The brain at rest (i.e., under no external stimulation and any sort of task) is not asleep but seems to be actively engaged, displaying highly structured spatiotemporal patterns of neural activity known as restingstate networks (RSNs) [1]. The study of RSNs has become a central focus of brain network science. Evidence from numerous studies has demonstrated significant correlations between restingstate functional connectivity (FC) and structural connectivity (SC) [2]. Note that FC, which is derived from restingstate functional magnetic resonance imaging (fMRI) unveils functional patterns among brain regions, and SC, which is inferred from diffusion tensor/spectrum imaging (DTI/DSI), shows direct anatomical connections among distinct brain regions. However, the relationships between structural and functional connectivity are not straightforward. Two regions that are structurally bonded tend to show a functional connection, but those that are not structurally bonded can also show a functional connection. In fact, there are studies reporting the observation of strong FC among regions that are not directly structurally linked [3][5]. Though the prediction of restingstate FC from SC remains unclear, a number of models have been proposed to investigate the role of SC in shaping restingstate FC, which will be valuable for further studies [2], [6][15]. For example, simple models based on Euclidean distance and topological measures of SC have been proved to be efficient to investigate the impressive range of topological properties of functional brain networks [12], [15]. Another theoretical model [13] proposes that analytic measures of network communication extracted from SC help to predict the strength of FC among both structurally connected and unconnected regions. Nevertheless, these models may not have fully explored the underlying network dynamics of brain activity of neuronal populations. In consideration of the spontaneous dynamics of interacting brain areas, neural mass models coupled with anatomical architecture are developed to understand the emergence of restingstate fluctuations [5]. One mainstream computational neural mass model is the dynamical mean field (DMF) model which is a reduction of the detailed spiking model [1]. This DMF model consistently summarizes the realistic dynamics of a detailed spiking and conductancebased synaptic largescale network [2]. To predict FC from SC, the model should be followed by the BalloonWindkessel model to transform neuronal activity into the blood oxygen level dependent (BLOD) signal [4], [16], which increases the complexity of the prediction of FC. In the DMF model, when global network dynamics operate at a critical point, the interplay between SC and restingstate FC reaches its maximum [4].
In this article, we use a simple dynamic model combined with the susceptibleinfectedsusceptible (SIS) theory [17][22] and the shortest paths [13], [23] to predict FC from SC. We focus on the shortest paths as the principal routes to transmit signals. Thus we first simplify the structurally connected network into an efficient propagation network in terms of the shortest paths. Then, we combine SIS infection theory with the efficient network to simulate the dynamic process of human brain activity. Previous studies show that FC simulated on an empirical structural brain network by means of SIS infection dynamics resembles the empirical FC [14]. Considering the shortest paths rather than structural network as effective transmission routes, our experiments on two different resolution databases suggest that the predictive power of FC simulated by the dynamic model embedded in the efficient propagation network is better than that simulated by a model embedded in the structural brain network. Finally, we make an extensive comparison of the dynamic models and the DMF model. We conclude that the dynamic model simulated on shortest paths can predict FC among both structurally connected and unconnected node pairs. Compared with the DMF model and previous dynamic model, the predictive capacity of the dynamic model based on an efficient network is found to be better.
Ⅱ. PRELIMINARIESSince the 1990s, complex network analysis has been attracting a growing number of investigators who are engaged in exploring complicated issues via networks in various areas. For instance, many biological and social systems can be expressed as networks, i.e., connected graphs formed by a set of nodes (which represent entities) and edges (which represent interaction pathways among nodes). The study of networks is of great importance for solving some practical problems, such as controlling the spread of viruses among networks during epidemics [17][22].
