MATHEMATICS AND COMPUTING RESEARCH EXPERIENCES FOR UNDERGRADUATES AT IOWA STATE UNIVERSITY
supported by the National Science Foundation through
DMS 0750986, DMS 0502354, DMS 0353880

ISU Math REU Summer 2013

Thanks for a great summer!  We look forward to seeing many of you at YMC, SACNAS, and JMM.


Schedule

M - F 9A-5P Do research except for scheduled activities below and lunch break (even when no group lunch).

Red = food,  all REU students and sometimes whole group. 
Blue =
all REU students and sometimes whole group.
Purple = unusual time or place.


Faculty mentors have authority to excuse students from any scheduled activity to avoid disruption of research, but someone should notify Leslie Hogben and Julia Anderson-Lee if a student is excused to miss a whole group activity during the workweek.

Weekend and evening activities are optional.

Monday July 22
9 AM                research:
                          Combinatorial Matrix in 202 Carver
                          Analysis in 298 Carver
                          Algebraic Graph  in 268 Carver
                          Compressive Sensing in 244 or 174 Carver
noon                  Union Drive Marketplace Heritage room REU student lunch menu
                          REU student business meeting in UDM at 12:15

Tuesday July 23

9 AM                research:
                          Combinatorial Matrix in 202 Carver
                          Analysis in 298 Carver
                          Algebraic Graph  in 268 Carver
                          Compressive Sensing in 244 or 174 Carver
4:30 PM             cookies and conversation 400 Carver


Wednesday July 24
9 AM                research:
                          Combinatorial Matrix in 202 Carver
                          Analysis in 298 Carver
                          Algebraic Graph  in 268 Carver
                          Compressive Sensing in 244 or 174 Carver
noon                 Union Drive Marketplace in Mezzanine REU student lunch menu
                         REU student business meeting in UDM at 12:15


Thursday July 25
9 AM                research:
                          Combinatorial Matrix in 202 Carver
                          Analysis in 298 Carver
                          Algebraic Graph  in 268 Carver
                          Compressive Sensing in 400 or 174 Carver or Coover
4:30 PM             cookies and conversation 400 Carver


Friday July 26
9 AM                research:
                          Combinatorial Matrix in 202 Carver
                          Analysis in 298 Carver
                          Algebraic Graph  in 268 Carver
                          Compressive Sensing in 244 or 174 Carver or Coover
11:40                 Meet outside Union Drive for Virtual Reality Tour
                          lunch on your own


Saturday July 27

Sunday July 28

Monday July 29

9 AM                research:
                          Combinatorial Matrix in 202 Carver
                          Analysis in 298 Carver
                          Algebraic Graph  in 268 Carver
                          Compressive Sensing in 244 or 174 Carver
1:30 PM             sympoisum in 274 Casrver                       
                          Analysis
                           refreshment break 400
                          Algebraic Graph
3:45 PM             t-shirt distribution in 400 Carver                       
 
 

Tuesday July 30

9 AM                research:
                          Combinatorial Matrix in 202 Carver
                          Analysis in 298 Carver
                          Algebraic Graph  in 268 Carver
                          Compressive Sensing in 244 or 174 Carver
1:30 PM             sympoisum in 274 Carver                       
                          Combinatorial Matrix
                           refreshment break
                          Compressive Sensing


Wednesday July 31
9 AM                research:
                          Combinatorial Matrix in 202 Carver
                          Analysis in 298 Carver
                          Algebraic Graph  in 268 Carver
                          Compressive Sensing in 244 or 174 Carver
noon                  Union Drive Marketplace Mezzanine REU student lunch menu
                          REU student business meeting in UDM at 12:30


Thursday Aug 1
9 AM                research:
                          Combinatorial Matrix in 202 Carver
                          Analysis in 298 Carver
                          Algebraic Graph  in 268 Carver
                          Compressive Sensing in 400 or 174 Carver or Coover
5-5:30 PM         IINSPIRE-LSAMP poster presentation, S Ballroom of Memorial Union (incudes an REU poster)


