Random dynamic graph models in neuroscience
Abstract: This thesis presents two different types of stochastic processes on graphs, which
can be interpreted as descriptions for phenomena in neuroscience.
In the first part mean field limits for non-linear Hawkes processes on a q-Erdős-
Rényi-graph are derived. From the neuroscience perspective it is important to
introduce inhibition to those models. This leads to a distinction between a criti-
cal case, where excitation and inhibition is balanced, and a non-critical case. The
structure of the graph is fixed beforehand, while the shape of the multivariate
Hawkes-intensity allows us to introduce some dependence structure among dif-
ferent vertices.
The second part describes dynamic graph models, i.e. the graph itself changes
over time. We use Markov jump processes to describe the evolution of the edge
count matrix of a graph. The rate for the formation of new edges in this graph is
motivated by the configuration model. We derive limit results of these dynamic
models for a large number of edges and vertices. These limits can be thought of
as a possibility to implement Hebb’s rule for the formation of synapses in a brain
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Notes
-
Universität Freiburg, Dissertation, 2024
- Keyword
-
Graphentheorie
Zufallsgraph
Zufallsgraph
Mean-Field-Theorie
- Event
-
Veröffentlichung
- (where)
-
Freiburg
- (who)
-
Universität
- (when)
-
2024
- Creator
- DOI
-
10.6094/UNIFR/246449
- URN
-
urn:nbn:de:bsz:25-freidok-2464491
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
-
25.03.2025, 1:50 PM CET
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
Time of origin
- 2024
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