A. SIS ModelThe SIS model is the simplest epidemiological model which describes the spreading process of disease based on the social network [17],
[20]. In the SIS model, each individual is in one of two states: healthy (but susceptible) or infected. Healthy individuals would be infected at rate
$ \begin{eqnarray}\label{2} & {{S}_{i}}+{{I}_{j}}\xrightarrow{\alpha }{{I}_{i}}+{{I}_{j}} \nonumber\\ & {{I}_{i}}\xrightarrow{\beta }{{S}_{j}} \end{eqnarray} $  (1) 
where
The network, as stated above, can be expressed by a set of nodes
The algorithm [24] for the shortest paths between each node pair
It is worth mentioning that many studies have focused on the shortest paths as primary routes to communicate along the complex networks [13], [25][27]. They assume that short paths are efficient (faster and less noisy) and optimal for signal transmission. For example, Trusina's studies [25] have demonstrated that the ability to communicate in some realworld networks is favored by the network topology for small distances, but not favored at longer distances. Rosvall and his colleagues [26] made an assumption on the basis of the shortest paths to estimate typical traffic in a network, which thereby minimized the disturbance on other nodes. Goñi et al. defined analytic measures in 2013 which were needed to access or trace the shortest paths to investigate communication efficiency in complex networks [27]. Furthermore, Goñi et al. used four communication measures based on the shortest paths in 2014 [13] to explore the capacity of these measures to predict FC. He proposed to linearly combine the four primitives to form a predictor of functional connectivity matrix. From this perspective, we will consider the shortest paths as a principal factor for an efficient structural network to predict functional connectivity. Note that the model we developed as follows is geared towards simulating the dynamical signal propagation among each node pair, which will reflect the physiological characteristics, rather than just achieving linear fit by the aid of the communication measures described in [13].
Ⅲ. A DYNAMIC THEORETIC FORMULATION FOR FUNCTIONAL PREDICTIONHere, we propose a dynamic model embedded in the shortest paths on the basis of SIS theory to predict functional connectivity. We firstly introduce human brain structural and functional datasets and then use the dynamic model embedded in a structural brain network which has been illustrated in Stam's study [14]. Finally, the efficient dynamic model based on the shortest paths is developed.
A. DatasetsTwo datasets were used to test the proposed method for predicting FC from SC. One lowresolution dataset includes 66 ROIs (regions of interest); the other 90ROI dataset records networks of structural and functional connections of 90 parcellations of cerebral cortical areas. The lowresolution dataset has been described in detail in [7]. Each element in the SC matrix represents the density with which two different brain regions were connected. The restingstate FC matrix was examined by calculating the pairwise Pearson's correlation coefficients of corresponding fMRI BOLD signals obtained for each brain area during 20min. The 90ROI dataset was a dataset as described in [28]. Structural and diffusion MR volumes were parcellated into 90 cerebral cortical areas after diffusion tractography processing [29]. Then, fiber strengths produced by the streamline tractography algorithm were resampled into a Gaussian distribution. In this paper, for 90ROI dataset, 8 individual participants were selected to calculate the average FC and SC. All selfconnections (diagonal elements in the FC matrix in both 66ROI and 90ROI datasets) were excluded. The resulting empirical SC matrices and empirical FC matrices in the above two databases are shown in Fig. 1. Note that the upper left quadrant of the matrices represents connections in the right hemisphere, the lower right quadrant represents the left hemisphere, and the other two quadrants represent interhemispheric connections. The region names of 66ROI and 90ROI datasets are shown in Appendix A and Appendix B, respectively.
Download:


Fig. 1 Two datasets. (a) Empirical SC (SC 66), (b) empirical FC matrix (FC 66) in 66ROI dataset, (c) Empirical SC (SC 90), (d) empirical FC matrix (FC 90) in 90ROI dataset. 
Similar to what has been said above, the SC of a parcellation of the human cerebral cortical into
Download:


Fig. 2 Simplifying the structural networks according to the shortest paths. (a) Binary 66×66 structural matrix with red dots representing anatomical links and blue dots indicating the absence of links. (b) The efficient propagation matrix derived from the original 66×66 structural matrix according to the shortest paths. (c) Binary 90×90 structural matrix with red dots representing anatomical links and blue dots indicating the absence of links. (d) The efficient propagation matrix derived from the original 90×90 structural matrix according to the shortest paths. 