Friday Aug 2
8 AM                clean apartments
1 PM                poster session in Howe Hall
3 PM                clean apartments
4:30 PM          depart Freddy for Farewell Dinner at Hickory Park
5:00 PM         
Farewell Dinner at Hickory Park


Saturday Aug 3
10:45 AM        depart for airport


Participants

Photo Directory

Undergraduate Students
     
Dallas Albritton            Emory University
Jeremy Burke               Vassar
Cora Brown                 Carleton College
Josh Carlson                 Iowa State University
Chris Cox                     Iowa State University
Nathanael Cox             Saint Olaf College
Jason Hu                      University of California, Berkeley
Katrina Jacobs              Pomona College
Jonathan Lai                 University of Texas at Austin
Kathryn Manternach    Central College
Greg Michel                 Carleton College
Chris Sheafe                 Iowa State University
Trevor Steil                   Michigan State University
Hannah Turner             Ball State University
Caroline VanBlargan    St. Mary's Collge of Maryland
Xiaosheng Zhang         Iowa State University

Graduate Students 
(all Iowa State University)
Julia Anderson-Lee
Chassidy Bozeman
Jiali Li
Brian Lois
Katy Nowak
Kevin Palmowski
Nathan Warnberg

Faculty   (Iowa State University unless otherwise noted)
Leslie Hogben                     
Justin Peters

Sung-Yell Song
Namrata Vaswani
Michael Young
Adam Berliner                 St. Olaf College (MN)
Travis Peters                   Culver-Stockon College (MO)





Photos

REU students: If you want a high resolutuon version of picture(s), e-mail Leslie the names of the file(s) you want.

Analysis Cs
            Analysis Group                                                                                             Compressed Sensing Group
CMT
          Combinatorial Matrix Group

T-shirt design

Front                                                                                           Back
frontback


Ames Events

The following information is taken from the internet; these activites are not sponsored by the REU.
See http://www.visitames.com/events/ for more information.
Free unless noted otherwise.

All the time
Furman Aquatic Center (water park), $5 admission, 1-8 PM weather permitting
Ames/ISU Ice Arena $5 admission, $2.75 skate rental

Thursdays
5:30 PM Main Street (downtown) music
7 PM Ames Municipal Band concert in Bandshell park

Saturdays
8:00 a.m. - 1:00 pm Ames Main Street Farmers' Market, 400 block Main Street

Des Moines Arts Festival June 28-30

Useful Links

LaTeX template    Figure for template     Beamer template

NSF REU sites

AMS Undergrad page

MAA Undergrad page

SACNAS National Conference 

Young Mathematicians Conference

Involve

SIAM Undergraduate Research Online (SIURO)

Rose-Hulman Undergraduate Math Journal


Matlab Information has links to Matlab guides


Math Project Descriptions 2013 (original description)

Algebraic Graph Theory Group  Dr. Sung-Yell Song, Katy Nowak
 
Existence and Nonexistence of (Directed) Strongly Regular Graphs

A strongly-regular graph with parameters (v, k, λ, μ) is defined as an undirected simple graph G with v vertices satisfying the property:
“The number of common neighbors of vertices x and y is k if x = y, λ if x and y are adjacent, and μ if x and y are non-adjacent vertices.”
Let A denote the adjacency matrix of G, and let I and J  denote the v x v identity matrix and all-ones matrix, respectively. Then G is a strongly-regular graph with parameters (v, k, λ, μ) if and only if
(i) JA = AJ = kJ and
(ii) A^2 = kI + λA + μ(J-I-A)

A loopless directed graph D with v vertices and adjacency matrix A is called directed strongly-regular graph with parameters (v, k, t, λ, μ)  if and only if A satisfies the following conditions:
(i) JA = AJ = kJ and
(ii) A^2 = tI + λA + μ(J-I-A)

We are interested in constructing (directed) strongly-regular Cayley graphs of various classical groups with suitable generator sets. We are also interested in settling some problems related to characterization and classification of these graphs and related objects. So, the sample problems that we are tempted to
explore look like:
• Find (directed) strongly-regular graphs that can be obtained as Cayley graphs of classical groups.
• How many strongly regular graphs with parameters (64, 28, 12, 12) are there?
• Is there a directed strongly regular graph with parameters (24, 10, 5, 3, 5)?
• Characterize all tactical configurations that yield the directed strongly regular graphs with parameters ((n2 − 1)(n3 − 1)/(n − 1)2, n(n + 1), n, n − 1, n).


