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

- Symposium Schedule: Overview (lists all sesssions) Detailed (lists all student talks, nothing else)

- Schedule this week
- Participants
- Useful links

- Photos
- Projects

Blue = whole group. Red = food.

As long as you get your work done and attend scheduled activities relevant to your group, you can choose when/where to work unless instructed otherwise by your faculty mentor.

Faculty mentors have authority to excuse students from any scheduled activity to avoid disruption of research, but someone should notify the Director, Dr. Minnie Catral, if a student will miss a whole group activity during the workweek.

Weekend and evening activities are optional.

Sunday July 18

Monday July 19

9 AM research

noon Union Drive Marketplace REU student lunch menu

Tuesday July 20

9 AM research

3:30 PM cake, chips and conversation 400 Carver

4:00 PM SACNAS discussion, 250 Carver

Wednesday July 21

9 AM research

noon Union Drive Marketplace REU student lunch menu

Thursday July 22

9 AM research

3:30 PM cookies and conversation, 3105 Snedecor

Friday July 23

9 AM research

noon Union Drive Marketplace REU student lunch menu

Saturday July 24

Sunday July 25

Monday July 26

9 AM research

noon Union Drive Marketplace REU student lunch menu

8 PM Meet outside buildings 51 & 52 Freddy for rides to Jason's 3214 Nixon Ave. for S'Mores

Simple directions from Fredrickson are to take Stange north, the first stoplight is 24th. Right (east) on 24th, about one block past first stop sign, until Hoover. Left (north) on Hoover, about two blocks past first stop sign, until Wheeler. Right (east) on Wheeler, the first left is Nixon. Left (north) on Nixon, I'm the third house on the right. It is dark brown/green with bright red doors.

Tuesday July 27

9 AM research

3:00 PM t-shirt pick up

3:30 PM photo in REU t-shirts

3:35 PM corn and conversation, 400 Carver

Wednesday July 28

10 AM - 9 PM Symposium Schedule Overview Detailed Schedule

Thursday July 29

8 AM - 1 PM Symposium Schedule Overview Detailed Schedule

1 - 5 PM Pack and clean

5:30 PM Farewell dinner King Buffet

Marie Archer Columbia College

Millicent Grant Spelman College

Rana Haber Cal Poly Pomona

Ashley Johnson Florida A & M

Xavier Martinez-Rivera UPR-Mayaguez

Jared Mills Morehouse College

Antonio Ochoa Cal Poly Pomona

Timothy Pluta NC State

Matthew Temba Morehouse College

Travell Williams Morehouse College

Brian Wu Bowdoin College

Graduate Students

Josh Bernhard ISU (Stat)

Brenna Curley ISU (Stat)

Rafael Del Valle ISU (Math)

Craig Erickson ISU (Math)

Katrina Harden-Williams ISU (Stat)

Takisha Harrison ISU (Stat)

Maria Neco UPR-RP

Reza Rastegar ISU (Math)

Jason Smith ISU (Math)

Hector Torres-Aponte UPR-RP

Chad Vidden ISU (Math)

Faculty

Minerva Catral ISU (Math)

Leslie Hogben ISU (Math)

Mark Kaiser ISU (Stat)

Peng Liu ISU (Stat)

Fred Lorenz ISU (Stat)

Dan Nettleton ISU (Stat)

Dan Nordman ISU (Stat)

Alex Roitershtein ISU (Math)

Zhengyuan Zhu ISU (Stat)

Independence Day Picnic

Leslie's 2009 Alliance grant slides

LaTeX template Figure for template Beamer template

NSF REU sites

AMS Undergrad page

Young
Mathematicians Conference

SIAM Undergraduate Research Online (SIURO)

Rose-Hulman
Undergraduate Math Journal

Journal of Young Investigators

Matlab
Information has links to Matlab guides

The project is in the intersection of two fascinating mathematical areas, probability theory and game theory. No prior knowledge of any of them is required. A decent proficiency with the Calculus and any basic course in probability taken in the past would be an advantage. The project might (or might not) involve simulations in MATLAB.

Eventually Nonegative Matrices and Sign Patterns

The square real matrix A is eventually nonnegative if there is a positive integer k 0 such that for every k > k_0, A^k > 0. A sign pattern is a matrix whose entries are elements of {+, -,0}; it describes the set of real matrices whose entries have the signs in the pattern. This project investigated sign patterns that allow eventually positive or eventual;ly exponentially positve matrices.

Initially a subset Z of the vertices of a graph G are colored black and the remaining vertices are colored white. The color change rule is that if a black vertex v has exactly one white neighbor w, then change the color of w to black. 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 black. The zero forcing number is the minimum size of a zero forcing set. Zero forcing arose in the study of determining the minimum rank/maximum nullity among real symmetric matrices having nonzero off-diagonal positions described by the edges of a given graph (the zero forcing number is an upper bound for maximum nullitty. This project was proposed by students and investigated zero forcing numbers of cut complexes of hypercubes.

