Applied Mathematics

Summer Research Opportunities at UCLA

Overview

This is an opportunity to participate in an 8-10 week summer program in the Applied Mathematics group at UCLA. Students will have the opportunity to join an active research group with projects in image processing,  control theory,  fluid dynamics. and the interaction of mathematics and sociology. The successful applicant will work with faculty members from UCLA and Harvey Mudd College, postdoctoral fellows, graduate students and other undergraduates.

Students will start around June 18th and finish mid-August. Exact dates will be worked out with the faculty advisor. Students will generally be housed in the vicinity of UCLA.

Stipends and Support

Students will receive a stipend of roughly $4,000 for the summer and roughly $1,000 to cover housing and living expenses.

Application Process

Applicants should submit to Professor Bernoff (ajb @ hmc . edu) the following:
Applications received by April 6th will be given preference.

Project Descriptions

Tracking, Visibility and Mapping


UCLA has an ongoing project developing algorithms for tracking objects and  devloping control algorithms for autonomous vehicles. This year there will be at least two projects in this area.

  • Video tracking: A team of students will learn about real time video tracking algorithms. The goal will be to implement these methods on a platform with a real video camera and streaming data. The goal will be to track people walking across the field of view of the camera. 
  • Autonomous robots: a team of students will help to design, build, and implement a tracking algorithm using autonomous robots. The robots will be equipped with sensors to measure local environmental changes. The goal of the algorithm is to map out the environment using sensor data.
Last years autonomous vehicle groupTwo autonomous vehicles

Radio controlled and video-tracked autonomous vehicles on the test bed. For more information see:

http://www.math.ucla.edu/~bertozzi/lab/lab.html

Studying the Epidemiology of Crime


Projects on the modeling and analysis of automobile theft, residential break-ins, and gang activity are open for undergraduate research participation.  These projects will involve use of actual crime data from Los Angeles and Long Beach. The student will work on the mathematics of crime hotspot propagation. A better quantitative understanding of both of these processes will help with designing crime prevention strategies.


Auto Theft Hotspots

Auto Theft Hot Spots in Los Angeles from May 2003 to April 2004

Image Processing and Inpainting

UCLA has several ongoing projects studying image processing and inpainting of images (i.e. filling in missing information in partial images)
  • Hyperspectral Imaging:  This project involves remote sensing from satellites and airplanes. Objects on the ground are imaged using very fine scale information in the electromagnetic spectrum. The result is large volumes of data with spectral information about the materials on the ground. The project will design algorithms to identify the objects based on their spatial shape and high dimensional spectral data.
  • Image inpainting:  This project involves testing and design of algorithms for filling in missing information on images. Applications include text reconstruction, aerial imagery, and Hollywood special effects.
A damaged pictureThe restored version

An example of image restoration via inpainting. For more information see:

http://www.math.duke.edu/~bertozzi/inpaint/inpaint.html

Mudslides, Slurry Flows and Particle Tracking


Slurry flows are models of mudlslides; UCLA has on ongoing numerical, experimental and theoretical study of slurry flows. The experiment to produce behavior like the photos (below) obtained in Peko Hosoi's lab at MIT.  Glass beads of a uniform size are mixed into a less dense viscous fluid. The resulting slurry is poured into a reservoir at the top of an inclined plane. A controlled amount of the slurry is allowed to flow through a gate down the incline. At low inclination angles and concentrations, the particles tend to settle out of the mixture and stick to the surface of the incline, leaving a clear fluid to flow down the slope (left panel). At intermediate angles and concentrations, a well-mixed slurry flows down the slope (middle panel) producing the characteristic fingering pattern seen in visous films. At high inclination angles and particle concentrations (right panel) the beads tend to collect at the front of the film; their presence drastically changes the dynamics of the contact line, supressing fingering and producing a pronounced ridge. An
experimental apparatus  for studying these flows  is under development at UCLA; one project is to refine particle tracking software that allows one to determine the flow velocity in the fluid from experimental observation.


Experiments on slurry flows from the Hosoi lab at MIT

Experiments on slurry flows from the Prof. Anette "Peko" Hosoi's  lab at MIT For more information see:

http://www.math.ucla.edu/~bertozzi/lab/lab.html



Andrew Bernoff * Department of Mathematics * Harvey Mudd College
Page Maintained by Andrew Bernoff
Last modified:  March 6th,  2007