Markov Processes and Brain Network Hubs.
Saved in:
| Title: | Markov Processes and Brain Network Hubs. |
|---|---|
| Authors: | Murty, M. Ram1 (AUTHOR) murty@queensu.ca, Prasad, Asuri Narayan2 (AUTHOR) narayan.prasad@lhsc.on.ca |
| Source: | Resonance: Journal of Science Education. Jun2026, Vol. 31 Issue 6, p859-884. 26p. |
| Subject Terms: | Markov processes, Graph theory, Large-scale brain networks, Eigenvalues, Ergodic theory, Brain mapping, Brain imaging |
| Abstract: | Current concepts of neural networks have emerged over two centuries of progress, beginning with the neural doctrine to the idea of neural cell assemblies. Presently, neural network models involve distributed neural circuits of nodes, hubs, and connections that are dynamic across different states of brain function. Advances in neurophysiology, neuroimaging, and the field of connectomics have given impetus to the application of mathematical concepts of graph theory. Current approaches do have limitations and inconsistencies in the results they achieve. We model the neural network of the brain as a directed graph and attach a matrix (called the Markov matrix) of transition probabilities (determined by the synaptic strengths) to every pair of distinct nodes, giving rise to a discrete Markov process. We postulate that the network hubs are the nodes with the highest probabilities given by the stationary distribution of Markov theory. We also derive a new upper bound for the diameter of a graph in terms of the eigenvalues of the Markov matrix. [ABSTRACT FROM AUTHOR] |
| Copyright of Resonance: Journal of Science Education is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: ehh DbLabel: Education Research Complete An: 195365683 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Markov Processes and Brain Network Hubs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Murty%2C+M%2E+Ram%22">Murty, M. Ram</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> murty@queensu.ca</i><br /><searchLink fieldCode="AR" term="%22Prasad%2C+Asuri+Narayan%22">Prasad, Asuri Narayan</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> narayan.prasad@lhsc.on.ca</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Resonance%3A+Journal+of+Science+Education%22">Resonance: Journal of Science Education</searchLink>. Jun2026, Vol. 31 Issue 6, p859-884. 26p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Large-scale+brain+networks%22">Large-scale brain networks</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Ergodic+theory%22">Ergodic theory</searchLink><br /><searchLink fieldCode="DE" term="%22Brain+mapping%22">Brain mapping</searchLink><br /><searchLink fieldCode="DE" term="%22Brain+imaging%22">Brain imaging</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Current concepts of neural networks have emerged over two centuries of progress, beginning with the neural doctrine to the idea of neural cell assemblies. Presently, neural network models involve distributed neural circuits of nodes, hubs, and connections that are dynamic across different states of brain function. Advances in neurophysiology, neuroimaging, and the field of connectomics have given impetus to the application of mathematical concepts of graph theory. Current approaches do have limitations and inconsistencies in the results they achieve. We model the neural network of the brain as a directed graph and attach a matrix (called the Markov matrix) of transition probabilities (determined by the synaptic strengths) to every pair of distinct nodes, giving rise to a discrete Markov process. We postulate that the network hubs are the nodes with the highest probabilities given by the stationary distribution of Markov theory. We also derive a new upper bound for the diameter of a graph in terms of the eigenvalues of the Markov matrix. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Resonance: Journal of Science Education is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ehh&AN=195365683 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s12045-026-2012-5 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 26 StartPage: 859 Subjects: – SubjectFull: Markov processes Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Large-scale brain networks Type: general – SubjectFull: Eigenvalues Type: general – SubjectFull: Ergodic theory Type: general – SubjectFull: Brain mapping Type: general – SubjectFull: Brain imaging Type: general Titles: – TitleFull: Markov Processes and Brain Network Hubs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Murty, M. Ram – PersonEntity: Name: NameFull: Prasad, Asuri Narayan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 09718044 Numbering: – Type: volume Value: 31 – Type: issue Value: 6 Titles: – TitleFull: Resonance: Journal of Science Education Type: main |
| ResultId | 1 |