In Stam's study [14], each brain region can be in one of two states: an activated state or excitable state, which is corresponding to healthy (susceptible) and infected states in the SIS model. Excitable regions will become activated at a certain infection rate if these regions connect with any activated region directly. Likewise, activated regions will return to the excitable state at a certain recovery rate. There are two transition probabilities: infection probability (
Download:


Fig. 3 The dynamic propagation mode. (a) The dynamic schema. The node with orange color represents the brain region in the activated state coded as 1; the node with blue color represents the brain region in the excitable state coded as 0. Along the transmission routes, regions will change their states with two probabilities: infection probability determining the transition from an excitable state to an activated state and recovery probability determining the transition from an activated state to an excitable state. (b) The "connected" transmission diagram. The activated node 
By contrast, the dynamic prediction model proposed here is based on the shortest paths and signals spread among "connected" node pairs. Fig. 3 (b) shows the "connected" diagram. At time
The efficient propagation networks based on two databases are illustrated in Fig. 2. Fig. 2 (a) is a binary 66×66 SC matrix where red dots exhibit the existence of anatomical links, while Fig. 2 (b) is the simplified efficient propagation matrix where red dots exhibit the "connected" links. In accordance with the 66ROI dataset, Fig. 2 (c) and Fig. 2 (d) show the binary SC matrix and the corresponding simplified propagation network, respectively. The patterns shown in Fig. 2 indicate that the simplified matrices have fewer connections than the original structural matrices, which reduces the complication of the transmission network. More specifically, there are 1060 anatomical links in the binary SC between 66 nodes while the reduced 66×66 matrix contains only 216 "connected" links where nearly 80 percent of connections are eliminated. And for 90ROI dataset, only 35 percent (1006 links) are reserved in comparison with 2938 links in the binary SC matrix.
Along the structural edges (or along the "connected" paths), if the region is activated at time
$ \begin{equation} FC{{s}_{ij}}=\frac{\sum_{n=1}^{{{N}_{L}}}{({{X}_{n}}\bar{X})({{Y}_{n}}\bar{Y})}}{\sqrt{\sum_{n=1}^{{{N}_{L}}}{{{({{X}_{n}}\bar{X})}^{2}}}}\sqrt{\sum_{n=1}^{{{N}_{L}}}{{{({{Y}_{n}}\bar{Y})}^{2}}}}} \end{equation} $  (2) 
where the two series
The algorithm for dynamical propagation based on the efficient brain network is shown as follows:
In order to demonstrate the capacity of the shortest paths and the reduced network, we compare the results simulated on a structural network and the results simulated on an efficient network.
A. Settings and ResultsFig. 4 schematizes the results for the 66ROI dataset using above dynamic prediction models embedded in the binary structural networks and the reduced efficient network. The upper diagram in Fig. 4 plots the correlation coefficients between empirical FC and the simulated FC (
Download:


Fig. 4 Predicting FC by dynamic models based on the binary structural network and reduced network for 66ROI dataset. The diagram in the upper panel plots the correlation coefficients (fit) between the empirical FC and the simulated FC varying with the probability of activation 
The same processing is next applied to the 90ROI dataset. In Fig. 5, the upper panel shows the variation of the fit between empirical FC and simulated FC (
Download:


Fig. 5 Predicting FC by dynamic models based on the binary structural network and reduced network for 90ROI dataset. The diagram in the upper panel plots the correlation coefficients (fit) between the empirical FC and the simulated FC varying with the probability of activation 
To better assess the ability of the dynamic model based on the reduced structural network, we compared the capacity of the model with the DMF model. The correlations between empirical FC and simulated FC were computed for all pairs (
Table Ⅱ summarizes the correlation coefficients obtained from three different models for 90ROI dataset. In agreement with results on 66ROI dataset, each model performs well to predict FC and the ability of the dynamic model along the reduced structural network outperforms the dynamic model based on the structural links especially for the FC among the structurally connected regions. Unlike results from 66ROI dataset, the dynamic model based on reduced SC for 90ROI dataset shows the best predictive effectiveness for both structurally connected and unconnected node pairs among three models. Though the predictions by the dynamic model along binary SC are better than those by DMF model among BH regions, the correlations among two regions that are anatomically linked are extremely low, by comparison.
