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.

scholarly journals A study on small-world characteristics of Chinaäó»s high-speed railway networks

2016 ◽  
Author(s):  
Xin Yuan ◽  
Guo Liu ◽  
Kun Hui Ye
Keyword(s):  
High Speed ◽  
Small World ◽  
Clustering Coefficient ◽  
High Speed Rail ◽  
Attribute Data ◽  
The Social ◽  
The Difference ◽  
Global And Local ◽  
The Relationship ◽  
Space Method

The small-world model provides a useful perspective and method to study the topological structure and intrinsic characteristics of high-speed rail networks (HRNs). In this paper, the P-space method is used to examine global and local HRNs in China, meanwhile the adjacency matrix is developed, then the social network analysis and visualization tool UCINET is used to calculate the spatial and attribute data of HRNs at national and local levels in China. The small-world characteristics of whole HRNs are discussed, three networks which have different properties are determined, and a comparative analysis of the small-world effect is detected. Then, the relationship between the construction of high-speed rail and regional development of China is analysed. The results show that: 1) China's HRNs have small average path length ( L ) and large clustering coefficient (C ), representing a typical small-world network; 2) Local HRNs have a certain correlation with economic development. The reasons for the difference of HRNs with respect to characteristics among regions are eventually discussed.

Survivability of public transit network based on network structure entropy

2015 ◽  
Vol 26 (09) ◽  
pp. 1550104 ◽  
Author(s):  
Bai-Bai Fu ◽  
Lin Zhang ◽  
Shu-Bin Li ◽  
Yun-Xuan Li
Keyword(s):  
Network Model ◽  
Network Structure ◽  
Public Transit ◽  
Small World ◽  
Clustering Coefficient ◽  
Statistical Characteristics ◽  
Network Efficiency ◽  
Transit Network ◽  
Scale Free ◽  
The Public

In this work, we have collected 195 bus routes and 1433 bus stations of Jinan city as sample date to build up the public transit geospatial network model by applying space L method, until May 2014. Then, by analyzing the topological properties of public transit geospatial network model, which include degree and degree distribution, average shortest path length, clustering coefficient and betweenness, we get the conclusion that public transit network is a typical complex network with scale-free and small-world characteristics. Furthermore, in order to analyze the survivability of public transit network, we define new network structure entropy based on betweenness importance, and prove its correctness by giving that the new network structure entropy has the same statistical characteristics with network efficiency. Finally, the "inflexion zone" is discovered, which can be taken as the momentous indicator to determine the public transit network failure.

SYNCHRONIZATION IN THE FAMILY OF CHAOTIC SMALL-WORLD NETWORKS

2008 ◽  
Vol 19 (01) ◽  
pp. 111-123 ◽  
Author(s):  
LIANGMING HE ◽  
DUANWEN SHI
Keyword(s):  
Chaotic System ◽  
Average Distance ◽  
Small World ◽  
Clustering Coefficient ◽  
Small World Networks ◽  
Characteristic Path Length ◽  
Unified Chaotic System ◽  
The Family ◽  
Regular Networks ◽  
High Degree

In this paper we investigate by computer simulation the synchronizability of the family of small-world networks, which consists of identical chaotic units, such as the Lorenz chaotic system, the Chen chaotic system, Lü chaotic system, and the unified chaotic system (unit). It is shown that for weak coupling, synchronization clusters emerge in the networks whose disorder probabilities p are large but do not emerge in the networks whose disorder probabilities p are small; while for strong coupling under which the regular networks do not exhibit synchronization, all dynamical nodes, behaving as in the random networks, mutually synchronize in the networks which own very small disorder probability p and have both high degree of clustering and small average distance. Based on the concepts of clustering coefficient C(p), characteristic path length L(p) and global efficiency E(G), these phenomena are discussed briefly.

OPTIMAL INTERCONNECTION OF AD HOC INJECTION NETWORKS

2008 ◽  
Vol 09 (03) ◽  
pp. 277-297 ◽  
Author(s):  
GREGOIRE DANOY ◽  
ENRIQUE ALBA ◽  
PASCAL BOUVRY
Keyword(s):  
Ad Hoc Networks ◽  
Ad Hoc ◽  
Small World ◽  
Access Point ◽  
Clustering Coefficient ◽  
Mobility Patterns ◽  
Characteristic Path Length ◽  
Network Properties ◽  
Hoc Networks ◽  
Topology Control Problem

Multi-hop ad hoc networks allow establishing local groups of communicating devices in a self-organizing way. However, when considering realistic mobility patterns, such networks most often get divided in a set of disjoint partitions. This presence of partitions is an obstacle to communication within these networks. Ad hoc networks are generally composed of devices capable of communicating in a geographical neighborhood for free (e.g. using Wi-Fi or Bluetooth). In most cases a communication infrastructure is available. It can be a set of access point as well as a GSM/UMTS network. The use of such an infrastructure is billed, but it permits to interconnect distant nodes, through what we call “bypass links”. The objective of our work is to optimize the placement of these long-range links. To this end we rely on small-world network properties, which consist in a high clustering coefficient and a low characteristic path length. In this article we investigate the use of three genetic algorithms (generational, steady-state, and cooperative coevolutionary) to optimize three instances of this topology control problem and present initial evidence of their capacity to solve it.

