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Potential research projects


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The biomechanics of Aplysia mouth movements How do neural control and biomechanics interact during control? To address this question, students will analyze the biomechanics and neural control of a well-studied system, the feeding apparatus of Aplysia, and develop mathematical and computational models of the structure, as well as of its neural control.
Comparative analysis of network motifs in systems biology Molecular systems biology is an emerging discipline aimed at understanding cellular function at the systems level. A prerequisite to this systems level understanding will be to understand the relationships between proteins, DNA and RNA. These relationships can be identified in terms of physical interactions that underlie various cellular processes (e.g., metabolism, signaling, regulation of molecular activity), as well as indirect functional association, such as genetic interactions or synthetic lethality. These relationships are often abstracted using network models, which provide high level descriptions of the organization of the cell. Graph theoretical analyses of molecular networks show that...
Analysis of topographic maps in the cortex

The occipital (visual) cortex of mammals contains topographic maps of the visual field, such that a stimulus in the shape of an X will produce neural activity which, when viewed on a flattened representation of the cortex, also looks like an X. Topographic maps form because it is less metabolically costly for highly interconnected neurons to lie next to each other on the cortical surface. Topographic maps therefore reveal important information about the computations carried out in different parts of the brain.

It has been hypothesized that many other areas, outside occipital cortex, also contain topographic maps. However, research has stalled because there are presently no quantitative tools available for assessing topographic organization....

Mathematics of brain activity mapping by MEG This project is an introduction to the mathematics of magnetoencephalography (MEG). Some of the standard models and inversion algorithms are reviewed, and students get a hands-on experience on simulating and interpreting MEG data. Real MEG data will be provided by the MEG laboratory of the Epilepsy Center of the Cleveland Clinic, where methods are developed and tested for localizing the focus of the onset of epileptic seizures....
Single cell psychophysics: gradient sensing in neutrophils P. Thomas (Mathematics, Biology & Cognitive Science) and H. Baskaran (Chemical Engineering & Biomedical Engineering) have formed a new collaboration investigate quantitatively the dynamics of information processing and decision making in biochemical signaling networks controlling eukaryotic chemotaxis. The proposed work will combine experimental, computational and theoretical approaches to studying the chemotactic response to precise spatially and temporally controlled chemical stimuli. Specified spatiotemporal patterns of chemical signals will be prepared by a microfabricated fluidic control device. Single cell responses will be measured through cell motility assays and fluorescence measurements of intracellular signaling protein spatial distributions...
Cognitive networks and memory Despite decades of research into the nature of memory, many basic questions about the mechanisms of learning, information storage and retrieval in the human brain remain unanswered. In the proposed year-long RIBMS project, a team of two undergraduate students will work with an interdisciplinary team at the Memory and Cognition Center at Case Western Reserve University to study fundamental mechanisms of memory based on analysis of controlled word association and recall tasks. Specifically, the students will develop computational models and analyze experimental data to explore the concept of semantic space from both mathematical and biological perspectives....