Across two different resolution datasets, these findings suggest that: ⅰ) with the increase of the infection possibility, the fluctuations of the activity would tend to be stable, yielding temporal correlations that best match the empirical FC; ⅱ) the dynamic model simulated on the reduced SC can predict FC among both structurally connected and unconnected node pairs; ⅲ) the fact that the performance of the dynamic model simulated on the efficient propagation network is better than that on the structural network demonstrates the effectiveness of the shortest paths; ⅳ) in comparison with the DMF model, the dynamic model embedded in the shortest paths is found to perform better to predict FC for 90ROI dataset with higher efficiency.
Ⅴ. CONCLUSION AND DISCUSSIONIn the present study, we investigate the availability and capacity of a simple dynamic model contributed by SIS theory and the shortest paths, to predict resting FC. In line with the SIS model and Stam's study [14], there emerges a critical transition probability (an infection probability with a fixed recovery probability) that plays an important role in the whole system. At the critical point, the observed fluctuations of the rate of activation are more stable, in comparison with sharp decreases in fluctuations during 5000 steps below the critical probability. In this paper, we combine this phenomenon with the simulated FC and compare simulated results with empirical data quantitatively. Experiments on two different resolution datasets suggest that the critical transition probability reflects the best correlation between simulated FC and empirical FC. The fact that the brain operates at the critical point of a bifurcation resembles the previous studies [1], [2], [8], [10], [32][34] which proposes the edge of instability yields spatial fluctuations reproducing FC maps optimally during rest.
In this work, we consider the shortest paths as the efficient routes to propagate signals. Thus, we reduce the structural network to the simplified network in the light of the shortest paths which specify the direction of transmission. After simplification, there exist fewer links in the network which, however, achieve better simulation of FC. In order to create a stable system, a larger critical infection possibility is needed due to the lower density of the network. Nevertheless, better performance of prediction demonstrates that some anatomical connections are redundant or even play a negative role in shaping functional connections. Eliminating some less efficient links and accessing the shortest paths to transmit signals are helpful for exploring the functional interactions among different regions. To better analyze the prediction capability of the dynamic model based on the reduced binary SC, a neural mass modelDMF model is used for further comparison. As expected, for 90ROI dataset, the dynamic model reduced network outperforms the DMF model and the dynamic model embedded in the original binary structural network. For the dataset with 66 regions, the resulting correlation coefficients derived from the dynamic model along reduced SC are nearly the same as the DMF model, with a relatively lower prediction among structurally connected pairs and a higher value among structurally unconnected regions. However, combining this with a sophisticated BalloonWindkessel model [16] and searching for an optimal coupling strength [2] to reproduce FC are of great complexity, which leads to generous calculation and lower time efficiency of the DMF model. Hence, using the dynamic model based on the reduced SC to predict FC is better from the perspective of computation efficiency.
Our studies have some limitations. First, all predictors perform poorly across structurally unconnected regions of cortex, possibly due to the limitation of the SC matrix. Though the dynamic model describes the signal propagation imitating the process of the epidemic transmission, which makes up few deficiencies, the fact that signal transmits along structural network restricts the performance of the models in agreement with the previous view, a large part of FC cannot be explained by SC alone [35], [36]. Hence, the analysis of intrinsic human brain neuronal interactions [2], [20], [37][39] and the combination with SC seem to be critically necessary. Second, for simplicity, only the binary reduced SC along the shortest paths is considered to explore the influence on FC. However neuronal communication should rely on the weight of "connection" links. Thus, a weighted "connection" network will be considered further. Third, the simplified network only considers the shortest paths as primary propagation pathways which ignore the influence of the other ways, such as the local detours along the shortest paths which may lead to the accumulation of signals and amplification of FC. Finally, the inaccuracy of SC which is inferred from fiber tractography [40][43] might impose restrictions on the predictions of FC. It has been documented that there is an inherent limitation in determining longrange anatomical projections in SC by diffusion MRI tractography [44].
In the end, we should note that the predictions of FC for structurally connected regions using the dynamic model based on the shortest paths across two differentresolution datasets are relatively strong. These results indicate the feasibility and capability of the model to predict FC. Moreover, this result may enable researchers to further understand the relation between structure and behavior [45] as well as offer help for future health and disease studies [45][49].
ACKNOWLEDGEMENTWe are thankful to Olaf Sporns for sharing the 66ROI Dataset; to Farras Abdelnour for sharing the 90ROI Dataset; and to Gustavo Deco for providing the code of DMF Model.
