Jarod Hart's Homepage  

Contac
t information:
 

Office:  521 Snow Hall
Email:  jvhart@ku.edu
Phone:  785-864-5186
Office hours: 


My Research in Harmonic Analysis
 
My CV

Math 596: Math in Biomedical Research, Fall 2016
 

Math 596 students should go to the Blackboard page for this course.  You can download course materials and submit assignments there.

Fall 2017, Math 596 Syllabus
 
Fall 2017, Math 596 Schedule
 
Math 596 Course Advertisement
 
Math 596 Course Summary



Undergraduate Research
 

The following are summaries of some undergraduate research projects that I've advised.  These are undergraduate research projects completed as part of either the Math 696: Transition in Math class (offered at KU fall 2009 through spring 2013) or Math 596: Math in Biomedical Research (offered at KU spring 2016 and currently).  Professor Estela Gavosto and I taught the Transitions in Math course, and I teach the Math in Biomedical Research course.  Some modification and additions were made to the original project for these summaries.  These courses were/are supported by the Initiative for Maximizing Student Development (IMSD) grant from the National Institutes of Health (NIH-NIGMS 5R25GM062232).  The PIs of the IMSD grant are Professors Estela Gavosto (Mathematics Department) and James Orr (Biology Department).  We are happy to share these projects, and welcome those who are interested to use them for capstone courses or undergraduate research advising.  We'd love to hear about your results and extensions related to these projects, and in some cases, will provide some support for the projects.  Please contact Jarod Hart at jvhart@ku.edu with any questions and/or comments about these project summaries.

1
. Time-frequency analysis of music using short-time Fourier analysis
 
    Supplementary files:    Two piano notes                                                                   Spectrogram, .wav
                                       
Happy Birthday Song                                                           Spectrogram, .wav
                                        Für Elise, Ludwig van Beethoven:                                        Spectrogram, .wav
                                        The Entertainer, Scott Joplin:                                               Spectrogram, .wav
                                       
Moonlight Sonata, Ludwig van Beethoven:                          Spectrogram, .wav
                                        Flight of the Valkyries, Wilhelm Richard Wagner:                 Spectrogram, .wav



2. Stochastic SIR models for inhomogeneous populations
 
   
Supplementary files:    SIR demonstration models
                                          beta=gamma=1, r=.1, uniform Lambda:                            Lambda 1, SIR plot 1
                                          beta=gamma=1, r=.1, .75 random Lambda:                      Lambda 2, SIR plot 2
                                          beta=gamma=1, r=.1, .2 random Lambda:                        Lambda 3, SIR plot 3
                                          beta=gamma=1, r=.1, .01 random Lambda:                      Lambda 4, SIR plot 4
 
                                        Three neighbor graph demonstration
                                          beta=gamma=1, r=.1, 1 initially infected:                           Lambda 1, SIR plot 1, SIR video 1
                                          beta=gamma=1, r=.1, 1 initially infected:                           Lambda 2, SIR plot 2, SIR video 2
                                          beta=gamma=1, r=.1, 4 initially infected:                           Lambda 3, SIR plot 3, SIR video 3
 
                                         Continental United States map and Lambda selection
                                          N=500: Map selection,
Lambda
 
                                        Continental United States SIR model
                                          beta=gamma=1, r=.1, NE initially infected:                       
SIR plot 1, SIR video 1
                                          beta=2, gamma=3, r=.25, NE initially infected:                  SIR plot 2
, SIR video 2
                                          beta=gamma=1, r=.1, 1 region initially infected:               
SIR plot 3
, SIR video 3
                                          beta=1, gamma=5, r=.2, 3 regions initially infected:          SIR plot 4, SIR video 4
 
                                        Continental United States SIS model

                                          beta=1, gamma=10, r=.3, 1 initially infected:                     SIS plot 1, SIS video 1

 

                                        World map and Lambda selection
                                          N=750: Map selection, Lambda
 
                                        World SIR model
                                          beta=gamma=1, r=.2, mainland US initially infected:        SIR plot 1, SIR video 1
                                          beta=2, gamma=1, r=.3, mainland US initially infected:    SIR plot 2, SIR video 2
 
                                        World SIS model
                                          beta=1, gamma=2, r=.25, mainland US initially infected:  SIS plot 1, SIS video 1



3. Artificial Neural Networks
 
    Supplementary files:   Multi-Layer ANN Binary Classification Examples:
  
                                          Example 1: Decision Contour, Decision Shaded, 3D Plot, Squared Error
                                          Example 2: Decision Contour, Decision Shaded, 3D Plot, Squared Error
                                          Example 3: Decision Contour, Decision Shaded, 3D Plot, Squared Error
  
                                        Multi-Layer ANN Four Group Classification via Binary Classifiers Example:
                                           Example: Decision Contour, Binary Decisions Shaded, 3D Plot, Squared Error

  
                                        Multi-Layer ANN Function Approximation Example:
                                           Example: Approximation of f(x,y)=(sin(x)cos(xy)+sin(2y))/2 on [-3,3]x[-3,3], Function Plot, Samples, ANN Approximation, Squared Error

4.  ODE Models of Pendulums
 
     Supplementary files:   Single Pendulums:
 

                                           Example 1: Video, Angle Plot, Angular Velocity Plot
                                           Example 2: Video, Angle Plot, Angular Velocity Plot  
 
                                         Double Pendulums:
 
                                            Example 1: Video, Video with Plots
                                            Example 2: Video, Video with Plots
                                            Example 3: Video, Video with Plots
 

Last Updated: 3/21/2017