scholarly journals Uniting functional network topology and oscillations in the fronto-parietal single unit network of behaving primates

eLife ◽  
2016 ◽  
Vol 5 ◽  
Author(s):  
Benjamin Dann ◽  
Jonathan A Michaels ◽  
Stefan Schaffelhofer ◽  
Hansjörg Scherberger
Keyword(s):  
Single Neuron ◽  
Low Frequency ◽  
Small World ◽  
Functional Communication ◽  
Neuron Network ◽  
Active Behavior ◽  
Network Function ◽  
Rich Club ◽  
Spiking Networks ◽  
Unit Network

The functional communication of neurons in cortical networks underlies higher cognitive processes. Yet, little is known about the organization of the single neuron network or its relationship to the synchronization processes that are essential for its formation. Here, we show that the functional single neuron network of three fronto-parietal areas during active behavior of macaque monkeys is highly complex. The network was closely connected (small-world) and consisted of functional modules spanning these areas. Surprisingly, the importance of different neurons to the network was highly heterogeneous with a small number of neurons contributing strongly to the network function (hubs), which were in turn strongly inter-connected (rich-club). Examination of the network synchronization revealed that the identified rich-club consisted of neurons that were synchronized in the beta or low frequency range, whereas other neurons were mostly non-oscillatory synchronized. Therefore, oscillatory synchrony may be a central communication mechanism for highly organized functional spiking networks.

BURSTING TYPES AND STABLE DOMAINS OF RULKOV NEURON NETWORK WITH MEAN FIELD COUPLING

2013 ◽  
Vol 23 (12) ◽  
pp. 1330041 ◽  
Author(s):  
HONGJUN CAO ◽  
YANGUO WU
Keyword(s):  
Parameter Space ◽  
Single Neuron ◽  
Complex Dynamics ◽  
Mean Field ◽  
Flip Bifurcation ◽  
Neuron Network ◽  
Square Wave ◽  
Field Coupling ◽  
The Mean ◽  
Stable Domains

Based on the detailed bifurcation analysis and the master stability function, bursting types and stable domains of the parameter space of the Rulkov map-based neuron network coupled by the mean field are taken into account. One of our main findings is that besides the square-wave bursting, there at least exist two kinds of triangle burstings after the mean field coupling, which can be determined by the crisis bifurcation, the flip bifurcation, and the saddle-node bifurcation. Under certain coupling conditions, there exists two kinds of striking transitions from the square-wave bursting (the spiking) to the triangle bursting (the square-wave bursting). Stable domains of fixed points, periodic solutions, quasiperiodic solutions and their corresponding firing regimes in the parameter space are presented in a rigorous mathematical way. In particular, as a function of the intrinsic control parameters of each single neuron and the external coupling strength, a stable coefficient of the Neimark–Sacker bifurcation is derived in a parameter plane. These results show that there exist complex dynamics and rich firing regimes in such a simple but thought-provoking neuron network.

scholarly journals Nonlinear growth: an origin of hub organization in complex networks

2017 ◽  
Vol 4 (3) ◽  
pp. 160691 ◽  
Author(s):  
Roman Bauer ◽  
Marcus Kaiser
Keyword(s):  
Real World ◽  
Preferential Attachment ◽  
Fibre Tract ◽  
Nonlinear Network ◽  
Network Function ◽  
Nonlinear Growth ◽  
Rich Club ◽  
Spreading Dynamics ◽  
Classical Models ◽  
Generic Representation

Many real-world networks contain highly connected nodes called hubs. Hubs are often crucial for network function and spreading dynamics. However, classical models of how hubs originate during network development unrealistically assume that new nodes attain information about the connectivity (for example the degree) of existing nodes. Here, we introduce hub formation through nonlinear growth where the number of nodes generated at each stage increases over time and new nodes form connections independent of target node features. Our model reproduces variation in number of connections, hub occurrence time, and rich-club organization of networks ranging from protein–protein, neuronal and fibre tract brain networks to airline networks. Moreover, nonlinear growth gives a more generic representation of these networks compared with previous preferential attachment or duplication–divergence models. Overall, hub creation through nonlinear network expansion can serve as a benchmark model for studying the development of many real-world networks.

scholarly journals The trend of disruption in the functional brain network topology of Alzheimer’s disease