APPENDIX A[1]  G. Deco and V. K. Jirsa, "Ongoing cortical activity at rest: criticality, multistability, and ghost attractors, " J. Neurosci., vol. 32, no. 10, pp. 33663375, Mar. 2012. http://www.ncbi.nlm.nih.gov/pubmed/22399758 
[2]  G. Deco, A. PonceAlvarez, D. Mantini, G. L. Romani, P. Hagmann, and M. Corbetta, "Restingstate functional connectivity emerges from structurally and dynamically shaped slow linear fluctuations, " J. Neurosci., vol. 33, no. 27, pp. 1123911252, Jul. 2013. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3718368/ 
[3]  M. A. Koch, D. G. Norris, and M. HundGeorgiadis, "An investigation of functional and anatomical connectivity using magnetic resonance imaging, " NeuroImage, vol. 16, no. 1, pp. 241250, May 2002. http://www.sciencedirect.com/science/article/pii/S1053811901910523 
[4]  G. Deco, A. R. McIntosh, K. Shen, R. M. Hutchison, R. S. Menon, S. Everling, P. Hagmann, and V. K. Jirsa, "Identification of optimal structural connectivity using functional connectivity and neural modeling, " J. Neurosci., vol. 34, no. 23, pp. 79107916, Jun. 2014. http://www.ncbi.nlm.nih.gov/pubmed/24899713 
[5]  J. Cabral, M. L. Kringelbach, and G. Deco, "Exploring the network dynamics underlying brain activity during rest, " Progr. Neurobiol., vol. 114, pp. 102131, Mar. 2014. http://www.ncbi.nlm.nih.gov/pubmed/24389385 
[6]  C. J. Honey, R. Kötter, M. Breakspear, and O. Sporns, "Network structure of cerebral cortex shapes functional connectivity on multiple time scales, " Proc. Natl. Acad. Sci. U. S. A., vol. 104, no. 24, pp. 1024010245, Jun. 2007. http://www.ncbi.nlm.nih.gov/pubmed/17548818 
[7]  C. J. Honey, O. Sporns, L. Cammoun, X. Gigandet, J. P. Thiran, R. Meuli, and P. Hagmann, "Predicting human restingstate functional connectivity from structural connectivity, " Proc. Natl. Acad. Sci. U. S. A., vol. 106, no. 6, pp. 20352040, Feb. 2009. http://www.ncbi.nlm.nih.gov/pubmed/19188601 
[8]  A. Ghosh, Y. Rho, A. R. McIntosh, R. Kötter, and V. K. Jirsa, "Noise during rest enables the exploration of the brain's dynamic repertoire, " PLoS Comput. Biol., vol. 4, no. 10, pp. Article ID e1000196, Oct. 2008. http://www.ncbi.nlm.nih.gov/pubmed/18846206/ 
[9]  E. Bullmore and O. Sporns, "complex brain networks: Graph theoretical analysis of structural and functional systems, " Nat. Rev. Neurosci., vol. 10, no. 3, pp. 186198, Mar. 2009. 