A NOVEL SMALL-WORLD NETWORK MODEL: KEEPING CONNECTIVITY WITHOUT ADDING EDGES

2008 ◽  
Vol 22 (29) ◽  
pp. 5229-5234 ◽  
Author(s):  
XUHUA YANG ◽  
BO WANG ◽  
WANLIANG WANG ◽  
YOUXIAN SUN
Keyword(s):  
Network Model ◽  
Regular Ring ◽  
Nearest Neighbor ◽  
Small World ◽  
Clustering Coefficient ◽  
The Novel ◽  
Small World Network ◽  
Characteristic Path Length ◽  
Large N ◽  
Novel Model

Considering the problems of potentially generating a disconnected network in the WS small-world network model [Watts and Strogatz, Nature393, 440 (1998)] and of adding edges in the NW small-world network model [Newman and Watts, Phys. Lett. A263, 341 (1999)], we propose a novel small-world network model. First, generate a regular ring lattice of N vertices. Second, randomly rewire each edge of the lattice with probability p. During the random rewiring procedure, keep the edges between the two nearest neighbor vertices, namely, always keep a connected ring. This model need not add edges and can maintain connectivity of the network at all times in the random rewiring procedure. Simulation results show that the novel model has the typical small-world properties which are small characteristic path length and high clustering coefficient. For large N, the model is approximately equal to the WS model. For large N and small p, the model is approximately equal to the WS model or the NW model.

scholarly journals Shorter TR Combination with Finer Atlas Positively Modulate Topological Organization of Brain Networks: A Resting State fMRI Study

2020 ◽  
Author(s):  
Yan Zhang ◽  
QILI HU ◽  
Jiali Liang ◽  
Zhenghui Hu ◽  
Tianyi Qian ◽  
...  
Keyword(s):  
Temporal Resolution ◽  
Path Length ◽  
Brain Networks ◽  
Small World ◽  
Clustering Coefficient ◽  
High Temporal Resolution ◽  
Small World Networks ◽  
Planar Imaging ◽  
Characteristic Path Length ◽  
Topological Organization

Abstract BackgroundThe simultaneous multislice echo planar imaging technique can shorten the repetition time (TR) of blood oxygen level-dependent acquisition and thus acquires more information. However, little is known about the influence of higher temporal resolution on functional networks. Whether the topological organization of small-world networks is modulated in the multispectra at high temporal resolution is still unclear. Results: The network reconstruction based on the shorter TR and the finer atlas, showed significant (p<0.05, Bonferroni correction) increases in normalized clustering coefficient, small-worldness, clustering coefficient, local efficiency and global efficiency, and reductions in normalized characteristic path length and characteristic path length. ConclusionsThe shorter TR coupled with the finer atlas can positively modulate topological characteristics of brain networks. Although five multispectra present properties of small-world networks, the properties of the network in 0.082-0.1 Hz are weaker than those in 0.01-0.082 Hz. These findings provide new insights into the topological patterns of brain networks and have implications for the study of brain connectomes and their applications in brain disease.

scholarly journals Quantitative Controllability Index of Complex Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lifu Wang ◽  
Yali Zhang ◽  
Jingxiao Han ◽  
Zhi Kong
Keyword(s):  
Complex Networks ◽  
Condition Number ◽  
Random Network ◽  
Small World ◽  
Scale Free Network ◽  
Scale Free ◽  
Network Topologies ◽  
Free Network ◽  
The Relationship ◽  
Controllability Index

In this paper, the controllability issue of complex network is discussed. A new quantitative index using knowledge of control centrality and condition number is constructed to measure the controllability of given networks. For complex networks with different controllable subspace dimensions, their controllability is mainly determined by the control centrality factor. For the complex networks that have the equal controllable subspace dimension, their different controllability is mostly determined by the condition number of subnetworks’ controllability matrix. Then the effect of this index is analyzed based on simulations on various types of network topologies, such as ER random network, WS small-world network, and BA scale-free network. The results show that the presented index could reflect the holistic controllability of complex networks. Such an endeavour could help us better understand the relationship between controllability and network topology.

scholarly journals Alterations in brain network organization in adults with obesity as compared to healthy-weight individuals and seniors

2019 ◽  
Author(s):  
J. Ottino-González ◽  
H.C. Baggio ◽  
M.A. Jurado ◽  
B. Segura ◽  
X. Caldú ◽  
...  
Keyword(s):  
Small World ◽  
Brain Network ◽  
Premature Aging ◽  
Clustering Coefficient ◽  
Healthy Weight ◽  
Degree Relative ◽  
Characteristic Path Length ◽  
Centrality Metrics ◽  
Network Composition ◽  
Unhealthy Weight

