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State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

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Modeling the Functional Network for Spatial Navigation in the Human Brain

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Published on: October 13, 2023

Geo-Mamba: Geometry-informed state-space learning of functional brain organization.

Yuwei Cao¹, Tingting Dan², Yang Yang¹

¹School of Information Science and Technology, Yunnan Normal University, Kunming, 650500, Yunnan, China.

Medical Image Analysis

|April 17, 2026

Summary

This summary is machine-generated.

Geo-Mamba introduces a novel geometric approach for analyzing brain connectivity data from functional magnetic resonance imaging (fMRI) and electroencephalography (EEG). This method enhances accuracy and robustness in neuroimaging analysis, paving the way for clinical applications.

Keywords:

Brain functional connectivity Geometric deep learning Riemannian geometry State space model

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Last Updated: Apr 19, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

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Published on: October 13, 2023

Functional Mapping with Simultaneous MEG and EEG

Functional Mapping with Simultaneous MEG and EEG

Published on: June 14, 2010

Concurrent EEG and Functional MRI Recording and Integration Analysis for Dynamic Cortical Activity Imaging

Concurrent EEG and Functional MRI Recording and Integration Analysis for Dynamic Cortical Activity Imaging

Published on: June 30, 2018

Area of Science:

Neuroimaging
Machine Learning
Computational Neuroscience

Background:

Functional connectivity (FC) from fMRI is often represented on non-Euclidean spaces, such as Riemannian manifolds of symmetric positive-definite (SPD) matrices.
Conventional Euclidean sequence models are ill-suited for these complex, non-Euclidean data structures, limiting the analysis of brain networks.

Purpose of the Study:

To introduce Geo-Mamba, a novel geometric variant of the Mamba model designed for neuroimaging data residing on Riemannian manifolds.
To develop a dual-path selective state-space model that effectively handles high-dimensional, non-Euclidean neuroimaging data like fMRI and EEG.

Main Methods:

Geo-Mamba utilizes a dual-path design: a stacked path for hierarchical feature aggregation and a distillation path for geometry-aware dimensionality reduction.
A GeoMix operator fuses complementary outputs, creating compact and discriminative SPD representations essential for manifold-based analysis.
The model was evaluated on seven fMRI datasets (Alzheimer's, Parkinson's, Autism, contact sports study) and three EEG datasets.

Main Results:

Geo-Mamba demonstrated consistently competitive accuracy and robustness across diverse neuroimaging benchmarks, including fMRI and EEG data.
The model effectively captures short- and long-range dependencies while managing high-dimensional SPD inputs through geometry-aware reduction.
Validation on clinical datasets suggests significant potential for detecting subtle brain changes and disease-related alterations.

Conclusions:

Geo-Mamba offers a powerful new tool for analyzing complex neuroimaging data by leveraging Riemannian geometry.
The dual-path manifold modeling approach provides a robust and scalable solution for functional connectivity analysis.
This work highlights the potential of geometric deep learning models for advancing neuroimaging research and clinical translation.