[10]  G. Deco, V. Jirsa, A. R. McIntosh, O. Sporns, and R. Kötter, "Key role of coupling, delay, and noise in resting brain fluctuations, " Proc. Natl. Acad. Sci. U. S. A., vol. 106, no. 25, pp. 1030210307, Jun. 2009. http://www.ncbi.nlm.nih.gov/pubmed/19497858 
[11]  G. Deco, V. K. Jirsa, and A. R. McIntosh, "Emerging concepts for the dynamical organization of restingstate activity in the brain, " Nat. Rev. Neurosci., vol. 12, pp. 4356, Jan. 2011. http://www.ncbi.nlm.nih.gov/pubmed/21170073 
[12]  P. E. Vértes, A. F. AlexanderBloch, N. Gogtay, J. N. Giedd, J. L. Rapoport, and E. T. Bullmore, "Simple models of human brain functional networks, " Proc. Natl. Acad. Sci. U. S. A., vol. 109, no. 15, pp. 58685873, Apr. 2012. http://www.ncbi.nlm.nih.gov/pubmed/22467830 
[13]  J. Goñi, M. P. van den Heuvel, A. AvenaKoenigsberger, N. V. de Mendizabal, R. F. Betzel, A. Griffa, P. Hagmann, B. CorominasMurtra, J. P. Thiran, and O. Sporns, "Restingbrain functional connectivity predicted by analytic measures of network communication, " Proc. Natl. Acad. Sci. U. S. A., vol. 111, no. 2, pp. 833838, Jan. 2014. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3896172/ 
[14]  C. J. Stam, E. C. W. van Straaten, E. Van Dellen, P. Tewarie, G. Gong, A. Hillebrand, J. Meier, and P. Van Mieghem, "The relation between structural and functional connectivity patterns in complex brain networks, " Int. J. Psychophysiol., vol. 103, pp. 149160, May 2016. http://www.sciencedirect.com/science/article/pii/S0167876015000410 
[15]  M. Kaiser and C. C. Hilgetag, "Modelling the development of cortical systems networks, " Neurocomputing, vol. 5860, pp. 297302, Jun. 2004. http://www.sciencedirect.com/science/article/pii/S0925231204000554 
[16]  K. J. Friston, C. D. Frith, R. Turner, and R. S. J. Frackowiak, "Characterizing evoked hemodynamics with fMRI, " NeuroImage, vol. 2, no. 2, pp. 157165, Jun. 1995. http://www.sciencedirect.com/science/article/pii/S105381198571018X 
[17]  R. M. Anderson and R. M. May, Infectious Diseases of Humans.. Oxford, UK: Oxford University Press, 1992. 
[18]  C. Castellano and R. PastorSatorras, "Thresholds for epidemic spreading in networks, " Phys. Rev. Lett., vol. 105, no. 21, pp. Article ID 218701, Nov. 2010. http://www.ncbi.nlm.nih.gov/pubmed/21231361 
[19]  M. Boguñá, C. Castellano, and R. PastorSatorras, "Nature of the epidemic threshold for the susceptibleinfectedsusceptible dynamics in networks, " Phys. Rev. Lett., vol. 111, no. 6, pp. Article ID 068701, Aug. 2013. http://www.ncbi.nlm.nih.gov/pubmed/23971619 
[20]  J. Joo and J. L. Lebowitz, "Behavior of susceptibleinfectedsusceptible epidemics on heterogeneous networks with saturation, " Phys. Rev. E, vol. 69, no. 6, pp. Article ID 066105, Jun. 2004. http://www.ncbi.nlm.nih.gov/pubmed/15244665 
[21]  H. J. Wang, Q. Li, G. D'Agostino, S. Havlin, H. E. Stanley, and P. Van Mieghem, "Effect of the interconnected network structure on the epidemic threshold, " Phys. Rev. E, vol. 88, no. 2, pp. 022801, Aug. 2013. http://www.ncbi.nlm.nih.gov/pubmed/24032878 
[22]  Y. L. Lu and G. P. Jiang, "Backward bifurcation and local dynamics of epidemic model on adaptive networks with treatment, " Neurocomputing, vol. 145, pp. 113121, Dec. 2014. http://www.sciencedirect.com/science/article/pii/S0925231214007176 
[23]  V. Latora and M. Marchiori, "Efficient behavior of smallworld networks, " Phys. Rev. Lett., vol. 87, no. 19, pp. Article ID 198701, Oct. 2001. http://www.ncbi.nlm.nih.gov/pubmed/11690461 
