**Model of an Intestinal Muscle Cell**

Contact: Jennifer Young, jjyoung@rice.edu, x2049

The contraction and relaxation of muscle cells contributes to a myriad of bodily functions such as circulation, respiration, motion and digestion to name a few. The purpose of the smooth muscle cells found in the intestine is to propel food along the intestinal tract during digestion. Individual muscle cells contribute to this propulsion by utilizing myosin fibers to slide and pull actin filaments over one another to contract the cell. This contraction is both a mechanical and biochemical process. When the intestine is under a great deal of stress (due to some trauma or disease) the ability of the muscle cells to contract can decrease. A project for this summer would be to study muscle contraction dynamics from both the mechanical and biochemical perspective and to create a single cell model of muscle contraction under normal conditions. Phase two of the project would be to experiment with the model to see how it behaves when the cell is under an imposed external stress.

**Properties of Viscoelastic Materials**

Contact: Sean Hardesty, hardesty@caam.rice.edu, x4805

The project is to measure damping properties of viscoelastic materials. The apparatus is already built, but is in need of some
basic electronics (a charge amplifier circuit). It excites one end of
a cylindrical sample with a piezoelectric transducer, and measures the
response at the other end. The results would then be processed using a
Finite Element Method (FEM) simulation, and an optimization routine to
produce actual damping constants. This project thus serves to expose
the student to a wide variety of problems in applied mathematics
within an experimental context.

**Biological testing of mathematical intuition: a study of complexity**

Contact: Yuri Dabaghian, dabaghian@rice.edu, x6073

In early 2009, mathematician V.I. Arnold (one the creators of the
fundamental KAM theorem of classical mechanics, one of the founders of
the theory of bifurcations, the author of the famous "Mathematical
methods of Classical mechanics" book, etc.) wrote a short paper in
which he discussed the complexity of finite binary sequences. The
paper starts with a simple question: "Sequence 010101 is simpler than
011010. How to capture this mathematically?" In it, Arnold proposes a
certain scheme for ordering finite binary sequences according to their
complexity.

Is the proposed classification of the binary sequences fundamentally

correct? Does it provide an objective measure of complexity? Is there

a way to verify his result empirically?

One can approach this problem biologically. From a biological point of view, a "simple" sequence is easier to learn, for an animal or a human, than a "complex" sequence. If a mouse or a rat or a human would have to learn different binary sequences, would they find the ones that are more complex in Arnold's sense harder to learn than the ones that are less complex? The goal of this study is to probe some experimental biological methods in the context of the emerging complexity theory.

Prerequisites:

1) Interest in contriving physical and computational instruments for

biological experiments (involves building an experimental setup)

2) Previous exposure to MATLAB

3) Basic analytical skills

**Oscillating between sleep and consciousness:
analysis of the EEG data**

Contact: Yuri Dabaghian, dabaghian@rice.edu, x6073

One of the major sources of our knowledge about the brain functions
comes from the analysis of the EEG patterns. The information about the
state of the brain obtained from the EEGs is surprisingly intricate
and specific, and it can tell us a lot about functioning of the brain
as a whole (e.g. sleep vs. conscious state) and about the functioning
of its individual parts.

The information is contained in the complex dynamics of the EEG signal, so extracting this information requires creative application of the discrete Fourier analysis, wavelet analysis, time series analysis and so on. This scope of questions will constitute the project for this summer: searching for new patterns in the EEG data from mice (transgenic and wild type) and humans (sleep and awake states). One of the research goals here is to develop a computational model of the human EEG sleep activity.

Prerequisites:

1) Creativity and interest in neurobiology

2) Familiarity with MATLAB

** Computational Model for Spatial Memory**

Contact: Katie Ward, kw5@rice.edu

This project involves refining an existing computational model to study spatial memory. Activity of networks of specialized neurons in the brain form internal representations, or maps, of the external environment. We are developing a model with a parallel implementation to study the stability of these maps due to small changes in the environment. One key mechanism in the model is synaptic plasticity, or changes in the strength of connections among neurons. The synaptic plasticity model currently implemented has hard lower and upper bounds, which is not biologically realistic.

The project is to implement a more biologically realistic model of synaptic plasticity that requires no hard bounds. Then, run simulations to examine the final structure of the connections among neurons and the stability of the neuronal map. Compare the results to those obtained using the current synaptic plasticity model.

**Hedge Funds**

Faculty lead: Katherine Ensor (ensor@rice.edu)

Graduate Student: Jeffrey Berglund (Jeffrey.D.Berglund@rice.edu)

Hedge funds operate in a general independent and non-transparent manner. The VIGRE group will seek to uncover patterns in hedge fund returns, identifying different market exposures and the geographical relationships between hedge funds. The ultimate goal is to quantify the economic value of transparency or opacity. This pfug will begin May 16 and run through July 15th.

**Visualising uncertainty**

Faculty lead: Hadley Wickham (hadley@rice.edu)

When you look at a plot, how do you calibrate for uncertainty? How do
you know if a signal is real? How do you know how when you've made
your histogram/spinogram bins too small? What is the variability
associated with the properties that you look at?

Objective: create plots that have the ability to display uncertainty baked in. We'll focus on area and density plots and resampling to start, and then work out way up to smooth uncertainty tours.

**Documenting data**

Faculty lead: Hadley Wickham (hadley@rice.edu)

Most datasets have associated metadata: variable names, possible
values, data sources etc. There is currently no standard way of
storing this data, and no cross-software standard.

Objective: build off the qnch file format, incorporating important additional features and provide a reference implementation in R.

**Develop R packages for Statistical Learning Applications**

Faculty lead: Genevera Allen (gallen@rice.edu)

Students will learn how to produce statistical software from algorithms by writing R packages for existing R, Matlab and Python code. The algorithms follow from the general area of statistical learning. Participating students will learn critical components of the research and how to efficiently publicize research. Programming, linear algebra, base statistical knowledge, and the ability to write and communicate effectively is required.

**Problems in minimizing functionals**

Contact: Leobardo Rosales (rosales.leobardo@gmail.com)

Our goal is to study several minimization problems, by considering related functionals. We work by analogy from the Dirichlet problem and the Plateau problem: the former asks to find the function, given boundary data on a domain, which minimizes the Dirichlet energy, or the integral of the square of the gradient; the latter asks to find the function, again given boundary data on a domain, with graph minimizing surface area. Using methods in the study of these problems, we will work on similar minimization problems with given constraints. This shall necessitate an introduction to the harmonic and minimal surface equation.

Dates: May 24-July 15