Publications and Software

Publications

Technical Reports

Expository Papers and Pre-Prints

Notable Software

  • DifferentialEquations.jl
    Author: Rackauckas C
    DifferentialEquations.jl is a package for solving numerically solving differential equations in Julia by Chris Rackauckas. The purpose of this package is to supply efficient Julia implementations of solvers for various differential equations. Equations within the realm of this package include ordinary differential equations (ODEs), stochastic ordinary differential equations (SODEs or SDEs), stochastic partial differential equations (SPDEs), partial differential equations (with both finite difference and finite element methods), differential algebraic equations, and differential delay equations. It includes well-optimized implementations classic algorithms and ones from recent research, including algorithms optimized for high-precision and HPC applications.
  • TBEEF, Triple Bagged Ensemble Ensemble Framework
    Authors: Rackauckas C, Cai W, Jarvis C, Xu C, Ching A
    Last Updated: August 2013.
    In the spring of 2013, Baidu, Inc. hosted a competition for teams to develop new algorithms for movie recommendation systems. The purpose of the competition was to develop better models for rating prediction and suggest methods for incorporating social media data into the prediction models. The goal of our project was to use the information disseminated by the top competitors of the contest to develop new algorithms for recommendation systems. Noting the prevalence of ensemble methods employed on factorization models, our team developed a doubly ensemble framework named TBEEF, a software framework with a plugin interface through which factorization and ensemble models could be easily developed and ran.
  • Bayesian Robust Multiple Linear Regression
    Author: Chris Rackauckas. Adapted from John Kruschke
    Last Updated: June 2013.
    This program performs a Bayesian Robust Multiple Linear Regression by utilizing a Student's t-distribution for the likelihood. It is written in R and requires the use of the rjags package and the JAGS (Just Another Gibbs Sampler) program for the numerical estimation of the posterior distributions. Included is the dataset used in the paper An Application of Robust Regression to Bernanke's Analysis of Nonmonetary Effects in the Great Depression. Credit goes to John Kruschke for developing the Bayesian Multiple Linear Regression script which was adapted to make this program.
  • Animated Water Quality Map
    Source Code
    Authors: Chris Rackauckas and Jeffrey Rackauckas
    Last Updated: June 2013.
    The Maryland Department of Natural Resources utilizes monitoring stations throughout the Chesapeake Bay and its surrounding tributaries in order to asses the quality of the water. These monitoring stations collect data on parameters that are important for life to thrive in the waters such as dissolved oxygen, dissolved carbon, etc. The purpose of this map is to show how these parameters change over time.
  • Jormungand Climate Model MATLAB Scripts
    Author: Chris Rackauckas
    Last Updated: April 2013
    This is a set of MATLAB scripts for generating graphs of the h function for the Budyko-Widiasih model. These are the scripts used in the Jormungand Climate State paper. Included are two programs: one which uses numerical methods to solve for h given any albedo function and another which solves for h using the finite Legendre expansion with geometric singular perturbation theory approximation for an arbitrary smooth alpha_ice.
  • ARIMA Analysis
    Author: Chris Rackauckas. Adapted from Harry Hurd
    Last Updated: April 2013
    This MATLAB script analyzes time series data, plots graphs of the residuals, autocorrelation fucntions, and partial autocorrelation functions for the best fitting ARIMA models, and presents the user with a printout of the Akaike Information Criterion and the Ljung-Box p-values. This script is an updated version of Harry Hurd's doarima.m. It is known to work with MATLAB R2012a and requires the System Identification Toolbox.
  • ARIMA Forecaster
    Author: Chris Rackauckas.
    Last Updated: April 2013
    This MATLAB script estimates the specified ARIMA(p,d,q) model and generates a forecast. It can be used to analyze an ARIMA forcast against real data by setting a portion of your data as the validation data. If you wish to only forecast, simply turn the validation step off (VALIDATE=0). One can specify a second ARIMA model estimated using a subset of the dataset by setting TWOARIMA=1 and the program will plot the estimation errors of both models for comparison. It is known to work with MATLAB 2012a and requires the Econometrics Toolbox.
  • Water Quality Analysis GUI for the Department of Natural Resources
    Authors: Authors: Le R, Rackauckas C, Ross A, Ulloa N.
    Last Updated: February 2013
    This tool was developed by students at the University of Maryland, Baltimore County NSA/NSF funded REU Site. This GUI allows researchers to be able to easily generate graphs and perform the necessary statistical analyses on the water quality readings taken by Maryland's Department of Natural Resources of the Chesapeake Bay.

Presentation Slides

Posters

Mathematical Art

Websites

These are the website I have created and/or maintained.