[24]  S. Hougardy, "The FloydWarshall algorithm on graphs with negative cycles, " Inform. Process. Lett., vol. 110, no. 89, pp. 279281, Apr. 2010. http://www.sciencedirect.com/science/article/pii/S002001901000027X 
[25]  A. Trusina, M. Rosvall, and K. Sneppen, "Communication boundaries in networks, " Phys. Rev. Lett., vol. 94, no. 23, pp. Article ID 238701, Jun. 2005. http://www.ncbi.nlm.nih.gov/pubmed/16090509 
[26]  M. Rosvall, A. Grönlund, P. Minnhagen, and K. Sneppen, "Searchability of networks, " Phys. Rev. E, vol. 72, no. 4, pp. Article ID 046117, Oct. 2005. http://www.ncbi.nlm.nih.gov/pubmed/16383478 
[27]  J. Goñi, A. AvenaKoenigsberger, N. V. de Mendizabal, M. P. van den Heuvel, R. F. Betzel, and O. Sporns, "Exploring the morphospace of communication efficiency in complex networks, " PLoS One, vol. 8, no. 3, pp. Article ID e58070, Mar. 2013. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3591454/ 
[28]  F. Abdelnour, H. U. Voss, and A. Raj, "Network diffusion accurately models the relationship between structural and functional brain connectivity networks, " NeuroImage, vol. 90, pp. 335347, Apr. 2014. http://www.sciencedirect.com/science/article/pii/S1053811913012597 
[29]  N. TzourioMazoyer, B. Landeau, D. Papathanassiou, F. Crivello, O. Etard, N. Delcroix, B. Mazoyer, and M. Joliot, "Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI singlesubject brain, " NeuroImage, vol. 15, no. 1, pp. 273289, Jan. 2002. http://www.ncbi.nlm.nih.gov/pubmed/11771995?access_num=11771995&link_type=MED&dopt=Abstract 
[30]  P. A. Bandettini, A. Jesmanowicz, E. C. Wong, and J. S. Hyde, "Processing strategies for timecourse data sets in functional MRI of the human brain, " Magn. Reson. Med., vol. 30, no. 2, pp. 161173, Aug. 1993. https://onlinelibrary.wiley.com/doi/abs/10.1002/mrm.1910300204 
[31]  B. Biswal, F. Zerrin Yetkin, V. M. Haughton, and J. S. Hyde, "Functional connectivity in the motor cortex of resting human brain using echoplanar MRI, " Magn. Reson. Med., vol. 34, no. 4, pp. 537541, Oct. 1995. https://www.ncbi.nlm.nih.gov/pubmed/8524021 
[32]  A. Ghosh, Y. Rho, A. R. McIntosh, R. Kötter, and V. K. Jirsa, "Cortical network dynamics with time delays reveals functional connectivity in the resting brain, " Cogn. Neurodyn., vol. 2, no. 2, pp. 115120, Jun. 2008. https://link.springer.com/article/10.1007/s1157100890442 
[33]  J. Cabral, E. Hugues, O. Sporns, and G. Deco, "Role of local network oscillations in restingstate functional connectivity, " NeuroImage, vol. 57, no. 1, pp. 130139, Jul. 2011. http://www.sciencedirect.com/science/article/pii/S1053811911003880 
[34]  J. Cabral, E. Hugues, M. L. Kringelbach, and G. Deco, "Modeling the outcome of structural disconnection on restingstate functional connectivity, " NeuroImage, vol. 62, no. 3, pp. 13421353, Sep. 2012. http://www.sciencedirect.com/science/article/pii/S1053811912005848 
[35]  J. S. Damoiseaux and M. D. Greicius, "Greater than the sum of its parts: a review of studies combining structural connectivity and restingstate functional connectivity, " Brain Struct. Funct., vol. 213, no. 6, pp. 525533, Oct. 2009. http://www.ncbi.nlm.nih.gov/pubmed/19565262 
[36]  A. Messé, D. Rudrauf, H. Benali, and G. Marrelec, "Relating structure and function in the human brain: Relative contributions of anatomy, stationary dynamics, and nonstationarities, " PLoS Comput. Biol., vol. 10, no. 3, pp. Article ID e1003530, Mar. 2014. http://www.ncbi.nlm.nih.gov/pubmed/24651524 
[37]  S. L. Bressler and E. Tognoli, "Operational principles of neurocognitive networks, " Int. J. Psychophysiol., vol. 60, no. 2, pp. 139148, May 2006. http://www.sciencedirect.com/science/article/pii/S0167876006000092 
