaluating neural network architectures and classical machine learning techniques for the classification of mammograms. Due to relatively small amounts of data (as is often the case with medical data), we explored different methods for data augmentation and transfer learning. Details about the entire project can be found in this article. Slides about this work are found here. The article I just linked, along with a bunch of interesting things (problems, articles, etc.), can be found in the UMass Math & Stats 2016-2017 Department Newsletter.}

• A Matroid Generalization of Sperner's Lemma
  Team Members: Gabriel P. Andrade, Andrés Rodríguez Rey, Alberto Ruiz
  Advised By: Prof. Francis Su & Prof. Mutiara Sondjaja
  

  ^{I conducted this work as part of a summer REU at MSRI. In a team of three, we spent the summer working to improve a bound given in a paper from 1980 by Prof. László Lovász. In that paper he generalized Sperner's lemma for matroids by showing that triangulations of a d-simplex, labeled with elements of a matroid M, must contain at least one "basis simplex". We found a small counterexample to Prof. Lovász's claim, made an addenda so that the statement holds, uncovered properties of matroids and the labeling which influence the bound, and more. All of our results from that summer are recorded in this manuscript. A video of a talk we gave on this work can be found here.}

  ^{I would like to mention that this work was done at the MSRI-UP 2015 REU. I encourage any undergraduate student with an interest in math to seek out more information about MSRI-UP. My summer there had a huge impact on my research interests, academic maturity, and career plans. In addition to being academically/professionally enriching, it was just an incredible way to spend a summer (arguably one of the best times I've had in my life).}