AbstractLife expectancy and obesity rates have drastically increased in recent years. An unhealthy weight is related to long-lasting biological deregulations that might compromise the normal course of aging. The aim of the current study was to test whether the network composition of young adults with obesity would show signs of premature aging. To this end, subjects with obesity (N = 30, mean age 32.8 ± 5.68), healthy-weight controls (N = 33, mean age 30.9 ± 6.24) as well as non-demented seniors (N = 30, mean age 67.1 ± 6.65) all underwent a resting-state MRI acquisition. Functional connectivity was studied by means of graph-theory measurements (i.e., small-world index, clustering coefficient, characteristic path length, and mean degree). Contrary to what expected, obesity in adults was related to disruptions in small-world properties driven by increases in network segregation (i.e., clustering coefficient) as compared to elders. Also, this group showed alterations in global and regional centrality metrics (i.e., degree) relative to controls and seniors. Despite not mimicking what was here shown by seniors, the topological organization linked to an obesity status may represent a flaw for cognitive functions depending on the rapid combination between different modular communities.

scholarly journals Altered Small-World Functional Network Topology in Patients with Optic Neuritis: A Resting-State fMRI Study

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Ke Song ◽  
Juan Li ◽  
Yuanqiang Zhu ◽  
Fang Ren ◽  
Lingcan Cao ◽  
...  
Keyword(s):  
Resting State ◽  
Path Length ◽  
Small World ◽  
Brain Network ◽  
Clustering Coefficient ◽  
Control Group ◽  
Network Efficiency ◽  
Characteristic Path Length ◽  
Brain Functional Connectivity ◽  
The Brain

Aim. This study investigated changes in small-world topology and brain functional connectivity in patients with optic neuritis (ON) by resting-state functional magnetic resonance imaging (rs-fMRI) and based on graph theory. Methods. A total of 21 patients with ON (8 males and 13 females) and 21 matched healthy control subjects (8 males and 13 females) were enrolled and underwent rs-fMRI. Data were preprocessed and the brain was divided into 116 regions of interest. Small-world network parameters and area under the integral curve (AUC) were calculated from pairwise brain interval correlation coefficients. Differences in brain network parameter AUCs between the 2 groups were evaluated with the independent sample t -test, and changes in brain connection strength between ON patients and control subjects were assessed by network-based statistical analysis. Results. In the sparsity range from 0.08 to 0.48, both groups exhibited small-world attributes. Compared to the control group, global network efficiency, normalized clustering coefficient, and small-world value were higher whereas the clustering coefficient value was lower in ON patients. There were no differences in characteristic path length, local network efficiency, and normalized characteristic path length between groups. In addition, ON patients had lower brain functional connectivity strength among the rolandic operculum, medial superior frontal gyrus, insula, median cingulate and paracingulate gyri, amygdala, superior parietal gyrus, inferior parietal gyrus, supramarginal gyrus, angular gyrus, lenticular nucleus, pallidum, superior temporal gyrus, and cerebellum compared to the control group ( P < 0.05 ). Conclusion. Patients with ON show typical “small world” topology that differed from that detected in HC brain networks. The brain network in ON has a small-world attribute but shows reduced and abnormal connectivity compared to normal subjects and likely causes symptoms of cognitive impairment.

scholarly journals Percolation Distribution in Small-World Quantum Networks

2022 ◽  
Vol 12 (2) ◽  
pp. 701
Author(s):  
Jianxiong Liang ◽  
Xiaoguang Chen ◽  
Tianyi Wang
Keyword(s):  
Percolation Threshold ◽  
Network Structure ◽  
Percolation Theory ◽  
Small World ◽  
Entanglement Swapping ◽  
Quantum Networks ◽  
Communication Links ◽  
Network Topologies ◽  
Entanglement Distribution ◽  
Percolation Thresholds

Quantum networks have good prospects for applications in the future. Compared with classical networks, small-world quantum networks have some interesting properties. The topology of the network can be changed through entanglement exchange operations, and different network topologies will result in different percolation thresholds when performing entanglement percolation. A lower percolation threshold means that quantum networks require fewer minimum resources for communication. Since a shared singlet between two nodes can still be a limitation, concurrency percolation theory (ConPT) can be used to relax the condition. In this paper, we investigate how entanglement distribution is performed in small-world quantum networks to ensure that nodes in the network can communicate with each other by establishing communication links through entanglement swapping. Any node can perform entanglement swapping on only part of the connected edges, which can reduce the influence of each node in the network during entanglement swapping. In addition, the ConPT method is used to reduce the percolation threshold even further, thus obtaining a better network structure and reducing the resources required.

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