[38]  V. Pernice, B. Staude, S. Cardanobile, and S. Rotter, "How structure determines correlations in neuronal networks, " PLoS Comput. Biol., vol. 7, no. 5, pp. e1002059, May 2011. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3098224/ 
[39]  G. Deco, M. Senden, and V. Jirsa, "How anatomy shapes dynamics: A semianalytical study of the brain at rest by a simple spin model, " Front. Comput. Neurosci., vol. 6, pp. Article ID 68, Sep. 2012. http://www.ncbi.nlm.nih.gov/pubmed/23024632 
[40]  J. L. Vincent, G. H. Patel, M. D. Fox, A. Z. Snyder, J. T. Baker, D. C. Van Essen, J. M. Zempel, L. H. Snyder, M. Corbetta, and M. E. Raichle, "Intrinsic functional architecture in the anaesthetized monkey brain, " Nature, vol. 447, no. 7140, pp. 8386, May 2007. http://www.ncbi.nlm.nih.gov/pubmed/17476267 
[41]  D. S. Margulies, J. L. Vincent, C. Kelly, G. Lohmann, L. Q. Uddin, B. B. Biswal, A. Villringer, F. X. Castellanos, M. P. Milham, and M. Petrides, "Precuneus shares intrinsic functional architecture in humans and monkeys, " Proc. Natl. Acad. Sci. U. S. A., vol. 106, no. 47, pp. 2006920074, Nov. 2009. http://www.ncbi.nlm.nih.gov/pubmed/19903877 
[42]  M. P. van den Heuvel, R. C. W. Mandl, R. S. Kahn, and H. E. Hulshoff Pol, "Functionally linked restingstate networks reflect the underlying structural connectivity architecture of the human brain, " Hum. Brain Mapp., vol. 30, no. 10, pp. 31273141, Oct. 2009. http://www.ncbi.nlm.nih.gov/pubmed/19235882 
[43]  C. J. Honey, J. P. Thivierge, and O. Sporns, "Can structure predict function in the human brain?, " NeuroImage, vol. 52, no. 3, pp. 766776, Sep. 2010. http://www.ncbi.nlm.nih.gov/pubmed/20116438 
[44]  C. Thomas, F. Q. Ye, M. O. Irfanoglu, P. Modi, K. S. Saleem, D. A. Leopold, and C. Pierpaoli, "Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited, " Proc. Natl. Acad. Sci. U. S. A., vol. 111, no. 46, pp. 1657416579, Nov. 2014. http://www.ncbi.nlm.nih.gov/pubmed/25368179 
[45]  E. I. Barakova, A. Spink, and N. Fujii, "From neuron to behavior: evidence from behavioral measurements, " Neurocomputing, vol. 84, pp. 12, May 2012. http://www.sciencedirect.com/science/article/pii/S0925231211007417?np=y 
[46]  B. S. Bhattacharya, Y. Cakir, N. SerapSengor, L. Maguire, and D. Coyle, "Modelbased bifurcation and power spectral analyses of thalamocortical alpha rhythm slowing in Alzheimer's disease, " Neurocomputing, vol. 115, pp. 1122, Sep. 2013. http://www.sciencedirect.com/science/article/pii/S0925231212008600 
[47]  S. A. R. B. Rombouts, F. Barkhof, R. Goekoop, C. J. Stam, and P. Scheltens, "Altered resting state networks in mild cognitive impairment and mild Alzheimer's disease: an fMRI study, " Hum. Brain Mapp., vol. 26, no. 4, pp. 231239, Dec. 2005. https://www.ncbi.nlm.nih.gov/pubmed/15954139 
[48]  S. A. R. B. Rombouts, J. S. Damoiseaux, R. Goekoop, F. Barkhof, P. Scheltens, S. M. Smith, and C. F. Beckmann, "Modelfree group analysis shows altered BOLD FMRI networks in dementia, " Hum. Brain Mapp., vol. 30, no. 1, pp. 256266, Jan. 2009. http://www.ncbi.nlm.nih.gov/pubmed/18041738 
[49]  M. M. Schoonheim, J. J. G. Geurts, D. Landi, L. Douw, M. L. van der Meer, H. Vrenken, C. H. Polman, F. Barkhof, and C. J. Stam, "Functional connectivity changes in multiple sclerosis patients: a graph analytical study of MEG resting state data, " Hum. Brain Mapp., vol. 34, no. 1, pp. 5261, Jan. 2013. http://www.ncbi.nlm.nih.gov/pubmed/21954106 