Integrating simplicial complex structures into statistical models for brain health
About This Grant
Project Abstract This proposal aims to develop statistical models that associate brain connectivity with human health outcomes. It uses a mathematical framework that quantifies not only pairwise co-activation of brain regions (nodes), but also encodes three-way and higher-order interactions, and their densities, using the mathematical framework of simplicial complexes (SCx). The methods developed here will enable the statistical analysis of cognitive function in large neuroimaging studies by modeling connectivity patterns in ways that are more extensive than those currently used. These methods will provide new insights into the complexities of brain-related health conditions because they quantify neuro-activation patterns in new and interpretable ways. Aim 1, extends the investigators’ previous scalar-on-matrix regression to include generalized linear and mixed models, then moves beyond adjacency matrix predictors to upper-adjacency edge (UAE) matrices, defined via three-way co- activation. These higher-order analogues of connectivity matrices involve edge relationships and have a low- rank structure not captured by standard approaches. They also lead to a new concept of edge communities (1- simplexes) that share a triangle (2-simplexes), or maximal edge communities (MEC). In Aim 2, estimated health-associated connectivity patterns in penalized regression models also incorporate higher-order simplicial structures—as predictors and regularizers. These model path structure by viewing node-pairs as boundaries of paths, and modeling their effective resistance (ER), which quantifies network-wide robustness of communication among nodes. Aim 2 leverages the UAE matrix to define a “lifted graph”, and the corresponding lifted-graph Laplacian is used for penalized regression on edges. These models encompass kernel-based methods that involve subject similarities based on simplicial structures. Aim 3 considers matrix- on-scalar regression models to estimate community-level associations between scalar predictors and adjacency-matrix responses. Rather than regressing based on prescribed mesoscale structure associations this form of model is extended to higher-order adjacencies structures, including MECs and other SCx structures. Aim 4 explores the recent concept of persistent Laplacians. This new operator relates the properties of two simplicial complexes when one is embedded in another. This allows analysis of a population of networks/simplices, which do not necessarily share all edges or triangles, by relating them to a common “core” SCx. Participant-wise discrepancies from this core, using the SCx algebra framework, leads to a new type of analysis. Successful completion of the proposed research will provide urgently needed extensions to current analytical methods with new models and software tools aimed at understanding common neurobiological disorders.
Grant Summary
Integrating simplicial complex structures into statistical models for brain health is a NIMH - National Institute of Mental Health grant providing up to $832K for university, nonprofit, healthcare org. Applications are due 2031-02-28 (open). Check eligibility and apply with FindGrants.
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Up to $832K
2031-02-28
- 1Confirm your organization is eligible for Integrating simplicial complex structures into statistical models for brain health from NIMH - National Institute of Mental Health, checking organization type, location, and any population or project requirements.
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Integrating simplicial complex structures into statistical models for brain health: Frequently Asked Questions
Who is eligible for the Integrating simplicial complex structures into statistical models for brain health?
Integrating simplicial complex structures into statistical models for brain health is offered by NIMH - National Institute of Mental Health and is generally open to university, nonprofit, healthcare org. It is open to organizations nationwide unless the funder specifies otherwise. Review the specific eligibility terms before applying, since funders set their own requirements around organization type, location, and the population or project being served.
How much funding does the Integrating simplicial complex structures into statistical models for brain health provide?
Integrating simplicial complex structures into statistical models for brain health provides up to $832K per award from NIMH - National Institute of Mental Health. Actual award sizes depend on the scope of your project, available program funds, and the number of applicants, so build a budget that reflects realistic, allowable costs rather than the maximum figure.
When is the Integrating simplicial complex structures into statistical models for brain health deadline?
Applications for Integrating simplicial complex structures into statistical models for brain health are due 2031-02-28 (open). Because deadlines can change, verify the date with the funder, NIMH - National Institute of Mental Health, and give yourself enough time to prepare a complete, competitive application before the close date.
How do you apply for the Integrating simplicial complex structures into statistical models for brain health?
To apply for Integrating simplicial complex structures into statistical models for brain health, confirm your eligibility, gather the required documents, and prepare a narrative and budget that address the funder's priorities. FindGrants guides you step by step and can draft each section, then exports a submission-ready application pack for this grant from NIMH - National Institute of Mental Health.