2021 ◽  
Author(s):  
Alireza Fathian ◽  
Yousef Jamali ◽  
Mohammad Reza Raoufy
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Functional Connectivity ◽  
Small World ◽  
Brain Network ◽  
Cognitively Normal ◽  
Functional Brain ◽  
Rich Club ◽  
Functional Brain Network ◽  
Progressive Disorder

Abstract Alzheimer’s disease (AD) is a progressive disorder associated with cognitive dysfunction that alters the brain’s functional connectivity. Assessing these alterations has become a topic of increasing interest. However, a few studies have examined different stages of AD from a complex network perspective that cover different topological scales. This study analyzed the trend of functional connectivity alterations from a cognitively normal (CN) state through early and late mild cognitive impairment (EMCI and LMCI) and to Alzheimer’s disease. The analyses had been done at the local (hubs and activated links and areas), meso (clustering, assortativity, and rich-club), and global (small-world, small-worldness, and efficiency) topological scales. The results showed that the trends of changes in the topological architecture of the functional brain network were not entirely proportional to the AD progression, and these trends behaved differently at the earliest stage of the disease, i.e., EMCI. Further, it has been indicated that the diseased groups engaged somatomotor, frontoparietal, and default mode modules compared to the CN group. The diseased groups also shifted the functional network towards more random architecture. In the end, The methods introduced in this paper enable us to gain an extensive understanding of the pathological changes of the AD process.

scholarly journals Complex Brain Network Analysis and Its Applications to Brain Disorders: A Survey

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-27 ◽  
Author(s):  
Jin Liu ◽  
Min Li ◽  
Yi Pan ◽  
Wei Lan ◽  
Ruiqing Zheng ◽  
...  
Keyword(s):  
Network Analysis ◽  
Brain Networks ◽  
Small World ◽  
Brain Regions ◽  
Brain Network ◽  
Brain Diseases ◽  
Brain Disorders ◽  
Comprehensive Overview ◽  
Rich Club ◽  
New Perspective

It is well known that most brain disorders are complex diseases, such as Alzheimer’s disease (AD) and schizophrenia (SCZ). In general, brain regions and their interactions can be modeled as complex brain network, which describe highly efficient information transmission in a brain. Therefore, complex brain network analysis plays an important role in the study of complex brain diseases. With the development of noninvasive neuroimaging and electrophysiological techniques, experimental data can be produced for constructing complex brain networks. In recent years, researchers have found that brain networks constructed by using neuroimaging data and electrophysiological data have many important topological properties, such as small-world property, modularity, and rich club. More importantly, many brain disorders have been found to be associated with the abnormal topological structures of brain networks. These findings provide not only a new perspective to explore the pathological mechanisms of brain disorders, but also guidance for early diagnosis and treatment of brain disorders. The purpose of this survey is to provide a comprehensive overview for complex brain network analysis and its applications to brain disorders.

IDENTIFYING NEURAL NETWORK TOPOLOGIES THAT FOSTER DYNAMICAL COMPLEXITY

2013 ◽  
Vol 16 (02n03) ◽  
pp. 1350032 ◽  
Author(s):  
LARRY S. YAEGER
Keyword(s):  
Neural Network ◽  
Network Structure ◽  
Complex Dynamics ◽  
Small World ◽  
Clustering Coefficient ◽  
Characteristic Path Length ◽  
Physical Constraints ◽  
Network Function ◽  
Network Topologies ◽  
The Relationship

We use an ecosystem simulator capable of evolving arbitrary neural network topologies to explore the relationship between an information theoretic measure of the complexity of neural dynamics and several graph theoretical metrics calculated for the underlying network topologies. Evolutionary trends confirm and extend previous results demonstrating an evolutionary selection for complexity and small-world network properties during periods of behavioral adaptation. The resultant mapping of the space of network topologies occupied by the most complex networks yields new insights into the relationship between network structure and function. The highest complexity networks are found within limited numerical ranges of clustering coefficient, characteristic path length, small-world index, and global efficiency. The widths of these ranges vary from quite narrow to modest, and provide a guide to the most productive regions of the space of neural topologies in which to search for complexity. Our demonstration that evolution selects for complex dynamics and small-world networks helps explain biological evidence for these trends and provides evidence for selection of these characteristics based purely on network function—with no physical constraints on network structure—thus suggesting that functional and structural evolutionary pressures cooperate to produce brains optimized for adaptation to a complex, variable world.

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