The REU program in Computational and Applied Math (including the NSF funded UCLA REU site in Mathematical Modeling) at UCLA provides funded 8 week summer research opportunities for students to work on frontier level problems in Applied Math with UCLA faculty. Applications for the 2019 Computational and Applied Math REU are now open. Apply through at this URL.

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In Summer of 2019 we plan to offer a set of projects that will include the following areas. The list will be continuously updated as new projects are added.

Blood flow in microvascular networks

Microvascular networks; made up of the narrowest blood vessels, deliver red blood cells continuously throughout the human body. We will use experimental data (from zebrafish, mice brains and retinal imaging) to model blood flow, and to determine how vessels are organized to solve difficult mathematical optimization problems, such as being resistant to damage, and ensuring that every part of a tissue receives an even amount of oxygen.

Organization of fungal cells

Fungal cells are organized very differently from animal (or plant) cells. Rather than having a single nucleus sitting in a cell, and directing the cell’s behaviors, a fungal cell may contain tens or even thousands of nuclei, all sharing a single cytoplasm. How do these nuclei work together to control the cell’s behavior? In this project, we will follow two lines of inquiry — 1. developing our own image analysis tools and running experiments, to understand cell cycle: the cues that nuclei use when making the decision to divide. 2. We will study data produced by our collaborators at UNC Chapel Hill and UC Berkeley, mapping out the nuclei, and the proteins that produce in fungi that are grown in microfluidic devices that deliver different environmental cues to different parts of the fungus. In both projects the goal is to understand how different nuclei that receive different cues from the fungus’ environment pool their information to make decisions together.

Fluid mechanics

(Provisional topic). We will develop a tool for predicting how small particles move around within a class of lab on a chip devices called inertial microfluidic devices. Although these devices are used in industry and university labs for hundreds of applications, there is no theory that is capable of predicting how particles such as cells move within devices. Our goal is to create a fast computational tool based on a successful theoretical model of particle motion that has been known about for 30 years. We will figure out how to computationally implement the method of solution, using finite element methods. Our goal is to create a tool that can be easily used by any experimentalist, and that will finally allow for theoretical design of these devices. This project is particularly suitable for students with interests either in physics or in Partial Differential Equations.

Machine learning for Los Angeles homicide narratives

What makes two homicides different? Is it something about the victim, the suspect, the place where it happened, motive?  These features of homicides often appear in text narratives describing the event.  The purpose of this project is to understand this high dimensional space and identify patterns.