| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | September 8, 2013 |
| Latest Amendment Date: | September 8, 2013 |
| Award Number: | 1311755 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Junping Wang
jwang@nsf.gov (703)292-4488 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 15, 2013 |
| End Date: | August 31, 2017 (Estimated) |
| Total Intended Award Amount: | $184,937.00 |
| Total Awarded Amount to Date: | $184,937.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
4300 MARTIN LUTHER KING BLVD HOUSTON TX US 77204-3067 (713)743-5773 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
651 Phillip G Hoffman Houston TX US 77204-3008 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): |
Cross-BIO Activities, MATHEMATICAL BIOLOGY, MSPA-INTERDISCIPLINARY, Modulation |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
A major challenge in neuroscience is to understand how the brain reliably completes cognitive tasks, despite a great deal of intrinsic variability. Cognitive tasks often require coordinated spatiotemporal activity, which experimentalists can measure using multiple electrodes, voltage sensitive dye, and optical techniques. The main goal of this research project is to develop mathematical tools to study how spatially structured networks in the brain produce reliable activity in the face of noise. Specifically, we will be interested in how the spatial architecture of synaptic connections interacts with noise on multiple scales to influence network activity. Thus, linking our theory with experimental data will require the development of new techniques in stochastic and nonlinear analysis, multiscale methods, and symmetric bifurcation theory. Neuronal network models that incorporate space often assume synaptic connectivity depends only on the distance between neurons. Such dynamical systems tend to be marginally stable, so solutions diffuse in the presence of noise. More realistic models of neuronal connectivity do not produce such degeneracies. We propose to examine how spatial heterogeneity can improve or limit the robustness of neuronal networks. We will analyze models that encode neural activity linked to working memory, decision making, and place localization. Our work will contribute mathematical methods to other current research areas in math biology concerned with analyzing the effect of noise on spatially extended systems.
Everyday, humans make decisions, use memory, and navigate their environment. Spatially structured activity in the brain underlies all these processes. Spatially localized "bumps" of activity are thought to encode short term memories of spatial position. Propagating waves of activity represent visual inputs and the movement of limbs. These activity patterns must be generated in networks of the brain that are fraught with noise. Despite the noisiness of the brain, we execute cognitive tasks faithfully. How does this happen? We will develop mathematical techniques to address this major question. Mainly, we will explore how neuronal networks can be structured to support robust spatiotemporal dynamics. Insight into the robustness of cognitive processes can be used to develop therapeutic solutions for various mental disorders. Alzheimer's, dementia, and Parkinson's present more commonly as human lifespans grow. Treatments are not possible without well-developed theory. Our analysis of spatiotemporal neural coding will also help understanding of how spatial arrays of multielectrodes should best be designed for applications like neural prosthetics.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
Working memory is central to cognition, but has a number of limitations. Speaking, reading, driving, and competitive sports are all examples of tasks that require working memory, and our performance is improved by a more precise working memory system. For example, a football player will be able to evade defenders much better if they can hold in mind their relative locations on the field, as well as a movement plan. Therefore, it is of interest to understand the mechanisms the brain uses to make working memory robust to noise and perturbation. The outcomes of this project focus on key features of neuronal network architecture that can help to dampen the effects of fluctuations during the storage period of working memory. We have demonstrated that interactions between multiple layers of a network reduce noise. Multilayer networks also allow for for sensory feedback, and the memory-guidance of spatial navigation. When performing searches of their environment, organisms integrate information from memory and the sensory system when determining where to move next to find food or evade predators. We have also demonstrated that noise can serve to correlate activity across multiple layers of a network, which can be helpful in coordinating activity such as movement initiations. Our results have also touched on the effects of delay as a form of memory. In a multilayer network with delayed coupling between layers, a stored signal representing a remembered location is further stabilized for longer and longer delays in coupling. This is because delays allow the system to look back at previous information that is less corrupted by noise. Most recently, our results on working memory have explored the origins of cognitive bias, such as interference. There are a wide variety of cognitive biases humans tend to exhibit, and it seems likely that many of these have some evolutionary advantage that is not featured in the artificiality of a laborator environment. For instance, interference leads individuals to exhibit responses in working memory tasks that are biased in the direction of responses on the previous trial. This makes sense in an environment where trial stimuli are correlated, but is a nuisance to performance when they are not. We have shown that short term plasticity, which temporarily reshapes the structure of the network encoding the memory, can lead to this cognitive bias. Looking forward, we think that more experimental studies that are able to identify the detailed dynamic network connectivity of areas involved in cognitive tasks will help to elucidate the neural mechanisms responsible for accuracies and errors. In doing so, we think the field of neuroscience can contribute to prosthetic and pharmacological treatments of cognitive disorders, as well as contribute to the growing industry of machine intelligence. The brain is a remarkably efficient approximation machine, and lessons from its biology will help developers come up with better solutions for energy efficent artificial intelligence.
Last Modified: 11/03/2017
Modified by: Zachary P Kilpatrick
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