| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | September 20, 2011 |
| Latest Amendment Date: | September 20, 2011 |
| Award Number: | 1122106 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Mary Ann Horn
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | October 1, 2011 |
| End Date: | September 30, 2015 (Estimated) |
| Total Intended Award Amount: | $130,422.00 |
| Total Awarded Amount to Date: | $130,422.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
4333 BROOKLYN AVE NE SEATTLE WA US 98195-1016 (206)543-4043 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
4333 BROOKLYN AVE NE SEATTLE WA US 98195-1016 |
| 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): | MATHEMATICAL BIOLOGY |
| 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
New recording methods allow researchers to probe the structure of neural activity with unprecedented scope and detail. As a result there is an explosion of interest in understanding the patterns of activity that emerge in entire neuronal populations and relating these patterns to the function of the nervous system. However, the overwhelming range of different sensory inputs that these populations receive -- and the vast range of different responses that these inputs evoke -- make it impossible to achieve this goal based on empirical observations alone. This challenge is compounded due to the nonlinearity of neuronal network dynamics, which makes it difficult to predict patterns of activity by extrapolation from observations of simpler systems. Predictive mathematical modeling and a deeper understanding of the dynamics of neuronal circuits is therefore required. With previous NSF support, the investigators developed numerical and analytic tools at the interface of statistics, stochastic analysis and nonlinear dynamics, to understand the genesis and impact of correlations in simple, but fundamental microcircuits. They build on these results by extending the underlying mathematical theory to more complex and realistic networks. Using this approach, the team of researchers examines how collective activity is controlled by network architecture, cell dynamics, and stimulus drive in a set of neural networks that typify structures across the nervous system.
Answering these questions will open the door to contemporary biological applications and will meet key theoretical challenges posed by recent technological developments in experimental neuroscience. The key innovation lies in the understanding the collective dynamics of large neural networks that cannot be decomposed into their isolated parts. Through continued interactions with a broad set of experimental collaborators, these ideas are introduced and tested by a broad community of neuroscientists. In the longer term, results on coding in the presence of collective network dynamics will impact the design of neural prosthetics, which code sensory signals via cortical, retinal, and thalamic implants.
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.
The brain presents an extraordinary challenge for the computational and mathematical sciences: a complete model would require ~10^11 highly nonlinear neurons, interacting nonlinearly and stochastically through rapid voltage fluctuations (called “spikes”) on a complex network. This network is of an even more astonishing size, with orders of magnitude more connections than neurons themselves.
How can we cut this description down to a manageable size, in which the network features that drive the underlying network function can be itemized, measured, and compared among different brains and brain areas? Achieving this goal requires linking tractable features of network structure (the architecture of connectivity) with the network dynamics (the evolution of network elements over time).
Here, we advanced this goal of achieving a tractable link between the structure and dynamics of spiking networks. Envision a large, hugely complicated web of interactions. What are the building blocks of this network? The number of individual connections is the first ingredient: knowing how many of these exist is the most basic characterization of how connected a network is. But from here, there is an explosion of different ways to describe how this given number of links is assembled to form the network as a whole. In a series of papers, we show how this problem can be tamed by counting small network substructures, or motifs, and using mathematical formulas for coupled stochastic processes to extrapolate from these motif counts to predict overall levels of coherent dynamics in the network. Thus, there is a direct and concrete link between a small and tractable list of network characteristics and the overall strength and timing with which neurons’ spikes are coordinated on the whole-network scale. We believe this result will open doors to linking structure and function in real neural circuits, a procedure we demonstrate using recent connectivity data from mouse thalamo-cortical systems.
Achieving the aim of linking network structure and dynamics demands a synergy among several scientific fields and disciplines, from systems engineering to statistics to applied mathematics. It also demands collaboration among multiple institutions, in our case three universities located across the country. As such it is an ideal topic for training graduate and undergraduate students to attack complex modern problems, and this grant supported the work of several such trainees. Trainees as well as the PI gave presentations nationally and locally and published papers that share our findings in journals, online repositories, and science newsletters, and gave talks to share this work with practicing scientists, graduate students, and undergraduates just starting to explore the world of scientific research.
Last Modified: 12/30/2015
Modified by: Eric T Shea-Brown
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