scholarly journals Cluster-based network modeling—From snapshots to complex dynamical systems

2021 ◽  
Vol 7 (25) ◽  
pp. eabf5006
Author(s):  
Daniel Fernex ◽  
Bernd R. Noack ◽  
Richard Semaan
Keyword(s):  
Nonlinear Dynamics ◽  
Statistical Physics ◽  
Network Modeling ◽  
Network Connectivity ◽  
Dimensional Subspace ◽  
Data Driven ◽  
Lorenz Attractor ◽  
Universal Method ◽  
Time Resolved ◽  
Kolmogorov Flow

We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM describes short- and long-term behavior and is fully automatable, as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict, and control complex systems in all scientific fields.

Investigation on nonlinear dynamics of ZnO using time-resolved pump-probe technique with phase object

2011 ◽  
Author(s):  
Lirong Ge ◽  
Min Shui ◽  
Xiao Jin ◽  
Zhongguo Li ◽  
Yinglin Song
Keyword(s):  
Nonlinear Dynamics ◽  
Phase Object ◽  
Time Resolved ◽  
Pump Probe ◽  
Probe Technique

DEVELOPMENT OF THERAPEUTIC BRAIN STIMULATION TECHNIQUES WITH METHODS FROM NONLINEAR DYNAMICS AND STATISTICAL PHYSICS

2006 ◽  
Vol 16 (07) ◽  
pp. 1889-1911 ◽  
Author(s):  
PETER A. TASS ◽  
CHRISTIAN HAUPTMANN ◽  
OLEKSANDR V. POPOVYCH
Keyword(s):  
Nonlinear Dynamics ◽  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Essential Tremor ◽  
Brain Stimulation ◽  
Brain Function ◽  
Statistical Physics ◽  
Delayed Feedback ◽  
Phase Resetting ◽  
Feedback Mechanisms

Synchronization processes may severely impair brain function, for instance, in Parkinson's disease, essential tremor or epilepsies. We present three different effectively desynchronizing stimulation techniques which have been developed with methods from nonlinear dynamics and statistical physics. These techniques exploit either stochastic phase resetting principles or complex delayed feedback mechanisms. We explain how these methods work and how they can be applied to therapeutic brain stimulation.

Flocking of multiple autonomous agents with preserved network connectivity and heterogeneous nonlinear dynamics

2013 ◽  
Vol 115 ◽  
pp. 169-177 ◽  
Author(s):  
Miaomiao Wang ◽  
Housheng Su ◽  
Miaomiao Zhao ◽  
Michael Z.Q. Chen ◽  
Hongwei Wang
Keyword(s):  
Nonlinear Dynamics ◽  
Autonomous Agents ◽  
Network Connectivity

scholarly journals Data Driven Exploration of Network Connectivity in task-fMRI of Focal Hand Dystonia

2021 ◽  
Author(s):  
Noreen Bukhari-Parlakturk ◽  
Michael Fei ◽  
James Voyvodic ◽  
Andrew M. Michael
Keyword(s):  
Basal Ganglia ◽  
Motor Performance ◽  
Time Course ◽  
Network Connectivity ◽  
Data Driven ◽  
Functional Networks ◽  
Primary Role ◽  
Data Driven Approach ◽  
Task Time ◽  
Writing Task

Background: Dystonia is a network level brain disorder with limited understanding of interactions between functional networks. Prior studies have demonstrated abnormalities both between and within functional networks. However, these findings were based on a hypothesis driven region of interest (ROI) approach or used resting state fMRI to extrapolate network differences in task-specific dystonia called writers cramp (WC). As a result, it remains unclear if these same networks would be active during the actual performance of a dystonic task. It's also unclear from prior studies which networks play a role in the primary disease versus a compensatory region. Lastly, neuroimaging studies have used sequencing tapping task with equal motor performance to study networks changes due to concern that differences in motor performance during the dystonic writing task may confound the findings. Objective: The aim of this research study was: 1) to use a data driven approach on a task-specific focal dystonia to understand network level interactions during task-fMRI, 2) to determine if differences in observed network level could distinguish between brain regions of primary vs compensatory change in task-specific dystonia, and 3) if sequence tapping task captured similar level network changes as the dystonic writing task. Methods: We used the data-driven independent component analysis to compare functional network correlation with task time course and network connectivity during 3 motor tasks of writing, sequence tapping and finger flexion-extension. Results: Our analysis shows that in WC there is significantly decreased correlation of the basal ganglia and increased correlation of the orbitofrontal network to the writing task time course. Analysis of network connectivity showed significantly decreased connectivity of the basal ganglia to the left sensorimotor network specifically during the writing task in WC patients. We also showed significantly increased correlation of the cerebellum to the orbitofrontal and parietal networks. Conclusions: Collectively, our analysis supports a global network disorders in which the basal ganglia plays a primary role in the disease mechanism while the cerebellum plays a role as a compensatory network, partially through increased connectivity to the orbitofrontal network, a region important in motor planning. Our analysis also shows that the sequence tapping task does not capture the same network level dysfunction as the primary dystonic task. Our study is the first to apply a purely data-driven approach to understand network interactions in WC dystonia patients during task performance.

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