ISU Stat REU

Each statistics participant has an individual project that s/he investigates under the supervision of faculty and graduate student mentors. Possible projects are listed below.

ISU Stat Project Descriptions 2010

Spatial Sampling Design with Ancillary Information Dr. Zhengyuan Zhu

In many applications one need to observe a random process over some
space at a set of sample locations, and make inference about some
functions of the process. Examples include surveys of soil materials,

air pollution monitoring, ecological survey, Geological Survey for Oil
and Gas Resources, etc. Since the number of locations one can sample is
almost always constrained by available resources, it is of great

importance to find efficient spatial sampling design which can lead to
accurate and unbiased inference. In practice, ancillary information is
often available which is related to the variable of interests. For

example, in digital soil mapping, the soil properties of interests are
related to some ancillary soil and environmental variables which can be
obtained cheaply over large areas through remote sensing. We will

study how to use ancillary information to improve the efficiency of
spatial sampling, and develop innovative design approaches which can be
implemented in practice. A digital soil mapping dataset will be used

as a test bed to compare different approaches. This project will involve statistics and computation.

Development of Statistical and Computational Methods for Analysis of RNAseq Data Dr. Peng Liu

The next-generation sequencing technology allows digital
measurements of gene expressions. The resulting RNAseq data provide
much richer data about gene expressions than microarray technologies
and calls for novel statistical analysis. This summer research project
involves the development of statistical and computational methods for
assessing RNAseq data. The project will involve descriptive and
inferential statistics about RNAseq data and some computational
activity.

Analysis of Data from the Family Transition Project Dr. Fred Lorenz

During the past two decades, the Family Transition Project
has been following a panel of over 500 rural Iowa families. The
objectives are to study family resilience to economic and family
stress and to trace

continuity in behaviors between one generation and the next. Lorenz's
specific interests are in modeling change over time and in modeling the
relationship between observer ratings and questionnaire reports of
behavior.

Statistical Analysis of Microarray Data on Gene Expression Dr. Dan Nettleton

Microarray technologies allow researchers to simultaneously measure
the expression of thousands of genes in multiple biological
samples. By examining how genes change expression across
different types of samples or

samples collected under different conditions, researchers gain clues
about how genes act together to carry out important biological
processes. Genes can be organized into groups based on past
research. Genes in a group may share a function or act together
in the same biological process. Researchers often

wish to learn whether known groups of genes change their behavior in
response to new conditions. This summer research project involves
the development of statistical and computational methods for assessing
evidence of group expression change in response to stimuli. The
project will involve mathematics, statistics,

and computation. Although biological data will be used, no special background in biology is required.

The Effect of Nonconstant Variance on Spatial Prediction Dr. Mark Kaiser

Spatial prediction of phenomena such as weather variables, groundwater
contamination, or mineral deposits (and many more) is often approached
through the use of what statisticians call {\it geostatistical}
methods. The standard form of predictors developed in a
geostatistical analysis make a number of simplifying assumptions about
the process being observed. In particular, it is often assumed
that the process has a constant mean across all locations, a constant
variance across all locations, and a covariance that depends only on
distance (rather than, for example, direction). Of these, a good
deal of work has been conducted on what happens when the assumptions of
constant mean and covariance depending only on distance are
violated. Much less is known about the effects of nonconstant
variance. The goal of this project, most likely to be approached
through Monte Carlo simulation, is to investigate the behavior of the
standard methods when the true process being modeled has constant mean
and covariance depending only on distance, but violates the assumption
of constant variance. To undertake this project, the student will
need to become familiar with basic geostatistical tools such as
variograms and kriging predictors, and will be required to develop the
skills needed to conduct a simulation study using the language R.

Limnology is the study of lakes, focusing largely on the variables that govern the water quality in lakes, both natural and manmade (called reservoirs). Limnologists often sample a lake several (3 or 4) times during the summer and compute a ``seasonal mean'' as the average, and that value may be judged against water quality standards or regulations to determine the status of a lake.

There are questions about what a seasonal mean actually represents relative to what happens in a lake over the course of a year. This project will use data from a study in which 3 lakes were sampled every day from mid-May to mid-September. The data form a time series, as illustrated for one of the lakes in Figure 1 for the variables of phosphorus and chlorophyll (two of the primary indicators of water quality). Even visual examination of these plots suggests that the values of these variables over time should not be considered independent. In addition, what is the true mean, that limnologists attempt to estimate by sampling 3 or 4 particular days?

In this projet we will apply a statistical technique called subsampling to estimate the mean over the entire data record and provide a measure of uncertainty (standard error) for that estimate. The basic idea is to use portions of the data record (subsamples) that are short enough to give sufficient replication (number of subsamples) but long enough to preserve the dependence structure of the entire data record within each subsample. We can then examine a number of sampling strategies that might be used by limnologists through a Monte Carlo study. This project will introduce students to statistical dependence in time series, the techniques of subsampling, and hopefully an assessment of practical value for scientists and managers.

Mathematics
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Hogben