Analysis Group   
Dr. Justin R. Peters, Jiali Li
We will be investigating two unrelated problems. Both problems will require some background in introductory analysis. One of the problems will have a large computational compenent. Students may choose to be involved in one or both projects.

1) Given a transcendental function f(x), let p_n(x) be its nth Taylor polynomial. We will investigate the behavoir of the zeroes of pn in the complex plane. We will be asking questions such as, do the zeroes of p_n lie in some region we can determine? Do the zeroes of p_n accumulate on some curve, possibly after renormalization? How are the zeroes of p_n related to those p_1? Is there some way in which the zeroes of p_n approach the zeroes of f? Is there a minimum distance between the zeroes of p_n, which is independent of n? In the case f(x) = exp(x) this has been investigated and has led to some nice results.

2) Which Cauchy sequences {a(n)}_n>1 with a(n) > 0, n=1,2,... have the property that the sequence {b(n)}_n>1 is also Cauchy, where
    b(1)=a(1), b(2)=a(2)^b(1), ..., b(n+1)=a(n+1)^b(n)?
We note that the case where a(1) = a(2) = a(3) = ... = a > 0 has been solved, and the solution is both surprising and interesting, though the arguments involved use nothing more than elementary calculus.


Combinatorial Matrix Theory Group 
Dr. Leslie Hogben, Dr. Adam Berliner, Dr. Travis Peters, Dr. Michael Young, Nathan Warnberg
Minimum rank, maximum nullity, and zero forcing on a graph

The graph of a real symmetric matrix A=[a_ij] has an edge between i and j if and only if a_ij is nonzero.  Finding the maximum multiplicity of eigenvalue 0 among symmetric matrices having a given graph is the same as finding the maximum nullity and is equivalent to finding the minimum rank among symmetric matrices having the given graph.  Initially a subset Z of the vertices of a graph G are colored blue and the remaining vertices are colored white.  The color change rule is that if a blue vertex v has exactly one white neighbor w, then change the color of w to blue.   The set Z is a zero forcing set if after applying the color change rule until no more changes are possible, all the vertices of G are blue.  The zero forcing number is the minimum size of a zero forcing set.  The zero forcing number is an upper bound for the maximum nullity of a graph, and arose independently in the study of control of quantum systems in physics, where it is called graph infection or propagation.   This project will investigate problems related to minimum rank, maximum nullity, and zero forcing number.

Students involved in this project will be part the ISU Combinatorial Matrix Theory Research Group; more information is available on that page. This group regularly publishes its results (see list of papers).

Linear algebra is a prerequisite for this project, graph theory is an advantage, and a strong theoretical mathematics background (usually including abstract algebra or real analysis) is expected.  The software we use is Sage and Mathematica, so knowing one or both of these in advance is helpful, but you can learn one or both of here.

Automated Recursive Projected CS (ReProCS) for Real-time Video Layering and Performance Guarantees  Dr. Namrata Vaswani, Dr. Leslie Hogben, Brian Lois, Kevin Palmowski, Chassidy Bozeman

A large class of video sequences are composed of at least two layers - the foreground, which is a sparse image that often consists of one or more moving objects, and the background, which is a dense image, that is either constant or changes gradually over time and the changes are usually global. Thus the background sequence is well modeled as lying in a low dimensional subspace that can slowly change with time; while the foreground is well modeled as a sparse "outlier" that changes in a correlated fashion over time (e.g., due to objects' motion). Video layering can thus be posed as a robust principal components' analysis (PCA) problem, with the difference that the "outlier" for PCA is also a signal-of-interest and needs to be recovered too. Real-time video layering then becomes a recursive robust PCA problem. We will develop algorithms using a novel approach called Recursive Projected Compressive Sensing (ReProCS) to solve this problem and we will try to bound their performance under practically motivated assumptions. In particular, we will study how to handle temporal correlations in the low-dimensional part (background).



Mathematics Department Homepage

Web page maintained by Leslie Hogben