Markov Processes and Brain Network Hubs
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 the model of neural networks involves distributed neural circuits of nodes, hubs, and connections that are dynamic in 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 carry limitations and inconsistency in results achieved. 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 (continuous) 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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Differentially Categorized Structural Connectome Hubs are Involved in Differential Microstructural Basis and Functional Implications and Contribute to Individual Identification
Human brain structural networks contain sets of centrally embedded hub regions that enable efficient information communication. However, it remains largely unknown about categories of structural brain hubs and their micr…
Diffusion MRICorrelation of Correlation Networks: High-Order Interactions in the Topology of Brain Networks
To understand collective network behavior in the complex human brain, pairwise correlation networks alone are insufficient for capturing the high-order interactions that extend beyond pairwise interactions and play a cru…
Mapping multiplex hubs in human functional brain network
Typical brain networks consist of many peripheral regions and a few highly central ones, i.e. hubs, playing key functional roles in cerebral inter-regional interactions. Studies have shown that networks, obtained from th…
Generative Modeling of Hidden Functional Brain Networks
Functional connectivity refers to the temporal statistical relationship between spatially distinct brain regions and is usually inferred from the time series coherence/correlation in brain activity between regions of int…
Functional ConnectivityTime SeriesTime Series AnalysisFunctional complexity emerging from anatomical constraints in the brain: the significance of network modularity and rich-clubs
The large-scale structural ingredients of the brain and neural connectomes have been identified in recent years. These are, similar to the features found in many other real networks: the arrangement of brain regions into…
Functional Connectivity